Archief Mekelweg 2, 2628 Deift Tel: 015-2786873/Fax:2781836 Waterjet-Hull Interaction

TECIINTSEE UNEVERSITEIT Scheeps bydromechani ca Archief Mekelweg 2, 2628 Deift Tel: 015-2786873/Fax:2781836 Waterjet-Hull Interaction

door Tom J.C. van Terwisga

Samenvatting

Doelstelling van dit werk is het ontwikkelen en valideren van gereedschappen voor de analyse van waterjet-romp interactie.

Hoewel erreeds een aanzienlijkehoeveelheid kennis bestaat omtrent de afzonderlijke componenten in het waterjet-romp systeem, bestaat er een hiaat in onze kennis met betrekking tot de wederzijdse interactie. Als gevoig daarvan worden verschilleninhet vermogen-snelheidsverband tussen prototype en voorspelling vaak aan interactie toegeschreven.

Een van de belangrijkste oorzaken voor misverstanden op het gebied van waterjet voortstuwing lijkt de afwezigheid van duidelijke definities te zijn. Hoofdstuk i laat zien dat er in de literatuur veel verwarring bestaat over definities en beschrijving van waterjet-romp interactie. Dit werk begint derhalve met een theoretisch model waarmee een complete beschrijving van waterjet-romp interactie mogelijk is. Het interactie effect op de romp wordt uitgedrukt in een 'resistance increment' factor. Het interactie effect van de waterjet wordt uitgedrukt in een 'thrust deduction' factor en een impuls interactie- en een energie interactie-efficiency. De beide laatste rendementen verdisconteren de verandering in ingenomen impuls- en energieflux ten gevolge van de verstoring door de romp.

Hoewel een ruwe procedure voor voortstuwingsproeven met waterjets reeds voorgesteld is door de ITTC in 1987, leidt deze aanpak gemakkelijk tot grote systematische fouten, waardoor het nut van de proeven dubieus wordt. Bovendien was devoorgesteldeverwerkingsproceduregebaseerd op een incompleet theoretisch model. In dit werk wordt een verbeterde experimentele procedure beschreven die gebaseerd is op ijking van de opnemers tijdens een paaltrek proef, tezamen met een verwerkingsprocedure die bepaling van de interactie factoren mogelijk maakt.

Gedetailleerde stromingsberekeningen en LDV metingen zijn gemaakt aan de stroming in en rondom de intake. De resultaten geven inzicht in de geldigheid van de aannamesdiegemaaktzijnindeverwerkingsprocedurevanvoort- stuwingsproeven. Zij tonen aan dat een rechthoekige dwarsdoorsnede van de stroombuis met een breedte die 30% groter is dan de geometrische intake breedte, een adequate representatie van de ingenomen stroming geeft. Zij tonen eveneens aan dat de 'thrust deduction' factor tijdens het droogvaren van de spiegel niet verwaarloosbaar is.

Berekeningen met een potentiaalprogramma en de methode van Savitsky zijn gedaan voor een berekening van de interactie effecten. De resultaten hiervan komen echter niet bevredigend overeen met de experimentele resultaten. Een empirisch model wordt aangeraden voor een bepaling van interactie effecten in voorlopige vermogensberekeningen.

Dit werk biedt een consistente verzameling van definities en relaties, waarmee zowel de voortstuwingseigenschappen van de romp en de waterjet, als ook hun interactie termen volledig beschreven worden. Een experimentele methode met een groter betrouwbaarheidsniveau dan tot nu toe beschreven in de openbare literatuur wordt eveneens voorgesteld. Deze resultaten kunnen bijdragen tot een bredere acceptatie van het waterjet systeem en tot een betere afwikkeling van contractuele onderhandelingen. Immers, de te verwachten voortstuwingseigenschappen van het schip zijn hierdoor beter voorspelbaar. STELLINGEN

De interactie tussen de romp en het waterjet systeem kan het gevraagde motorvermogen tot meer dan 20% beïnvloeden.

Voor een juisteselectie van voortstuwer systeem voor een bepaalde toepassing, dienen de effecten van romp-voortstuwer interactie meegewogen te worden.

De interactie term 'thrust deduction' suggereert dat de stuwkracht verminderd wordt als gevoig van de aanwezige romp. Bij een waterjet-romp systeem is dit deels het geval. Bij een schroef-romp systeem is dit echter per definitie onj uist.

De beschrijving van waterjet-romp interactie met dezelfde interactie termen zoals algemeen aanvaard voor de beschrijving van propeller-romp interactie, is principieel onjuist.

Waterjet-romp interactie effecten worden bet meest nauwkeurig bepaald door middel van modeiproeven.

In een potentiaalstroming is er in het algemeen meer nul dan je denkt. Door bet toenemend gebruik van numerieke analyse methoden wordt dit steeds vaker over bet hoofd gezien.

Interactie-verschijnselen zijn effecten die bij de gratie van door de mens geschapen (te) simpele denkmodellen in het technisch jargon bestaan. De natuur zelf kent ze niet.

AIs we het vanzelfsprekend vinden dat met name jongeren fouten maken waarvan ze kunnen leren, dan moeten we het ook accepteren dat een complexe en jonge organisatie als de VN fouten maakt. Een opvoeder die dit proces bewaakt is echter onontbeerlijk. De afwezigheid hiervan vormt daarom het grootste probleem bij bet voiwassen worden van de VN.

Het zou het welzijn van de individuen van beide seksen als ook die van organisaties ten goede komen, wanneer we de psychologische verschillen tussen mannen en vrouwen niet krampachtig ontkennen, doch er dankbaar gebruik van maken. 10 Eén van de meest gemaakte menselijke fouten is het oordelen op basis van een té eenvoudig denkmodel van de werkelijkheid. Als deze fout tijdens een borrel gemaakt wordt is er een excuus, zijn de consequenties gering en kan het de gezelligheid stimuleren. Bij alle andere gelegenheden kan het echter verstrekkende gevolgen voor ons welzijn hebben.

De volgende redeneer mechanismen kunnen naar afnemende mate van betrouwbaarheid van het resultaat genoemd worden: wiskunde, statistiek, fuzzy reasoning, en 'no reasoning at all'. Het redeneren van de mens bevindt zich in het algemeen tussen de twee laatstgenoemde mechanismen.

Door de complexiteit en de veelheid van processen in het menselijk lichaam, zijn er talrijke mogelijkheden voor ongewenste interacties tussen deze processen en medicijnen. Door gebruik te maken van de lichaamseigen processen, geeft de horneopathie inherent een kleinere kans op bijwerkingen dan de allopathie.

Het succes van het in de logistiek gehanteerde JIT principe (Just In Time) leidt tot een groter aantal vrachtwagenkilometers per ton produkt. Dit leidt tot een grotere stroperigheid en verstoppingskans van bet verkeer, waardoor het uT principe uiteindelijk via het JTL (Just Too Late) principe za] overgaan in het NNA (Not Needed Anymore) principe.

Hetveelgehoordeargument'1khebgeentijd',heeftpasenige overtuigingskracht nadat de spreker ervan is overleden. En zeifs dan is het discutabel.

Stellingen behorend bij het proefschrift van T.J.C. van Terwisga: "Waterjet-Hull Interaction'. 25 april 1996 TECHNISCHE UVERSITET t.aboratorium voor Scheepshydromechanica Archief Mekeiweg 2, 2628 CD Deft 11L015-786873-Fax015-781333 Waterjet-Hull Interaction

Torn J.C. van Terwisga Printed by: Grafisch Bedrijf Ponsen & Looijen BV, Wageningen Waterjet-Hull Interaction

Proefschrift

ter verkrijging van de graad van doctor aan de Technische Universiteit Deift, op gezag van de Rector Magnificus Prof.ir. K.F. Wakker, in het openbaar te verdedigen ten overstaan van een commissie, door het College van Dekanen aangewezen, op donderdag 25 aprii te 13.30 uur

door

Thomas Jan Cornelis VAN TERWISGA

scheepsbouwkundig ingenieur

geboren te Sneek Dit proefschrift is goedgekeurd door de promotor:

Prof.dr.ir. G. Kuiper

Samenstelling promotiecommissie:

Rector Magnificus, voorzitter Prof.dr.ir. G. Kuiper, TU Deift, promotor Prof.dr.ir. J. Pinkster, TU Deift Prof.Dr.Dipl.-Ing. C. Gallin, TU Deift Prof.dr.ir. A. Hermans, TU Deift Prof.dr.ir. L. van Wijngaarden, U-Twente Prof.Dr.-Ing. C. Kruppa, TU Berlin Dr. A.J. Bowen, Canterbury University, New Zealand

ISBN 90-75757-01-8 Aan mijn ouders fac intha Table of Contents

Introduction 1 .1 Aim and motivation i 1 .2 Historic setting 2 1.3 Outline of work 4 1.4 Description of waterjet system 8 1.5 Relations with other propulsors 13 1.5.1 Comparison with propeller 13 1.5.2Comparison with gasturbine jet system 17 1.6 Review of previous work 22 1.6.1 Parametric models 23 1.6.2Experimental procedures 34 1 .6.3 Computational procedures 43 1 .7 Summary of present work 48 1.7.1 Theoretical model 48 1.7.2Experimental procedure 49 1.7.3Computational analysis 50

2 Theoretical model 53 2.1 Systems decomposition 53 2.1.1Definition of jet system control volume 54 2. 1.2 Analysis of overall powering characteristics 58 2.2 Basic equations 64 2.2.1 Thrust 65 2.2.2Power 68 2.2.3Free stream conditions 71 2.2.4Lift 78 2.3 Interaction 80 2.3.1 Momentum interaction efficiency 8 1 2.3.2Energy interaction efficiency 88 2.3.3Quantitative assessment and comparison with previous work 90 2.3.4Hull resistance increment 94 2.4 Conclusions 96 3 Experimental analysis 99 3.1 Propulsion test procedure 99 3.2 Flow rate measurement 105 3.2.1 Flowmeter selection 106 3.2.2Calibration procedure 119 3.2.3Bollard pull verification tests 139 3.3 Uncertainty analysis 144 3.4 Propulsion test results 154 3.4.1 Thrust deduction 155 3.4.2Momentum and energy interaction efficiencies 164 3.5 Extrapolation method 166 3.6 Conclusions 168

4 Computational analysis 171 4. 1 Free stream intake analysis 171 4.1.1 Intake flow analysis 172 4.1.2Intake induced drag and lift 189 4.2 Computational prediction of interaction 196 4.2.1 Resistance increment for hump speed 197 4.2.2Resistance increment for design speed 210 4.3 Analysis of propulsion test procedure 215 4.3.1 Effect of intake geometry on interaction efficiency .... 216 4.3.2Effect of hull and free surface effects on t1 assumption 219

5 Conclusions and recommendations 229 5.1 Methods and tools 230 5.2 Physical mechanisms 233 Appendices

Al Derivation of relations for ideal efficiency 235

A2 Expressions for the computation ofcm and Ce 239

A3 Outline of uncertainty analysis 243

A4 Description of facilities and models used for experiments 253

AS Description of potential flow panel codes HESM' and DAWSON 259

A6 Description of performance prediction code PLANE' 263

A7 Description of LDV experiments in the MARIN large cavitation tunnel 265

References 271

Nomenclature 23

Summary 291

Acknowledgement 293

Curriculum Vitae 295 Chapter 1

1 Introduction 1.1 Aim and motivation

Aim of this work is 'the development and validation of tools to analyze interaction effects in powering characteristics of waterjet-hull systems'.

Interaction may be regarded as the phenomenon that is responsible for deviations in the actual characteristics of two or more integrated subsystems, from a synthesis of properties of the merely matched subsystems. Interaction phenomena are only revealed after one has a theoretical model to derive interaction terms, or after one has the means to observe interaction effects from measurements. And interaction is only explained and used effectively in design, after one has the tools to analyze the responsible mechanisms in detail. The search for the aforementioned instruments forms the incentive of this work.

What's new? Propeller-hull interaction is a well developed field of research in propulsion hydrodynamics where many researchers have made useful contributions, see e.g. Morgan [1992]. What makes waterjet-hull interaction different is the degree of integration of hull and propulsor system, rendering the definition of interaction less straightforward, causing complications in experimental techniques, and finally, rendering the interaction mechanisms different from those observed with propeller-hull operation. Chapter 1Introduction During the first propulsion tests with waterjet propelled hulls, it appeared that waterjet-hull interaction could affect the overall efficiency by well over 20%. This finding in itself would probably be sufficient to justify research on this topic. Moreover, the interaction effect on thrust sometimes appears to create an unfortunate combination of working regions for both the pump of the jet system and the hull. Such a combination may prohibit the jet-hull combination to reach its design working point and may result in a maximum speed of the craft that is several knots lower than could be expected from pure matching of the two single systems.

Apart from this technical motivation, an economic motivation may be extracted from present industrial developments. A growing number of waterjet applications and waterjet manufacturers can be observed from the literature. Apart from the increase of these numbers, there is also an increase in waterjet size perceptible. And with this increase in scale, one can simply see the growing financial risks and the consequent request for performance warrants.

1.2Historic setting

An obvious question one may ask when being confronted with such an effort into waterjet-hull interaction, is the one on 'Why it is only now that interaction raises this interest'. The following section seeks for a plausible explanation.

In the development of a new concept, technicians are initially only concerned with the performance and the relations governing the isolated system. Interac- tion between this new system and other systems is consequently neglected. As such, the development of the waterjet-hull system can be regarded to have already started in the ancient times during the development of the first hull forms. The first achievement was the actual building and operation of the corresponding vessel. Building and operation were based on experience, necess- arily gained after having learnt how certain ideas failed to work. Improvements were gradually implemented after an empirical evaluation of the new idea.

Archimedes (287-212 BC), presumably puzzled by the appearance of floating vessels, found a rational theory to describe this phenomenon. With his theory, new ideas and improvements could more easily, and with greater certainty be evaluated. His contribution undoubtedly speeded up the development in naviga- tion and shipbuilding. In the course of times, a wealth of knowledge became available on the subsystem 'hull'.

2 1.2 Historic setting Another historical event of probably similar importance, was the development of mechanical ship propulsion. This could be achieved after the availability of mechanical power, which came within reach with the introduction of steam engines. Talented engineers subsequently concentrated on the propulsor system to convert the available mechanical power from the engine to a propelling force for the ship.

Since the beginning of the 17th Century, written reference is made to waterjet propulsion.In 1631, a Scot called David Ramsey acquired English Patent No. 50, which included an inventionto make Boates, Shippes and Barges goe against Stronge Winde and Tyde". This was at a time when there was great interest in using steam to raise water and to operate fountains, so there is good reason to suppose Ramsey had a type of waterjet in mind' (Dickinson [19381)... A more explicit reference to the waterjet is made in a patent granted to Toogood and Hayes [1661] for their invention of "Forceing Water by Bellowes together with a particular way of Forceing water through the Bottome or Sides of Shipps belowe the Surface or Toppe of the Water, which may be of singuler Use and Ease in Navagacon".

'The theory of waterjet propulsion was subsequently investigated and discussed by the Frenchman Daniel Bernoulli in 1753. He suggested (Flexner [1944]) that if a stream of water was driven out of the stern of a boat below the waterline, its reaction on the body of water in which the boat floated would drive the vessel forward. By pouring water into an L-shaped pipe stretching to the aft end, Bernoulli's simple model experiment confirmed the principle of waterjet propulsion, yet left others to determine how to force the water from the vessel' (Roy [1994]).

Up until the mid-nineteenth century, there has been little or no development on waterjet propulsors. 'Because of the limitations of technology and lack of understanding of the principles of propulsion , waterjet propulsors were unable to compete with paddle wheels and, later, propellers' (Allison [1993]).

From the early days of waterjet development, attempts to improve the propulsor concentrated on a better understanding and a consequent improved design of the propulsor system itself. Interaction effects may not have been noted due to a limited accuracy of measurements or due to the absence of a physical model which showed that the effect searched for, could only be explained by interac- tiOfl.

3 Chapter 1Introduction As with the first propeller propelled vessels, waterjet systems have long been used successfully before technical interest focused on a proper description and prediction of interaction effects between propulsor and hull. This interest could also have been slumbering for quite a period, because the first waterjet projects often allowed for extensive trials or initial model testing. Problems due to interaction effects could thus timely be solved experimentally.

Nowadays, the design procedure of a waterjet propelled vessel isdifferent. Because of the availability of a large number of well developed waterjet systems, the designer is confronted with a selection of existing waterjet units, more than with the integrated design of the waterjet itself. Due to the success of waterjet propulsion development, times and budgets available for the vessel development have been reduced significantly.

Having less time available, it is the responsibility of the ship designer to select the most appropriate waterjet system for the vessel under development. For an optimal selection of the propulsor installation, the evaluation of candidates should not only be made on an evaluation of separate systems, but should also take into account possible interaction phenomena that interfere with the vessels overall performance.

1.3Outline of work

Philosophy in approach

The basic philosophy underlying this study is taken from what is called Systems Theory.

'For centuries, science has sought for insight by analysing, by breaking down more complex matters into series of simpler problems. Thesolution of the total problem would then be equal to the sum of the solutions of the partial problems. Partial problems are thereby studied independently. More and more, also basic, elements being identified. At the same time, the field of science is widened, causing a growth inthe amount of phenomena that need to be explained. The analysis getting keener and deeper. Caused by this increasing amount of knowledge, spread over numerous disciplines,synthesis has become increasingly difficult.

These days, the subsystems or elements are largely known and their properties have been well investigated. Various combinations of elements or systems are being studied now. But often,insightinthe mutual interaction between

4 1.3. Outline of work elements is limited. This is partly caused by the classical scientific dogma: 'Only change one variable at a time'.' (translated from [In't Veld, 1981]).

Description of concepts

Systems may be described by an enumeration of their constituting elements,or by a set of properties or 'attributes' of the system. This latter way is appropriate when interaction between systems is to be described.

According to the concepts adopted in Systems Theory, 'interaction' between two (sub)systems occurs when the attributes of one system are affected by the attributes of the other system. The distortion causing the interaction, is passed through by the environment of the subject system. Analogous to the way in which interaction occurs between two systems, it may occur directly between the system and its environment (see e.g. In 't Veld [1981]).

The attributes are quantified by the so-called 'state variables'. A set of state variable values consequently defines the 'state' of the system. The values of these state variables are constrained by the set of relations governing the system in its environment.

To be able to quantify interaction, the 'isolated' system's condition is introduced (Fig. 1.1). This condition is defined by the set of attributes and relations describing the system in a predefined undisturbed environment. The undisturbed environment will in this work be referred to as the'free stream condition'. Examples of free stream conditions are the later defined free stream condition for the waterjet system and the 'open water' condition for propellers.

Before looking at a complete integration of two systems with mutual interaction,an intermediatesystem's conditionisintroduced.Inthisso-called matched condition', there is no interaction between the two systems yet. The systems do however limit the range of values of the state variables of each system. The state itself is not affected, only the number of states that can occur is limited. The possible states are governed by the 'matching relations'.

The situation in which interaction occurs is referred to as the 'united condition' of the combined system. In addition to matching relations, 'interaction relations' determine the possible states of the systems involved. It can be inferred from Fig. 1.1 that interaction between two systems is caused by a change in the environment through the action of the other system.

5 Chapter 1Introduction

Isolated Condition

Matched Condition

United Condition

Fig. II Relation between the degree of integration and interaction between two systems

Waterjet-hull interaction as meant throughout this work, refers to the interaction between the waterjet system and the hull system only. That is, to a change in values of the relevant attributes due to the presence of the other system.

The following gives an example on the use of the three conditions described above. The isolated systems condition or free stream condition is used for the quantification of the bare hull resistance as a function of speed. Similarly, the jet system's thrust production can be determined in its isolated condition for varying values of flow velocity and flow rate. In the matched condition, the thrust of the waterjet should balance the resistance of the hull. However, no interaction effects on thrust or resistance are accounted for yet. We speak of the united condition after interaction effects have been accounted for. In this situ-

6 1.3. Outline of work ation, the resistance of the hull is affected by the distorted flow due to the waterjet action, and vice versa, the thrust delivered by the waterjet for a certain impeller rotation rate is affected by the hull distortion in ingested flow.

It should be noted that the matched condition is a conceptual condition which only occurs in reality when it coincides with the united condition. This is when interaction between both systems does not occur. The reason for considering this condition is that a rough indication of the attributes of the combined system can easily be obtained during synthesis activities. A second reason is that for analysis activities the concept of interaction is defined more precisely.

Scope

This thesis deals with interaction effects in the hydrodynamic relations that may occur in the relations of either the jet or the hull system. Interaction effects in the geometrical or constructional relations of either system are consequently not dealt with.

We speak of hydrodynamic interaction when for instance the equilibrium position of the jet-hull system is different from that of the bare hull resistance test. This change in balance is caused by the jet action, causing a change in the hull's environment. Interaction effects can be described in terms of integrated variables, such as in the above example. They can however also be expressed in terms of state variables of the environment, such as fluid pressures and velocities.

The present work is concerned only with steady operation of the jet-hull system. Unsteady operation occurs for instance during acceleration of the vessel and duringoperationina seaway. Unsteady operations caninitiallybe approached by a quasi-steady analysis for each time step considered. 1f such an approach does not yield the requested correspondence with experimental observations. the next step would be to also take into account time derivatives of the state variables. However, as a first step, we will concentrate here on interaction during steady operation.

Although the above limitations are considered necessary from a practical point of view, it should at the same time be realized that the quasi-steady approach should be considered with care. Doctors et aI. [19721 for example, show that both the height and the corresponding Froude number of the hump in the wavemaking drag of a Surface Effect Ship depend on the acceleration of the vessel. This change in resistance characteristics may consequently lead to a change in thrust requirements.

7 Chapter 1Introduction

Uptonow,theunsteadytypeofoperationduringacceleration(and deceleration) has not emerged to the author as a field of industrial interest.

This is different for the unsteady operation of a vessel in a seaway. Engine damage problems have been reported on High Speed Marine Vehicles by Meek- Hansen [1991]. Possible reasons for these damage problems are believed to be caused by either air ingestion by the intake, by separation of the flow in the intake or by a combination of both (ITTC [1993]).

Waterjet systems occur with various versions of the intake geometry. The three basic configurations are shown in Fig. 1.3, viz, the flush type intake, the ram type and the scoop type intake. This work is restricted to waterjet systems with a flush type intake. The theoretical model describing waterjet-hull interaction, as well as the experimental procedures can however be used for ram and scoop type intakes as well, with only minor modifications.

1.4Description of waterjet system

General principle

The general principle underlying the thrust production of the jet propulsor is tersely summarized in the conservation law of momentum. A consequence of this physical law is, that an action force is required to accelerate a certain amount of fluid. This action force is exerted on the fluid by an actuator. For a waterjet system, the actuator normally consists of a mechanical pump. In steady conditions, the action force has to be counterbalanced by a reaction force exerted by the fluid on the actuator. This reaction force can be identified as a thrust vector Tg:

Tg 4mnmi where = momentum flux vector subscripts n and i denote the nozzle and intake area respectively.

The minus sign for the gross thrust has been added because the thrust is defined as the reaction force to the force associated with the increase in momentum.

The momentum flux for a uniform flow can be written as: (1.2) fll= P

8 1 .4 Description of waterjet system where p= specific mass of fluid volume flow rate through control volume u,n= momentum velocity vector.

Although various propulsor concepts acting in a fluid or a mixture of fluids are available, they all share this common principle. Examples of such propulsors are for instance the classical propeller and all its derivatives, the gasturbine jet used inairplanes and thewaterjetfor marine applications.Analogies in propulsor-hull interaction with propellers and gasturbines will be discussed in the next section, to ensure that research results on propulsor-hull interaction for similar propulsors are used whenever possible.

To obtain a better understanding of the way in which interaction occurs and how it can be treated, a description of the waterjet system is provided in the following. The elements and fundamental processes areshortly addressed, without pursuing completeness.

Description of waterjet system

A general scheme of the waterjet propulsor is presented in Fig.1 .2. A suitable control volume that is required for e.g. the thrust computation from eq. (1.1), is discussed in detail in Chapter 2.

Fig. 1.2GeneraI scheme of waterjet propulsor

Water from the jet system's environment is ingested by the intake, accelerated by the actuator and discharged through the nozzle. The actuator usually consists of a mechanical pump, which may have a range of characteristics. The first waterjet systems were primarily equipped with centrifugal pumps, offering a relatively low pump efficiency. Modern waterjet systems mostly apply axial flow or mixed flow type pumps at improved pump efficiencies. An alternative

9 Chapter 1Introduction actuator that has recently raised some interest is the Magneto Hydrodynamic Pump [Doss and Geyer, 1993] and [Tasaki et al., 1991]. Due to its current low efficiency, it has only been applied in experimental craft.

A further distinction of waterjet systems can be made after the type of intake applied. Two basic types of intake exist. One being an intake with an opening that is situated flush in the vessel's hull and consequently approximately parallel to the local flow. The other being an intake with an opening that is situated at approximate right angles to the local flow. Based on these two basic concepts, various hybrid forms may be conceived. The basic concepts are sketched in Fig. 1.3.

flush intake

ram intake

planing scoop intake scoop intake

Fig. 1.3Basic intake concepts (from Kruppa et al. [1968])

lo 1.4 Description of waterjet system Both types of intake have their specific area of application. An advantage of the flush intake is that it does not suffer from any drag due to protruding parts,as in the case of a ram type intake. Due to its position in the hull's bottom however, it may become subject to air ingestion, either caused by large relative motions and a shallow submergence, or by entrained air in the flow under the hull. These disadvantages are avoided with a ram type intake, which can be situated at a more favourable position in the flow.

The flush type intake is presently the most frequently applied intake. Ram intakes are mounted in Hydrofoil craft or in other craft where the flush intake would be situated too close to the water surface. Hybrid forms are not often applied any more. They may be used wherever the disadvantages of flush type intakes are considered too serious, but the drastic ram intake solution is considered overdone.

Process per element

The most important part of the jet system governing both the size of the unit and its overall efficiency, is the nozzle. This part of the jet system converts the potential (pressure) energy in the flow, added by the pump, into kinetic energy, used for thrust production.

For a given thrust and speed requirement, the nozzle area determines the thrust loading coefficient CT,,:

Tg CT,, = (1.3) -p UA where =gross thrust as defined by eq. (1.1) o =ship speed or free stream velocity =nozzle exit area. lt will be demonstrated in Chapter 2 that the ideal efficiency of the jet system only depends on the magnitude of CT,,. The ideal efficiency largely determines the overall efficiency. Thus, in analogy with propellers, the lower the thrust loading, the higher the efficiency of the system. This implies an increase in efficiency with increasing nozzle area.

The nozzle is usually shaped such as to have the vena contracta of the discharged jet coinciding with the nozzle exit. The vena contracta of the jet coincides with the position where the average static pressure in the jet equals

11 Chapter 1Introduction the ambient pressure of the medium in which it is discharged. Some jets are equipped with a clearly converging or Pelton type nozzle, causing the vena contracta of the jet to be situated outside the physical boundaries of the jet system (Fig. 1.4).

parallel throat nozzle Pelton type nozzle

jet boundary jet boundary

Vena contracta Fig. 1.4Distinct nozzle geometries

The function of the pump in the waterjet system is to add potential energy to the flow, resulting in a pressure rise over the pump. The most suitable type of pump depends on the jet's thrust loading coefficient CTfl. For highthrust loading coefficients, the ratio between nozzle velocity and free stream velocity is large, causing a relatively high head at low flow rate requirement. In extreme cases, the radial flow pump would offer the best pump efficiency.Nowadays, jet systems are usually selected at a lower thrust loading coefficient to obtain the highest efficiency. This design condition demands a high pump efficiency at a relatively low head but large flow rate. For theserequirements, the mixed flow and the axial flow pump offer a better performance.

The function of the intake and consecutive ducting to the pump inlet area is to provide sufficient flow to the pump. Intake design requirements relate to a maximum energy recovery from the flow about the hull and minimum energy losses within the intake. Another important requirement for the intake is that it should present, as good as possible, a homogeneous flow to the pump. The intake should further be as small as possible to minimize the weight of its construction and of the ingested water.

The intake and ducting mostly feature bends and a diffusing or contracting cross sectional area along the intake/ducting. It should be notedthat for most

12 1 .4 Description of waterjet system operational conditions, diffusion or contraction of the ingested flow already starts ahead of the intake. 1.5Relations with other propulsors

The waterjet, the marine propeller and the aeronautical jet engine share the same principle for thrust production. The latter two propulsors have furthermore been subject to a longer time of scientific interest than the marine waterjet. In this period, well established theories of and procedures for the assessment of interaction effects have become available. When investigating interaction effects in and about waterjets, due attention has therefore to be paid to these related propulsors.

Before discussing interaction aspects of the propeller and the gasturbine jet, the most salient similarities and differences between the propulsors are discussed.

1.5.1Comparison with propeller

The major hydrodynamic difference between a propeller and a waterjet system occurs in the state of the flow passing the actuator, and therefore the risk of cavitation. The state of flow can be characterized by the state variables static pressure and velocity as a function of their position.

Restricting ourselves to the steady process, we are not concerned with variations of these parameters in time. Averaging these parameters over the disk area just in front of the actuator, yields the two parameters that govern the cavitation number G: i-pv ±p2 (1.4) 2 where = vapour pressure.

The higher this cavitation number, the better the resistance in the actuator disk against cavitation.

Using a required thrust production at a given speed as a starting point for our comparison, the cavitation number of the propeller can only be increased by decreasing the velocity through its disk area. This conclusion is simply verified through the use of Bernoulli's theorem. Lowering the velocity through the disk area can only be accomplished by increasing the disk area.

13 Chapter 1Introduction The cavitation number just in front of the impeller disk of the waterjet is similarly controlled by the average velocity through this disk. This average velocity is however not only controlled by the impeller diameter itself, but also by the nozzle diameter. This is because the flow rate through the impeller disk is controlled by the nozzle area. For this resulting flow rate, the average velocity through the actuator disk is subsequently controlled by the impeller diameter. The smaller the nozzle area, the smaller the flow rate. And the bigger the impeller diameter, the lower the average velocity.

As we have seen in the preceding section, decreasing the nozzle area results in a decrease of ideal efficiency. This process of increasing the resistance against cavitation by decreasing the flow rate through the system is consequently at the cost of efficiency. This implies that when the jet is designed such as to have a better resistance against cavitation than the propeller, the propeller shows the better efficiency.

This lower efficiency of the waterjet is partly compensated for by the absence of appendage drag, which does occur for submerged propellers. This appendage drag can reach values at high hull speeds of over 20% of the bare hull drag, causing a major effect in power requirements.

Fig. 1.5 shows the trends in thrust loading coefficient CTfl and non-dimensional appendage drag as a function of the non-dimensional speed FnL.

12 0.25

t L)

o 0

0.2 0.4 0.6 0.8 1 1.2 1.4 6 FnL I-t

Fig.I .5Thrust loading coefficient and appendage drag contribution as a function of non- dimensional speed

14 1 .5 Relation with other propulsors As discussed before, the decreasing thrust coefficient results in an increase in waterjet efficiency. At the same time, the increasing importance of the appendage drag to the overall efficiency benefits the waterjet. If one furthermore considers the deteriorating effects of cavitation at the higher speeds on overall powering performance, it becomes clear that the waterjet system is especially suitable for the higher speeds, when purely evaluated in terms of cavitation and efficiency.

Propeller-hull interaction

The most frequently used model for the description of propeller-hull powering performance is based on the overall performance of the combined system, and the performance of the isolated systems in predefined conditions. This theoretical model provides a parametric description of the interaction. For this reason, it is a suitable model for application in preliminary ship design. A short description of the model is given below.

The powering characteristics of the isolatedhullareeither computed or measured during a resistance test. The powering characteristics of the isolated propeller are measured or computed for a uniform inflow. The performance characteristics of the propeller are then represented in a so-called hopen water diagram'. This diagram provides the relations between non-dimensional propeller speed of advance J, with non-dimensional thrust KT and torque KQ.

Considering the combined propeller-hull system, the propeller normally operates in the wake of the hull. The effective propeller inflow velocity thereby differs from the ship speed. By definition, the relation between thrust coefficient and propeller advance speed isset equal to that in free stream conditions. The advance ratio subsequently derived from the thrust coefficient as obtained from self propulsion tests, can now be compared with that based on ship speed (see Fig. 1.6, Newman [19891). The difference with the corresponding advance ratio as obtained from the open water characteristics is accounted for in the 'Taylor wake fraction' WT according to: U = UO(l-wT) (1.5) where U= effective propeller speed of advance U0 =free stream velocity or ship speed.

15 Chapter 1Introduction

i difference in US-* 1 W »1 = UEI/UMODEL

I I

I I (KQ )O I I difference in KQ S * I (KQ)SP

SQSP s.

UEJ UMODEL U - nD

KT = thrust coefficient KQ = torque coefficient

Subscripts O = open water condition SP = self propelled condition

Fig. 1.6Relationship between self propelled and open water propeller characteristics (from Newman [1989])

Because the propeller open water characteristics may differ from the propeller characteristics in the 'behind hull' condition, and because we have assumed identical thrust coefficients KT in both conditions for a given advance ratio J, a generally small discrepancy occurs in the torque coefficient KQ. This discrepancy is accounted for by the relative rotative efficiency iR (see Fig. 1.6):

K20 (1.6) iR KQ where K0 =propeller torque coefficient subscript O indicates open water conditions.

Usually, a discrepancy exists between the thrust T delivered by the propeller and the resistance R that was measured during the resistance test. This discrepancy is accounted for by the thrust deduction fraction t:

16 i .5 Relation with other propulsors

(T-R) (1.7) T

The overall efficiencyfluA can now be obtained from the open water efficiency and the interaction contribution

flOA 1Oib1NT (1.8) where ib = open water efficiency fl/NT =interaction efficiency, and the interaction efficiency can subsequently be written as:

(l-t) flINT - fiR (1.9) (1 WT)

The fraction occurring on the right-hand side of this equation is often referred to as the hull efficiency flH

As can be observed from the above model, the interaction between the propeller and the supporting hull is defined on a basis of the propeller open water characteristics. Characteristics that were obtained from thrust and torque measurements or computations. The idea of relating interaction to the free stream characteristics of the systems involved can also be used in a model for the description of waterjet-hull interaction. But because the waterjet free stream characteristics are obtained in a different way than practised for propeller propulsion, it is not obvious to use the same terminology and relations. 1.5.2Comparison with gasturbine jet system

First, a short description of the basic elements and processes of the gasturbine jet will be given. Having reviewed the working principle, a comparison is made between the elementary processes of the waterjet and the gasturbine jet. Finally, the applicability of the analogy with waterjet-hull interaction is addressed.

The description of aeronautical or gasturbine jet systems will be concentrated on subsonic jet engines. The physics involved in the corresponding processes is better comparable to those of waterjet systems because of the absence of shock waves.

17 Chapter 1Introduction Although the jet-fuselage configuration is not directly comparable to jet-hull systems, similarities occur. Hush intake type waterjets may be compared with similar intakes of jet engines embedded in the fuselage. Ram intake type waterjets as occur on hydrofoil craft may be compared with podded jet engines underneath the wings or mounted on the fuselage.

Description of gasturbine jet

A general scheme of the gasturbine jet is presented in Fig. 1.7.

a 1 2 34 intake compressor combustion camber turbine nozzle

a-1 ram.effect 2 adiabatic compression p(N/m2) 2 . 3: continuous burning at even pressure 3 .4 :adiabatic expension 4 . 5 adiabatic expansion in a convergent or convergent- divergent nozzle to excition of jet a o S(J/(kgK)) volume entropy

Fig. 1.7GeneraI scheme of gasturbine jet system (Bodegom, W. Van [19981)

In the actuator of a gasturbine jet (viz, the combustion chamber), chemical energy is directly converted into kinetic and internal energy in an essentially isobar process (path 2-3 in Fig. 1.7). By expanding the exhaust gases in the aft part of the jet system, most of the internal energy is converted into kinetic energy that can be used for thrust production (path 5-6 in Fig. 1.7).

This direct conversion of chemical energy within the jet can only occur in a compressible fluid, governed by thermodynamic principles. Burning fuel in the actuator of the waterjet would initially only result in a rise of the water temperature, without the flow being able to retrieve this energy for thrust purposes.

18 1.5 Relation with other propulsors Because of the compressibility of air,the distinct elements constituting the gasturbine jet system are characterized by a greater variety of physicalpro- cesses than in the case of waterjet propulsion. These processes are schematically presented in the ideal pV and TS-diagrams shown in Fig. 1.7.

The function of the ram intake of the gasturbine jet is to ingest the required mass flow from the external flow at a maximum energy recovery. Apart from maximum energy recoveryata minimal external drag, another condition imposed on inlet design relates to an even velocity distribution in front of the compressor mouth, so that an even force distribution on the compressor is obtained. At subsonic airspeeds, the process of air ingestion and compression in the intake is isentropic (path a-I in Fig. 1.7). Analogous to the waterjet intake, diffusion or contraction of the ingested flow already starts upstream of the physical intake opening.

Before entering the combustion chamber, the ingested air is further compressed by a compressor, performing an adiabatic compression (path 1-2 in Fig. 1.7). A high pressure of the ingested air is favourable for the thermodynamic efficiency of the combustion process.

The pressure increase in inlet and compressor is of great importance to the total efficiency. The pressure rise in the intake is about1 .6 times the free stream pressure. The pressure increase over the compressor is subsequently 12-15 times the pressure just in front of the compressor. For supersonic speeds, the pressure rise over the intake alone can even reach values in excess of 20 times the free stream pressure.

After the combustion chamber, the flow enters the turbine, where part of the energy is converted into mechanical power (path 3-4 in Fig. 1.7). This power is used to drive the upstream compressor. In the turbine, the exhaust gas is expanded, resulting in a decrease of gas temperature and pressure and an increase of flow velocity.

The final stage of the jet system consists of the nozzle, in which the potential energy of the flow is completely converted into kinetic energy (path 4-5 in Fig. 1.7). The discharged exhaust gases adopt the ambient pressure at a higher temperature (or internal energy) than ambient.

Comparison with waterjet

A remarkable difference with the waterjet propulsor is the conversion process of chemical into kinetic and potential energy. incorporated within the jet system

19 Chapter 1Introduction itself. As a consequence, the ingested medium is not equal to the discharged medium. The ingested flows consist of air and fuel, the discharged flow of exhaust gases.

The ingestion of a uniform velocity distribution by the intake is more important than it is for waterjets. The origin for this difference is that the specific mass of the ingested flow rate increases with speed, due to the compressibility of air and the increasing ram pressure with speed. This effect results in a thrust-speed relation thatis markedly distinct from the same relation for waterjets (see Fig. 1.8). Increasing the mass flow through the system for a given speed and thrust requirement, decreases the nozzle velocity ratio NVR. And a decrease of this parameter implies a higher ideal efficiency, as will be discussed further in Chapter 2.

thrust - speed relation for thrust - speed relation for incompressible fluid compressible fluid (waterjet) (gasturbine jet)

Resultant of A &B

E E-

ingested watervelocity ingested airvelocity

Fig. 1.8Thrust-speed relations for waterjet and gasturbine jet system

The compressor, mainly responsible for the pressure rise, requires a uniform inflow for an efficient and balanced performance. As a consequence of this uniform flow requirement, the inlets are either podded or fuselage integrated in such a way that no appreciable amount of low energy or vortex flow is likely to be ingested (Antonatos et al. [1972]). This is contrary to what is practised in marine jets (see Photo 1.1).

Despite the aforementioned differences, a remarkable correspondence occurs in operational conditions, expressed in Nozzle Velocity Ratio values NVR. Oper- ational values for this ratio occur between 1.5 and 5 for both jet systems (Borg et al. [19931). Consequently, their ideal efficiencies are comparable.

20 1.5 Relation with other propulsors

Courtesy Royal Dutch Air Force

Courtesy Lips Jets BV

Photo 1 .1Comparison of intakes of a gasturbine jet and a waterjet

21 Chapter 1Introduction It is concluded that the compressibility of air causes major differences in the processes of the gasturbine and the waterjet. Additional complications for the marine jet are furthermore the possibility of cavitation and consequent performance degradation, and the presence of an interface between the two media (water and air) in which the vessel operates.

Analogy with aeronautical jet-fuselage interaction

Fuselage interference effects on jet performance are of prime importance for aircraft designed for supersonic speeds. Due to the close interrelation between fuselage and jet engine in the case of flush intakes, the jet system design is closely integrated in the whole aircraft design process (Ferri [1972]).

To the knowledge of the author, there are no parametric models available to quantify jet-fuselage interaction effects for airplanes. Taking into account the broad attention that is paid to the jet-fuselage integration in the design process, and the requirement for uniform flow ingestion, the need for such a description may not be so evident.

Due to the marked differences in processes taking place in the marine jet and the aeronautical jet, as discussed in this section, aerodynamic publications have a limited significance as far as the marine jet is concerned. Nevertheless, sorne useful information can be obtained from this discipline. The work of Mossman et al.[1948] on flush type intakes may in this respect serve as a classical example.

1.6Review of previous work

A large number of publications dealing with the hydrodynamics or aerodynam- ics of jet propulsion has been published since jet propulsion started to raise interest. Because the interest was first excited in aeronautics, the first publications have an aeronautical origin. As concluded in Section 1.5, these publications have only a limited significance for the present work.

Waterjet technology has in the past particularly been pushed in Germany, Italy, New Zealand, the United States and Sweden. These countries have provided also most of the available literature.

This review of previous work is split up into a review of parametric models, experimental procedures and numerical procedures.

22 1 .6 Review of previous work 1.6.1Parametric models

For a meaningful set up of procedures and interpretation of the experimental and numerical information, parametric models are indispensable.

Description of parametric models

A parametric model is a special form of a more generic theoretical model. A theoretical model is a set of symbols and relations, describing both the elements and the processes occurring in the systems considered. The Navier-Stokes equations are generally considered as a basic theoretical model governing all flows that may be described as a continuum. These equations can be written in a differential form, describing the equations of motion for an infinitesimal volume, or in its integral form, describing the equations of motion for a certain control volume (Fig. 1.9).

Newton's second law as applied to fluid mechanics

Differential equation (Flow field) analysis Integral analysis

Non-viscous flow Viscous flow

Navier-Stokes equations

Differential form Integral form

parametric model

1 CFD applications Insight in relevant physics Storage of data for empirical use Analysis of model tests

Fig. 1.9Place and relevance of a parametric model in fluid dynamics

A parametric model of these equations can be extracted from the integral form for a simplified description of specific processes. This is done by substituting parametric expressions for integral expressions. Such a model is useful to gain insight in the relevant physics for a given process. It furthermore allows for an efficient storage of data on the process, consequently allowing for empirical

23 Chapter 1Introduction approaches. A third application of such a model is the analysis of data obtained from model tests.

Organization of review

As can be inferred from Fig. 1. 1, a complete description of interaction phenomena is only obtained after the subsystems involved are completely defined. This includes their relations with the undisturbed environment.

This condition is considered to be satisfied for the powering characteristics of the hull system. The hull's resistance has been studied for many decades now. An example of a detailed analysis of the hull's resistance is given by Paffett [1972]. Model test procedures for measurement of the hull's resistance are well defined (see e.g. HSMV report of ITTC [1987]).

The definition of the powering characteristics of the waterjet system in an undisturbed environment is more complicated however. This is illustrated by the confusion that exists in the literature about the control volume defining the waterjet system and the corresponding intake drag of flush waterjet systems. This consequently results in confusion about the defined gross thrust (eq. 1.1) and the actual net thrust that is available to propel the hull. Interaction is originated at the boundaries of the system and appears as a change of powering characteristics. A change in environment resultsin a change in stress distribution on, and changes in mass, momentum and energy fluxes through its boundaries. The attention related to interaction on waterjet performance will therefore be discussed first in terms of definitions of control volume and free stream characteristics, and subsequently in terms of changes in stresses and fluxes due to the hull action.

Although there seems to be little specific interest in jet-hull interaction in the literature, the subject is addressed several times as part of an overall performance description. Within the themes mentioned in the precedingparagraph, the literature is reviewed in temporal sequence.

In reviewing the work that has been done on parametric models, we will concentrate on jet-hull interaction for flush intakes, in line with the rest of this work. Subsequently, due attention will be paid to jet-hull interaction for ram intake systems. We will close the review on parametric models with a consideration of an original contribution by Schmiechen to the field of propulsor-hull interaction.

24 1.6 Review of previous work Flush waterjet system

Definition of jet system and free stream powering characteristics

The generally quoted waterjet gross thrust T is usually defined as the force that results from the change in momentum fiuthrough a certain control volume (eq. 1.1). The selected control volume also determines the difference between defined gross thrust and actual net thrust exerted by the jet upon the hull. A logical first step in defining jet system characteristics therefore seems to be an explicit definition of this control volume. Such a definition has long been missing in literature however.

Early parametric models for the description of waterjet performance are given by e.g. Brandau [1967], Kruppa et al. [1968] and Gao et al. [1969]. Emphasis in these theoretical models is put on the description of powering characteristics of the jet system in free stream conditions. Explicit definitions of control volumes are omitted, but implicit reference is made to a control volume with an intake area infinitely far upstream (control volume A in Fig. 1.10).

To the knowledge of the author, Bowen [1971] was the first author in the marine field, to bring about a discussion on the control volume that should be considered as a model of the jet system with flush intake. He discusses the difference between a generally applied definition of gross thrust and the actual thrust acting upon the hull. Analogous to the practice in the aeronautical field (Jakobsson [1951]), he designates the difference between these definitions as a 'pre-entry thrust', and derives an estimate of this thrust contribution for ram inlets. Bowen thereby also applies Control Volume A (Fig.1.10) for the description of the jet system.

An early parametric model including an explicit definition of the waterjet control volume is presented by Etter et al. [1980]. The definition of their control volume corresponds to volume C (Fig. 1.10). The free stream characteristics of the waterjet system are not elaborated. The emphasis is placed on a separation of jet system net thrust and hull resistance.

The discrepancy between jet system gross thrust and the bare hull resistance is expressed in an inlet system drag. This intake drag is derived from model tests with a self propelled model, and therefore also incorporates a change in hull resistance due to the jet action. in a recent publication by Allison [1993], a complete review of existing relations to describe waterjet performance is given, including a review of interac-

25 Chapter 1Introduction tion effects. Implicit use is made of control volume A (Fig.1.10). Allison includes an inlet drag allowance in the jet efficiency, to allow for the difference between gross and net thrust, but omits a definition. He mentions that this term tends to zero for truly flush intakes.

X 4 /y

z y pump

/ AA // r / / / B' B

fixed (material) boundaries variable (imaginary) boundaries in the flow

A = intake leading edge (imaginary) = ramp tangency point I'BC =lower dividing streamline C = stagnation point D = intake trailing edge or outer lip tangency point EE intake throat area

Possible waterjet control volumes:

CV A : II'CFF'I

CV B : A'FF'A CVC : A'B'CFF'A' Fig. 1.10 Definitions of jet system's control volume used in the literature (see also fold-out at the back)

Intake drag Many authors refer to the difference between defined gross thrust and a net thrust acting upon the hull as an intake drag. Although the intake drag is

26 1 .6 Review of previous work addressed several times (e.g. Mossman etal. [1948], Arcand etal.[1968], Hoshino et al. [19841), little attention is paid to its definition. An exception to this rule is the contribution by Etter et al. [1980], as discussed in the previous section.

Mossman and Randall [1948] determine the intake drag for a number of flush type intakes in a wind tunnel. They implicitly use control volume A (Fig. 1.10). It will be shown in Section 4.1.2 however, that their intake drag consequently includes a significant frictional drag contribution of the tunnel wall in front of the intake.

Arcand and Comolli [1968] use the same definition in their data reduction. They state however that they believe that a better definition of the 'real external drag' of the intake is possible. Although their idea is not elaborated in detail, it can be inferred that their improved definition gets rid of the major part of the tunnel wall contribution.

Hoshino and Baba [19841 define the intake drag as the difference between gross thrust required to propel the ship and its bare hull resistance. This intake drag consequently not only accounts for a discrepancy between gross and net thrust for the jet system, but also for a change in hull drag due to the jet action. The authors implicitly use Control Volume A (Fig. 1.10) for the definition of gross thrust.

Confusion about external intake drag and internal jet system forces is illustrated by statements in Okamoto et al. [1993] and Kim et al. [1994]. Okamoto et al. state that 'the intake duct shows a thrust generation mechanism' for certain operational conditions. Whereas Kim et al. state that 'the pressure distribution along the intake lip is responsible for additional appendage drag'.

Interaction effects

Effects on thrust and power

Using an equal flow rate through the system as a basis for comparison, both distortions in the local velocity distribution and distortions in the local pressures affect the ingested and the discharged momentum and energy fluxes through the waterjet system. These fluxes govern the associated thrust production and the power requirement respectively.

Only a few publications address the problem of waterjet-hull interaction in detail. The first accounts of interaction effects on waterjet performance relate to

27 Chapter 1Introduction the ingestion of boundary layer flow. This flow shows a decelerated velocity relative to the free stream velocity.

Although the effects of pressure distortions on jet performance are acknowledged in an early stage (see e.g. Kruppa [19681), much confusion arises as to how it should be accounted for in a parametric model, as noticed by Kruppa [1992].

Kruppa et al. [1968] account in their parametric model for the effect of the boundary layer velocity distribution on the ingested momentum and energy flux. The authors introduce momentum and energy wake fractions. The authors note that, whenever a pressure gradient occurs between the undisturbed free stream and the intake area of the waterjet, these wake fractions should be corrected for pressure terms. The correction for the momentum wake fraction is not elaborated however. The difference between gross thrust and bare hull resistance is referred to as a parasitic drag. This parasitic drag consequently includes a drag contribution of the intake and a change in hull resistance due to the waterjet action. Wilson [1977] gives a detailed account of the state of the art knowledge on waterjet-hull interaction in that time. The parametric model used by Wilson is based on schemes presented by Johnson et al. [1972] and Barr [1974]. The essential relationships are outlined by Miller [1977].

Miller describes waterjet-hull interaction in terms of ingested momentum and energy velocities, accounting for differences in the respective fluxes relative to the corresponding free stream fluxes. The effects considered are solely caused by the boundary layer velocity profile. The other interaction parameter is referred to as an intake drag, being equal to the difference in net thrust and calculated gross thrust. The intake drag is to be determined experimentally, implying that this drag component not only accounts for a net force acting on the intake part of the jet, but that it also accounts for a change in hull drag due to the jet action.

A more complete description of the parametric model by Miller is presented by Etter et al. [1980]. This model is adopted by the High Speed Marine Vehicle Committee of the 18th ITTC [1987]. The model describes the powering performance of the combined jet-hull system. without breaking it down in the per- formances of the isolated systems and their mutual interaction. The relation between intake drag and a thrust deduction fraction is elaborated.

28 1.6 Review of previous work Haglund et al. [1982] express a waterjet-hull interaction efficiency as a hull efficiency, analogous to the same efficiency used in propeller-hull theory. The same control volume for the waterjet system is used as described by Etter et al. [19801 (CV C in Fig. 1.10). The effect of the boundary layer velocity profile on momentum and energy flux is only taken into account by the use of an average volumetric intake velocity.

Later, Svensson [1989] includes a pressure term in the jet efficiency, accounting for the static pressure contribution in the ingested energy flux.

Hoshino et al. [19841 only account for interaction by using a thrust effectiveness (1-t). The authors do not account for the ingested boundary layer flow.

As a further development to the model proposed by Kruppa et al.[1968], Masilge [1991] breaks the distortions in ingested momentum and energy fluxes down into a pressure contribution and a velocity contribution. The requirement for a pressure term in the ingested fluxes was also noted and a model suggested by Van Terwisga [1991].

As a sequel to their 1968 paper, Kruppa [19921 presents a relation for overall efficiency based on thrust (thrust power efficiency), in which he incorporates the potential flow and viscous flow interaction effects separately, as proposed earlier by Van Terwisga [1991]. He notes the lack of a pressure term in the momentum equation for thrust and consequently observes that the equations for thrust power efficiency for ram type inlets on the one hand and flush type inlets on the other hand are not compatible. Based on this observation, Kruppa queries a conclusion by Svensson [19891, where the positive effect of a retarded potential flow wake on thrust power efficiency is noted.

Allison [1993] gives a review of interaction effects. Similar to the hull-efficiency in propeller-hull interaction, an interaction efficiencyis used in the overall efficiency equation, according to:

(l-t) 11= (1.10) (1-w) wheret =thrust deduction fraction w =volumetric wake fraction. lt is emphasized by Allison that this efficiency is not directly comparable to the hull efficiency used in propeller-hull theory. Contrary to the model for propel-

29 Chapter 1Introduction 1cr-hull interaction, where no interaction terms occur in the propeller efficiency, interaction terms remain present in the efficiency of the jet system.

Effects on lift

Svensson [1989] mentions a net lifting force on the stern of the vessel with active waterjet. This conclusion was obtained from pressure measurements on the hull in the vicinity of the waterjet system (see Fig. 1.11). He states that 'the total lifting force generated by the inlets can be in excess of 5% of the displacement for a high speed craft. The total lifting force can thus exceed the weight of the units. This will be recognized as a negative thrust deduction caused by a reduction of the vessels resistance'.

BOTTOM PLATING B =I .5D

BOTTOM PLATING B= D

INLET INLET VELOCITY RATIO (IV R) D = NOMINAL INLET DIAMETER B = BREADTH OF BOTTOM PLATING

Fig. I Il Lifting force due to pressure on the bottom plating and inlet for a KaMeWa waterjet installation (from Svensson [1989])

The issue of lift production caused by waterjet-hull interaction will be treated in Chapter 2.It will be shown that the jet system itself does not generate a lift force, provided the jet is discharged parallel to the hull's bottom.

30 1.6 Review of previous work Determination of ingested momentum and energy fluxes

An important problem in determining interaction effects on the waterjet performance, is the assessment of ingested amount of momentum andenergy for a flush intake operating in a non-uniform velocity field. For this particular problem, a strong analogy occurs between the flow in and about a flush intake ofa waterjet system and the intake of a condenser scoop system.

Spannhake [1951] presents a detailed theoretical analysis of the flow througha condenser scoop system. He defines clear control volumes for both the inlet and the outlet scoop. He also introduces an expression for the imaginary intake area of the protruding streamtube (area AB in Fig. 1.10). This expression is based on data obtained from flow visualisation studies about the intake as published by Hewins et al. [1940].

Quantitative experimental information on the shape of this imaginary upstream intake area for a waterjet is provided by Alexander et al. [1993]. These data will be reviewed in more detail in Section 4.3.1 of this work.

Interaction effects ou hull performance

Interaction effects on the hull are caused by a change in the flow about the hull due to the jet action. It can be expressed as a change in the hull resistance. This change in resistance is in the literature expressed in a thrust deduction fraction or an intake drag, as discussed in the foregoing. A possible change in lift production on the hull as mentioned by Svensson [19891 could, if present, also be ascribed to interaction.

Several authors, e.g. Hothersall [19921, Allison [1993], Van Terwisga [1992], mention the effect of waterjet weight on the hull performance. The weight of the jet system does not affect the hydrodynamic environment for a given hull loading condition, and does therefore not cause a true hydrodynamic interaction effect. As it does affect the vessel's weight breakdown, one should account for it in the jet selection process.

Interaction in ram type intake jets

Sherman and Lincoln [1969] discuss the optimization of the ram type intake for waterjet systems in detail. They include clear definitions of the net and gross thrust and the external drag of the jet system. They thereby implicitly consider the control volume AHFF'H'A' (see Fig. 1.12).

31 Chapter 1Introduction

nozzle F

F -- .

hull

strut

The net thrust, available to propel the hull is obtained from the vector summation of gross thrust and external drag:

Tnet Tg+Dext whereTnet = net thrust Tg = gross thrust Dext = external drag.

Their gross thrust is defined as:

Tg mnniO+(PnPO)An (1.12)

where = momentum flux p = pressure A = nozzle area subscriptn = nozzle O = free stream condition.

32 1 .6 Review of previous work

This definition grossly corresponds to the basic definition given ineq. (1.1), but is extended with a pressure force term over the nozzlearea. It will be demonstrated in Chapter 2 that this term is also present for flush waterjet intakes, but is included in a thrust deduction fraction t there.

The external drag of the system consists of the sum of the external forceFEXT, a so-called pre-entry drag DPE and a possible interference drag DINT:

DEXT FEXT+DPE+DINT (1.13)

The external force FEXT acts on the material external part of the waterjetsystem (AHH'A' in Fig. 1.12). It is obtained from the summation of allpressure and frictional forces in x-direction, associated with the ram inlet system from the stagnation line around the external surface to the termination of the system.

The pre-entry drag DPE acts on the protruding part of the streamtube ahead of the material intake. This is the same component that was introduced in the discussion on the net thrust of flush type waterjets by Bowen [1971] and discussed in the foregoing. It is caused by external diffusion or contraction of the ingested streamtube. As a consequence thereof, a discrepancy occurs between the actual net thrust and the defined gross thrust after the external forceFEXT and a possible interference drag DINT have been accounted for.

The interference drag DINT can be interpreted as a drag component accounting for a change in hull drag due to the presence of the waterjet.

A discussion on the subject of thrust definition and actual net thrustwas held during the 20th ITTC in and about the Report of the High Speed Marine Vehicle Committee {ITTC, 1993].

Because the flow is ingested at a certain distance from the hull, interaction between hull and intake is usually small. The hull drag may be affected by the pressure distortion by the intake or by an interference drag due to the strut piercing through the hull.

Parametric model due to Scizmniechen

An original approach tothe propulsor-hullinteraction problem isdue to Schmiechen [1968, 1970]. He presents a generic system of criteria to evaluate thepoweringperformanceofpropulsor-hullsystems.Heseparatesthe propulsor-hull system, thereby only providing a definition of the propulsor

33 Chapter 1introduction system. A definition of the hull system is not presented explicitly. As a consequence, a physical interpretation of the concept of resistance is not clear.

The propulsor system in free stream conditions is defined as an actuator through which the same mass flow rate is flowing and the same power is absorbed as for this system integrated in the combined propulsor-hull system. A physical system boundary is only described in broad terms. The outlet plane through which mass flow, momentum and energy fluxes are discharged, is situated in the far field for both the isolated and the integrated propulsor system. The intake boundary is not clearly defined in geometrical terms, but is to be solved for any particular case.

His definitions of efficiency that are introduced are not directly related to an effective/absorbed power ratio. The concepts of power that are introduced do furthermore not all have a physical interpretation, as momentum and energy fluxes are used indifferently. If one allows for this new-speak, it is probably possible to use these definitions in a system of relations that is consistent in itself.

Conclusions

It is concluded from the review of parametric models, that there is no model available that explicitly and completely accounts for waterjet-hull interaction with flush type intake. The usefulness of such a model is illustrated by the generally accepted parametric model for propeller-hull interaction, as discussed in Section 1.5.1.

Probably due to the absence of explicit relations for waterjet-hull interaction, there is widespread confusion about the effect of interaction between a flush type waterjet and its supporting hull. This confusion becomes apparent in the use of intake drag, thrust deduction, lift production and interactioneffects on waterjet performance.

1.6.2Experimental procedures

An analysis of model tests with a self propelled model provides quantitative information on interaction. Such an analysis involves a comparison of the results of the combined system with measured or computed properties of the constituting systems, viz, hull and waterjet(s). The work reviewed here concen- trates on procedures for propulsion tests.

Bare hull resistance tests are conducted by a wide variety of towing tanks and

34 1.6 Review of previous work various procedures have been published (see e.g. Reports of the ITTC Resis- tance Committee or the High Speed Marine Vehicle Committee).

Performance tests of isolated waterjet systems are less common. Although this latter type of tests is not considered to be part of this work, itis addressed shortly in this section for the sake of completeness. This deliberate thrift is justified by the fact that jet manufacturers have usually done extensivecompu- tations and measurements on their designs.

Propulsion tests

The High Speed Marine Vehicle (HSMV) Committee of the 18th ITTC [1987] provides a procedure for propulsion tests with waterjets. This procedure is based on the measurement of flow rate and the subsequent reduction ofmomen- tum and energy fluxes in and out of the jet system contained by the hull. The procedure is schematically presented in Fig. 1.13 and is outlined below.

The HSMV Committee states that the ship model should be equipped with scaled waterjet inlet and nozzle systems. They emphasize the needlessness of geometric scaling of the jet systems pump. A pump able to provide the required flow rate through the inlet and nozzle system is sufficient. This approach could be referred to as a 'black box' approach, as the precise characteristics of the pump are not relevant.

The HSMV Committee furthermore emphasizes the importance ofan accurate flow rate measurement as the basis for meaningful thrust andpower values. Apart from flow rate measurements, the ingested velocity profile ahead of the intake opening should be measured or estimated. This information is essentialto derive ingested momentum and energy fluxes from the measured flowrate. Thrust and power data can subsequently be obtained from these fluxes.

In addition to flow rate transducers, the committee states that the model should also be equipped for measurements of impeller thrust, torque,rate of revolutions, and hull towing force and running trim.

The Committee recommends a sequence of two similar tests after calibration of the flow rate transducers. In the first series of tests, the required flowrate should be measured at the pump rate of revolutions causinga residual towing force to the model equal to the calculated one. This forcecan be calculated with e.g. the procedure presented by Savitsky et al. [19811. In the second series, at pre-set model speed and impeller rotation rate, the velocity profile ahead of the intake should be measured with the Prandtl tube rake.

35 Chapter 1Introduction

EXPERIMENT DATA PROCESSING RESULTS

Q-calibration -VREF

VREF - VM Propulsion test i

u(z) -VM Propulsion test 2

Data reduction method

T(VM),'s (Vs)

Extrapol. method

T(V), JSE(Vs)

Jet system tests KH KMas f(KQ)

Matching prop & jet system data

'ir. (Vs), n(V5)

Fig. I . 1 3 Basic propulsion test procedure as recommended by the 18th ITTC

36 1 .6 Review of previous work In contrast with this 'black box' approach, there are a few accounts of propulsion tests with completely scaled waterjet units. Mavlyudovet al. [1975] and Lazarov etal.[1987] report of propulsion tests where the jet system was mounted rigidly within the hull. A set-up which does not allow fora separate thrust measurement of the jet-unit through force transducers. This set-up is supposed to allow for a measurement of required power on thepump impeller that can directly be extrapolated to full scale.

Mavlyudov et al. [1975] determine the discharged momentum fluxes from the nozzle and the intake through total pressure measurements with pitot rakes in the respective areas. An effective nozzle area is determined froma bollard pull test, where both the pulling force and the average velocity through the nozzle are measured.

In an alternative experimental set-up, forces between the jet unit and the hull are passed through by force transducers. All other connections between the jet unit and the hull are made flexible, so as to prevent them from passing through any forces or moments. Such attempts are reported to have been pursued by MARIN (ITTC [1987]) and Bassin d'Essais des Carènes (ITTC [1993]). A full scale experiment with this set-up is reported by Coop et al. [1992].

Flow rate measurements

Haglund etal.[1982] report on tests of a waterjet mounted on top of a cavitation tunnel and on full scale tests. They measured the local velocity distribution in front of the impeller disk (no impeller present). The flow rate was subsequently found from integration over the gauged cross section. As a check on this procedure, static pressures were also measured between the nozzle area and the stator. By applying the continuity equation and Bernoulli's theorem between the measuring section and the nozzle outlet, the flow rate could be calculated. The two methods were reported to give practically thesame result.

Hoshino et al. [1984] consider three ways of flow rate measurement:

The discharged flow rate from the nozzle is collected over a certain time interval, and the weight of water over this time interval is measured. These measurements provide a mass and, after accounting for specific mass, a volume flow rate. 2. Measurement of the jet velocity distribution through a pitot rake. After integration of the velocity field over the nozzle area a flow rateis obtained. This method is comparable to the one applied by Haglund et al. 11982].

37 Chapter iIntroduction

3. Direct measurement of the discharged momentum flux from the nozzle by measurement of a reaction force on a so-called reaction elbow. This procedure has been evaluated for a specific test set up by Eilers et al. [1977].

The authors selected procedure i because of its simplicity and accuracy of measurement. A sketch of the test set-up is shown in Fig. 1.14.

Towing Carriage

Guidea

Craft Model Jet Flow Measurement Tank

Propeller Rudder

Fig. 1.14 Test set-up for flow rate measurement: water collecting tank (from Hoshima et al. [19841)

As a check, they also conducted a bollard pull test at zero forward speed and compared the measured pulling force with the computed thrust. The results of this comparison are presented in Fig.1.15. Although computed and measured thrust are within 2% for one model, they differ some 20% for the other model. This discrepancy is ascribed to a scatter in the discharged jetfiow. The discrepancy between thrust derived from the flow rate measurementsand the directly measured thrust was accounted for by the introduction of an effective nozzle area in the thrust derived from flow rate measurements.

The HSMV Committee of the 18th ITTC [19871 also mentions three techniques for flow rate measurements:

1. Determination of an average nozzle velocity through venturi pressure taps in the nozzle.

38 1.6 Review of previous work Measurement of flow rate through paddle wheels or turbine flow rate transducers in the outlet nozzle. Weighing the discharged flow from the nozzle that is collected in a tank behind the model over a certain time interval.

-4 =5

0 5 10 et = PQÜn[kgf]

Fig. 1 .15 Comparison of thrust derived from flow rate measurement and directly measured thrust at bollard pull test (Hoshino et al. [1984])

Method 3, where a collecting tank is used, is reported to be an accurate method. It is however only a suitable method if the nozzle is sufficiently free from the water, so as to avoid a distortion of the water collecting gear on the flow about the ship model. This implies that this method is not suitable for low speeds or for arrangements where the water is leaving the nozzle at or below the water surface.

Itis suggested by Rönnquist Il983I1 to apply a convenient combination of a calibration of flow rate transducers at speed zero with a water collecting tank, and an actual flow rate measurement with these calibrated transducers during the propulsion test.It is suggested that either venturi pressure taps or paddle wheels be used for this procedure.

The HSMV Committee of the 20th ITTC [19931 mentions that 'major difficulties are experienced in flow rate measurements during self propulsion tests with waterjets'.

39 Chapter 1Introduction

Flow rate measurements at SSPA (Swedish Model Basin) are reported to consist of flow rate calibrations at speed zero (Allenström [1990]). The flowrate calibration is conducted by weighing the collected water over a certain time interval. This measured flow rate is calibrated with pressure taps in the nozzle anda paddle wheel imbedded in the wall of the nozzle. During the actual self propulsion tests, the calibrated relation from speed zero is used to derive actual flow rates.

Flow rate measurements at MARINTEK (Norwegian Model Basin) are also based on calibrations using a water collecting tank (Aarsnes [1991]). The measured flow rate is calibrated with three pitot tubes, situated in the intake and yielding an average local velocity. This local velocity was found to be more suitable for reference purposes than impeller rotation rate. Calibration between flow rate and these pitot signals is conducted for a range of speeds and impeller rotation rates, so that the actual propulsion test condition is covered. This was deemed necessary as deviations in the calibrated relation appeared for different speeds and impeller rates. After the calibration has been finished, free running propulsion tests are conducted.

The HSMV Committee flotes the difficulty in assessing the ingested momentum and energy fluxes when a clear three-dimensional flow about the intake is experienced. Such a flow condition is likely to occur if the intake is situated in large deadrise bottoms of e.g. SES or catamarans.

In their contribution to the workshop on waterjets of the 20th ITTC, Hoshino et al. [19931 present a number of procedures applied during several propulsion tests conducted in Japan. Apart from techniques that have already been mentioned in the foregoing, he gives an account of propulsion tests on a ram type intake. Apart from a venturi type velocity transducer, working over two distinct cross sections in the nozzle, the reaction force acting on a wedge situated in the discharged jet was measured (Fig. 1.16). The relation between the reaction force and the waterjet thrust had been calibrated at bollard pull condition. The authors state that the agreement in derived thrust from both measurements was good.

The difficulty of a good flow rate measurement is clearly illustrated by the large number of different flow rate measuring procedures. Up until the time this review was prepared, there does not seem to be consent over a robust and validated flow rate measurement technique.

40 1.6 Review of previous work

Lifter

Towing Carriage L:i1r-

I L-

Load Cell Pressure Gauges Dummy Hull / / Waterj' P pump Motor

Wedge Load Cell

Inlet Fig. 1. 16 Arrangement of venturi type velocity transducer and reaction force transducer for a pod-strut with a waterjet system (Hoshino et al. [1993])

Extrapolation method

Having addressed the issue of propulsion test procedures, the issue of extrapolating the model powering data to full scale values remains. The power demand by the waterjets is most logically obtained from the effective power demand by the full scale hull, the full scale jet powering characteristics and the full scale interaction effects. The corresponding powering data obtained from the model could be scaled with Froude's scaling principle, provided no scale effects were present. This procedure warrants dynamic similitude between gravitation and inertia forces.

The HSMV Committee of the 18th ITTC [19871 considers two scale effects important. One relatestothe differenceinfrictionalresistance, which is accounted for by an additional towing force during the propulsion test. A second scale effect relates to the difference in ingested boundary layer. The full scale boundary layer thickness and velocity distribution should be obtained from computations to allow for this difference.

The difference in bare hull resistance and measured thrust, accounted for by the thrust deduction fraction, is assumed to be free of scale effects and thus retains the same value for both model and full scale.

41 Chapter 1Introduction From the above assumption, the full scale thrust can be obtained from the measured thrust on model scale. With an extrapolated boundary layer velocity profile just ahead of the waterjet intakes, the flow rate can be determined that is required to generate this full scale thrust. Once the flow rate and the full scale jet system and interaction characteristics are known, the required pump head can be determined. Flow rate and pump head subsequently determine the working point of the pump, and with that, the efficiency and power requirement.

Jet system tests

The HSMV Committee of the 18th ITTC [1987] provides two different testing techniques to determine the powering characteristics of the jet system.

The first one is a procedure where the jet characteristics are obtained from propulsion tests with a waterjet-hull model. The hull can either be a model of the actual hull or a model of a specific test boat. For this purpose, all components of the jet system incorporated in the hull need to be scaled geometrically. This is in contrast with the black box approach, where only overall or interaction effects are studied.

Basic measurements for the determination of the jet system's powering characteristics are the flow rate, impeller torque and rotation rate. For a proper reduction of the jet system's free stream characteristics, itis essential to know the velocity profile ahead of the intake. Although not mentioned by the ITTC [1987], interaction effects should be accounted for in the derivation of the measured results to free stream characteristics.

The second procedure consists of tests on the isolated waterjet system in a water or cavitation tunnel. This set-up has the advantage that free stream conditions are approached, so that corrections for jet-hull interaction or jet-set-up interaction are small, and consequently so for the corresponding errors.

Conclusions

It is concluded from the review on experimental procedures that a broad procedure for self propulsion tests with waterjet propelled models is proposed by the ITTC [1987]. Within this procedure there is uncertainty about:

- robust and accurate flow rate measurement procedures; - the relation between flow rate and ingested momentum and energy flux, and thus thrust and power; - assumptions in the extrapolation method, especially with regard to the

42 1 .6 Review of previous work absence of scale effects in the thrust deduction fraction; - isolation of waterjet-hull interaction effects.

The latter uncertainty has been treated in the previous section.

1.6.3Computational procedures

Similar to the objective of experimental procedures, computational procedures seek to quantify interaction effects. In addition to propulsion tests, where integral quantities are obtained, computational methods provide a detailed insight in the flow phenomena. Often this latter aspect is worth the trouble of going through all the work, despite the sometimes doubtful quantitative results.

This review will first address the CFD work related to the analysis of the waterjet's free stream characteristics, which is addressed by the majority of the literature. Secondly, the literature dealing with a prediction of waterjet-hull interaction effects is discussed.

Free stream intake characteristics

Most publications on a computational analysis of the free stream characteristics address the performance of the intake. Initially, attention has been focused on a prediction of the pressure distribution along the intake ramp and the intake lip. This information is relevant for a prediction on the occurrence of cavitation, which may occur in the initial part of the intake. Nowadays, now that full RANS codes are available, attention is extended to the prediction of boundary layer separation, which may occur at the intake ramp, and the prediction of viscous energy losses and flow field at the pump inlet. A review of the relevant publications is given in this section, in an order of increasing complexity and potential resemblance with reality.

One of the first publications providing computed streamlines in the intake region is due to Kruppa et al. [19681. These authors compute the flowlines near 2D scoop and flush intakes through a conformal mapping procedure. This procedure allows for alimited number of mathematically defined intake geometries.

Kashiwadani [1985, 19861 presents well documented results on a potential panel code for 2D intake geometries. The purpose of his work is to analyze and optimize the initial part of the waterjet intake (ramp and lip) for cavitation free operation at high speeds. The author has developed a potential flow code where a continuous description of the geometry of the intake is obtained with a rda-

43 Chapter 1Introduction lively small number of points. In this respect, his method differs from the work of Hess and Smith [1966] and Ishikawa [1983]. The limited number of input points was desired for geometry optimization.

The continuous surface description was desired for a continuous and accurate pressure computation on the jet surface. The original method by Hess and Smith has been demonstrated to be less accurate for internal flows, such as occur in the waterjet intake (Hess [1975]). The original method applies a surface description by a distribution of quadrilateral panels. Each panel uses a constant source strength distribution over its surface. The boundary conditions are imposed in the so-called null point of each element. This point is taken as the point where the element itself has no effect on the tangential velocity. The velocities are computed only in these null points and velocities at other positions on the surface are obtained from interpolation in the known null points.

Kashiwadani [1985] uses a 2D integral equation to describe the source distribution over the material boundaries. The flow velocity vector iZ(x,y) is then given by the following equation: r (x,y) = U T-_ +Jf(s)L ds (1.14) 2m wheres =girth length along the boundary C (see Fig. 1.17) =position vector from (x,y) to point on boundary C =position vector from (x,y) to suction source with strength Q

i =unit vector in x-direction.

- U

Fig. 1.17 Nomenclature and definitions in waterjet model used by Kashiwadani [19851)

44 1 .6 Review of previous work Although the method compares good with an exact solution and with the results from Ishikawa [1983], a rather poor correlation with experimental results from a wind tunnel set-up is reported. Wind tunnel tests with a model having an aspect ratio of the intake throat of w(h=2 (compared to for the 2D computations) were conducted. The differences in pressure distribution are considered to be caused by 3D effects during the experiments and by viscosity effects, not present in the potential flow computations. The discrepancies within the intake are furthermore more significant than those just outside the intake. The supposed large effects of viscosity and 3D flow are enforced by the infinitely small lip radius of the tested model.

In a second report, Kashiwadani [19861 optimized the 2D intake on a maximum inception speed criterion. The optimized geometry showed a more rounded lip. This optimized geometry was again tested in a wind tunnel set-up, where a large number of static pressures was measured along the centreline of the intake. The correspondence between measured and computed pressures just outside the intake area appeared to be good, whereas correspondence within the ducting was poor again, except for the trends. The difference in C value within the ducting appeared to be similar for both cases (approx. 0.7). The effect of three-dimensionality of the flow was checked by sparse pressure transducers off the centreline. These transducers showed similar signals to the centreline ones however. The aspect ratio of the duct w/h was approx. 3 this time.

Førde et al. [1991] attempt to compute the flow field in the intake and the pertinent energy losses. They solve the Euler equations with a code suitable for both internal and external compressible flows. The time dependent Euler equations are solved by a time marching method. Grid generation is done by a multi block transfinite algebraic method. A geometry generation procedure has been developed by the authors, based on a simple description by three characteristic contour lines. A surface is subsequently modelled between the defined lines using Bezier surfaces.

In an attempt to compute the viscous losses in the intake as well, a thin layer Navier-Stokes code has been used. No further description of this method is given however. In their discussion on results, the authors conclude that the grid that was used is probably too coarse to give a representative computation of the viscous losses. The analysis of results is partly biased by a misconception on the ingested momentum by the intake. The authors correct the ingested momentum for the angle of the mean ingested flow vector. It will be shown in Chapter 2 however, that there is no loss in momentum associated with the angle under which the flow is ingested for a flush type intake.

45 Chapter 1Introduction Pylkkänen [1994] has analyzed a 2D intake with a RANS solver (FLOW3D). His main purpose was to find out whether the flow in the intake would cavitate or whether separation would occur. He verified whether a satisfactory solution in the 2D domain was obtained by checking the computed results with wind tunnel measurements on 2 intake geometries. He found deviations in static pressure between computations and measurements from 2 to 15% on the ramp and on the lip. The agreement on the ramp was generally better than on the lip surfaces. The measured top speeds at the impeller plane were further l-11% higher than predicted by the 2D calculations. Pylkkänen presumed that the deviations were caused by the typical 3D flow ingestion, which is not modelled in the 2D computations. He further presumes that the impeller shaft should be modelled in order to find reliable predictions.

The reported deviations in the internal pressure coefficient Gp as obtained from the viscous computations by Pylkkänen, are significantly better than the deviations obtained from the 2D potential computations by Kashiwadani. This indicates that the neglect of viscous effects has a bigger effect on the results (on the centreline intake) than the 2D modelling of the reality.

Waterjet-hull interaction

Kim et al. 111994] perform potential flow computations on a waterjet-hull combination. Their objective is to determine the pressure distribution and cavitation inception characteristics in the intake. To this end, the authors consider a mathematical hull form and an intake built up from cylindrical sections. The free surface boundary condition is approximated by its high speed limit:

onz=O (1.15) where = perturbation potential function.

Special attention has been paid to an accurate representation of the geometry by the use of higher order boundary elements. These elements use cubic spline interpolation functions for the source distribution over each panel.

The authors conclude that the pressure distribution is strongly affected by the ship's hull. They furthermore conclude that the pressure distribution along the ramp centreline is more critical to cavitation inception than along the lip. They state that the pressure distribution along the lip is directly responsible for additional appendage drag.

46 1 .6 Review of previous work Their conclusion about the importance of the ship's hull on the intake's pressure distribution is likely to be caused by either the mathematical hull form, not representative for realistic hulls, or by the computational method. From experiments at MARIN, changes in velocity near the intake due to the hull appear to reach maximum values of approx. 5%, whereas the authors show a value of 14% at the nose of the intake ramp (ramp tangency point), increasing to a difference of 22% with free stream velocities further along the ramp.

Their conclusion about the effect of the lip's pressure distribution on appendage drag is incorrect as will be discussed in Chapters 2 and 4.

Latorre et al. [1995] study the intake flow from a waterjet-hull combination. They consider the effect of trim on intake pressure distribution and cavitation inception by using a 2D RANS code, described by Miyata [1988]. The authors found a significant reduction in the minimum C (approx. 0.4) on the internal part of the intake lip due to a change in trim by the hull.

The paper suggests that the distance from the keel to the lower boundary of the computational domain is only some 20% of the hull's length. This, together with the 2D approach and the relatively short length of the hull in front of the intake is likely to cause significant deviations from representative 'real world' conditions. The authors furthermore conclude a significant influence on intake efficiency, which is not justifiable from the presented results.

Okamoto et al. [19931 present pressure measurements in the intake of a jet-hull model, measured during propulsion tests. Although these data cannot be interpreted to overall performance, as is done by the authors, they may serve a purpose in the validation of CFD results.

Conclusions

It is concluded from the review on computational procedures, that most of the computational work is directed towards intake flow analysis. Aspects of interest are the viscous energy losses, the flow field at the pump inlet and the detection of cavitation inception. A few attempts are reported that deal with waterjet-hull interaction. The conclusions drawn from these computations are not in agreement with the experience and insight that is obtained from the present work however.

47 Chapter 1Introduction 1.7Summary of present work

When starting an investigation into a rather abstract physical phenomenon, such as waterjet-hull interaction, one first needs to search for tools. A theoretical model providing a description of a phenomenon can in this respect be regarded as an essential tool. Other tools that are considered essential are experimental and computational procedures.

To illustrate the strong interrelation between a theoretical model and an experimental procedure, we consider the following approach for an investigation. One could, for example, start observing by experimenting. From these observations a lot can be leaint about the adequacy of an available physical or theoretical model. After a subsequent evaluation of experimental results one may have to adapt the theoretical model, and after having done this, one may be forced to revise the experimental procedure. It is this iterative way of working that has been gone throughout the present work. For the readers tranquillity of mind, he or she will not be teased with a presentation of this work in a similar whimsical way.

After having done the first propulsion tests with waterjet propelled models, three conclusions gradually emanated. One conclusion referred to the difficulty of the experimental procedure required to measure the powering characteristics of a waterjet propelled model. A second conclusion referred to the absence of a theoretical model, fully and explicitly expressing the interaction effects. And finally as a third conclusion, interaction appeared to be able to affect the required power with well over 20%.

1.7.1Theoretical model

Because of the observed lack of a theoretical model describing all possible interaction effects on hull resistance, jet system thrust, power required and thus overall efficiency, such a model is discussed first. Perhaps the main difference between this model and previously published models is that waterjet-hull interaction effects are accounted for completely and explicitly. As part of the model, a clear definition of the jet system's free stream conditions isproposed, together with a definition of the bare hull powering characteristics. These definitions link up with those proposed by the High Speed Marine VehicleCommittee of the 18th ITTC [198711.

In the proposed theoretical model, the difference between waterjet gross thrust and net thrust is accounted for by a true thrust deduction fraction t1, which is a property of the jet's free stream characteristics. This thrust deduction fraction is

48 1 .7 Summary of present work thus not an interaction parameter, contrary to the generally applied definition of thrust deduction in propeller-hull theory. The thrust deduction fractionas introduced here, may be subject to interaction effects itself. The change in hull resistance due to the jet action is captured in a so-called resistance increment fraction r.

The flow that is ingested by the intake and sometimes the flow that isdischarged from the nozzle area, is affected by thepresence of the hull. These distorted flow effects are accounted for by so-called momentumand energy interaction efficiencies. These efficiencies account for the effect that is caused by distorted ambient velocities and pressureson momentum and energy fluxes, relative to those in the free stream condition.

Explicit relations for the thrust deduction fraction, resistance increment fraction and momentum and energy intake efficiencies are derived from integralcon- siderations of the conservation laws of momentum andenergy. Consistent relations are derived for the free stream characteristics of the jetsystem. 1.7.2Experimental procedure

Having constructed a theoretical framework, quantification of therelevant parameters is a logical next step. Before starting a detailed analysis of all possible contributions, it is preferable to obtain quantitative informationon the major parameters, indicating the overall significance of interaction.This overall quantification of interaction is obtained from model propulsion tests.

Despite the well developed procedures for propulsiontests with propeller propulsion, such procedures cannot be applied for waterjet propelledmodels. The main reason for this set-back is the close integration between waterjetand hull system. The forces on the impeller of the jet only partly account for thepower- ing characteristics of the complete jet system. Forcesare also passed through to the hull by the ducting and pumphousing. The deliveredpower by the impeller is furthermore only representative for the prototype deliveredpower if a completely scaled jet system has been used in the model tests. In addition,such a model jet would need to be sufficiently large to avoid uncontrollable scale effects.

During propulsion tests with waterjet propulsors,a geometrically scaled hull model with a model stock jet having geometrically scaled intake and nozzle openings proceeds at a scaled speed through the model basin. As willbe discussed in Chapter 3, the most effective way tomeasure powering characteristics of a waterjet system is to measure volumetric,momentum and energy fluxes

49 Chapter 1Introduction through intake and nozzle areas. This requires a highly accurate method for the measurement of flow rate through the waterjet model.

A satisfactory technique to do this is searched for and various options experimentally evaluated. One method, using a built-in averaging static pitot tube was selected as most reliable and accurate transducer for flow rate measurements. A discussion on accuracy and reliability of the methods considered is presented in Chapter 3.

Three sources for scale effects can be acknowledged when extrapolating model propulsion tests. One source for scale effects is the hull's resistance. The other source is embedded in the powering characteristics of the model jet system. A third source is formed by the interaction effects between jet system and hull.

As for the extrapolation of the hull performance, a wealth of information and proceduresisavailable to make satisfactory assessments of possible scale effects. Therefore no specific attention will be paid to this subject in the present work.

After more knowledge on the jet system free stream characteristics and the waterjet-hull interaction mechanism became available during the project, a better assessment of possible scale effects came into reach. This knowledge is reworked in both the experimental and extrapolation procedure. The proposed ITTC procedure for propulsion tests (ITTC [19871) is hereby used as a starting point. The assumptions in this model are checked and procedures are elaborated in more detail. In addition to an extensive discussion on the experimental procedures considered, some quantitative results from the propulsion tests are discussed. This discussion serving the purpose of directing further research.

1.7.3Computational analysis

Three incentives for a detailed computational flow analysis grew during the study. These incentives are:

- The requirement for a detailed insight in the jet system free stream characteristics. - The urge to assess the validity of computational procedures for a determination of the overall powering characteristics and separate interaction effects.

50 1.7 Summary of present work

- The necessity to study the validity of initial simplifications andassump- tions that are made in the propulsion test procedure.

Insight in the jet system free stream characteristics is needed to identify and quantify possible sources for interaction. It is also required to investigate the validity of assumptions in the extrapolation procedure proposed by the ITTC [19871.

A potential flow panel code for the analysis of non-viscous flows is usedto study the flow in the intake region. A validation studywas conducted using detailed flow measurements on a flush intake in the MARIN large cavitation tunnel. From this validation study, it appears that for an importantrange of working conditions, a satisfactory prediction of the flow just outside the intake can be obtained. The results are also used in an assessment of the jet's thrust deduction fraction t1. The computed results are furthermore used to gain knowledge about the virtual intake area of the chosen control volume.

A potential flow code incorporating linearized free surface effects, is usedto study the effect of flow ingestion by the intake on the equilibrium position and the pressure drag of the hull. For the higher speed region, a modified Savitsky method is used for this purpose.

For the reduction of thrust, power and efficiency, from propulsiontests, assumptions need to be made with regard to the relation between volume flow rate and ingested momentum and energy fluxes. For such relations and for a better understanding of the relation between gross and net thrust of the jet system, a detailed study of the flow in and around the flush intake is conducted.

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52 Chapter 2

2 Theoretical model 2.1Systems decomposition

In analysing complex systems, but also in designing them, decomposing the total system leads to a better insight in the performance of the constituting systems. In decomposing a complex overall problem into smaller partial problems, mutual constraints between the partial problems have to be acknowledged, so as to guarantee a proper functioning of the overall system.

For the present case, the waterjet-hull system is decomposed intoa bare hull and a waterjet system. The bare hull is equal to the hull of the combinedsys- tem with the exception that the waterjet is not present. The weight and the position of the centre of gravity however correspond to those of the combined system in operation. The weight of the hull thus includes the jet system's weight including entrained water. This definition corresponds to the proposed ITTC procedure for model propulsion tests (ITTC [19871).

The waterjet system can be subdivided into a pump system anda ducting system. The pump system is the driving heart of the waterjet, converting mechanical power into hydraulic power. The ducting system leads the required flow rate from the external tiow to and from the pump again into the environment.

53 Chapter 2 Theoretical model The pump and ducting system of the waterjet are usually an integral part of the hull. Therefore, the total jet thrust exerted on the hull and the corresponding required power cannot be measured or computed so easily as in the case of propeller propulsion. An indirect way of measuring thrust and power has to be followed. In doing so, it appears that the powering characteristics are most appropriately obtained from integral considerations of the conservation laws over a suitably chosen control volume.

Although the overall powering characteristics are basically independent of the subdivision of the total system, clear definitions of the subsystems are essential in avoiding inconsistencies in the description of interaction.

2.1.1Definition of jet system control volume

Control volumes are preferably chosen such that the required forces are passed by. or required fluxes are passing through their boundaries. Furthermore, the boundaries are chosen such that knowledge about forces or fluxes acting on them or passing through them is obtained easily. Apart from these theoretical considerations, one may impose that the control volume selected for a waterjet system corresponds to that part of the flow that is strongly affected bythe waterjet system. In this way, interaction effects between the flow about the hull and that through the waterjet are relatively small. Consequently, the overall performance of the composed system is largely determined by the performance of the individual systems. The working point of the waterjet-hull system is determined by the thrust required by the hull and the net thrust delivered by the waterjet system. Having defined a control volume, the thrust generated over this volume can be obtained from the conservation law of momentum. An obvious definition of thrust is then given by the net rate of change of the momentum flux in x-direction. This so-called gross thrust Tg is generally not equal to the thrust acting on the hull however. This latter thrust is made up from the total hydrodynamic stresses (both normal and tangential) acting directly upon the material (fixed)boundaries of the waterjet system. It will be referred to as net thrust Tnet in the following.

General agreement seems to exist in the marine literature on the definition of gross thrust T. Most definitions correspond to the oneused by the High Speed MarineVehicle Committee of the 18th ITTC [1987]:

(2.1) Tg = tnni: -mix

54 2.1 Systems decomposition where = momentum (m) flux from the nozzle (n) in x-direction mix momentum flux ingested through the intake area (i)inx- direction.

Less agreement is found however on the boundaries over which the integral consideration is made, as was discussed in Section 1.5.1. This can easily lead to serious differences in results.

One of the possible control volumes is designated volume A in Fig. Fig. 2.1. This control volume is used by a.o. Bowen [1971]. An advantage of this control volume is the knowledge that is available on the flow characteristics in the intake region. A disadvantage is however, that a large part of the jet system is now positioned along the hull and in the hull affected stream. As a consequence, external forces can affect the thus defined internal jet flow over a large part of the jet system's boundaries, resulting in a strong dependency of the jet system's performance on the hull containing the jet.

A second alternative is represented by control volume B, spanned by the points A'DCFF'A' (Fig. 2.1). This is a practical definition of the control volume when thrust measurements are obtained from a set-up where the complete waterjet (model) is separated from the hull model and only attached to it through force transducers. A description of such a set-up is for example given by the ITTC [1987] and Alexander et al. [1993]. If the required power is to be measured from model tests, a proper model of the complete waterjet unit is required. The size of the jet model needs to be sufficiently large so as to avoid large scale effects in the internal flow, hampering a proper scaling of measured input power.

In this definition of waterjet control volume, the gross thrust is identical to the net thrust acting upon the hull (provided no net force results from the pressure terms over the nozzle area). It is difficult however to determine the thrust from momentum flux considerations on the ingested flow, as the velocity distribution in the intake area A'D is highly irregular. For this reason, and because the pressure in this area shows a similar irregularity, estimates of power through evaluation of the net change of energy fluxes is also difficult and inaccurate.

The most frequently used control volume is referred to as volume C, and is represented by the points A'B'CFF'A'. The intake area A'B' is typically situated at the intake's ramp tangency point A'. This control volume is implicitly used by Wilson [1977] and Miller [1977]. A more accurate description of the control volume and appropriate theoretical model is presented by Etter et al. [1980], which is also used by the ITTC [1987].

55 Chapter 2 Theoretical model

z 8 r

A'A I -Jl U0

fixed (material) boundaries variable (imaginary) boundaries in the flow

A = intake leading edge (imaginary) A' = ramp tangency point I'BC lower dividing streamline C = stagnation point D = intake trailing edge or outer lip tangency point EE' = intake throat area

Area I A1 = imaginary intake area Area 2 = A2 dividing stream surface Area 4 = A4 = outer lip surface Area 6 = A6 = internal material jet boudary Area 7 A-j = boudary area of pump control volume Area 8 = 8 =nozzle discharge area Volume P = Vp = pump control volume

Suitable waterjet control volumes: CVA: II'CFF'I CVB: A'DCFF'A' CV C: A'B'CFF'A' CV D: ABCFF'A

Fig. 2.1Definition of jet system's control volume (see also fold-out at the back)

56 2.1 Systems decomposition This control volume offers good possibilities for a survey of the flow in the intake region A'B'. The material (fixed) boundary of the waterjet system does not coincide with the external hull, and the jet system boundary exposed to the external flow is relatively small.

A more uniform velocity distribution in the intake area A'B' is obtained when the intake area is shifted slightly ahead of the intake's ramp tangency point (A'). In this way, most of the effect of the intake ramp curvature on the flow in the intake area is avoided. It is furthermore more logical that the flow strongly affected by the waterjet geometry, belongs to its internal flow. The corresponding control volume is designated volume D (Fig. 2.1).

Although the extent of the ramp curvature effect is a function of the curvature, the distance A'A may be more uniquely defined as a part of the intake length A'D. Point D is determined by the intake geometry and is referred to as the intake trailing edge or outer lip tangency point. From potential flow computations and Laser Doppler Measurements that were made at MARIN on an intake with a relatively small radius of curvature, it was concluded that a distance A'A of 10% of the intake length A'D is efficient in smoothing the 3-D velocity profile in the intake area. The resulting velocity field is presented in Section 4.1.1.

Having selected control volume D, the ducting system is partly defined by the fixed (material) boundaries of the jet system, partly by a dividing stream surface ahead of the physical intake opening. This dividing stream surface (A2 in Fig. 2.1) is an imaginary surface in the flow, through which no transport of mass occurs by definition.

The geometry of the areas 1 and 2 depends on the point of operation of the waterjet. It may also be affected by the external flow, e.g. in the case where a longitudinal pressure gradient exists.

The flow is discharged through area 8, representing the nozzle area. Further- more, the flow is bounded by area 6, representing the physical ducting of the waterjet system. All forces, including pump forces, exerted by the waterjet system on the hull can only be passed through this area and through the pump control volume VP.

An interesting observation can be made when the control volume A is studied in a free potential flow. This is a potential flow that is not distorted by the hull nor by free surface effects. In this particular case, it can be demonstrated that the net thrust, is equal to the gross thrust (Van Gent, [1993]). This observation

57 Chapter 2 Theoretical model is used in the derivation of the ideal efficiency as discussed in the previous section. It can also be used for the derivation of an expression for the thrust deduction fractiont., both in free stream and operational conditions. Using these relations, it wili be demonstrated in Section 2.3.1 that under certain conditions, the gross thrust of control volume A equals the net thrust in operational conditions.

2.1.2Analysis of overall powering characteristics

Dominant parameters in the powering characteristics are thrust and power. The working point of the jet system is determined by the equilibrium between the required thrust by the hull, and the actually delivered thrust by the jet.

The effective power delivered by a system is often expressed in its non-dimensional form. An efficiency is thus obtained that can generally be defined as:

'doute (2.2)

where '3oute = effective power delivered by system Pin = power input in system P, =

loss = power losses. The efficiency of the overall system can be obtained from the efficiencies of the subsystems from which itis composed. The process of energy conversion through each subsystem of the combined waterjet-hull system is sketched in Fig. 2.2, and will be discussed in the following.

When matching two distinct subsystems, the overall performance is generally not equal to the overall performance that results from the free stream characteristics after matching both systems. The difference being referred to as interaction. For the purpose of design or analysis of such a combined system, it is desirable to have the interaction effects explicitly defined. The overall efficiency of the combined system can then be obtained from the free stream efficiency n0 and an interaction efficiency nINT according to:

OA = nonlNT (2.3)

58 2. 1 Systems decomposition

JSE pump system ducting system

jet system TE 11et U

mI l+r hei

bare hull system

Fig. 2.2Decomposition of energy fluxes through waterjet-hull system

The performance of the jet system in free stream conditions will now be worked out first, followed by an analysis of the waterjet-hull interaction components.

Jet system

The actual thrust delivered by the waterjet should match the required thrust by the hull. Usually, a gross thrust Tg is introduced, which generally differs from the actual thrust Tnet. The reason for the introduction of a new definition of thrust is that this thrust is more easily computed or measured over a suitably chosen control volume.

To facilitate conversion from gross thrust to net thrust, these two definitions of thrust can be related to each other by a single parameter. A logical reference to this parameter isthrust deduction fraction' t1, according to:

Tg(l t1) = Tnet (2.4)

A simple expression for the quantification of the jet's thrust deduction fraction will be discussed in the applications section.

The thrust deduction has been used here in the same form as it is commonly used in propeller-hull theory. The distinction is that the thrust deduction fraction accounts here only for the difference in gross and net thrust of a waterjet oper-

59 Chapter 2 Theoretical model ating in free stream conditions. In propeller-hull theory, the thrust deduction fraction accounts for the additional resistance of the hull due to the propeller action, and as such, is an interaction parameter.

The primary objective of the jet system is to convert the hydraulic power delivered by the jet systemJSEinto a thrust acting on the hull. The effective jet system power J5Ecan be regarded as the power required to transport a certain flow rate Q from the intake (AB) to the nozzle, and can be obtained from:

JSE =QH5 (2.5) whereHjs = waterjet system head. The appropriate energy levels at the nozzle and the intake, determining the jet system head, are strongly affected by the flow conditions in the environment of the waterjet system.

The power appropriate to the jet system's thrust production can be designated as effective thrust power PTE: (2.6) TE TnetU

where U0 =hull's speed or free stream velocity. The conversion from hydraulic power to thrust power is accompanied by axial kinetic energy losses, which are usually accounted for in a so-called momentum or jet efficiency. The jet efficiency used by Etter et al. [19801, isdefined as:

T,U0 (2.7) 11JET - rD JSE where Tg = gross thrust. The free stream condition of the waterjet system is now defined as the condition where the jet operates in an undisturbed flow with uniform velocity U0 in x-direction. Such a condition can for example be created in CFD codes or on a test stand in a water tunnel. The centre of the nozzle area issituated on the free surface.

For this condition, the product of jet efficiency and thrust effectiveness (1-t1) can be transformed into the ideal efficiency Ti,:

60 2.1 Systems decomposition

TgOUØ(1 1i -t10) (2.8) = JSE0 where subscript O indicates free stream conditions.

The advantage of selecting the free stream conditions such that this product develops into the ideal efficiency, is that two simple relations can be derived for this efficiency:

2 nl = (2.9) i +NVR where NVR= nozzle velocity ratio; NVR = u,/U0 or 4 iii (2.10) 3+Jl +2CT where CTfl thrust loading coefficient; CTfl = T/(½pUO2A) A =nozzle area.

The efficiency of the conversion process by the jet system from hydraulic jet system powerJSEto effective thrust power ATE' is thus expressed by the ideal efficiency 1:

TEO Iii = (2.11) JSE0

This ideal efficiency represents an important part of the overall efficiency of the jet-hull system.

The hydraulic jet system powerJSEresults from the effective pump powerPE after accounting for the energy losses due to the ducting. The energy losses occurring in the ducting system can be accounted for by a ducting efficiency 1ducr

'3JSE (2.12) PE

61 Chapter 2 Theoretical model

The pump system converts the delivered mechanical power Dinto hydraulic power, designated here as the effective pump powerPEThe efficiency appropriate to this conversion process is designated pump efficiency rjp:

PE lip - (2.13) 1D

Interaction

So far, the hull and the waterjet system have been discussed from the viewpoint of free stream characteristics. When these two systems are fit together, they interfere with each others performance.

The bare hull resistance is changed due to a distortion in the flow about the aft body. At higher speeds, this distortion can furthermore cause a distinct equilibrium position of the hull, thus causing another change in resistance. In an equilibrium situation, the actual resistance of the hull balances the net thrust delivered by the jet system. The change in hull resistance can now be expressed by a 'resistance increment' factor I +r, according to:

Tnet i +7 = (2.14) RBH

Similarly, the jet system performance is affected by the flow distortion caused by the hull. Due to this distortion, a boundary layer is ingested through the intake area and the local flow velocity is likely to differ from the free stream or the hull's velocity. This affects the ingested momentum and energy fluxes, and thus the delivered thrust and power. Analogous to interaction effects in the intake region, interaction effects may also occur in the nozzle region. This occurs for instance when the nozzle is submerged in the transom flow instead of in air. Corrections on these fluxes can be applied by introducing a momentum interaction and an energy interaction efficiency respectively.

Interaction effects on momentum fluxes affect the thrust production. They can be accounted for by a momentum interaction efficiency 1lmI according to:

Tnet (2.15) T,11

62 2.1 Systems decomposition Interaction effects on the energy tiuxes directly affect the power balance. These effects can be accounted for by an energy interaction efficiency11e1' according to:

= JSEO (2.16) JSE

The overall efficiency of the waterjet-hull system can be defined in the usual way, according to:

PE lOA = (2.17) "D where E =effective hull power;E = RBHUO. After substitution of equations (2.6) and (2.11) to (2.16), the following relation for the overall efficiency is obtained:

11e! (2.18) 10A = li1 ductlP(1 +r)lj

This overall efficiency may subsequently be decomposed into the product of the free stream efficiency 1lü and the interaction efficiency11JNT' where

110 = lIli ductlP (2.19) and

11e! li/NT (2.20) (1 +rYq,1

Note that a change in net thrust, expressed here inr, also affects the ideal efficiency. This is caused by a corresponding change in thrust loading coefficient. This could be regarded as a secondary interaction effect, which is not incorporated in the interaction efficiency.

63 Chapter 2 Theoretical model 2.2Basic equations

Relations for the delivered thrust and corresponding required power will now be derived from the conservation laws of momentum and energy respectively. For this derivation, we will consider the conservation laws in their integral form, for a control volume fixedinthe coordinate system. A body-fixed Cartesian coordinate system is used, with the x-ordinate oriented parallel to the local buttock (parallel to AD) and the z-ordinate pointing downward (Fig. 2.3). For reasons of simplicity, it is assumed here that the jet, discharged from the nozzle area FF' is oriented parallel to the x-ordinate.

x, y, z hull fixed coordinate system X', y', z'earth fixed coordinate system rotated coordinate system x, y. z (hull fixed)

Fig. 2.3Definition of coordinate systems

Tensor notation is used throughout the equations with the Cartesian summation convention. In any product of terms, a repeated suffix is held to be summed over its three values 1, 2 and 3 (or x, y and z). A suffix notrepeated in any product can take any of the values 1, 2 or 3.

The pump system of the waterjet is represented by a system of one or more actuator disks. They are contained in control volume V and exert a force per unit mass on the fluid and deliver a power D to thefluid.

64 2.2. Basic equations 2.2.1Thrust

The thrust is a force vector that can be quantified through use of the conservation law of momentum.

The conservation law of momentum in words reads that the net rate of change of momentum for a given control volume equals the sum of the forces exerted by surface forces and volume forces. This yields for a stationary situation, the following momentum equation in i-direction, in its integral form:

J J pu(u)dA=fJ (2.21) A1+A8 A1A2A6A8 V1 V where¡Ip u(uknk)dA= net momentum flux through control volume ffodA = external force acting on surface of the control volume IffpFdV = external force acting on the mass contained in the control volume fIfpF1dV = pump force acting on fluid

Fig. 2.1 lists the designations of the surfaces and volumes.

In examining eq. (2.21), note that by convention, the normal vector on a surface always points in a direction out of the control volume. Hence, when ialso points out of the control volume, the product un is positive. The flow is then physically leaving the control volume, i.e.itis an outflow. An inflow in the control volume consequently shows a negative contribution.

The external force acting on the surface is made up from the total mean stress in a turbulent flow:

JJYdA =JJn1dA (2.22) where =total mean stress; -p& + p =time averaged pressure = Kronecker delta (equal to 1 if i=j and O otherwise) =total shear stress tensor; t1' + t11' =viscous stress; 2pS p = dynamic viscosity of fluid

65 Chapter 2 Theoretical model

Sf,, = time averaged rate of strain = contribution of turbulent motion to the stress tensor; Reynolds stress tensor.

Because the surface normal vector is positive when pointing out of the control volume, an external pressure force acting upon this volume is positive (because of the minus sign of p in The sign of the force that occurs in the equation when written in Cartesian coordinates, depends on the direction of this force in the coordinate system.

In search for a relation between the physical flow model (streamtube) and the geometrical model (waterjet surface), we will now consider the momentum balance in x-direction. We will define the thrust pertinent to the streamtube as gross thrust:

The gross thrust Tg is defined as the force vector pertinent to the change in moinen turn flux over the selected control volume, acting on its environment.

Because we are mainly interested in the x-component of this thrust, the gross thrust will refer in the following to the x-component of this force vector Tgt and will shortly be written as Tg This definition of gross thrust corresponds essentially to that proposed by the ITTC [1987]. The definition of gross thrust in tensor notation subsequently reads:

Tg = J puX(uk)dA (2.23) A1 +A

The minus sign in the right-hand term occurs because the gross thrust is defined as the reaction force that is exerted by the control volume on itsenvironment. In this way, the gross and the net thrust point in the same direction.

Similarly, the net thrust vector refers to the material boundaries of the waterjet:

The net thrust Tnetis defined as the force vector acting upon the material boundaries of the waterjet system, directly passing the force through to the hull.

Analogous to the adopted symbol for the gross thrust, we will consider here the component of the net thrust in x-direction Tnetx, which will be abbreviated to Tnet in the following. A possible lift exerted by the jet on the hull (Tnetz or L) will be discussed later.

66 2.2. Basic equations The definition of net thrust in tensor notation subsequently reads:

Tuer dA-JJJpFdV = J J (2.24) A4A6 VP

The minus sign in the right-hand term occurs because of the orientation of the normal vectors, pointing out of the flow or control volumes.

With the adoption of the above definitions of gross and net thrust, we may write eq. (2.21) as

- Tg= Tnet+Jf dA -JJcYdA +JjjpgdV (225) A1+A,+A A4 V

The mass force acting on the fluid in the volume V is the gravity force; F.=g.

The difference between the net thrust and the gross thrust can now be expressed in a true thrust deduction fraction, which is defined by the following relation:

Tnet=Tg(l-t1) (2.4)

This thrust deduction fraction t1 can consequently be written in terms of forces acting on the streamtube model, by using eq. (2.25):

=_L{fJ dA-JJodA+JjJpgdVl (2.27) g A1+A2+A8 A4 V

The thrust deduction expresses the discrepancy between the gross thrust Tg and the net thrust T,iet. The net thrust is smaller than the gross thrust whenever a positive thrust deduction occurs. This is the case when the total stress force acts in negative x-direction upon the combined protruding streamtube boundaries (A1A2-f A8) and in positive direction on the material jet boundary (A4) respectively.

It should be noted that the thrust deduction fraction t.,as defined above, is different from the same used in propeller-hull theory. ?n the latter,taccounts (by definition) for the increase in hull resistance, caused by the propeller action. In this context it merely accounts for the difference between the actual net thrust acting on the hull, and the defined gross thrust.

67 Chapter 2 Theoretical model 2.2.2Power

In analogy with the derivation of the thrust equation, the equation for the required power is derived from the conservation law of energy.

The conservation law of energy in words reads that the rate of change of the total energy per unit time for a certain amount of mass equals the sum of the work per unit time, done by the forces acting on the surface, and the amount of external energy that is supplied per unit time.

The total energy e per unit mass can be written as:

(2.28) e=ek.inepot etnt where ekfl =kinetic energy; ½u2 ep0,=potential energy =internal energy.

The conservation law of energy can now be written in the following integral form:

JJJP.±dV=JjuojdA+jjJpqdV (2.29)

where f//p(de/dt) dV =rate of change of total energy contained in volume V ffuodA =rate of work done on the volume's surface fffpq dV =rate of external energy exchange with volume.

For a waterjet system in a stationary incompressible flow, this equation can be reworked into:

ccp(...... 0l, cc(-pun+ut1JnJ)dA+PD (2.30) j J J j A1A2+A8

The following observations and assumptions have been made in the derivation of this relation:

The potential energy e0 is determined solely from the gravity field; li=-gz', where the z' ordinate is pointing vertically downward.

68 2.2. Basic equations Because transport of mass only occurs through the areas A1 and A8, only these areas contribute to the transport of kinetic and potential energy through the volume boundaries.

The rate of change of internal energy for an incompressible fluid can be written as:

Wdiss=fJjlt,u dV (2.31)

This term represents the viscous energy losses within the flow, which are converted into heat.

The contribution of the work done by surface forces, acting on the boundaries of the control volume, is represented by the first term on the right-hand side of eq. (2.30). No work is done by the surface tension forcesdA within the ducting of the waterjet, due to the non-slip condition at the corresponding surfaces. A similar observation can be made for the pressure forces acting perpendicular to the dividing stream surface.

If itis furthermore assumed that there is no exchange of heat through the volume boundaries, the external rate of change of energy that is supplied to the system is therefore solely due to the pump, and can be referred to as

Pump system

In the following, we will write the velocity and normal vectors in the components of a new Cartesian coordinate system. to better distinguish between the useful and the lost kinetic energy. The new Cartesian coordinate system is obtained from the body-fixed system x,y,z by rotating the system about the y- axis until the e-axis is aligned with the local centreline intake (see Fig. 2.3).

The input power Dis given by eq. (2.30). The effective power delivered by the pumpPE canbe described as the power required to deliver a pressure head for a certain flow rate:

cc 1 2 PE =jjp(_u-+J)undA (2.32) A7 p The first term in the right-hand side of eq. (2.32) represents the change in kinetic energy in axial direction. The second term represents the change in potential energy, and the third term in the same integrand represents the transport of energy by the pressure p.

69 Chapter 2 Theoretical model The power losses associated with the pump can be written as:

loss JJp (-u +u)undAWdjss_JJ(u t)ndA (2.33) A7

The first term on the right-hand side of eq.(2.33) represents the kinetic rotational and radial losses and the second term '1Jd55 represents the viscous energy losses. The third term represents the transport of mean flow energy by the total stresst,representing both viscous shear and turbulent flow stresses.

Ducting system

The effective power that is delivered by the jet system JSEis analogous to the effective pump power:

JSE JJ (2.34)

The power losses in the ducting system are given by an equation similar to eq. (2. 33), with the relevant system boundaries applied:

Pi055 (2.35) = J J J A1--A,+A8

The last term in equation (2.35) not only yields a contribution over the intake and nozzle area A1 and A8 respectively, but also over the dividing streamplane A2.

Jet system

The power output by the jet system is given by:

TgV0 (2.36)

where Tcan be referred to as thrust power. The gross thrust in this power term is defined by eq. (2.23).

70 2.2. Basic equations The jet efficiency can subsequently be defined as:

11JET (2.37) JSE

If the average pressure p in the intake is equal to that in the nozzle area after correction for submergence, and the nozzle centreline is situated in the free stream water surface, the jet efficiency reduces to the often quoted ideal efficiency ,.This will be illustrated in Section 2.2.3. 2.2.3Free stream conditions

Before treating the subject of interaction, let us first have a closer look at the waterjet system in free stream conditions. The objective of doing so is to obtain a better insight in the mechanisms governing thrust and power, and to aim at simplifications in the relations discussed in the previous sections.

Let us define the free stream condition for the waterjet system as the condition where a waterjet, mounted on an infinitely extended flat plate, operates in a uniform velocity U0 (Fig. 2.4). The flat mounting plate is situated in the x-y plane, which coincides with the horizontal plane x'-y'. The nozzle centre is situated in the free stream surface (z0=O).

The free stream velocity is directed in x-direction. The pressure at the free surface is designatedPoand the potential force field N' is made up from the gravity: N' = -gz (2.38)

Although the free stream flow is fully viscous, viscous energy losses caused by the jet system's environment do not occur by definition. If they do occur in a practical test set-up, for instance in a tunnel, correction for these energy and momentum losses should be made.

Thrust

One of the most intriguing issues related to waterjet thrust, is the relation between gross and net thrust. For gross thrust is easily computed or derived from measurements, but itis the net thrust that should be matched with the hull's resistance.

71 Chapter 2 Theoretical model

ZflO = O 4X z = O, p0

j..! free stream condition IziO 4 --I U0

Z= O, Po

yzi - operational condition

Fig. 2.4Difference between free stream and operational condition

Thrust deduction

The relation between net thrust and gross thrust is defined by eq. (2.26). The thrust deduction fraction is expressed in terms of force contributions by eq. (2.27). For reasons of simplicity, the change in resistance due to the missing surface force on the nozzle area A8 is transferred to the relation for the jet's thrust deduction fraction t. This step will be explained in Section 2.3.4 on the hull's resistance increment. Equation (2.27) then develops into:

= _{JJ (2.39) gA1+A, A8 A4 V where 5 = total mean stress tensor in x-direction, acting upon the hull for the flow condition without waterjet mounted.

If we consider the jet system's free stream conditions, the integrand for the nozzle area A8 equates to zero, because This follows directly from the definition of free stream conditions.

72 2.2. Basic equations Furthermore the volume force due to the gravity term g vanishes, as there is no gravity term in the horizontal x-direction.

The remaining contribution to the jet system's thrust deduction fraction, now referred to as tis the force in x-direction, acting upon the protruding part of the streamtube and the part of the intake lip that is exposed to the external flow. We will refer to this force as FXABCD in the following:

FBcD = -JJdA +J J dA (2.40) A4 A1+A.,

A positive value of FBcD can be interpreted as an intake dragD,pertinent to the jet system. The relation between intake drag and thrust deduction in free stream conditions is now given by: D. = t10Tgo (2.41)

Intake drag

As indicated in Section 1.5 (review of previous work), several authors have addressed the issue on intake drag. Intake drag for flush intakes as meant in the present context, is perhaps most completely treated by Mossman and Randall [1948]. These authors derive an intake drag from wake survey measurements on a number of flush intake geometries. It will be demonstrated in Section 4.1.2 that their definition of intake drag includes a significant contribution of the tunnel wall in front of the intake area. It will be demonstrated here that the intake drag FßcD of a flush intake in a potential flow equals zero for a suitably chosen control volume of the waterjet.

Let us consider a flush intake operating in a potential flow. It was noted by Van Gent [19931 that the net force, acting upon the dividing streamline in x- direction, should be zero according to the Paradox of d'Alembert. Van Gent noted the similarity between the dividing streamline and a flow line in the field made up by a source in a uniform flow (see Fig. 2.5).

73 Chapter 2 Theoretical model

-Q Fx s ink mix Fxl

Fig. 2.5Flow line about a single sink in a uniform onflow

The dividing streamline I'C (Fig. 2.1) and part CD of the intake lip prone to the external flow, can now be modelled by a flow line in a field consisting of a suitable set of sinks and sources in a uniform flow. A double model of this flow line is shown in Fig. 2.6, where the streamline is minored about a horizontal line through the stagnation point C. We have now obtained a half open symmetrical flow line model.

Centre Line

Fig. 2.6Double model of streamline I'CD

For a study on the net pressure force on the half body, we will study a similar body that is built up from one sink. Fig. 2.5 shows a resulting flow line, where point C is the stagnation point again. We can now study the momentum balance for the inner part of the half body. The integrated pressure forces on the upper and lower streamlines of the half body are designated and F respectively. For symmetry reasons, these two pressure force components are identical. The sink with strength -Q, exerts an internal force on the control volume, which can be obtained from Lagally's theorem (Weinblum [1951]):

FXSjflk = -pQU0 (2.42)

74 2.2. Basic equations The momentum balance for the internal control volume subsequently reads:

mix= Fxsink+Fxu +Fxl (2.43)

Because 4,nix equals the force exerted by the sink, the sum of the pressure forces on the half body equals zero. As these forces are equal, the individual components should also be equal to zero. In the same way, it can be shown that the momentum balance can be written in the same form for any set of sinks and sources. The internal sinklsource forces are simply obtained from the sum of the Lagally forces. The interaction forces between the distinct sinks and sources cancel each other. The momentum flux is in the same way built up from the sum of momentum fluxes of the individual sinks and sources, so that the net pressureforce onthe flowlinesequals zerofor any half open body. Consequently, the force FBcD equals zero in free stream conditions, provided the imaginary intake area AB is situated outside the jet systems flow distortion.

An important consequence of the above observation is that the net thrust is equal to the gross thrust for control volume A. We will refer to the gross thrust pertinent to this control volume as Tgin the following, and write this conclusion as:

Tpîet = Tgoj (2.44) where subscript O indicates free stream conditions; indicates the imaginary intake area AB to be positioned infinitely far upstream.

Note that the gross thrust for Control Volume A (Tg) is equal for both free stream conditions and operational conditions. The index O for free stream conditions will therefore be omitted.

For intake areas that are situated more closely to the intake's ramp tangency point, such as for the selected control volume D in Fig. 2.1, the flow distortion by the intake causes the mean momentum velocity through the intake area to deviate from the free stream velocity. It will be shown in Section 4.1.1, that even in the case where the intake area is situated 10% of the physical intake length A'D in front of the ramp tangency point, the average intake velocity deviates noticeably from the free stream velocity.

For this case, we can find an expression for the thrust deduction fraction or for the intake drag, from a consideration of the force acting on the streamline I'BCDJ (Fig. 2.1) and a momentum consideration on control volume II'BAI.

75 Chapter 2 Theoretical model The resulting expression for the thrust deduction then reads:

i -IVR0 (2.45) NVR -I VR0 whereIVR0 = intake velocity ratio through area AB; uK/UO = mean volumetric velocity through intake area NVR = nozzle velocity ratio.

Strictly speaking, we would have to use the mean momentum velocity through the intake area in the above expression. Assuming a small difference between the minimum and maximum velocity inthisarea however, the difference between the mean volumetric and the mean momentum velocity is negligible.

It is seen from eq. (2.45) that for an imaginary intake situated in the undisturbed flow, the thrust deduction t0 becomes zero. This corresponds to the previous observation that the gross thrust equals the net thrust.

Power

It will be shown in the following, that the product of jet efficiency as used by Etter et al. [19801 and thrust deduction factor (1-ti) reduces to the ideal efficiency for the selected Control Volume D in free stream conditions.

For these conditions, the relation for the effective jet system power JSE0 reduces to:

pnO I -, Pio = (2.46) JSE0

where e = average energy velocity p = pressure z = vertical distance from free surface U0 = uniform free stream velocity subscript n denotes nozzle area (area 8), i denotes intake area (area 1) and O denotes free stream conditions.

For the sake of simplicity,it will be assumed that the nozzle is completely effective in converting pressure energy into kinetic energy, so that the pressure at the nozzle area equals the ambient pressure p0, provided the jet isdischarged

76 2.2. Basic equations in air. Should this not be the case, the mean nozzle velocity should be replaced by the mean jet velocity that occurs in the vena contracta. Consequently, the jet area in this vena contracta should be used instead of the nozzle area.

The flow in front of the intake was defined as a non-viscous flow. The energy level at the intake in this free stream condition can now be expressed in free stream variables using Bernoulli's theorem:

1-2Pio 1 _uj0+__gzj0=_U(f. (2.47)

The effective jet system power in free stream conditions JSEO canthen be rewritten into

JSEO=pQ!(ii-U)+pQ(-gz0) (2.48)

It is seen from eq. (2.48) that the potential force fieldN' only contributes to the power demand if the centre of the nozzle area does not coincide with the free (undisturbed) surface (z0=O). By defining the free stream condition as the condition where the centre nozzle is situated in the free stream surface, the gravity term is cancelled.

The jet efficiencyJETconsequently reduces to the ideal efficiency 1:

U0(iZm U0) Iii = (2.49) 1 -" 2 ...... (u -U0)

If the nozzle centreline is oriented parallel to the x-ordinate and the velocity distribution in the nozzle area is uniform, the ideal efficiency can be reduced to either of the following relations:

= 2 (2.50) 1 +N%/R where NVR=nozzle velocity ratio; NVR=u,/U0 or

77 Chapter 2 Theoretical model

4 ri1= (2.51) 3 Ii +2CT,1

where CTfl=thrust loading coefficient; CTfl=TgJ(½PUO2Afl) A =nozzle area.

A derivation of these relations for the ideal efficiency is given in Appendix 1.

2.2.4Lift

A net lifting force on the stem of the vessel with an active waterjet has been suggested by Svensson [1989. This conclusion was obtained from pressure measurements in the intake and on the hullin the vicinity of the intake. According to Svensson, this lifting force, generated by the inlets, can be in excess of 5% of the displacement of a high speed craft.

This section aims to explain that there is no net lift contribution from the pressure field about the intakes, as long as the bottom plating about the intake is sufficiently wide.

To study the net lift production of a waterjet unit in free stream conditions, we will mount the unit on an infinitely large horizontal plate and let it operate in a potential flow. A potential flow assures a proper modelling of the flow, provided the boundary layer about the real hull is thin. This is a realistic assumption for most hull forms fitted with waterjets. And because we focus on the induced lift production by the intake, we consider the jet to be discharged horizontally again.

To find an expression for the net lift force on the jet-plate system (or z-component of the net thrust vector), we consider the momentum balance for the control volumes indicated in Fig. 2.7. Because there is no change in the vertical momentum flux for Control Volume A, the sum of the vertical forcesacting upon this volume equals zero:

FZJAF/Fc+FzJ/c= o (2.52) where subscriptzdenotes the force component and capitals refer to the corresponding lines in Fig. 2.7.

78 2.2. Basic equations

pump

A / CVA 7 1.1 -/ /

cv i

J.,

Fig. 2.7Control volumes used for derivation of intake drag and lift

A similar momentum balance can be worked out for Control Volumei In contrast to Control Volume A, there needs to be an exchange of mass through the lower boundary J"..!', to replenish the flow rateQthat is ingested by the intake. This replenishment cannot take place through the downstream boundary J"J, as there needs to be a uniform velocity field at this boundary, for we have seen in Section 2.2.3 that there is no net horizontal force acting within the control volume.

The momentum balance for Volume i subsequently reads:

FZCDJ+FZ (2.53) in order to find a parametric description for the lift force on the hull, we will write the vertical momentum flux as:

nzi'j PQmpI4z (2.54) where = momentum flux velocity coefficient in a potential flow.

The mean z-component of the velocity ¿ is obtained from the conservation law of mass:

Q (2.55) AJ//J//

79 Chapter 2 Theoretical model The net lift force Tnetz is made up from the sum of the vertical forces FZIAFFC and FZCDJ, which can now be written as:

Tnetz = PQCmpl7z (2.56)

To study the behaviour of the lift force, a non-dimensional lift coefficient CL is introduced: T CL (2.57) pQU0

Keeping in mind that the flow rate Q can be expressed as the product of the intake throat area the intake velocity ratio lVR and the free stream velocity U0, we have found an expression for the lift coefficient CL as a function of the ratio between intake throat area and plane area A1:

Cml VRAit (2.58) CL-- /-Il II

The momentum velocity coefficient Cm has a value less than one for a non- uniform velocity field (see also Appendix 2). Representative values for the intake velocity ratio IVRE are of 0(1). It can thus easily be seen that the lift coefficient CL vanishes for sufficiently large areas ¡"J' in relation to the intake throat area.

The net lift force on the waterjet-hull configuration may attain finite values when the bottom plane is limited. This situation may for example occur in actual vessels, where the intake is situated just in front of the transom stem. A quantitative discussion on this phenomenon is postponed to Chapter 4.

2.3Interaction

As we have seen in Section 2.1, the interaction effects in the powering characteristics can be expressed in the momentum and energy interaction efficiencies for the effect on waterjet performance, and in resistance increment for the effect on hull performance. Parametric expressions that can beused in either a computational or an experimental study will be derived in the following.

80 2.3 Interaction 2.3.1 Momentum interaction efficiency

Hull interaction effects on waterjet thrust are accounted for in the so-called momentum interaction efficiency, which is defined by (see also Section 2.1.2):

Tnetü TI mi (2.59) Tnet

For reasons discussed in Section 2.1, the net thrust is most practically obtained from the product of gross thrust Tg and jet system thrust deduction t:

Tnet = Tg(l_tj) (2.4)

As a consequence, the momentum interaction efficiency can be written as:

/ lI (2.61) TI = fl,11,11,111 with

/ Tg - (2.62) Tg and

i, (l-t10) (2.63) =(l-;)

subscript O indicates free stream conditions.

It will be shown in the following that, for control volume D in a potential flow, the net thrust in free stream conditions equals the net thrust in operational conditions for the same flow rate and a negligible free surface induced pressure gradient over AD. As a result, the momentum interaction efficiency equals unity.

Contributions to the thrust deduction by the nozzle area A8 and the trim angle (eq. (2.39)) are thereby neglected. which is a good approximation for most operational conditions. The effect of this simplification will be discussed in Section 4.3.2.

81 Chapter 2 Theoretical model

Momentum interaction efficiency TI,,ÇJ

To get rid of the integral term in the definition of the gross thrust (eq. (2.23)), the momentum flux mjthrough the intake area A1 will be expressed in global flow parameters and coefficients: dmi = PQUmjx (2.64) where

mix =CvpCmUø (2.65) and = potential flow velocity coefficient; U/U0 Cm =momentum velocity coefficient due to boundary layer velocity distribution U =local potential flow velocity outside the boundary layer U0 =free stream velocity in x-direction.

Expressions for the momentum velocity coefficient as a function of the boundary layer parameters are given in Appendix 2.

Assuming an effectively uniform velocity profile in the jet at the nozzle exit, the discharged momentum flux can be written as:

= p Qu,71 (2.66) where i7, = mean nozzle velocity at nozzle exit area 8.

Substituting the above parametric expressions in the first term of the momentum interaction efficiency r,, we obtain:

NVR-1 / (2.67) l_lin! = NVR I VRmi where IVR,77=intake momentum velocity ratio through intake area A1; u1JU0.

Momentum interaction efficiency rÇj

Let us now consider the second term of the momentum interaction efficiency; r. This term is defined by eq. (2.63). An expression for thethrust deduction

82 2.3 Interaction fraction in free stream conditionst was already derived in Section 2.2.3 eq. (2.45).

We will now focus on a relation for the thrust deduction fractiont1in operational conditions. The basic equation fort1is given in eq. (2.39). We will restrict ourselves to the first integral term over the protruding part of the streamtube and intake lip (ABCD in Fig. 2.1). The integral termsover the nozzle area and the enclosed volume are assumed to be negligible here.

To simplify the study oft.in operational conditions, let us break down the total flow field into a flow fiel1d pertinent to the jet action in free stream conditions, a flow field pertinent to a double model of the hull without free surface effects, and into a flow field consisting of the free surface distortion. In the potential flow considered, the total flow field potential function consists of thesum of the individual potential functions. Hence, the resulting velocity fields may be summed.

We will first consider a two-dimensional double model (mirrored about the free surface) of a waterjet-hull system in a potential flow (Fig. 2.8). This condition leaves free surface effects out of consideration. Depending on the hull shape, the jet system may be operating in an accelerated or a decelerated flow.

From its definition, the following expression for the thrust deduction fraction t1 can be derived (see eqs. (2.39) and (2.40)):

(2.68) T where FABcD =external force acting in x-direction on the protruding part of the intake (see Fig. 2.8).

A suitable expression for FßcD can be obtained from a consideration of the force in x-direction acting upon the streamline I'BCDJ anda momentum consideration on the control volume II'BASI forward of the imaginary intakearea AB.

The force on the streamline part BCD can be obtained from a consideration of the pressure force on the streamline I'BCDJ. Using the paradox of d'Alembert or Lagally's theorem, it can again be derived that the net pressure force in x- direction, acting upon this streamline equals zero. Consequently, the forceon BCD can be written as:

83 Chapter 2 Theoretical model

FXBCD = (2.69) where F = f_Pflx (2,70) and p = pressure = x-component of normal vector ds = infinitesimal line element.

// I, / U0

J A' A -J---- B X

Flow about isolated body Waterjet in free stream

+ 4- p, 4- U0 U0 po

Fig. 2.8Flow field decomposition for a waterjet-hull configuration

In the above expression, use is made of the adopted constraint that nequals zero along line element DJ.

From a momentum balance over the control volume Il'BASI, we find:

84 2.3 Interaction

pQ(U-U0) = FsJ+FXßA-FBcD (2.71)

where the pressure forces F are the forces acting upon the control volume.

The force FBcD can now be obtained from eq. (2.71), and reads:

FBcD = -pQ(U-U0)+ I-Pn ds (2.72) JASJ

It should be noted here that the force over AB as mentioned ineq. (2.71) where it acts upon control volume II'BASI changes sign when we consider thecone- sponding reaction force acting upon control volume ABCFF'A. Ina steady flow, its magnitude remains the same.

If the integral term over the streamline ASI in the right-hand side of thisequa- tion would be negligibly small, we would have obtained a simple expression for the thrust deduction. To study the character of this integral term,we decompose the total flow field into a free stream field for the jet system mountedon a flat plate, and the flow field about the hull without jet (see Fig. 2.8). The totalpressure p can now be linearized as the sum of the pressure p0, occurring when the half body is positioned in the free stream, anda perturbation pressure p', caused by the intake action:

P (2.73)

The integral term over AS! can now be written as:

J pn ds (2.74) ISA X JSAPOflSJSA

With Lagally's theorem, it can again be shown that the first integral termon the right-hand side of this equation equals zero if the body contour part AJ is oriented parallel to the x-coordinate. This condition is usually fulfilled for hull forms fitted with waterjets.

The second integral term on the right-hand side, or perturbation term due to the jet action, can be neglected whenever either the perturbation pressure p' is negligibly small, or whenever the normal in x-direction is negligibly small in the area where p' cannot be neglected. The first condition isa condition

85 Chapter 2 Theoretical model imposed on the flow induced by the intake, and is an argument to position the imaginary intake area AB slightly ahead of the ramp tangency point A'. The second condition imposes a geometrical constraint on the body containing the jet.

It is to be noted that the total pressure can only be obtained from the sum of the pressures of both flow fields, if one of the perturbation pressures is small.

With the neglect of the pressure integral over AS!, we have obtained a simple expression in terms of u,, U0 and NVR for the thrust deduction fraction t1 in operational conditions without free surface effects:

I -1VR (2.75) NVR-1VR

A similar relation was found for the thrust deduction fraction in free stream conditions t10 eq. (2.45).

We will now add the free surface velocity field. We will thereby consider the flow in the protruding part of the streamtube, configuring the jet system with intake AB (Control Volume D in Fig. 2.1). Using Bernoulli's theorem, free surface effects may be interpreted as a change in the relation between the magnitude of the velocity u and the pressure p due to the wave height Ç:

p =co_pu2_gÇ (2.76)

whereco =constant, determined by U0, p0 and z0 wave height (positive downward).

A constant change in wave height over the intake length AD results in a uniform change in pressure. Because the pressure integral over part ABCD is not affected by a uniform change in pressure, such a free surface effect does not affect the thrust deduction t3. Only in case a pressure gradient (or varying wave height Ç) over AD occurs, the thrust deduction will be affected. We will initially neglect the effect of a free surface induced pressure gradient. Its effect on the thrust deduction t1 for a representative case will bediscussed in Section 4.3.2, where more information about the dividing streamlines and a possible pressure gradient is available.

86 2.3 Interaction Substituting now eq. (2.45) and eq. (2.75) in eq. (2.61) shows that the contributions of îj and T1 neutralize each other, leading to a momentum interaction efficiency equal to unity in a potential flow.

Implications for net-gross thrust relation

The interpretation of the above discussion is that, as long as the pressure integral over AS! is negligible, the net thrust in operational conditions equals the net thrust of the jet system in free stream conditions for identical NVR value. The integral term is either negligible for an imaginary intake of the jet that is sufficiently far upstream of the ramp tangency point, or for a hull form in front of the intake area AB with a negligible component of the normal in thrust (x) direction. In case this integral term is not negligible, part of the hull's resistance is found back in the jet system's thrust or vice versa. This will lead to a redis- tribution in the values of the momentum interaction efficiency and the hull's resistance increment. The power requirement will however not be affected because there is no loss of energy involved.

An important implication for the computation of net thrust in a potential flow is, that the net thrust is equal to the gross thrust pertinent to control volume A (Fig. 2.1):

Tnet = Tgoo (2.77)

For a viscous flow, the ingested momentum should be corrected for a momentum deficit in the intake area AB, due to the viscous stresses acting on the hull bounded part of streamtube lI'BAI. The net thrustin a viscous flow can consequently be obtained from:

Tg=, = pQU0(NVR-c7) (2.78)

Because substantial deviations from the neglects of the nozzle contribution to t1 may occur during transom clearing (Section 4.3.2), we will use Tgoo as a good approximation of the net thrust over the greater part of the speed range. The parametric relation for the momentum interaction efficiency can now be written as: l-c7 - 1+ (2.79) 11ml NVR-1

87 Chapter 2 Theoretical model 2.3.2 Energy interaction efficiency

Analogous to the definition of momentum interaction, hull interaction effects on waterjet power are accounted for in the so-called energy interaction efficiency. This efficiency is defined by (see also Section 2.1.2):

JSEO 11e! = (2.80) JSE where JSE=effective jet system (hydraulic) power. As in the case of the momentum interaction efficiency, both the power in the free stream and in the operational condition refer to the same flow rateQ through the jet system. Introducing an average energy velocity iZ,, the effective jet system power can be written as:

= (2.81) JSE Q{p -p g(z -z) (p-p)}

In order to find a parametric expression for the energy interaction efficiency, the kinetic energy flux through the intake area will be written as:

1 222 (2.82) 4eki PQCvpÇUj0

where Ce = energy velocity coefficient due to theboundary layer velocity distribution =potential flow velocity coefficient; u/u0 u = local potential flow velocity, just outsidethe boundary layer =free stream velocity in x-direction through intake area.

The energy velocity coefficient can be determined when the ratio between the ingested flow rate and the flow rate that can be absorbed from the boundary layer are known. Appropriate relations are given in Appendix 2.

The effective jet system power in free stream conditions JSEOcan be obtained from eq. (2.48):

JSEO =pQ(ii-U) (2.83)

88 2.3 Interaction

We will now again assume that for operational conditions, the nozzle iscom- pletely effective in converting the pressure energy into kineticenergy, so that the pressure outside the nozzle is equal to the ambient pressurep0. Applying Bernoulli's theorem and taking into consideration that the centrepoint nozzle is situated on the water surface in free stream conditions, the following relation for the effective jet power is found:

JSE =JSEOP Qgz (2.84)

where =sinkage of the nozzle centrepoint relative to the free (undisturbed) surface.

The energy interaction efficiency1e1 in a potential flow can subsequently be written as: pQgz 1e1 = 1+ (2.85) JSE It is seen that the energy interaction efficiency adopts a value greater than i if the sinkage of the nozzle is positive (downward).

Applying the energy velocity coefficientsCe and cv,, the energy interaction efficiency in a viscous flow can be written as:

i gz cIVR(C-l) (2.86) Thi U(NVR2_l) (NVR2-1) 2 The second term on the right-hand side may be regarded as a typical potential flow effect in the interaction efficiency, which is caused by the change in elevation of the nozzle. This term may also be written as the ratio between the nozzle elevationZn and the required pump head H0 in free stream conditions, expressed in meters water column mwc; z,/H0.

The third term on the right-hand side represents viscous effects in the interaction efficiency. if there is no boundary layer present (Ce=l), this term vanishes. The potential flow velocity coefficient is seen to diminish the effect of the frictional boundary layer losses in a retarded potential flow. This can be understood if one recalls that the frictional energy losses are related to the kinetic energy contents. If all energy would be stored in potential pressure energy, there would be no viscous losses.

89 Chapter 2 Theoretical model Similar to the validity of the parametric relation for the momentum interaction efficiency î, the above relation is valid as soon as the nozzle discharges in air.1f the jet is discharged in a separated flow, Bernoulli's theorem is not applicable any more and corrections should be made.

2.3.3Quantitative assessment and comparison with previous work

Now that we have obtained parametric expressions for the interaction effects of the hull on the jet performance, we can make an assessment of its magnitude. Moreover, we can compare these findings with results obtained from models published by other authors. We will thus study first the interaction effects on jet performance in a potential flow, followed by viscous flow considerations.

In his search for a better physical understanding of waterjet-hull interaction, Jon Hamilton [1994] put the following thought experiment forward. 'imagine an infinitesimal wate rjet near the stagnation point of the hull. How will this affect the interaction efficiency?'.

This limiting case is considered a good test case for the aforementioned parametric models governing the overall efficiency. To keep the comparison as pure as possible, we will consider the jet-hull operating in apotential flow. As a consequence, the ducting losses are zero. It isfurthermore assumed that the pump efficiency equals unity, that the nozzlecentreline remains at the free stream water surface and that the resistance increment of the hull (1 +r)equals zero.

The overall efficiency lOA by Svensson [1989] now reduces to the following relation: 2p(l -c1,) (2.87) 10A l-p2 where p hull speed I nozzle velocity ratio; U./u c =potential flow velocity coefficient w'L70.

The wake fraction w, used by many authors, relates for a potentialflow to the velocity coefficient in the following way:

= l-w (2.88)

90 2.3 Interaction A relation between the pressure coefficient G used by Svensson and the velocity coefficient can be found using Bernoufi's theorem:

2 Gp = 1Cvp (2.89)

Similarly, the relation for overall efficiency11OA by Dyne et al.l994] reduces to: 2i fluA (2.90) 1

From the breakdown of the overall efficiency as proposed in this work, the following terms remain:

11e! 110A = ll (2.91) where

2 (2.92) =1+NVR NVR = nozzle velocity ratio u,/U0 or i/p.

Because we consider a potential flow, the momentum velocity coefficientCm equals unity. A representative value for IVR0 of 1.03 has been used.

The results of the above efficiency relations are plotted in Fig. 2.9 for a range of jet operating conditions (expressed in NVR value) and a strong flow retardation (c=O.l). lt can be seen that three of the quoted efficiency relations predict values for the overall efficiency in excess of 1.0, which is unrealistic. This would imply that we had found an original realization of the perpetuum mobile. The parametric expression that is discussed here shows values not exceeding unity, which is more realistic.

The effect of the above models on the interaction efficiency for a representative flow retardation (c =0.95) is shown inFig. 2.10. Although not explicitly given in the efficiency reIìtions of other authors, the interaction efficiencyflINTcould be computed from the following relation:

fi OA flINT = (2.93) Iii

91 Chapter 2 Theoretical model

- - . -Svensson[1989] Dyne [1994] - -. Terwisga[1993] 2 - modifiedmodel

0 05 15 2 25 35 NVR [-I Cvp = 0. 1. w= 0.9 nozzle elevation, intake, pump and nozzle losses equal zero

Fig. 2.9 Computed overall efficiencies for an infinitesimal waterjet near the stagnation point

1.2

-. -Svensson [1989] 1.15- Dyne [1994] - - -.Terwisga [1993] modified model * - E z S,.' 1.05 -

0.95 05 15 2 2.5 3 3.5 NVR [-1 Cvp0.95, w = 0.05 nozzle elevation, intake, pump and nozzle losses equal zero

Fig. 2.10 Computed interaction efficiencies for a waterjet in a retarded potential flow

92 2.3 Interaction Realizing that representative NVR values range fromapprox. 1.5 to 3, errors in interaction (and thus in overall efficiency) occur from 1.5to 2.5% (Dyne [19941) to 2.5 to 10% (Svensson [19891 and Van Terwisga [1993]). The parametric model presented in this work yields an interaction efficiency witha constant value of 1.0.

With the aid of eqs. (2.79) and (2.86), the effect of distortions in the viscous flow can be studied independently. This is done for a value of the NVR of 1.7, which is representative for design conditions. The velocity profile in the boundary layer is assumed to follow the n-th power law.

An example of the effect of the ingestion of boundary layer is given in Fig. 2.11, where the overall interaction efficiency is plotted as a function of the ratio of required flow rate and flow rate available from the boundary layer. Potential flow distortions are supposed to be absent. A maximum value in this case for the interaction efficiency due to the boundary layer of 1.06 is found for the condition where a maximum of boundary layer flow is captured (in thiscase the ingested flow rate amounts to 60% of the attainable flow rate from the boundary layer). For increasing flow rates at equal boundary layer flow rate, the interaction efficiency approaches a value of I asyniptotically.

1.25

1.20 NVR= 1.7 .15 n=9

1.10 I '11m1

I.05

1.00 OINT

0.95 leI 0.90

0.85

0.80 0.5 1.5 2 25 3 35 4

Q1QbI

Fig. 2.11 Effect of boundary layer height/ingested flow rate ratioQ'QhIon interaction efficiency

93 '!

Chapter 2 Theoretical model 2.3.4Hull resistance increment

In a steady situation, the net thrust Tnet is counterbalanced by an effective resistance RE. This equilibrium of forces yields:

RE Tnet (2.94)

The effective resistance with active waterjet mounted, can be derived from the bare hull resistance in the following way:

RE = (2.95) A3 A8

where total mean stress tensor in x-direction for the flow condition without waterjet mounted AR = change in hull resistance due to waterjet action. The integral terms in eq. (2.95) represent the effect of the change in hull geometry on the hull's resistance, due to the waterjet. It is again assumed here that the orientation of the x-ordinate is parallel to the hull's speed vector.

The integral over area A3 refers to the missing surface in the intake projected in the hull plane. This area is referred to as projected intake area. The integral term over the nozzle area A8 refers to a similar absence of area, where there would be a pressure force acting during a resistance test.

For reasons of simplicity, we will transfer the latter change in resistance due to the missing surface force on the nozzle area A8, to the relation between gross and net thrust. This results in an additional term in the relation for the thrust deduction fraction t1 (eq. (2.27)), which subsequently becomes:

t1 _LJJ dA +JJ(-o)dA -JJcYdA +JJJp gd%' (2.39) X A+A2 A8 A4 V

A non-dimensional change in resistance or resistance increment fraction r was defined in Section 2.1.2 as:

94 r---- 2.3 Interaction

r = _!_-f jYodA +AR} (2.97) RBH A1

where the resistance increment can now be written as:

Tnet 1 +r = (2.98) RBH

The resistance increment factor (1+r) is caused solely by the waterjet action and geometry, and can therefore be regarded as a factor accounting for a true interaction effect of the waterjet on the hull performance.

Apart from the change in resistance due to the geometrical changes as discussed above, the waterjet action causes a change in the local flow about the aftbody. This will change the pressure field, resulting in changes in wavemaking resistance. It may furthermore affect the equilibrium position of the hull. When this happens, an additional change in global flow pattern about the hull occurs and a change in overall hull resistance occurs.

The jet induced hull resistance increment (AR) may be estimated from potential flow panel codes, as will be discussed in Chapter 4.

An alternative method is provided by a set of resistance tests. For an estimate of the change in hull resistance due to the waterjet action (AR), we may assume that this change is built up from two independent contributions. One contribution being due to a change in the local flow pattern about the intake, the other contribution being due to a change in global flow pattern about the hull. The latter contribution is caused by a change in equilibrium position of the hull due to the jet action, and can be expressed in a change in rise of the hull (dz) and in a change in running trim angle (d'r).

The change in local flow about the intake, for a given intake geometry, is strongly dependent on the ingested flow rate Q. Assuming free stream conditions, and neglecting viscous effects, the flow pattern is uniquely determined by the intake velocity ratio ¡VR.

If the assumption on the independence between the changes in resistance due to the local and the global flow appears to be true, the change in resistance can be estimated from a linear development in a Taylor series:

95 Chapter 2 Theoretical model

AR(Q,dz,d'r) = AR(Q,0,0) _(Q,0 ,0)dz (2.99)

A further simplification may consist from the assumption that the derivatives of AR to the rise and trim angle are independent of the flow rate Q, so that we may write:

(Q,0,0) = (0,0,0) (2.100)

and

(Q,0,0) = .(0,0,0) (2.10 1)

The partial derivatives of the resistance to the change in rise and trim angle can now be obtained from resistance tests at varied displacement and position of the centre of gravity. This procedure will be used in Section 3.4.

2.4Conclusions

A systematic separation between waterjet and hull system appears to be possible. This results in a set of parametric relations, explicitly describing the free stream characteristics of the subsystems and their mutual interaction effects.

The overall powering characteristics and interactioneffectsare essentially independent of the choice of control volume, modelling the jet system. A skilful choice does however enhance the accuracy of measurements or needs fewer assumptions and simplifications in the derivation of the powering characteristics. The control volumes A and D in Fig. 2.1 are demonstrated to have useful hydrodynamic properties. Control volume B will be demonstrated in Section 4.2 to be advantageous in modelling the intake in computations.

The following conclusions relative to the physical interpretation of jet-hull interaction are drawn. These conclusions contradict many statements in the open literature.

There is no intake drag for a flush type intake operating in a potential flow.

96 2.4 Conclusions There is no interaction effect of the potential flow distortion by the hull on the jet performance, provided thereis no hull induced pressure gradient over the intake area AD (Fig. 2.1). Additional conditions are that the flow about the nozzle is not affected by the hull and that the hull has zero dynamic trim (see Section 4.3.2). There is no net contribution of the intake induced flow on the total lift force of the jet-hull system. provided the area around the flush intake opening is sufficiently extended.

97 This page intentionally left blank Chapter 3

3 Experimental analysis

The objectives of the present chapter are threefold. First, a propulsion test procedure is presented which deviates from the ITTC [1987] proposal (see Fig. 1.13) on a number of points. Major differences occur in the flow rate calibration procedure and the data reduction method. The modifications yield an improvement in both uncertainty and time required for the execution of the tests. This first objective is dealt with in the first two sections of this chapter. Secondly, an uncertainty analysis is presented in Section 3.3 with the aim to quantify the uncertainty in model propulsion tests, and to acknowledge those factors that dominate the resulting uncertainty. And thirdly, a selection of salient results will be presented in Section 3.4 that has been collected during the course of the present study. The physical interpretation of these results will be discussed, providing a natural transition to Chapter 4, where we will take a closer look at the mechanisms of waterjet-hull interaction.

3.1 Propulsion test procedure

Model propulsion tests provide a means to obtain an accurate assessment of the powering characteristics of the combined waterjet-hull system. Furthermore, it provides a means to separate the interaction effects if the powering characteristics of both systems in their isolated condition are known. We will refer to these latter characteristics as the free stream characteristics.

99 Chapter 3 Experimental analysis

In the present context, the term powering characteristics refers to thrust, delivered power and impeller rotationrateasafunction of vesselspeed.These characteristics of the combined system are preferably determined from a synthesis of the free stream attributes. That is; without interaction effects. The overall characteristics of the combined system can however not merely be obtained from matching the attributes of the isolated systems.

The propulsion test procedure as recommended by the HSMV Committee of the 18th ITTC [19871 has been used as a starting point. An argumentation for this choice and some remarks on this procedure are given in this section.

The basic ITTC procedure is presented in Fig. 1.13 (Section 1.6.2). The procedure is based on a black box approach as far as the pump of the jet system is concerned. The pump mounted in the model does not need to be scaled, but needs to be capable of delivering the required flow rate. Before focusing on the propulsion test procedure, this black box approach is discussed in comparison to propulsion tests with a completely scaled pump unit.

Selection of test set-up

Two possibilities to model the waterjet system in the model hull are schematically presented in Fig. 3.1. In option 1, mass, momentum and energy flux through the waterjet system boundaries are determined from measurements on flow rate and velocity distribution in the intake. The corresponding thrust and power requirement is obtained from the relations discussed in Chapter 2, Sections 2.3.1 and 2.3.2.

In option 2, the thrust and power delivered to the impeller are measured directly through force and torque transducers. The free stream powering characteristics of the jet system are then expressed in a similar manner as propeller open water characteristics. In this procedure, interaction effects can only be related to resulting interaction effects on the pump characteristics. This method prohibits a break down of interaction in terms of hull effects and waterjet system effects, because the boundaries between the two systems are situated well within the jet system. More precisely about the pump. A breakdown between jet system and hullis nevertheless desirable for an effective use of interaction data in preliminary ship design.

The latter option also imposes severe constraints to the test set-up. To be able to determine the powering characteristics of the combined waterjet-hull system, a hull model with an integrated and properly scaled waterjet unit should be used. This model should be large enough to avoid uncontrollable scale effects within the waterjet system.

100 3.1 Propulsion test procedure

Option i Option 2 Scaled intake and nozzle Fully scaled waterjet system black box pump

Flow rate Q

u(z)

Fig 3.1Possible approaches for waterjet modelling in propulsion tests

The delivered power to the impeller and impeller rotation rate are now measured directly. Correction for internal scale effects in the jet are necessary to arrive at a full scale prediction.

A practical disadvantage of option 2 is that a direct measurement of the thrust is complicated. This is because the total force of the waterjet system acting upon the hull is passed through to the hull through all points in which both systems are connected to each other. A solution to this problem is to put the complete waterjet system, including the driving motor, on a force measuring frame. Special care should be taken that the flexible connections between jet system and hull are unable to pass forces. These connections should be watertight sealings to avoid leakage. Fig 3.2 shows a set-up based on this modelling procedure that has been used in the early days of waterjet testing at MARiN. Because of its complexity, the adverse dynamic mass-spring characteristics of the measuring frame and the costs involved, it was decided to abandon further developments in this direction.

It may be clear from the description of the test set-up of option 2, that this procedure is both expensive and time consuming. Due to its technical complexity, it is sensitive to bias errorsduring the tests. Furthermore, it does not directly give interaction data between the bare hull and the jet system. Data which are useful in the selection of existing waterjet systems. For those reasons, this test set-up is not considered further in this work.

I) See Appendix 3 for definitions on accuracy and related terminology.

101 Chapter 3 Experimental analysis

connection to ship model drive force motor balance > equipment frame seal

flexible seal /flexible seal

i base line i

Fig 3.2Test set-up for complete model of waterjet system

Description of propulsion test procedure

The same modelling of the jet system and the same sequence of activities as proposed by the HSMV Committee of the 18th ITTC is used throughout this work (see Fig. 1.13, Section 1.6.2). The experimental method that results from the investigation described in this chapter, differs from the aforementioned ITTC procedure in essentially the flow rate calibration procedure and the data reduction method. A further deviation occurs in the way in which characteristics of the ingested flow are measured.

Flow rate measurement

The flow rate measurement procedure is extensively treated in Section 3.2.

Propulsion tests

After having a flow rate measurement procedure, the ITTC {1987] proposes two distinct propulsion tests (see Fig.1.13). The first propulsion test in the ITTC procedure is meant to determine the impeller rotation rate and the flow rate through the jet system. A second propulsion test is subsequently proposed where the velocity profile just in front of the open intake is measured with a pitot static rake. The velocity profile measurement is to be done with preset impeller rotation

102 3.1 Propulsion test procedure rate, as obtained from the first propulsion test. This is because minor differences in impeller rotation rate in the self propulsion point could occur because of the added resistance of the pitot rake.

It has been demonstrated in Section 2.3 however, that it is essentially the viscous energy and momentum deficit that needs to be measured during the propulsion tests. The simplest way to do thisis to measure the velocity profile in the boundary layer. The boundary layer thickness can be obtained by fitting a theoretical velocity profile through the experimental data (see Fig 3.3).

1.1

u . u 1 .0

Measured - Computed

0.9

0.8

model boundary layer: n = 7

0.7 I j

0 0.5 1 1.5 2 z/ö [-J

Fig 3.3Example fit between measured and computed boundary layer velocity profile

A suitable model for this velocity profile is given by the power law:

I/fl u(z) (Z (3.1) -u

103 Chapter 3 Experimental analysis Because the intake area AB (Fig. 2.1) is situated in the flow region with low intake induced velocities, the boundary layer characteristics can also be measured during a resistance test. That is; with closed intakes. Analogous to the vocabulary used in propeller hydrodynamics, we could speak here about the nominal wake field for the waterjet intake.

An alternative procedure is provided by Dyne et al. [1994]. These authors propose to determine a momentum and an energy frictional wake fraction from a set of velocity and pressure measurements. This method is however more elaborate and is unlikely to contribute to a lower uncertainty for the so-called thin boundary layers. In this context, a boundary layer is called thin if the pressure gradient perpendicular to the wall is negligible. This can be assumed for almost all waterjet propelled hull forms.

We have seen in Section 2.3 that the potential flow velocity just in front of the intake does not play an important role in overall powering characteristics. Only a modest contribution in the energy interaction efficiency could be discerned (eq. 2.86). If the potential flow component is obtained from measurements, one should take care that the intake induced velocity is not included, as this is not contributing to the interaction. It is therefore better to use the nominal wake velocity distribution, measured during the resistance test.

Data reduction method

The difference between the data reduction method proposed in this work and the ITTC [19781 procedure is mainly caused by the difference in parametric model (Chapter 2) and the different flow rate calibration procedures used. The data reduction method resulting from this work is schematized in Fig 3.4. The numbers in parentheses, given for the key data, refer to the relations needed for their computation.

Extrapolation method

The extrapolation method is discussed in Section 3.5

Final prediction

A final prediction of powering characteristics in terms of power delivered to the pump impeller and impeller rotation rate involves incorporation of the internal jet system characteristics. These characteristics can be obtained from experiments on the isolated jet system and matching of jet system data with extrapolated propulsion test data, as indicated in Fig. 1.13.

104 3.1 Propulsion test procedure

Model Geometry

Wi en

Calibration 5et' a0, a1

Propulsion test

u(z) Dp U0 Z

Data Analysis

RBH u(z) U01_ p A0 en Z0

cm(App.2) Ce (App.2)

TgL(3.10) JSE(3.36)

t (3.39) 1e1 (2.86)

(4.42) 1NT 11

numbers in brackets refer to equation numbers

Fig 3.4Flow chart of data required for propulsion test analysis

3.2 Flow rate measurement

As can be concluded from the HSMV Committee reports of the 18th [1987] and 20th [1993] ITTC meetings, it is difficult to carry out flow rate measurements with sufficient accuracy. This section gives an account of the search for such a method.

1 0 Chapter 3 Experimental analysis 3.2.1 Flowmeter selection

There are well over one hundred different types of flowmeters currently available and several other techniques are the subject of R&D around the world. Such a wide variety is making meter selection and correct application increasingly difficult (Fumess [1990]). The purpose of the work addressed in this section is to identify the most promising flowmeter in waterjet propulsion tests.

Three aspects in the selection of a flowmeter have been considered here:

Performance considerations Installation considerations Economic considerations.

As tothe economic aspects of a flowmeter, acquisition,operational and maintenance costs determine the overall costs. The operational costs refer to the costs required for the installation of the meter, its calibration for each set of experiments and its reliability. To keep the costs as low as possible, it was decided to initially focus in this work on robust flowmeters for which relatively much experience is available. Mainly for these reasons, attention was limited to the flowmeters from the Groups 1, 2 and 4 from Table 3.1.

Table 3.1 Classification of flowmeters (BSJ Guide 7405 [199lJ)* * refers to endnote on page 169

Group Flowmeter description

I Orifices, venturis and nozzles

2 Other differential pressure types

3 Positive displacement types

4 Rotary turbine types

5 Fluid oscillatory types

6 Electromagnetic types

7 Ultrasonic types

8 Direct and indirect mass types 9 Thermal types

10 Miscellaneous types

106 3.2 Flow rate measurements The first two groups consist of differential pressure transducers, Group 4 consists of rotary turbine type meters. Two of the three flowmeters mentioned by the HSMV committee (venturi pressure taps and paddle wheels) belong to these selected groups (Groups i and 4 respectively). The third meter, a water collecting container is not treated by the BSI. This type of flow measurement will be addressed in the section on flow rate calibration, together with an alternative 'weir' method.

We will concentrate in this section on reference flowmeters for installation within the model jet. In line with the ITTC recommendations, the flowmeter will be separately calibrated for each jet.

Performance considerations

Performance considerations deal with the required accuracy2" of the flowmeter and the expected range of flowrates to be measured. In the case of waterjet propulsion, the required accuracy is determined by the accuracy that is required for the thrust deduced from the propulsion tests. The model thrust is a suitable performance indicator, as this variable plays a dominant role in the extrapolation procedure and hence in the final power-speed prediction. As a first aspiration level for the accuracy of the thrust measurement, the error in direct thrust measurement on a propeller may be taken. To this end, we will use an estimate on the experimental standard error for propeller thrust measurements from model propulsion tests (ITTC [1978]), which is derived to be approx. i to 2% of the mean value.

To study the relation between uncertainty in waterjet thrust and flow rate, we will consider the relative sensitivity 06 pertinent to gross thrust, defined by:

¿ET - 0' (T) = _-__ (3.2) g QTg where the overbars denote average values.

This relative sensitivity is a measure for the propagation of an error in flow rate to the error in thrust. The relative sensitivity is a non-dimensional quantity, relating the non-dimensional error in flow rate to the non-dimensional error in thrust. A more detailed explanation on the propagation of errors is given in Appendix 3.

2) See Appendix 3 for definitions on accuracy and related terminology.

107 Chapter 3 Experimental analysis To find the sensitivity of thrust for errors in flow rate, we will use the following relation between thrust and flow rate (from eq. (2.78)):

P(QCmt1O) (3.3) n where p = mass density of water Q = flow rate A,1= nozzle area c,,1 = momentum velocity coefficient due to the velocity distribution in the intake U0 =free stream velocity.

The relative sensitivity of thrust for an error in flow rate is now found to be:

2NVR-c e'(T) 'n (3.4) Q g NVRCm where NVR =nozzle velocity ratio; u/U0.

A similar exercise for the effective jet system powerJSE canbe made, using eq. (2.81). After neglecting the contribution of the sinkage of the nozzle, we find:

3NVR2_c2 (35) 0(JsE)= 2 NVR Ce

Fig 3.5 shows the relative sensitivities of net thrust Tnet and effective jet system powerJSEfor errors in flow rate, as a function of the nozzle velocity ratio NVR. Representative values for the momentum velocity coefficient Cm and energy velocity coefficient c of 0.9 have been applied here.

It is seen that the relative sensitivity of the thrust increases drastically for ¡'[VR values smaller than about 2. Consequently, for most waterjet operational conditions where NVR adopts values between 1.5 and 3, an error of 1% in flow rate already causes an error of 3.5 to 2.4% in derived thrust. For the effective jet system power JSEerrors between 4.3 and 3.2% would result.

108 3.2 Flow rate measurements

I -8'Q (Tnet) I - - 9'Q(JSE L-II Cm =0.9, Ce2 = 0.9 o o 2 3 4 NVR [-1

Fig 3.5Relative sensitivities of thrust and power for flow rate

These values of the relative sensitivity emphasize the importance of an accurate procedure for the flow rate measurement.

Table 3.2 lists the performance for various types of flowmeters. Based on this review and the aforementioned economical considerations, it was decided to focus in some more detail on the venturi type flowmeter, using the nozzle geometry as venturi (Group 1), to the averaging pitot (Group 2), and to the insertion turbine flowmeter (Group 4).

Installation considerations

For afurtherselectionof flowmeters, we willconsider theinstallation considerations here.

Two installation constraints that should be met by the selected flowmeter can be acknowledged. One constraint is imposed by the jet model. It limits the allowable flowmeter distortion in order to have a reliable flow model for the full scale waterjet without flowmeter. The other constraint is imposed by the flowmeter in order to obtain reliable signals.

109 Chapter 3 Experimental analysis

Table 3.2 Performance factors in flowmeter selection (from BSI Guide 7405 [199 lI)*

PressureI) Group Type Linearity [%] Repeatability [%] Rangeahility drop at maximum flow

1 Orifice # # 3 or 4: I 3/4

Venturi # 3 or 4: 1 2

Nozzle 3 or 4: I 2/3

2 Variable area ±1 to ±5% FS ±0.5 to ±1% FS 10: 1 3 Target NS NS 3: I 3 Averaging pitot # ±0.05 to ±0.2% R # 1/2 Sonic nozzle ±0.25% ±0.1% 100: 1 3/4

3 Sliding vane ±0.1 to ±0.3% R ±0.01 to ±0.05% R 10 to 20: 1 4/5 Oval gear ±0.25% R ±0.05 to ±0.1% R 4 Rotary piston ±0.5 to ±1% R ±0.2 R 10 to 250: 1 4/5 Gas diaphragm No data No data 100: 1 2

Rotary gas ±1% ±0.2% 25: 1 2

4 Turbine ±0.15 to ±1% R ±0.02 to ±0.5% R 5 to 10: 1 3 Pelton ±0.25 to ±0.2% R ±0.1to ±0.25% R 4 to 10: 1 4 Mechanical meter No data ±1% ES 10 to 280: 1 3 Insertion turbine ±0.25 to ±5% R ±0.1 to ±2% R 10 to 40: 1 1/2

5 Vortex ±1% R ±0.1 to ±1% 1/ 4to 40: 1 3

Swirlmeter < ±2% R NS 10 to 30: 1 3

Insertion vortex ±2% ±0.1% R 15 to 30: 1

6 Electromagnetic ±0.5 to ±1% R ±0.1% R to 0.2% FS lOto 100: I

Insertion electro- ±2.5 to ±4% R ±0.1% R 10: 1 magnetic

7 Doppler No data ±0.2% FS 5 to 25: 1 I

Transit time ±0.1 io 1% R ±0.2% R to ±1% F5 10 io 300: 1

8 Coriolis NS ±0.1 to ±0.25% R 10 to 100: 1 2/5 Twin rotor No data No data 10 to 20: 1 3/4

9 Anemometer No data ±0.2% PS 10 to 40: 1 2

Thermal mass ±0.5 to ±2% FS ±0.2% F5 to ±1% R 10 to 500: 1 2

IO Tracer No data No data Up to 1000: 1 i Laser No data ±05% R Up to 2500: I I

Key: % Ris the percentage flow rate % ES is the percentage full scale NS indicates not specified is dependent on differential pressure measurement

U lis low; Sis high

110 3.2 Flow rate measurements Let us first address the constraints imposed by the waterjet system on the flowmeter. It is important that the flowmeter should not change the relation between the flow rate and thrust developed by the jet. This consequently implies that the influence of the flowmeter on the velocity distribution and the static pressure in the intake and the nozzle should be negligible. Another constraint is that it should not have large external protrusions that create additional drag. This may especially be important at the lower speeds, where the nozzle is fully or partially submerged.

Let us secondly consider the constraints imposed by the flowmeter. There are two main types of disturbances affecting the flowmeter performance; flow profile distortion and swirl' (Fumess [19901). Many flowmeters require therefore a certain undisturbed upstream pipe length in the order of JO diameters or more in front of the meter. A somewhat smaller length is usually required downstream of the meter (see Table 3.3). Often a flow straightener is required as well.

Profile distortions may for example be caused by an obstruction partially blocking the conduit, such as e.g. large flow separation or cavitation in the waterjet intake. Swirl may be generated by e.g. an impeller, a turbine or a stator. lt may also be caused by the ingestion of axial vorticity from the external flow, caused by appendages or chines ahead of the intakes (see e.g. Brennen [19941). Swirl is far more difficult to correct for than velocity profile distortion. Fig 3.6 shows that a swirl angle of 1 deg already causes a deviation in the calibration coefficient of a turbine meter of approx. 2%, leading to a similar deviation in flow rate. In contrast to the sensitivity of the turbine meter, Fig. 3.7 shows that a multiport averaging pitot has a tolerance of an angle of approximately 3 deg with the onset flow.

12 lo Liquid turbine meter

V o Gas turbine L) meter V L) 4

2 Q-) Q-3 o

C-) 10 20 30 40 50 Swirl angle, degrees

Fig 3.6Effect of swirl on turbine meters (from BSI Guide 7405 [1991])*

111 Chapter 3 Experimental analysis

Table 3.3 Flowmeter installation constraints (from BSI Guide7405[19911*

Quoted Quoted range range of Pipe Group Type Orientation Direction of upstream minimum Fil- bore range lengths downstream ter [mm] lengths

I Orifice H, VU, VD, I U, B SD/80D 2D/8D N 6 to 2600 Venturi H, VU, VD, I U 0.5D/29.5D 4D N > 6 Nozzle H, VU, VD, I U 3D/SOD 2D18D

2 Variable area VU U OD OD P 2 to 600 Target H, VU, VD, I U 6D/2OD 3.5D/4.5D N 12 to 100 Averaging pitot H, VU, VD, I U, B 2D/25D 2D/4D P > 25 Sonic nozzle H, VU, VD, I U > 5D > OD N 5

3 Sliding vane H, VU. VD. I U OD OD R 25 to 250 Oval gear H U OD OD R 4 to 400 Rotary piston H, VU. VD, I U OD OD R 6 to 1000 Gas diaphragm H U OD OD N 20 to lOO Rotary gas H. VU, VD, I U, B OD/IOD OD/3D R 50 to 400

4 Turhinc H. VU, VD. I U, B 5D/2OD 3D/1OD P 5 to 600 Pelton H. VU, VD. I U 5D SD R 4 to 20 Mechanical H, VU, VD, I U 3D/IOD ID/5D R 12 to 1800 meter 5 Insertion turhincH, VU, VD, I U. B JODI8OD D/IOD P > 75

5 Vortex H. VU. VD, I U lD/4OD SD N 12 to 200 Swirlmeter H, VU, VD, I U 3D ID N 12 to 400 Insertion vortex H, VU. VD, I U 20D SD N > 200

6 Electromagnetic H, VU, VD, I U, B OD/IOD OD/5D N 2 to 3000 Insertion electro-H, VU, VD, 1 U, B 25D 3D N > WO magnetic

7 Doppler H. VU. VD, I U. B IOD SD N > 25 Transit time H. VU, VD. I U, B OD/5OD 2D/5D N > 4

X Coriolis H, VU, VD, I U OD OD N 6 to 150 Twin rotor H, VU, VD, ¡ U 2OD SD N 6 to 150

9 Anemometer H. VU, VD, I U, B IOD/4OD No data R > 25 Thermal mass H. VU, VD, I U No data No data R 2 to 300

(1 Tracer H. VU, VD, I U, B # # N Unlimited Laser H. VU, VD, I U, B OD OD P

Key: H is horizontal flow U is uni-d irectional flow VUis upward vertical flow B is bi-directional flow VD is downward vertical flow R is recommended is inclined flow N is not necessary # is mixing length P is possible

112 3.2 Flow rate measurement..Q

I. 'i,

o o

Fig. 3.7 Installation guidelines for multiport averaging static pitot tube (from BSI Guide7405 [199 1I)*

Considering the installation constraints for the waterjet system, it soon becomes clear that in no part of the system a developed, swirl free and undisturbed velocity profile will occur. This observation implies that the fiowmeter used should be calibrated under the conditions for which it is used, and that it should show little sensitivity to flow profile distortions and swirl. Ideally, this means that before conducting the actual propulsion test, first a calibration test should be made at the same model speed and impeller rotation rate. This procedure is followed by the Norwegian towing tank, where pitot tubes in the intake are used as flowmeters (ITTC [1993]).

Flow rate calibration at non-zero speeds is a complicated and time consuming task however. We will therefore consider the consequences of calibrating the flow rate at zero speed in the following. It is thereby noted that the flowmeter is calibrated in its actual position, but at a slightly different operating condition of the jet.

Calibrating at zero model speed only yields reliable results if the distinct operating condition does not introduce significant deviations in the flowmeter reading. This is an essential constraint, because minor deviations in the pump's working point are known to occur due to this change in operation, which may consequently cause a minor change in velocity profile as well as in swirl.

113 Chapter 3 Experimental analysis

Apart from small variations in pump working point, deviations in the jet velocity profile may also occur through the occurrence of separation in the intake and changes in the ingested boundary layer (or velocity profile).

To minimize the effect of large changes in velocity profile, the best position for the flowmeter is situated between the stator of the pump and the nozzle exit area. Initial disturbances in the ingested flow are thus levelled out by the impeller and stator action.

Based on observed differences in working point between bollard pull and propulsion tests and the consequent deviations in swirl, it was decided to stop further evaluation of the insertion turbine meter at this point.

Jet velocity profile study

To obtain more insight in the differences occurring in velocity profile between the speed zero or bollard pull condition and the operational condition at non-zero speed, velocity measurements with a five fingered pitot static rake were conducted. To this end, the pitot rake was mounted in such a way that the stagnation pressure is measured in the nozzle discharge area (A8 in Fig. 2.1). A sketch of this set-up is shown in Fig 3.8.

Fig 3.8Nozzle geometry and pitot static rake position used for the jet velocity profile measurements

114 3.2 Flow rate measurements The shift in pump working point that occurs for changing model speeds (resulting in a change in non-dimensional flow rate K0), causes a change in the relation between flow rate and impeller rotation rate. To ensure that the velocity profile is compared at equal flow rate, a reference velocity transducer was mounted. The relation between flow rate and reference velocity was thereby assumed to be independent of model speed.

The reference velocity signal was obtained from a venturi flowmeter. The venturi fiowmeter consisted of four circumferential pressure tappings at each of two distinct cross sections in the nozzle (see Fig 3.9).

Fig 3.9Positions of venturi pressure taps and asp

The relation between reference velocity and local velocity in the nozzle was for each position found from linear regression analysis.

A review of the experimental programme on the jet velocity profile measurements is given in Table 3.4.

Impeller rotation rates at the self propulsion point of ship were selected, because this is the operating condition in which the flow rate is to be measured.

115 Chapter 3 Experimental analysis

Table 3.4 Review of jet velocity profile measurements

Condition Type of test Vni[rn/si Impeller n [rpm] Horizontal plan 0 800 1200 1600 2600 3100 3.1 2600 3.7 3100 Vertical plan 0 800 1600 2400 2600 (2*) 3.1 2600 3.7 3100 4.7 3600

The results of the velocity profile comparison between zero and non-zero speed at equal flow rate are presented in Fig 3.10. The measured velocity u in the jet at each of the five positions is expressed in the corresponding velocity u that would have occurred during the bollard pull test at speed zero. The latter velocity was obtained from the linear regression formulas. The local velocities for the two highest impeller rotation rates in the vertical cut are obtained by extrapolation of the linear regression relation.

vertical plane horizontal plane 1.6 -e-- n=2600, Vm=3.l

o.. - -- n=3600, Vm=4.7 1.0 --- n=2600, Vm=3.l - -4- n3 100, Vm=3.7 0.6 0.85 0 20 40 60 80 100 0 20 40 60 80 100 radial position from radial position from upper nozzle wall [mmj portside nozzle wall [mm]

Fig 3.10Effect of model speed on jet velocity profile

116 3.2 Flow rate measurements

For all pitot positions, all measurements could be used for the regression analysis, with the exception of the point in the vertical cut at a radial position of 68 mm. For this point, the two lowest impeller rotation rates were skipped because they disproportionally increased the standard error in the regression coefficient.

With these results, the deviation in average (momentum) velocity in the nozzle can be assessed when a five port averaging static pitot ('asp') would be used for flow rate measurements that is calibrated at speed zero. The mean momentum velocity is obtained from the square root of the asp pressure differential.

Because the signal of the asp is made up from the average of the local velocity pressures, this signal can be written as:

Lu (3.6) DPasp =

where Ç = asp calibration coefficient =local velocity at position i n = number of ports on asp.

The calibration coefficient Ç is supposed to be independent of model speed. The effect of model speed on the average momentum velocity can now be assessed by studying the ratio of the asp pressure differentials between bollard pull and propulsion test. In the case of true independency, the following equation should hold:

u )2/, = 1 (3.7) U jr1 I?/?

Table 3.5 shows the results of the computed pressure ratio values.

It is seen from this table that all values are within 1% deviation, except for the measurements in the vertical cut at a model speed of 3.1 mIs, where a deviation of some 4% occurs. A similar exceptional behaviour is observed from Fig 3.10 for this condition.

117 Chapter 3 Experimental analysis

Table 3.5 Results on five port asp check

Model speed / Type of test V[E(u/u1 bp)2'1 Vm [mIsi

Horizontal cut 3.1 0.990 3.7 1.002 Vertical cut 3.1 1.042 3.7 1.009 4.7 1.008

No simple explanation for the exceptional behaviour at this single point is readily available. It should be noted however, that due to the relatively large nozzle opening (see Fig 3.9), the pump is operating outside its design range, resulting in a lightly loaded pump operating at low efficiency. This condition may result in an unstable flow in the impeller, leading to more than one possible velocity field in the nozzle. The resulting deviation in velocity profile is clearly not sufficiently handled by a five port asp.

Flowrneter evaluation

Taking the preceding considerations on flowmeters into account, two types of flowmeters were tested on their suitability. These types are:

One and four tap venturis, making use of the nozzle contraction Multiport averaging pitot tube.

The positions where these transducers were installed in the nozzle are depicted in Fig 3.9.

Both venturi meters showed to be very sensitive to local distortions caused by other transducers. Similar distortions may occur in the lower speed region where the nozzle is not yet completely ventilated. These conditions would subsequently affect the relation between flow rate and venturi signal. The one tap venturi meter showed a greater sensitivity than the 4 tap meter, as could be expected.

118 3.2 Flow rate measurements

Furthermore, the precision error of the venturi meter signal appeared to beapprox. twice the precision error of the asp signal (2% versus 1% of themean signal).

In addition to the lower quality of the signal, the venturi meter ismore prone to systematic errors due to a skewed velocity profile relative to the calibration situation, as can be inferred from Fig 3.10.

The averaging static pitot (asp) was selected as the most promising flowmeter for the following reasons:

The asp only interferes to a limited extent with the flow in the nozzlearea (A8 in Fig. 2.1). The precision error of the asp signal appeared to be approximately half the error of the 4 tap venturi meter. It furthermore showed to be less sensitive to local flow distortions. The sensitivity of the asp for local flow distortions has been studied through the determination of the nozzle velocity profile and turned out to result in bias errors within 1%, where deviations in local flow velocityup to 10% occurred (Fig 3.10). According to the BSI Guide [1991], deviations in angle of attack (on the asp cross section) up to 3 deg due to swirl for example, do not significantly affect the meter calibration.

3.2.2Calibration procedure

Before conducting the propulsion test,the selected flowmeter needs to be calibrated, as mentioned in the previous section. From thesummary of previous work on flow rate measurement (Section 1.6.2), it is concluded that almost all procedures suggested in the course of time, attempt to accuratelymeasure the flow rate, in order to derive the thrust. A similar procedure was also attempted in the beginning of the present work. The uncertainty of propulsion test results however, largely depends on the uncertainty of the flow rate calibration. It appeared after many attempts, that although sufficiently accurate results were incidentally obtained, the uncertainty of this 'flow rate calibration procedure' is unacceptably high.

As a consequence, direct calibration of the thrust from the nozzle duringa bollard pull test was attempted. This procedure will be referred toas 'thrust calibration procedure'. It appeared to significantly improve theaccuracy of the thrust derived from propulsion tests.

119 Chapter 3 Experimental analysis A broad outline of both calibration procedures will be given first. Subsequently, each procedure will be described in more detail and obtained results will be discussed in terms of their contribution to the overall uncertainty. Finally, an evaluation of both procedures is made, based on the estimated uncertainty of their results, and the propagation of errors in the final thrust and power prediction.

Outline of Jlowmeter calibration procedures

Fig 3.11 shows schematically the activities and the results for both calibration procedures.

FLOW RATE CALIBRATION THRUST CALIBRATION

Flow rate calibration - V-notch weir Q-Dp - WC Container + Bollard pull thrust Bollard pull test __-øtp tbp calibration + + Propulsion test - T-V Propulsion test -T-V

Fig 3.11Scheme of flowmeter calibration procedures

The 'flow rate calibration procedure' consists of three activities. The first activity is the actual flow rate calibration. This calibration determines the relation between the flow rateQand the differential pressure Dp from the asp. The obtained relation is subsequently used in the bollard pull test (second activity), resulting in a thrust derived from the asp signal and a pulling force, directly measured on the model. A bollard pull thrust deduction fraction tbp is obtained, which is defined as:

(3.8) P T Jetx

120 3.2 Flow rate measurements where T. =thrust from jet (from discharged momentum) in x-direction 'xbp = pulling force acting on model in x-direction at bollard pull.

This bollard pull thrust deduction was used as a checkon the thrust derived from the asp. Based on experience with propeller driven hulls,it was known that representative values for the thrust deduction fraction shouldnot be much higher than 0.05. If the bollard puil thrust deduction fraction met this empirical criterion, the flowmeter calibration was considered successful.

The relation between flow rate and asp signalwas subsequently used in the propulsion tests, where the waterjet net thrust could be derived from the relation for gross thrust (see Section 2.3.1):

Tg COSOnPQCmUO (3.9)

where O, = nozzle centreline inclination relative to vessel fixed x-ordinate (see Fig. 2.3).

It will be derived and experimentally demonstrated later however (Section 3.2.3), that for most configurations, the thrust deduction fraction fora waterjet driven hull in bollard pull condition should approximately equalzero. With this knowledge, a direct relation between the asp-signal and the momentum flux from the nozzle, or jet thrust Tjetx could be obtained. Using eq. (3.9), the net thrust during the propulsion test can be approximated from:

TietxPA,i Tgoo ietxCn1UO (3.10) cosO

Apart from the net thrust, the effective jet system powerJSEcan be obtained from either the flow rate or the bollard pull thrust.

In the substitution of flow rate for jet thrust in the relations for net thrust and power, it is assumed that the jet velocity profile is sufficiently uniform to equate the mean momentum and energy velocities to themean volumetric velocity. Should this not be the case, the differences in mean velocitiescan be accounted for with momentum and energy velocity coefficients (Cm and Ce),as introduced in Section 2.3. The relation between jet thrust and flow rate is then given by:

121 Chapter 3 Experimental analysis

- (3.11) et Cnm A where c,, = momentum velocity coefficient in nozzledischarge area.

Flow rate calibration

A number of methods to measure the flow rate with the greatest possible accuracy and certainty have been investigated. The methods considered (in arbitrary order) are:

calibrated flowmeter in a straight pipe section direct mass flow measurement through weighing of collected water integration of velocity profile in the jet V-notch weir.

Calibrated flowmeter in a straight pipe

A calibrated flowmeter in a straight pipe can be used in a set-up where thepipe is connected to the nozzle of the waterjet unit. An advantage of this method is that an accurate flowmeter can be selected and canbe mounted in line with the appropriate installation constraints. Disadvantages are:

a relatively complicated test set-up forcalibration is needed more than one pipe diameter and flowmeter maybe necessary to cover the required range of flow rates (a range of 5 - 70 lIs was required).

Provided the installation constraints pertinent to the flowmeter are met (Section 3.2.1), this method of calibration is potentially satisfactory. Thecomplexity of the required test set-up and the acquisition costs were initially considered prohibitive for successful application.

This method has been used once in this work to calibrate aV-notch weir, which will be discussed later in this section. For this purpose, a turbineflowmeter was used.

122 3.2 Flow rate measurements Mass flow measurement through weighing

Collecting the water discharged from the nozzle and weighing it as a function of time has been used by several institutions (see e.g. ITTC [1993]). This method has been applied in the present work in two different set-ups.

The first set-up consisted of a large container, suitable of collecting water for a steady period of about 10 seconds at a flow rate of approx. 70 1/s. Because of the dimensions and the weight of the replenished container, this flow rate calibration could only take place at zero speed of the ship model. A practical disadvantage was furthermore that the container had to be emptied at regular intervals, making the whole calibration procedure time consuming.

Later on during this work, a smaller water collecting container (WC container) was designed for a smaller maximum flow rate calibration. This WC container had the advantage that it was so small and light that it could be mounted onto the carriage of the basin, thus allowing for a calibration at speed. Another advantage was the automated valve in the container, which could be adjusted to collect water over any required time interval. The valve opening angle could be measured as a function of time, thus giving the possibility to estimate the errors due to the lapse of time during opening and closing of the valve.

The WC container has been used during one sequence of tests, with the aim to obtain an indication of the start and stop errors, of the sensitivity to differences in collecting time and the repeatability of the measurements. A photograph of the WC container in operation is shown in Photo 3.1. The photo illustrates the whisker spray over the box, which potentially leads to a bias error. It can furthermore be seen that the sealing of the valve was not sufficiently adequate to guide the full jet into the container without losses. The corresponding leakage losseswere estimated to amount to approx. 0.3 L's.

Fig 3.12 shows some of the results obtained with the WC container. In this graph, the flow rate obtained from the WC container is plotted against the square root of the asp pressure reading. It clearly shows the scatter of the data, which was considered unacceptably large for accurate thrust measurements. Although the above mentioned defects could probably be reduced to a certain extent, the inherent uncertainty of the set-up was considered too large to render this a promising method.

123 Chapter 3 Experimental analysis

Photo 3.1 The water collecting container in operation

124 3.2 Flow rate measurements

14 A

aWCC. Vm=0, n=2500 12 o D WCC, Vm=0, n=3200

G WCC. Vm=2.53 / 5.36 o jet thrust, Vm=0

R lo 16 18 20 22 24 26

VDp asp [cmwcl

Fig 3.12 Comparison of flow rates WC container and bollard pull calibration

Integration of velocity profile

Based on the measurements mentioned in Section 3.2.1 on the jet velocity profile in the nozzle, an estimate of the discharged flow rate can be obtained from an integration of the measured velocity profile over the nozzle area. To this end, the pitot static rake was set at four different angular positions in the jet. The resulting velocity profiles are presented in Fig 3.13.

Due to the non-uniform and non-symmetric character of the velocity profile and the limited number of measured positions, the uncertainty in the velocity profile was considered too big to allow for an accurate flow rate from velocity integration. An important contribution to this uncertainty is due to the asymmetry of the axial velocity close to the nozzle centre (Fig 3.13). Both the symmetry and the uniformity of the velocity profile are expected to improve for smaller nozzle/pump diameter ratios. A further improvement is expected when the pump operates closer to or in its design range of working points.

125 Chapter 3 Experimental analysis

1.2 £ £ 1.1 . j D o D4Sdeg 0.9 . £ O 90deg O 0.8 £ I35deg - o l8Odeg 0.7 -0.5 0.5

Fig 3.13 Measured velocity profile at nozzle discharge opening

From the limited set of experiments conducted, it is concluded that flow rate measurement through velocity field integration is time consuming for sufficient accuracy. Furthermore, one should be ascertained of a steady and stableflow pattern in the nozzle if the velocity field is measured by timewise sequential velocity measurements.

V-notch weir

Flow rate measurement through weirs is common practice in civil engineering to measure flow rates through open channels. This techniqueis furthermore understood to be applied by pump manufacturers for accurate flowrate measurements.

A wide variety of weir types exists (see e.g. Bos [1990]). Of these types, the 'sharp crested V-notch weir' (Fig 3.14) was selected, because of its simplicity, its rangeability (5-70 1/s was required) and its expected accuracy.

For use in the calibration of jet discharged flow rate, the weir is mounted in a 4 m long container, as shown in Fig 3.14. The weir is mounted at one end ofthe container. The water supply is positioned at the other end. Two plates were mounted just after the water supply, to damp the turbulence and wave generation created by this supply.

126 3.2 Flow rate measurements

Source publication LRI no. 20 International Institute for Land Reclamation and Improvement Copyright: dimensions in Em]

Fig 3.14V-notch sharp crested weir (from Bos [1990]); V-notch weir container

Two distinct notches could be mounted, one having a notch angle O of 90 deg, the other having an angle corresponding to a quarter of the tangent of 90 deg (28 deg). This latter notch is considered more accurate for the flow rates in the lower range.

The flow rate for a V-notch weir (fully contracted) is obtained from:

(2g)tan(_) h2.5 (3.12) Q Ç 2 where Ce =coefficient of discharge; Ce =f(h1/p1, p1/B1 and O) (see Fig 3.14) = notch angle he =effective head; he = hj+Kh h1 =actual discharge head (see Fig 3.14) K17 =coefficient representing the combined effects of fluid properties.

By measuring the discharge height h1, the flow rate through the weir can be calculated.

Because of the importance of accurate flow measurements, the weir itself has been calibrated in order to reduce the bias error in the flow rate (Willemsen et al. [19921). Calibration of the weir was done with a certificated turbine flowmeter. This flowmeter was reported to have an uncertainty of 0.03% in calibration coefficient.

The uncertainty of the flow rate measurement through a weir can now be estimated from its calibration. The flow rate in an arbitrary weir test can be obtained from:

127 Chapter 3 Experimental analysis

Qm = Cweirh (3.13) where Qrn measured flow rate Cweir = calibrated weir coefficient h = measured water level height.

The coefficient Cweir is determined from the weir calibration and only depends on the weir geometry. The water level height was measured through a wave probe. The zero height reference level is determined at the beginning of each testing sequence. The height obtained from the wave probe signal can subsequently be written as: h = a1&-h0 (3.14) wherea1 = linear wave probe calibration coefficient = measured voltage over wave probe h0 = zero flow rate adjustment weir.

C weit uncertainty

The results of the weir coefficient from calibration are plotted in Fig 3.15. The figure clearly shows that the scatter in calibration coefficient for the 28 deg notch is clearly higher for a rising water level (increasing pump rotation rate) than for a falling level. This observation corresponds with a recommendation for the wave probe calibration procedure which suggests that the probe should be calibrated for falling water levels only.

The precision error in the weir coefficient could now be calculated from the sample presented in Fig 3.15. The results are summarized in Table 3.6.

Table 3.6 Precision of the V-notch weir coefficient

90 deg notch 28 deg notch Complete Falling water Complete Falling water sample level sample level

averageCweir [] 1.342 1.339 1.416 1.396 0.202 0.252 0.533 0.061 cwe,r

128 3.2 Flow rate measurements

1.08

L 1.06 0 90 deg, mer. rpm 90 deg, deer rpm L L 28 deg, incr. rpm 28 deg, deer. rpm L L L o o DL. .otòn . s 0.98 O 2 4 Thousands impeller rotation rate [rpm]

Fig 3.15V-notch weir calibration results

Precision of height measurement

The precision error of the height measurements is evaluated from three wave probe calibration experiments, each experiment consisting of 8 to 14 points. The average best estimate of the standard deviation of the height measurements of three calibration experiments on two distinct wave probes has been used.

h0 uncertainty

An estimate of the bias error in the zero adjustment of the weir was obtained from a number of repeated zero settings with the weir. The zero adjustment was visually read on the manometer scale. From these repeated zero readings, a bias error of approx.1 .5 mm was estimated.

The results of the above uncertainty analysis in the flow rate as measured from the weir are summarized in Table 3.7.

The importance of the scatter in the height measurements by the wave probe is clearly illustrated. Improvements in flow rate uncertainty by improving the uncertainty of the water height measurements is considered possible.

Fig 3.16 shows an example of typical bollard pull thrust deduction fractionstbp that were obtained from the above flow rate calibration procedure. Taking into

129 Chapter 3 Experimental analysis consideration that the uncertainty in the bollard pull thrust is twice the uncertainty in flow rate due to the corresponding sensitivity, the shown deviations from zero thrust deduction are explained by the uncertainty analysis from Table 3.7. Table 3.7 Uncertainty analysis of flow rate measurement from V-notch weir

Relative Bias error Precision Error source Error sensitivity error b [%J3) [%f3) 0[-1 ; 1.0 0.25 - cweir

-precision of height 2.5 1.0 measurement from wave probe

-zero height setting h0 Bho'l.S mm -2.5 0.54

Totals 1.35 2.51

URSS Qweir @ 95% 5.2% Example data Qm15 I/s e=28 deg h=279 mm

Thrust calibration

With regard to the large uncertainty in the flow rate measurement from the weir, and the difficulties experienced in using other methods, the idea originated to calibratethedischarged momentum fluxdirectlythroughpullingforce measurements on the model. For such a procedure we need some knowledge about the thrust deduction in bollard pull condition.

Hypothesis on thrust deduction

From simple potential flow considerations on the flow field about the intake during bollard pull condition, one can derive that the ingested momentum flux in x- direction for an arbitrary intake mounted on a flat plate equals zero (Fig 3.17).

3) Errors are expressed as a percentage of the Reading (R), unless indicated otherwise.

130 3.2 Flow rate measurements

0. 1 ---t 0.05

i' e test 50231, 1.19A0 -0.05 -o-test 50231,

-0.! 1000 500 2000 2500 3000 3500 4000 n [rpm]

Fig 3.16 Typical bollardpullthrust deduction fractions obtained from V-notch weir calibrations

A qj(xj,O) A' /P N o D R R I ''½Ae

Fig 3.17F!ow field about an arbitrary intake at boflard pu!! condition

131 Chapter 3 Experimental analysis

To illustrate this, let us consider a 2-dimensional intake in the x-z plane. The flow field can be modelled by a suitable set of sinks on the x-abscissa. Each sink has a strength -q and a potential p and is located in (x,O). The potential of the total flow field can be written as the sum of the potentials of the individual sinks:

= (3.15)

We would like to demonstrate that the ingested momentum flux 4)m3x through area 3 in x-direction equals zero at U0=O. Let us therefore first consider the circular control volume, spanned by the area Ae, containing the set of sinks representing the intake. The circle has a radius R, with the origin at the centre of gravity of the sink distribution. The momentum balance for this control volume can now be written as:

4)mex =JpndA (3.16) Ae

The external force in the right-hand side of the equation, is built up from the pressure force acting upon the external boundary Ae and the forces on the singularities representing the intake. These latter forces can be computed with Lagally's theorem. But because the free stream velocity equals zero in the bollard pull condition, the net Lagally force on the sink distribution equals zero. Internal forces between the sinks neutralize each other.

For an arbitrary distribution of n sinks on the x-abscissa. we can write the momentum flux in polar coordinates:

(3.17) mex=-J(v2cosO-7rVesin O)rdO where Vr = radial velocity V9 = angular velocity.

The second term in the integrand is caused by the fact that the potential function is made up from a sink distribution instead of one sink point. For increasing radii R, this second term quickly diminishes because of the vanishing contribution of y9.

132 3.2 Flow rate measurements

The radial velocity Vr can be obtained from the potential function:

Vr = (3.18) ¿fr

Remembering the potential function of a single sink in polar coordinates:

-q (p1= (3.19) 47tr1 the following relation for the momentum flux through Ae can be derived:

2it q1(R-xcosO) ,nex ]2RcosOdø (3.20) o ' 4it(R2+x22x1RcosO)5/2

This integral approaches zero if the term in brackets becomes independent of the polar coordinate O. This situation occurs for x.cR or for q1cQ.

This implies that if R is sufficiently large with respect to the intake length, the momentum flux in x-direction through Ae equals zero, and consequently the net pressure force acting upon Ac equals zero (eq. (3.16)).

To find the momentum flux Pm3x' we will now consider half the circular control volume spanned by Ac. The new boundary is situated just underneath the x- abscissa so that the set of sinks is just out of the control volume. The new boundary is made up from the plating area A and the projected intake area A3. The circumferential area is one half the original circumferential area Ae. The momentum balance for this volume reads:

ìn3xmex J pndA+ J pndA (3.21) A+A3 e 2

Use has been made of symmetry of the flowfield about the x abscissa. We have seen that both the momentum flux and the external net force in x-direction on the external area Ae vanish for a sufficiently large radius of the control volume R. Furthermore, the contributions of the surface forces on the surfaces A and A3

133 Chapter 3 Experimental analysis equal zero because n equals zero. Equation (3.21) consequently reduces to:

4m3x = (3.22)

Therefore, the net thrust during bollard pull is given by:

Tnet = Tjetx (3.23) where Tietx is the discharged momentum flux from the nozzle:

Tjetx - cosO (3.24) A,

It is assumed in the above relation that the velocity distribution in the jet is sufficiently uniform toneglect differencesin mean volumetric and mean momentum velocities. If thisis not the case, a similar momentum velocity coefficient c1 can be introduced as has been done to account for this effect in the ingested momentum flux in the intake (see Appendix 2).

Despite the above argumentation, differences between the jet thrust Tjetx and the measured pulling force on the model may occur for the following reasons:

The discharged jet induces a non-zero force in x-direction. The limited bottom area about the intake affects the intake flow. The viscous stresses acting on the bottom plating exert a non-zero component in x-direction.

These effects are assumed negligible in eq. (3.23).

Model tests have been conducted to check this assumption. The test set-up and the results will be described in the next section (Section 3.2.3). We will continue first with an estimate of the uncertainty in measured jet thrust Tjetx.

Thrust deduction uncertainty

The jet thrust can be obtained from a pulling force measurement during bollard pull conditions:

134 3.2 Flow rate measurements

Fx,neas Tietx = (3.25)

The uncertainty in jet thrust acting upon the hull is consequently built up from the parameters that occur in this relation.

The quintessential assumption inthe'thrust calibration'procedureisthe assumption that the jet thrust deduction fraction tbp is negligible. Based on the tests discussed in the next section, itis estimated that the bias error, due to this assumption is about 1% of the jet thrust.

Pulling force uncertainty

Generally speaking, an accurate force measurement is a much easier task to accomplish than an accurate flow rate measurement. This is expressed in the smaller uncertainty of a careful force measurement. For an estimate of this uncertainty, the error sources and much of the corresponding estimates are borrowed from the report of the High Speed Marine Vehicle Committee of the 20th ITTC 1993], and listed in Table 3.8.

Table 3.8 Estimates of uncertainty for measured force Fmeas for two transducers with different capacity

80 N Transducer 800 N Transducer Error sources Bias error B1Prec. error S Bias error B Prec. error S- - Transducer & A-D converter linearity error 1.60 102 N 1.60 lO N - A-D digital error 2.15 l02 N 2.15 lO N -Calibration 4.0 102 N 4.0 10' N -Filter 1.64 10-2 N 1.64 10-2 N - Measurement error 2.6 10-2 N 2.6 l02 N

Total (Ftneas=52.8 N) 0.1% 0.1% 0.5% 0.76% URSS F,nea @ 95% 0.2% 1.6%

It is noted that the precision error estimates for calibration and measurement are not copied. The authors cited take the measurement error as the precision error of the instantaneous signal, whereas we are only interested in the average of one

135 Chapter 3 Experimental analysis 'run', consisting of a large number of samples. Also the precision error in force estimate from the calibration test is considered to be too pessimistic. The values given here are based on standard MARIN practice. They also show a better agreement with the data presented by Lin et al. [19901

To illustrate the effect of a small and a large capacity transducer, an 80 N (full scale) force transducer and an 800 N transducer are considered.

The foregoing table shows that the difference in uncertainty between the small and the large capacity transducers is caused largely by the precision errorin calibration. We will assume that the most appropriate transducer has been fitted for the thrust calibration and consequently use the smallest uncertainty value.

The resulting uncertainty in jet thrust Tjetx is summarized in the Table 3.9.

Table 3.9 Uncertainty in jet thrust for calibration input

Relative Bias error Precision Error source Error sensitivity error 0 [-1 b [%] s [%] - Thrust deduction tb Sect. 3.2.3 1.0 1.0 - Transducer force Fmeas Table 3.8 1.0 0.1

Total 1.1 0.1 1.1% URSS 1il @ 95%

Evaluation of procedures

Performance considerations should play a dominant role in the selection of the most suitable procedure, apart from economic considerations. To this end, wewill use uncertainty in net thrust as a performance indicator.Consequently, both the precision and bias errors, as well as their propagation into the uncertainty of the net thrust should play a role in the selection of calibration procedure.

4) This estimate is based on the repeatability of the bollard pull force measurements in Section 3.2.3.

136 3.2 Flow rate measurements The non-dimensional confidence level for the result u, covering 95% probability, is given by (see also Appendix 3):

=/bk2+(too25(v)sk)2 (3.26) RSS @ 95%

whereb?= non-dimensional bias error in result = non-dimensional precision error in result.

The non-dimensional error in the result is caused by a propagation of several error sources occurring in the experimental procedure. The bias error in the result can be obtained from the following relation:

h = (3.27) N i=I where 0 = relative sensitivity of result for parameter i (see Appendix 3) b =non-dimensional bias error in parameter i.

A similar relation is found for the non-dimensional precision error.

The error source parameters follow from the parametric relations for the net thrust (equations (3.9) and (3.10) respectively). The uncertainties for flow rate and jet thrust that are used as input signals in the calibration procedure have been discussedinthepreceding. We will now systematically compare other contributions to the sensitivity of both calibration procedures.

Starting from the equations (3.9) and (3.10), the relative sensitivities 0 can be expressed as functions of the nozzle velocity ratio NVR and the momentum velocity coefficient in the intake Cm. The relative sensitivity for an error in the flow rate 0can now be compared to the relative sensitivity for an error in the jet thrust 0etx This is done in Fig 3.18 for a representative value of c,= 0.9. This figure shows that the jet thrust procedure shows a sensitivity that is half the sensitivity of the flow rate procedure over the complete NVR range.

A similar comparison on the relative sensitivity of net thrust can be made for the error contributions of the nozzle area A and the specific mass of water p. The sensitivity of both procedures for A is plotted in Fig 3. 18 for both calibration procedures. It shows that the difference between thrust calibration and flow rate

137 Chapter 3 Experimental analysis calibration is here considerable in the NVR region of practical interest (roughly for l.5<.NVR<3). With regard to the uncertainty in nozzle area, it is noted that the tolerance (bias error) in the nozzle diameter manufacture is about 0.05 to 0.1 mm. An additional error may however be caused by a possible vena contracta behind the nozzle discharge area (A8 in Fig. 2.1).

jetthrust calibration jet thrust calibration - - -flowrate calibration - - -flowrate calibration

e'Q

Cm0. Cm =0. ------

o 2 3 4 o 2 3 4 NVR[-] NVR [-J

jet thrust calibration - - -flowrate calibration

Cm= 0.9

o 2 3 4 NVR[-]

Fig 3.18 Relative sensitivities for bollard pull thrust and flow rate, for nozzle area A and for mass density p

A comparison on the relative sensitivity of net thrust for errors in specific mass is given in Fig 3.18. Again, the thrust calibration procedure shows the lower sensitivity in the practical NVR range. As regards the uncertainty in specific mass, it is noted that during a number of flow rate calibration tests with the V-notch weir, air bubbles were observed at the water supply in the container. Although the source of the air leakage was not revealed, it could have affected the specific mass within the waterjet. The risk for different values of specific mass in the flow rate calibration procedure is higher than it is in the thrust calibration procedure. This

138 3.2 Flow rate measurements is especially caused by the fact that the pump operating point differs more from the working point during the propulsion test in the first procedure. This is caused by the additional pump head by the hose between nozzle and container and the additional height recovery.

The relative sensitivities of net thrust for the model velocity U0 andCm show a similar relation with NVR, due to the similar form in which the source parameters occur in the thrust equations for both procedures. The uncertainties for both error sources are furthermore independent of the calibration procedure. in summary, the uncertainty in jet thrust (input in thrust calibration procedure) is only some 20% of the uncertainty in flow rate (input in flow rate calibration procedure). Furthermore, the thrust calibration procedure shows a favourable behaviour in propagating the errors in all error source parameters for the jet's operating region of practical interest. For these reasons, it was decided to select the thrust calibration procedure as the most accurate and reliable calibration procedure.

3.2.3Bollard pull verification tests

In the 'thrust calibration procedure', a necessary hypothesis was made that the thrust deduction fraction in bollard pull conditions equals zero for a hull with representative transom fitted waterjets. To verify this hypothesis, a series of bollard pull tests has been conducted.

The objective of these tests is to quantify the effects of the ingested flow in the intake and the discharged flow from the nozzle on the relation between thrust from the nozzle (1jetx or nozzle momentum flux) and measured pulling force acting upon the hull model.

The experiments consisted of a series of bollard pull tests on four model configurations, viz.:

Bare hull model Model with stern plate between jet and transom Model with intake pipe Model with both stern plate and intake pipe.

The second configuration consists of the bare hull with a so-called 'stern plate'. This plate is mounted on a separate transducer frame and positioned in between the discharged jet from the nozzle and the hull's transom (Fig 3.19).

139 Chapter 3 Experimental analysis

This 'stern plate' configuration enables the measurement of the jet induced force on a transom-like area. This submerged area is approx. 13 times the submerged transom area. The slot between the nozzle and the circular gap in the plate through which it protrudes is only 0.3 to 0.4 mm after fitting. The angle between thex- reference of the plate transducer frame and the baseline of the modelwas measured with an inclinometer to be only 0°40'.

force transducer

transom hull - 197 72IL-

O base line Istat. -. u plate il stiffener 750

dimensions in [mm] for model

Fig 3.19Test set-up for Hamilton test boat with stern plate

The third configuration consists of the bare hull with a so-called 'intake pipe'. A cylindrical pipe enclosing the intake and protruding vertically downward with a length of 2.7 times the local hull draft (Fig 3.20). The 'intake pipe' should warrant a symmetrical ingestion of the flow without inducing a flow about the hull. Under this condition, the ingested momentum flux in x-direction equals zero, and the jet delivered thrust consequently consists from the discharged jet contribution plus possible induced hull forces only.

The fourth configuration consists of the bare hull fitted with both the stern plate and the intake pipe. This configuration enables us to measure the pure thrust from

140 3.2 Flow rate measurements the nozzle Tjetx after accounting for a possible induced force on the stern plate Expiate: Tjetx = Fxmeas Fxpiate (3.28)

The tests have been conducted with the Hamilton Jet test boat. A brief description of this boat and itswaterjet installation is given in Appendix 4.

¡ stat. O

intake pipe

0210

Fig 3.20Test set-up for Hamilton test boat with intake pipe

To increase the precision of the experiments, and to get a better understanding of possible bias errors, a number of static load and repeat tests were conducted. The full testing program is given in Table 3.10.

Fig 3.21 shows that the forces measured on the stern plate are about 1.5% of the pulling force measured on the model. Test No. 50708 (with stern plate) shows an erratic behaviour in Fpiate. which is possibly due to unstable circulation about the plate. Coincidentally, this test happened to be the first test of the day.It furthermore appears that the additional fitting of the intake pipe does not affect the measured plate forces.

141 Chapter 3 Experimental analysis

Table 3.10 Review of bollard pull verification tests

Test Type of test No.

50706 -bare hull 50707 -static load on 6 comp. frame transducer 50708 -with stem plate 50709 -with stern plate and intake pipe 50710 -with intake pipe 50711 -bare hull 50712 -with stern plate 50713 -bare hull 50714 -static load immediately on 6 comp. measuring frame plate, no stern plate mounted 50715 -static load on 6 comp. frame, stern plate mounted again 50716 -with stern plate 50717 - bare hull

Notes: -The asp angle of attack (relative to centreline nozzle) was changed in between Test Nos.50712 and 50713 from 25 deg to 10 deg. - The static load tests with the stern plate mounted were conducted at impeller rotation rates of 0, 1500 and 2500 rpm. - The baseline of the model was kept horizontal during all tests. - The impeller rotation rate was increased during the tests from 1500 up to 3500 rpm during all bollard pull tests, except for Test No. 50717, where it was decreased from 3500 rpm downward.

0.05 -- test nr 50708 / sternplate 0.04 -- test nr 50712 / sternplate --- test nr 50709 / sternplate & intakepipe 9 testnr5ø7ló/sternplate 0.03

V - 0.02

0.01

O 'WAI A 1000 1500 2000 2500 3000 3500 4000 n [rpm] Fig 3.21 Measured Fxpiaje forces as a function of impeller rotation rate

142 3.2 Flow rate measurements Fig 3.22 shows a comparison of the pulling forces Fxmeas that were measured on the hull model. These forces are normalized with the force from Test No. 50706 with the bare hull model. It shows that the average difference in measured pulling force between the tests with and without stern plate is some 1.5%, the pulling force with stern plate being lower. This difference corresponds to the force measured directly on the stern plate. The configurations with intake pipe (Tests No. 50709 and 50710) do not show any significant difference with similar configurations without intake pipe.

1.04 test no. 50708 test no. 50709 itest no. 50710 1.03 without sternplate

1.02 C C

1.01 S plate --

0.99 1000 1500 2000 2500 3000 3500 4000 n [rpm]

Fig 3.22Comparison of measured-'I pulling forces Fxmeas as a function of impeller rotation rate

With regard to the uncertainty in the measured pulling force Fxnieaç the following observation is made. The scatter in Fxmeas for similar configurations appears to be within approx. 0.5% for impeller rotation rates in excess of 2000 (Fxmeas>lS% FS (Full Scale)). This is somewhat higher than the estimated uncertainty in Fneas in Table 3.8 of the previous section. The additional error contribution is attributed to the condition of the flow. The importance of the flow condition is also illustrated by the greater deviation in Test No. 50708 which also showed an erratic behaviour

143 Chapter 3 Experimental analysis in plate force Fxpiate.

Based on the above observations, it is concluded that the momentum flux through the intake (area A'D in Fig. 2.1) in bollard pull conditions equals zero for the subject model. This observation is likely to have a general validity, as the subject intake is mounted close to the transom stern in comparison to other representative waterjet systems. Especially the bigger mixed flow pump waterjets need to transport the ingested water to a higher level in the hull, consequently leading to a further separation of intake trailing edge and transom.

The jet induced force acting upon the stern plate amounts to approx. 1.5% of the measured pulling force. Because the submerged part of the stem plate is approx. 13 times the submerged transom area, it is assumed that the actual jet induced force on the transom is generally within 1%. The distance of the nozzle discharge to the transom plates,,is considered to be representative for most cases (s,/D=1.7).

3.3Uncertainty analysis

The importance of subjective judgement in uncertainty analysis is tersely expressed by P.H. Meyers. In the 1930's, he and his team had put several years of hard work at NBS into the determination of the specific heat of ammonia. They finally arrived at a value and reported the result in a paper. Toward the end of the paper, Meyers is said to have declared (Abernethy et al. [1985]):

"We think our reported value is good to one part in 10,000; we are willing to bet our own money at even odds that it is correct to two parts in 10,000; furthermore, f by any chance our value is shown to be in error by more than one part in 1000, we are prepared to eat our apparatus and drink the ammonia!'

Despite the important role of subjective judgement, uncertainty analysis is regarded as an effective means to demonstrate the relative importance of each error contribution. Furthermore, it allows for an improved interpretation of the results.

To arrive at a realistic estimate of the uncertainty in the net thrust and effective jet system power, derived from model propulsion tests, a complete review of the relevant relations and their parameters is now discussed. Figure 3.4 shows the data required to analyze the powering characteristics of the model based on the signals measured during the propulsion test. The data are classified after their origin and their relations are indicated.

144 3.3 Uncertainty analysis We will use the data analysis category as a starting point for the derivation of the uncertainty in net thrust prediction. The error contributions of each parameter will be discussed in the following. The propagation of the error sources into the approximation of net thrust Tg, is given by the relative sensitivities O', that can be derived from the following rèlation:

TjetxPAn Tgoo = TjetxC mU (3.10) cosO whereTjetx = thrust from nozzle in x-direction.

The uncertainty analysis is elaborated for a representative case, of which the results are presented in Tables 3.11 through 3.14. The case is characterized by a nozzle velocity ratio NVR=2 and an ingested flow rate to boundary layer flow rate ratio of 1.5.

The error contributions quoted in Table 3.11 are briefly discussed per source in the following. Table 3.11 presents the final uncertainty estimate in net thrust T,iet. The Tables 3.12 and 3.13 present the intermediate uncertainty results in j et thrust Tiet and intake momentum coefficient c,, respectively.

Derived jet thrust Tjetx

The value of T,ierx from the propulsion test is obtained from the following linear relation, obtained from a regression analysis on the bollard pull results:

Tjetx a0±a1Dp (3.30) where a1 =regression coefficient Dp =differential pressure signal from 'asp'.

145 Chapter 3 Experimental analysis

Table 3.11 Uncertainty analysis Tnet

Error Error s (0'b')+ (t 0's')2 source [% R] [% R] Tetx See Table 3.13 1.41 1.50 0.26 5.01 From ITTC [1993] -0.82 0.08 0.09 0.03 Cm See Table 3.14 -0.82 2.20 0.02 3.25 p From ITTC [1993], S=l.82102 0.41 0 0 B(D,)=0.2 mm 0.41 0.80 0.11 B=0.1 deg. 2.00 0 Totals 2.80 0.37 UÇ,5 @ 95% 2.90 Example data NVR =2 .980 C 4 60 U' = 5mis 40 - O, =Sdeg D =50mm 20 T:eto = 98 N o Tjetx Uo Cm P A 0n Error source

Table 3.12 Uncertainty analysis from propulsion tests

Error source o; s (0'b') + (t 0's')2 [%R] [%R] a0 0.01 20.00 0.10 a 1.00 0.20 0.16 lIp 1.00 1.00 0.04 1.01 calibration 1.00 1.10 1.21 Totals 1.49 0.26 U, @ 95% 1.57

Example data 60 -- -

= aaiD - =375 o20 II T.jex=80N o I a a1 !) 1pet calibration Error source

146 3.3 Uncertainty analysis

Table 3.13 Uncertainty analysis Cm

Error source Error 0 b s (O'b')2 + (t e's')2 [%RI [%R]

ErrorQbl U0 I .00 0.08 0.09 0.04 ¡.1

Totals 14.36 0.09

URSS @ 95% 14.36 Example data: n = 7.00

ErrorQ etx 1.00 1.49 0.26 2.48

Totals 1.49 0.26

URSS @95% 1.57

ErrorQb,'Q Q -1.00 1.49 0.26 2.48 Qh/ 1.00 14.36 0.09 206.29

Totals 14.44 0.27

URSS @ 14.45

Error Cm n 0.09 20.00 0 3.49 Q11/Q -0.08 14.44 0.27 1.35

Totals 2.20 0.02 URSS @ 95% 2.20

Example data:Q/Q11 =I .5

The precision error of consequently follows from the precision errors in the coefficients a and Dp.xpressions for the precision errors of the coefficients are given by (Barford [1987]):

147 Chapter 3 Experimental analysis

S0(a0) = (3.31) \/n(n-2)[nx 2(x)2J

n,1(y) S0(a1) = (3.32) (n-2)nx 2(Ex)2] where [nv-x>y]2 n22)= 2()2 (3.33) nx2_2

Estimates of the precision errors are based on the results of the bollard pull tests reported in Section 3.2.3, and are listed in Table 3.14.

Table 3.14 Precision errors in Tjett regression coefficients

Test No. n s, (a0) s,Ç (a1) a0 a1 [%J [%] [N] [N/cmwk]

50706 12 21 0.19 -0.833 0.251 50711 8 22 0.15 -0.711 0.252 50713 9 13 0.18 1.467 0.266 50717 8 196 0.20 -0.106 0.267

Estimated 37 20 0.2 mean value

When analysing the following data, it is seen that the a0 coefficient of Test No. 50713 does not compare well with that of Test No. 50717. This is attributed to the fact that this bollard pull test was the first test in the morning. At the lower impeller rotation rates the asp signal appeared to be l-2% lower than the corresponding signal from the subsequent tests. It should furthermore be noted that the coefficients of the first tests (50706 and 50711) are not directly comparable to that of the last tests (50713 and 50717) due to the fact that the orientation of the asp with respect to the mean flow was changed.

148 3.3 Uncertainty analysis The large precision error in a0 (196%) for test No. 50713 is caused by the small value of the coefficient itself. When comparing the absolute value of the precision error, it is of a similar magnitude as the error from the other tests.

For the contribution of asp signal Dp, the precision error of the average Pp value from a propulsion test is taken. This error appears to be negligible with a value of 0.04%.

Little information is available on the bias error in the asp pressure Dp. A bias error may occur if either the angle of attack or the velocity profile on the asp is changed relative to the calibration test. Such a change may occur if the working point of the pump is changed (expressed e.g. in a change in flow rate coefficient KQ) or may be due to the ingested boundary layer, which was not present during the calibration test.

Two experimental observations on this issue have been made. The first observation was made during the systematic series of bollard pull tests, where it was shown that the average asp signal decreased with some 7% after an axial rotation of the asp over 15 deg. The second observation relates to the degree of correspondence between two propulsion tests on the Hamilton test boat (see Section 3.4). The second series of tests were conducted about half a year after the first series, and a new asp was used for the second tests. The pressure ports in this new asp showed a distinct distribution over the length of the asp, and it was positioned under an angle of attack of 10 deg with the centreline nozzle instead of 25 deg as used during the first test. Despite these modifications to the asp, the deviation in final thrust values was within 1.5% of the original values. Based on this experience and experience with other propulsion tests, a bias error in Dp of approx. 1% has been assumed. This is believed to be a conservative estimate in most cases.

An additional bias error is present in the regression relation for jet thrust Tier. This error occurs during the bollard pull calibration test and is not incorporated in the uncertainty analysis of the coefficients a. The magnitude of the error is taken from Table 3.9, and is estimated to be about 1%.

Table 3.12 clearly shows the importance of the bias errors in the asp signal Dp and the jet thrust T1from the calibration. These errors contribute respectively approx. 40 and 50% to the total uncertainty in the jet thrust as derived from the propulsion test.

149 Chapter 3 Experimental analysis

Hull speed U0

Both the bias and the precision error for the hull speed have been borrowed from the HSMV Report of the 20th ITTC [1993], for a model speed of 5 mIs.

Momentum velocity coefficient Cm

For the selected case where the required flow rate Q exceeds the flow rate that is ingested from the boundary layer Q,1, the momentum velocity coefficient Cm is given by (see Appendix 2):

QhI (3.34) Cm 1- n +2 Q and the flow rate ingested from the boundary layer Qbj is given by:

n QbI = UofwWi (3.35) 11+1 wherew=geometric intake width

width effectiveness factor, due to the flow contraction ahead of the intake =:boundary layer thickness n =power from velocity profile power law.

The results of the uncertainty analysis on Cm are presented in Table 3.13. The estimates are based on a procedure where the boundary layer parameters and n are obtained from semi-empirical relations, as for instance given by Hoerner [19651. It is observed that the major uncertainty contributions to are again made by the bias error estimates on the width effectiveness factorf, the boundary layer thicknessand the velocity profile power n. The latter contribution was estimated at 20% resulting in an uncertainty contribution of approx. 75% in c,. The estimated bias error in the velocity power n results in values on model scale that are situated in the range from 5.6 to 8.4. A mean value of 7 has been used here (see e.g. Schlichting [1979]). At full scale, this power value will be closer to 9.

The estimated bias errors in J, and contribute equally to the uncertainty in boundary layer flow rate Qbl' but finally only contribute about 25% to the total uncertainty in Cm.

150 3.3 Uncertainty analysis

If the boundary layer parameters ö and n are obtained from a curve fittingprocess on a series of pitot rake measurements in the boundary layer, the bias errors in n and boundary layer thickness are estimated to reduce from 20 and 10% respectively to about 5%. An example of a curve fitting result on the boundary layer profile measurements is given in Fig 3.3.

The uncertainty in c,,7 decreases from 2.2% to a value of 1.0% due to the boundary layer measurements. This results in an improvement of the Tnet uncertainty from 2.9% to 2.4%. It is to be noted that the sensitivity for errors in c,,7 increases for the lower NVR values, consequently increasing the improvement in uncertainty.

Specific mass p

The precision error in the specific mass is borrowed from the HSMV committee report [1993] and is due to a precision error in the measurement of the water temperature.

As discussed in Section 3.2.3 on the thrust calibration procedure, a bias error occurs when during the bollard pull calibration a different amount of air is ingested than during the propulsion test. As the working point of the pump is approximately the same in both conditions for the proposed procedure however, this is not likely to happen. A bias error is therefore not further considered.

Nozzle area A,,

A manufacturing tolerance of 0.2 mm in diameter is assumed.

Nozzle inclination angle O,,

The nozzle inclination angle is assumed to be measured with the inclinometer. This meter has a tolerance of approx. 0.1%. Hence a bias error of similar magnitude is assumed.

Uncertainty in net thrust Tnet

Table 3.11 clearly shows that the bias error contributions by Tiet andcm govern the uncertainty in 1. The greatest contribution (approx. 60%) is provided by the bias error in the derived jet thrust Tj,. from the propulsion tests.

The total precision error in net thrust is assessed to amount to approx. 0.4%. This is of a similar order as the precision error quoted by English [19951 for propeller thrust measurements on slender monohulls. It is consequently concluded that the

151 Chapter 3 Experimental analysis precision of the instrumentation used during the propulsion tests is satisfactory. Great care is to be practised during both the calibration procedure and the propulsion test, so as to notice possibly unforeseen bias errors.

A total uncertainty in net thrust of approx. 3% results for an NVR value of 2. This assessment is however based on uncertain bias error estimates, especially in asp signal from the propulsion test and in jet thrust during the calibration procedure. The author is therefore not prepared to drink the model basin, nor is he prepared to eat the carriage should the uncertainty turn out to be slightly different.

Uncertainty in effective jet system powerJSE

A similar procedure as applied to the uncertainty prediction in Tnet can be followed for the powerJSEBecause the bias error in Tiet appears to be the dominant contribution in net thrust, and because the net thrust also largely determines the required power, we will focus here on the jet thrust contribution. Analogous to the form of the net thrust in eq. (3.10), the corresponding powerJSEcan he written as:

Tieti.AnP jetx (3.36) JSE = -'cU-gzj cos e 2pA,7cose,7

The relative sensitivity e' for an error in Tjeis consequently 1.8 for the present case (NVR=2, c'0.9). This is some 30% higher than the sensitivity for the net thrust.

Judgernent criteria for bias errors

As we have seen from the preceding uncertainty analysis, the major contributions to the final error are caused by bias errors. Errors that can only be prevented or acknowledged if sufficient knowledge on the physical process and the properties of the test set-up is available. To increase the certainty of the results in and JSE'derived from the experiments, a number of criteria can be defined that should be met.

A good check on the net thrust data is obtained after a comparison of the thrust with the bare hull resistance. If a number of propulsion test results is available, the margins within which the resistance increment r should lie are roughly given. Furthermore, if more knowledge on the physical mechanism causing the resistance increment is available, one could probably narrow this bandwidth.

152 3.3 Uncertainty analysis A second criterion is the physical requirement that the resistance increment fraction r should show a faired character when plotted against speed. Outliers in the results are easily identified in this way.

A third acceptance criterion is formed by the overloading and underloading tests, that are normally conducted for one or two speeds of interest. During these tests, typically 3 to 4 impeller rotation rates are adjusted for one speed. This gives a relation between thrust and pulling force FD as presented in Fig 3.23. If the pulling forces are varied within reasonable limits, a straight line is usually discerned through the self propulsion point of ship, defined by the coordinates (FDTSP). The point where this line intersects the thrust abscissa is the self propulsion point of model Tm. The line intersects the pulling force abscissa through a point that is usually situated close but not exactly on the value of the model resistance Rm. This point is referred to as FTO.

T Tm

= + i r aT

s' 's s' N N N N N N N N FD Rm FTO F Fig 3.23Thrust-Force diagram from overloading and underloading tests

If the intersection with the pulling force abscissa is assumed to be sufficiently close to the bare hull resistance, the line can consequently be expressed as:

T T,-F(l+r) (3.37)

It can now be observed that the resistance increment fraction r can be obtained from the inclination of the loading variation line, which can be determined through regression analysis. The resistance increment fraction is then obtained from:

JT r (3.38)

153 Chapter 3 Experimental analysis

The resistance increment fraction that can be obtained from these overloading and underloading tests should approximately match the corresponding values from the speed variation tests at the self propulsion point ship. To this end, the pulling force Dshould be adjusted as close as possible to its required value. Residual discrepancies between the actual pulling force and the required force ED should be corrected for, using the overloading and underloading relation obtained from the experiments.

3.4 Propulsion test results

This section presents collected results on interaction data obtained from a selection of propulsion tests that have been conducted at MARIN. The set of hull forms involved covers a wide variety, ranging from a low LIB monohull (L/B=3) to a high L/B catamaran (L/B demihull =15), and ranging from a small 7 m to a large 80 m vessel. The objective of this review is to give an idea of the importance of interaction. Due to the non-systematic nature of the data, it is not meant to provide design guidance.

The overall interaction effect is quantified by the interaction efficiency The envelope area, comprising all values of this interaction efficiency obtained from the above selection of waterjet propulsion tests, is plotted in Fig 3.24.

115

LOS

0.95

0.85

0.75 0 00 0.50 1 00 1 50 FnL H

Fig 3.24Collected total interaction efficiencies 1JNT as a function of Froude number

154 3.4 Propulsion test results 3.4.1 Thrust deduction

A total thrust deduction fractiontis obtained from resistance and propulsion tests in a straightforward manner. This total thrust deduction links the gross thrust Tg to the bare hull resistance RBH in the following way:

T(l-t) RBH (3.39)

To link up with the existing nomenclature in propeller hydrodynamics, we may refer to the resistance increment as the hull's thrust deduction fractiontr A corresponding thrust deduction factor may subsequently be defined as:

(4.32) ltr_l+r

This thrust deduction is built up from the jet system's thrust deduction fraction t1and the hull's resistance incrementt,.(see Section 4.3.2):

t = tj+tJ. (4.34)

Using the results from Section 2.3.1 where it was concluded that the thrust deduction fraction t1 equals zero under certain conditions, the total thrust deduc- tiontmay be regarded representativeforthehull's resistance increment expressed in trIt will be shown in Section 4.3.2 that this assumption is valid over most of the speed range of interest. Significant deviations betweentandtr may occur in the hump speed region however.

Fig 3.25 shows the total thrust deduction t plotted against Froude number based on waterline length (at zero speed). Although a wide variety of hull forms is incorporated, some general trends can be observed:

- Relatively high thrust deduction values are obtained for speeds in the region of the hump in the wavemaking resistance (around FnL=O.S). The thrust deduction shows the highest values (up to t=O.25) for the short L/B hulls and the lowest values for the high L/B hulls. The variation intis large. - For higher speeds in excess of FnL=O.S, all t values appear to be slightly negative, indicating a decrease in hull resistance. The bandwidth of the models indicated is about 5% of the total thrust.

155 Chapter 3 Experimental analysis

- For speeds corresponding to FnL>l, the total thrust deduction increases with increasing speed again.

0.3

0.2

0.l

-0.1 O 0.5 15 FnL H

Fig 3.25Collected total thrust deduction values t as a function of Froude number FnL

To unravel the mechanism governing t, further experimental analysis is pursued along the lines proposed in Section 2.3.4. It was suggested there to decompose the resistanceincrement into independent contributions of flow rate and hull equilibrium position. With the insight from this experimental analysis, a hypothesis is posed for the mechanism governing the resistance increment. This hypothesis is evaluated further in Chapter 4.

Mechanism of resistance increment

An experimental study was conducted with the aim to get a better understanding of the mechanism of the hull's resistance increment. To this end, a series of propulsion and resistance tests has been conducted. Systematic LCG variation tests were conducted during the resistance tests in an attempt to assess the hull's resistance increment from variations in hull equilibrium position. These variations have been made at two speeds, corresponding to Froude numbers of FnL=O.SO and 1.19. The experimental study was conducted with the HAMILTON Test Boat (see Appendix 4 for a description of the model).

156 3.4 Propulsion test results The total thrust deduction fraction t, as obtained from two independent propulsion tests under the same condition is presented in Fig. 3.26. It should be noted that the two tests indicated in the figure were conducted with about half a year interval, with distinct asp tubes, mounted at different angles of attack. The discrepancy between both tests attains a maximum at the higher speeds, where it amounts to approx. 1.5% of the thrust. This discrepancy is well within the uncertainty in thrust (approx. 3%) found in Section 3.3. It is probably caused by an extrapolation of the flow rate-Dp (asp) relation in the upper flow rate regime (Fig. 3.27).

0.3

-e-test no. 48820 -+-test no. 50781 0.2 .

0.1

-0.1 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 FnL H Results based on asp readings and jet thrust calibration

Fig 3.26Hull thrust deduction for the HAMILTON Test Boat

Fig. 3.28 shows a comparison of the thrust deduction fraction t and the change in trim and sinkage due to the jet action. A remarkable correspondence in tendencies is found at the steep fall of the thrust deduction at FnL=O.S. In the higher speed range, the relation between the tendencies in t, and equilibrium position becomes less clear. It is inferred from this plot that, at least for the lower speeds, the hull equilibrium is strongly related to the thrust deduction.

The photo series presented in Photographs 3.2 and 3.3 show that the steep decline in t and the clearing of the stern coincide.

157 Chapter 3 Experimental analysis

FnL = 0.43

FnL = 0.50

FnL 0.56

Photo 3.2Wave patern of Hamilton Test Boat for Speeds coinciding with the steep decline in thrust deduction t

158 3.4 Propulsion test results

FnL = 0.43

= 0.50

FnL = 0.56

Photo 3.3 Underwater photographs of Hamilton Test Boat for Speeds coinciding with the steep decline in thrust deduction t

159 Chapter 3 Experimental analysis

0.2

* -0.2 D Regression obtained from bollard pull test 50780 I- -0.4 D ? 0.6 C, range used in propulsion tests

-0.8 10 15 20 25 30 35 VDp [cmwcl

Fig 3.27Coverage of the calibrated asp signal with that obtained from the propulsion tests

15 0.8

10 0.4

5 to I dz o -0.4

-5 -0.8 0.2 0.4 0.6 0.8 1.2 1.4 1.6 FnL [}

Res, test nr. 50221 and Prop. test. nr. 50208

Fig 3.28Comparison of the total thrust deduction t with the change in trim and sinkage due to the waterjet action

160 3.4 Propulsion test results A linearized estimate for the hull's resistance increment as a function of equilibrium position (see Section 2.3.4), can now be obtained from the LCG variations in the resistance test. A review of the series of tests is given in Table 3.15.

Table 3.15 Review of resistance test variations on HAMILTON Test Boat

Condition Speed range tested Remarks Test No. [kni A0, LCG0 6.5 -9.5 Baseline condition 50208 15.0 - 22.0 LCG variation tests A, LCGJ 7.5. 18 'r0-1.0 deg 50211 A0, LCG2 t00.5 deg 50212 ¿ LCG3 to+O.5 deg 50213 A0, LCG4 to+1.0 deg 50214 c is trim angle for baseline condition at speed O

Originally two displacement variations were tested as well, because at this time it was thought that the jet system could contribute to a significant lift force acting upon the hull (Alexander et al. [1994]). However, as the induced lift on the hull is approximately zero (Section 2.2.4), it can be argued that the change in dynamic position of the hull should preferably be obtained at the same displacement.

To this end, regression analysis was applied to find the coefficients in the following linearized relation for the resistance increment:

1+r ao+ai(t-'to)+a2(za-zau) (3.32) where 't=trim angle (dynamic plus static) za =sinkage of transom stern (dynamic plus static) subscript O indicates value at the resistance test.

The results of the regression analysis and a comparison of the linearized estimate of r with that obtained from the propulsion tests is given in Table 3.16:

161 Chapter 3 Experimental analysis

Table 3.16 Comparison of linearized estimate and experimentally determined values for the hull's resistance increment

FnL=O.50 FnL= 1.19 Regression results

a0 1.008 1.004 a1 5.33 l0 2.11 102 a2 8.37 l0 -2.29 l0 S(y) 7.10 l0 4.90 10

Estimated l+r 1.06 1.00 Experimental result

Derived 1+r 1.17 0.99

Table 3.16 shows that a reasonable correspondence occurs between the linearized estimate and the experimental value for the highest Froude number of 1.19. The correspondence for the lowest Froude number of 0.50 is poor however. It is to be noted here that the expression for the resistance increment proposed in Section 2.3.4, also included a resistance term depending on the flow rate Q. This term has been neglected in the preceding consideration, but may become important for the lower speeds.

One way to include the effect of local flow contributions to the change in hull resistance is to perform potential flow computations including free surface effects. This approach will be considered further in Chapter 4.

Some thoughts on the physical mechanism controlling the hull's resistance increment are now put forward. The same three speed regions as discussed before will be used.

Hump speed region

Thrust deduction fractions t may reach significant values (up to 0.25 has been derived from propulsion tests). The behaviour of t with speed is similar to that of the transom sinkage in this region. The resistance increment consists largely of transom pressure drag and wavemaking drag. The local flow distortion in the aftbody, depending on aftbody geometry and ingested flow rate Q, plays an important role in the resistance increment.

162 3.4 Propulsion test results Post hump speeds up till FnLl

Thrust deduction fractions t show mainly negative values between O and -5% of the bare hull resistance. This is the speed region where the wavemaking resistance contribution decreases and the frictional and spray resistance become more important. The transom stem is fully ventilated and the viscous pressure drag by the transom is hence equal to zero.

For speeds just above FnLO.S, the wavemaking resistance is sufficiently sensitive to show the effect of local flow distortions in the aftbody. With increasing speeds, this sensitivity decreases and the equilibrium position of the hull becomes more important in the determination of the wavemaking resistance or pressure drag.

lt is an empirical finding, that in this speed region, a lower hull resistance can be obtained by decreasing the aftbody volume and by decreasing the running trim angle. By mounting an active waterjet (at equal hull displacement), an effective decrease in aftbody volume is obtained. Furthermore, the waterjet action often decreases the running trim angle. These two mechanisms are considered to be responsible for the negative resistance increment of the hull.

Planing speeds FnL>l

The total thrust deduction t starts to increase again. In this speed region, the hull resistance is primarily affected by hull equilibrium position. For prismatic hull forms, the wavemaking resistance or pressure drag is simply obtained from:

R/) = Ltant (3.43) where t=trim angle (in earth-fixed coordinate system).

Itis an empirical finding that a certain optimal trim angle exists from the resistance point of view. This trim angle being hull form dependent. For lower trim angles, the resistance caused by the spray at the bow (both pressure and frictional resistance) increases. For higher trim angles, the pressure drag expressed by eq. (3.43) increases. It should also be noticed that the wetted surface area changes with changing equilibrium position. hence changing the frictional drag.

If the trim angleis optimized based on resistance considerations without accounting for the effect of the jet on running trim, the usual decrease in trim angle due to the jet action will cause an increase in hull resistance.

163 Chapter 3 Experimental analysis 3.4.2 Momentum and energy interaction efficiencies

The collected values of momentum and energy interaction efficiencies are plotted as a function of the Nozzle Velocity Ratio NVR in Fig. 3.29 and Fig. 3.30 respectively.

1.2

1.15

0.95 I 00 2.00 3.00 4.00 5.00 NVR l-1

Fig 3.29 Collected momentum interaction efficiencies as a function of Nozzle Velocity Ratio NVR

Fig. 3.29 shows that the trend for all cases is similar. Some scatter in the absolute values occurs, which is due to differences in ratio between required flow rate and boundary layer flow rate Qb1 The effect of this ratio is shown in Fig. 2.11. The case with the lowest lÍq,711 values featured a ratio of approx. 3, whereas the case with the highest values showed a QQb/ ratio less than 1.

Similar observations can be made from Fig 3.30. Contrary to the momentum interaction efficiency however, which is only controlled by viscous effects, the energy interaction efficiency is also affected by potential flow effects. This effect is expressed as a function of the nozzle sinkage relative to the still waterline (see Section 2.3.2). Hence the greater scatter in absolute values of T1eJ

To obtain an indication of the importance of both the potential and the viscous contributions, the case with the highest values and the one with the lowest values of lei are studied in more detail. To this end, two speeds per case are considered. One speed being around hump speed (FnLO.5). the other speed being the design speed.

164 3.4 Propulsion test results

1.05

0.95

0.9

0.85 loo 2.00 3.00 4.00 5,00 NVR [-]

Fig 3,30 Collected energy interaction efficiencies as a function of nozzle velocity ratio NVR

The results are presented in Fig 3.31. It is seen that the potential part may contribute as much as 10% to the energy interaction efficiency. This occurs for the lower speed, where the transom sinkage is relatively large. For increasing speeds, the transom sinkage decreases as well as the flow rate ratio QQb1 This latter phenomenon causes the viscous contribution to increase. It should also be noticed that the potential and viscous contributions counteract each other, the potential contribution contributing to a higher interaction efficiency (notice that the reciprocal value of1e1 is plotted).

0.04

Q ; o Q o

Q Q C_) -0.15 .0.04 0.43 0.89 0.40 1.34 Fn [-] Fn [-1

Fig 3.31Subdivision of potential and viscous contributions to energy interaction efficiency

165 Chapter 3 Experimental analysis 3.5 Extrapolation method

Extrapolation is required for the powering data representing the waterjet system, the hull and the mutual interaction. Specific tests on the waterjet system have been shortly addressed in Section 1.5.2. The full scale data are further considered to be available here. Extrapolation of the bare hull resistance is a daily task for model basins and is therefore also not further elaborated. This leaves the extrapolation of the interaction data, expressed in hull thrust deduction tr momentum and energy interaction efficiencies.

The basic principles for extrapolation as proposed by the HSMV of the 18th ITTC [1987] are followed. With the relations developed in Chapter 2 of this work, the effect of extrapolation on the interaction data can be explicitly evaluated.

The extrapolation procedure is schematized in Fig 3.32. The procedure uses the Froude scaling principle as a starting point and applies corrections for viscous scale effects. Such corrections are necessary on the viscous part of the bare hull resistance, and consequently on the boundary layer thickness and velocity profile within this layer.

RBHm ö1. u(z) model

RBHS E,. u(z) full scale

'Ir i Qbl

'jr Cm. Ce

JI, flmlflel

Fig 3.32Scheme of extrapolation procedure

Hull thrust deduction t,.

Analogous to the proposal by the ITTC [19871, the hull thrust deduction fraction is considered free of scale effects. This assumption, made without justification by the ITTC [1987], is justified here with reference to the hypothesis on the hull thrust deduction as discussed in the previous section. Studying the definition of the

166 3.5 Extrapolation method resistance increment (eq. (2.97)) (equivalent to the hull thrust deduction), shows that at least one term prone to viscous scale effects consists:

Jfxo' (3.44) A3 which represents the change in hull resistance due to the missing area projected in the hull plane. As this contribution is 0(1%) of the bare hull resistance, and the scale effect on resistance, expressed in FD is typically of 0 (10%) of the resistance, the viscous scale effect on the intake plane contribution is neglected.

Moinentun and energy interaction efficiency

The momentum and the energy interaction efficiencies and Tle/ are given by the equations (2.79) and (2.86) respectively (Section 2.3). The momentum interaction efficiency is seen to be a function of NVR and momentum velocity coefficient Cm. For a given waterjet system, the nozzle velocity ratio depends on the flow rate Q and the hull velocity U0. The flow rate is governed by the thrust requirement, as expressed in eq. (2.78). It is to a lesser extent affected by the momentum velocity coefficient Cm which in turn depends on the flow rate and the boundary layer characteristics. Consequently, an iteration process is required to match flow rate, net thrust requirement and momentum velocity coefficient (see Fig 3.32).

The boundary layer characteristics in tetijis of thickness S and velocity distribution u(z) within the boundary layer can be measured on the model with a closed intake (nominal intake field). Alternatively, the boundary layer characteristics can be estimated from a semi-empirical formula. In the latter case, care should be taken that the uncertainty in the estimate does not dominate the overall uncertainty in the experiment (see Section 3.3).

Extrapolation of the boundary layer characteristics is done through a Reynolds dependent relation for the thickness. The velocity profile is considered to follow the power law, where the local velocity can be found from eq. 3.1. The power coefficient n for the model can be matched from the measured velocity profile in the imaginary intake area. A power value for n of approx. 9 for the full scale situation is suggested.

After the flow rateis solved from the above process, the energy velocity coefficient is readily available. The nozzle sinkage term in the energy velocity coefficient is considered free of scale effects and is therefore simply obtained from Froude scaling.

167 Chapter 3 Experimental analysis 3.6 Conclusions

An accurate (high precision) and robust (small risk of bias errors) procedure for the experimental determination of waterjet-hufl powering characteristics has been searched for. The following conclusions can be drawn from this study:

In selecting a flowmeter for reference measurements during the actual propulsion test, one should take into consideration that both the swirl and the velocityprofileinany placeinthe jetsystem may differ froma corresponding condition during speed zero. The reference flowmeter should therefore show a low sensitivity to changes in flow pattern. It is concluded that an averaging static pitot tube (asp) meets this criterion. lt has proven to be a reliable transducer during many propulsion tests. Calibrating the reference velocity transducer in the jet system with flow rate easily leads to uncertainties that render the meaning of propulsion tests doubtful. Calibratingitwith model pulling force during bollard pull conditions yields both a better uncertainty in calibration input signal, but also provides a much weaker, or at most an equal propagation of all relevant error sources into the final thrust and power prediction. Applying the thrust calibration procedure, the errors in jet thrust (momentum flux from the nozzle) and in ingested momentum flux or cause the largest errors in the final results. Their relative contributions have been quantified in Section 3.3.

The results of a selected set of waterjet-hull combinations, incorporating monohulls and catamarans from 7 up till 80 m length, show that the total interaction efficiencylINT may reach values between 0.75 and 1.15. The lower values occur in the hump speed region, around FnL=O.S. For slightly higher Froude numbers, the interaction efficiencies adopt values in between 1.0 and 1.15 (see also Fig. 3.24).

Based on the trends observedinthe hull'sresistanceincrement and an experimental study on a possible mechanism, a hypothesis for the resistance increment mechanism is put forward. Based on this hypothesis and on the mechanisms governing the momentum and energy interaction efficiencies, scale effects in the extrapolation method can be identified.

168 Extracts from BS 74051991 are reproduced with the permission of BSL Complete editions of the standards can be obtained by post from BSI Customer Services, 389 Chiswick High Road, London W4 4AL or through national standards bodies

169 This page intentionally left blank

170 Chapter 4

4Computational analysis

The global objective of this work is 'the development and validation of tools'. It would however be of little use to study the validity of an arbitrary set of available tools without giving due consideration to the problem that is to be solved. Keeping in mind that the problem definition should be the driving force behind the selection of tools, this chapter is subdivided into three problem areas, viz:

Analysis of free stream intake characteristics Computational prediction of interaction effects Validity of assumptions and simplifications made in propulsion tests.

Each of the above problem areas has been analyzed with computational tools that are available at MARIN. To validate the detailed flow characteristics that become available from CFD calculations, detailed LDV flow measurements on a representative intake have been conducted. Integral properties following from the computations are compared to results obtained from propulsion tests. Final- ly, due attention is given to a physical interpretation of results.

4.1Free stream intake analysis

A full comprehension of the waterjet free stream characteristics, as defined in

171 Chapter 4 Computational analysis Chapter 2, is not obvious. Misunderstandings on intake drag occur frequently in the literature (Sections 1.6.1 and 2.2.3). Supposed intake induced lift forces have been published in recent literature (Section 1.6.1), whereas itis demonstrated in Section 2.2.4 that there is no intake induced lift in free stream conditions.

4.1.1Intake flow analysis

For the present work, a better understanding of the external flow pattern and the internal flow pattern in the initial part of the intake is indispensable. This flow pattern needs to be known to quantify the difference in intake characteristics between free stream and operational conditions. Furthermore, a detailed knowledge about the local flow in the intake region is necessary to simplify the intake model in CFD computations on jet-hull interaction.

Taking the above requirements in mind, it was decided to use the MARIN potential flow code HESM. This panel code uses a flat panel distribution to model the intake geometry with a constant source strength per panel (zero order panel code). Experiments were conducted in the MARIN large cavitation tunnel on the same intake as computed, to validate the results of this panel code. These experiments resulted in pressure readings along the intake and detailed velocity fields measured with 3D LDV equipment.

The comparison between the potential flow results and the full viscous experimental results provided insight in the importance of viscous effects in free stream conditions. Furthermore, the intake drag could be determined in a viscous flow. It was already demonstrated in Section 2.2.3 that there is no intake drag in a potential flow.

A description of the potential flow panel code HESM is given in Appendix 5. The LDV tests and set-up are briefly described in Appendix 7. This section first deals with a validation of the computed results with the LDV measurements, and subsequently discusses the interpretation of the results.

Modelling of problem in HESM

The intake geometry that has been used, together with the 2D planes in which the flow has been computed andlor measured is presented in Fig. 4.1.

HESM computations were made on two panel distributions representing the intake geometry. One coarser distribution consisting of a total of 931 panels and one fine distribution of 2018 panels (see Fig. 4.2).

172 4.1 Free stream intake analysis

E-

>E-

o E

Li Li Li

Fig. 4. iIntake geometry analysed by HESM computations and LDV measurements

173 Chapter 4 Computational analysis

Fig. 4.2Panel distribution on intake model (2018 panels)

The most difficult region to model is the intake lip. In this region a large velocity gradient occurs, necessitating a fine grid. Details of the lip region for the fine panel representation are given in Fig. 4.3.

Fig. 4.3Panel distribution on intake lip

174 4.1 Free stream intake analysis The operating condition of the intake in a potential flow is defined by the intake velocity ratio in the intake throat ¡VR,. Two operating conditions have been computed, representative for design speed and hump speed (IVR,=0.6 and 0.9 respectively).

The requested operating condition was adjusted by a so-called 'propeller disk', positioned at the end of the intake (Fig. 4.4). This disk is covered witha dis- tributioji of source (or sink) panels of constant strength. Thesource strength varies in radial direction, corresponding to the thrust distribution of arepresen- tative propeller.

source distribution in propeller disk for smaller IVRt

Fig. 4.4Modelling of pump through a source disk in the intake

The strength of the propeller disk is adjusted through a thrust loading coefficient CT,,:

Tpropeiier (4.1) p pUA

It is to be noted here that the relation between propeller force and source distribution in the present model is not as simple as that between the thrust and source strength for a propeller in a free stream. This is caused by the flow through the propeller disk, which is not purely axial here (Fig. 4.4). This flow direction causes radial components that need to be incorporated in the Bernoulli equation, in order to find the pressure jump over the propeller disk. The required IVR, ratios have consequently been obtained from interpolation in the empirical relation between CT,, and JVR,. Thrust loading coefficients CT,, of -4.6 and +4.6 were required for ¡VR, values of 0.6 and 0.9 respectively.

i 75 Chapter 4 Computational analysis Sensitivity of leakage for panel density

Two distinct planes in the intake have been used to check the volume flow rate through the intake. These planes are designated plane 1 and 2 in Fig. 4.5. Hess and Smith [1966] already noted that their method is less accurate for concave streamlines and internal flows. To account for the lesser accuracy, they advised to take a finer panel distribution for these type of flow problems.

-300 symmetric plane waterjet propellerdisk plane I plane 2 -200 intake area (Ait)

E E -100 N

100 0 -100 -200 -300 -4(X) -500 x [mml

Fig. 4.5Definition of cross sectional planes within the intake

The effect of the number of panels on the flow rate through the planes i and 2 has been studied. The results of which are presented in the Table 4.1 below.

Table 4.1 Computed flow rates through two cross sections for two distinct panel distributions. The flow rates are given relative to the flow rate in plane 2 with the 2018 panels

IVRE = 0.6 !VR1 = 0.9 Plane I Plane 2 Plane I Plane 2 931 panels 0.87 1.02 1.03 0.99 2018 panels 0.85 1.00 1.02 1.00

176 4.1Free stream intake analysis lt is observed that the difference in flow rates for the two panel distributions is within2%.A discrepancy of some 15% in flow rate through plane 1 and2 occurs however for the condition whereIVR1=0.6.

This discrepancy is attributed to the proximity of plane 1 to the boundaries of the elements modelling the intake. These boundaries are singularities in the mathematical model, causing unrealistic velocities in their proximity. This effect gets stronger when the source strengths of neighbouring panels differ stronger. This effect causes the deviation for theIVREof0.6,where a strong pressure gradient over plane I exists (Fig. 4.6), whereas this gradient is much smaller for the condition where IVR=0.9 (Fig. 4.7).

Validation of internal intake flow

The computed pressures will be compared with pressure readings from the intake ramp and lip centrelines. The results are shown in Fig.4.8for a design IVR1=O.62and in Fig.4.9for an off-designIVR=O.94.

Fig.4.8shows that the results for the ramp agree qualitatively, but that the discrepancy between measured and computed pressure increases when travelling inward. A maximum difference in C, value of about0.4is found. At the lip, the computed results do not show the drop in G downstream of the stagnation point as shown by the experimental results. A maximum difference in G, between measured and computed results of approx.0.7occurs. This poor correlation shows a remarkable correspondence with the results of Kashiwadani [1986]for his2Dpotential flow code. He made a similar comparison for an ÍVR1of0.68.

Fig.4.9shows a comparison as in Fig.4.8at an IVR=O.94. The comparison of the pressures at the ramp and at the lip show the same trend. The difference in C, value is larger here however (maximum difference in C is about 1.2).

The difference in computed and measured G is likely to be caused by different positions of the stagnation point at the lip. The experimental stagnation point is likely to be somewhat more outside the intake, causing a suction peak just on the inner side of the intake lip. The suction peak is clearly present in the experimental results for anIVR,=0.94(Fig. 4.9), but a similar tendency can be observed from Fig.4.8for theIVR=0.62.

177 Chapter 4 Computational analysis

0.500

0.000

-0.200

,--.---- -

Fig. 4.6Comparison of measured and computed C1!, distributionin centreplane VL1 for IVR=O.6

178 4.1 Free stream intake analysis

- -r-.- -t--s--._

Fig. 4.7Comparison of measured and computedÇdistribution in centreplane VL Ifor IVR=O.9

179 Chapter 4 Computational analysis

Ramp, IVRt = 0.62 Intake lip, IVRt = 0.62 0.8 1.5 - computed - computed measured measured . U o .

-0.8 -100 0 200 400 -60 0 40 80 girth coordinate from girth coordinate from ramp LE [mm model] lip LE [mm model]

Fig. 4.8Comparison of measured and computed static pressures for iVRO.62

Ramp, IVRt = 0.94 Intake lip, IVRt = 0.94 0.4 --computed omeasured T A O L) - - computed omeasured -0.8 -lOO 0 200 400 -60 0 40 80 girth coordinate from girth coordinate from ramp LE [mm model] lip LE [mm model]

Fig. 4.9Comparison of measured and computed static pressures for IVR,=0.94

The more outward stagnation point in the tests can be attributed to the displacement effect of the boundary layer at the ramp, which is not accounted for in the computations. This displacement effect causes a reduction of effective area in the throat of the intake. At an equal flow rate, the intake will therefore effectively operate at a slightly higher IVRE than for the corresponding computations.

Another viscous effect that is not included in the potential flow computations is the vortex that is shed from the sharp lateral edge of the intake. This vortex has been observed from the LDV measurements in the internal transverse plane VT5 (Fig. 4.1). Fig. 4.10 clearly shows the clockwise rotation just in the intake, downstream of the lateral edge. It also shows the decelerated axial velocity in the nucleus of the vortex.

180 4.1 Free stream intake analysis

transverse coordinate y [mm]

-60 -50 -40 -30 -20 -IO O 0 \\\\ \ \ i-10 N

-20 transverse coordinate y [mm] t- -60 -50 -40 -30 -20 -IO O o -30 H o o II -40- N 10

-50 -20 o o o

. -30 >

-40

Fig. 4.10 Measured velocity distribution in internal plane VT5 for IVR=0.62

Kashiwadani [1985, 1986] explained the discrepancy between calculated and measured static pressure within the intake by viscous and 3D flow effects. He did not measure a significant rotation within the intake however (Kashiwadani [1986]). He also found no significant deviations in the off-centreline pressure transducers compared to the centreline transducers. Thus, the hypothesis on the importance of 3D flow effects was not confirmed.

Kashiwadani subsequently hypothesized that the discrepancy in static pressure was mainly caused by the quickly increasing boundary layer displacement thickness near the intake throat. This effect causes a decrease of effective intake throat area, causing an increase in average flow velocity and therefore a decrease in static pressure. A comparison of measured and computed velocity profiles in the intake throat by Kashiwadani is presented in Figure 4.11.

Conclusions

It is now concluded that the zero order panel method as implemented in HESM yields results that give comparable deviations as the higher order method developed by Kashiwadani [1985]. The discrepancies with the measurements in the internal part of the intake are caused by the absence of viscous effects in the

181 Chapter 4 Computational analysis calculations. These begin to play a dominant role in the internal pressure and velocity distribution.

(side view) U0

1.5 Measured Calculated

1.0

0.5

0.5 1.0

ramp wall lip wall

Fig. 4.11 Comparison of measured and computed velocity profiles in intake throat area A4 for various IVRE values (from Kashiwadani [19861)

Validation of external intake flow

It has been demonstrated in the preceding observations that the validity of the potential panel code HESM is limited as far as the internal intake flow is concerned. Because viscous effects are considered less important in the flow just outside the intake, a better correspondence between experiments and computed resultsis expected here. This expectation is confirmed by the findings by Kashiwadani [198611 (see Section 1.6.3).

182 4.1 Free stream intake analysis To validate the HESM results, LDV measurements have been made fora number of 2D planes just outside the intake. The results for two vertical longitudinal planes (VL1 and VL2) and one horizontal plane Hl will be presented here (see Fig. 4.1).

A comparison of the C distribution in plane VL1 for IVRE values of 0.6 and 0.9 is presented in the Figs. 4.6 and 4.7 respectively. It can be observed from these figures that a broad correspondence appears between the computed and the measured results. Noticeable differences occur at the ramp in the boundary layer and near the stagnation point on the intake lip. The outward shift of the stagnation point from the measurements in comparison to the computed results can be observed.

Fig. 4.12 shows a comparison of the C distribution in the horizontal plane Hl for an IVRE of 0.6. This plane is situated at the very beginning of the intake, in the region where viscous effects just start to become important. The same trend as observed for plane VL1 is noticeable here. The extent of the accelerated region at the ramp is about equal for both the measured and computed results. Toward the lip, the computed results show a stronger deceleration, corresponding to the more inward position of the stagnation point. The slightly higher velocities at the lateral edge are likely to be caused by the flow ingested over the sharp edge. This accelerated region is situated slightly away from the lateral edge in the measured results, likely to be due to the presence of the boundary layer.

The correspondence of the measured and computed Cdistribution in the imaginary intake area (plane VTO) for IVR=O.6 can be observed from Fig. 4.13.

A more detailed comparison of results is obtained when we compare the shape and pressure distribution of the dividing streamlines. The streamlines can be traced from the detailed flow fields available by considering the stream function iii. The stream function is defined such that no transport of mass occurs through lines (or planes) of equal value. Hence, the dividing streamlines can be obtained by solving the differential equation:

(4.2) ¿h where s= girth coordinate.

183 Chapter 4 Computational analysis

0500

0 000 I-0 200

------5- \ 1 -u------il i'Li -1 --_u r . j / r , L!L ...--

wIlrr hulL rniw

Fig. 4.12Comparison of measured and computed C,, distribution in horizontal plane HI for JVR=O.6

184 4.1 Free stream intake analysis

0. 000

-0.220

C p_p r

II. 1 79

0.000

-0.176

Fig. 4. 13Comparison of measured and computed ('i, distribution in vertical plane VTO for JVR=O.6

185 Chapter 4 Computational analysis In the x-z plane, this equation can be written as:

aN! dx dz (4.3) axds azds= o

The following relations can be obtained from the continuity equation:

_=-w&NJ andaN! =u (4.4) ax az where u and w are the x and z-components of the local velocity. After substitution in equation (4.3) we find:

dz w (4.5) dx u

This equation can now be solved for any 2D x-z plane.

As a starting point for a dividing streamline, the point with the highest G1,, value in the lip area was searched for. Starting from this point eq. (4.5) was numerically solved in the following way. Because a residual velocity was available in the point with the highest GP, the velocity gradient w/u could be obtained. The next point for which eq. (4.5) is solved, is found by searching the two nearest points following (see Fig. 4.14). The velocities pertinent to this point are obtained by interpolating in these two neighbouring points. This process is repeated several times until the required streamline is found up to the desired length.

Dividing streamline tracing was performed for both the set of computed and experimental data. The resulting streamlines are presented in Fig. 4.15 for JVR values of 0.6 and 0.9 respectively. It is seen that the dividing streamlines almost coincide at the imaginary intake area AB, but that the streamline from the experimental data is positioned lower in the flow further downstream. The lines from computed and experimental data seem to approach each other again near the stagnation point. This discrepancy is in line with the findings from the internal flow. It has been found there that the displacement thickness of the boundary layer on the ramp quickly increases toward the intake throat. This increasing displacement thickness forces the dividing streamline further outward.

186 4.1 Free stream intake analysis

-J- grid point tvelocity vector in z-direction dividing streamline velocity vector in x-direction

Fig. 4.14Tracing of dividing streamlines

IVRt=0.6 IVRt=0.9 300 300 computation - - -. computation - - -. experiment - - experiment - -

O O

100 100 o -500 O -500 x [mm] x [mm]

Fig. 4. 15Comparison of dividing streamlines traced from HESM and LDV results (/VR0.6 and 0.9)

The pressure coefficient G pertinent to the dividing streamlines is plotted for both the computed and experimental data in Fig. 4.16, again for IVRE values of 0.6 and 0.9. Maximum deviations in Gr, of the order of 0.1 occur in the same region where deviations in streamline position were found.

To provide some more insight in the change of dividing streamlines with lateral position, the streamlines for the three computed planes VL1 through 3 (Fig. 4.1) are plotted in Fig. 4.17. It is observed that at the lowest IVR1 of 0.6, the dividing streamline approaches the intake lip from the inside of the intake, whereas

187 Chapter 4 Computational analysis for the higher IVRE of 0.9, the dividing streamline shows a rather straight character, approaching the lip from the outside.

IVR=0.6 IVRt=0.9 1.0 1.0 computation- - - computation- --. experiment experiment

ç-)

-0.4 -0.4 -100 -500 -100 -500 x [mm] x [mm]

Fig. 4.16 Computed and measured pressure distribution along dividing streamline in plane VL1 (IVR=O.6 and 0.9)

IVRt = 0.6 TVR1 = 0.9 300 300 plane VLI plane VLI- - -. plane VL2 - - plane VL2 - - plane VL3 plane VL3 E E N

100 100 o -500 o -500 x [mm] x [mm]

Fig. 4.17Dividing streamlines traced from HESM results for three longitudinal planes VLI,2 and 3 (IVR=0.6 and 0.9)

The results on the external flow fields will be used in the following sections.

Conclusions

The potential flow panel code HESM yields acceptable results for the external flow about a waterjet intake, if the ingested boundary layer is relatively thin (Q1QhI> approx. 1).

188 4.1 Free stream intake analysis 4.1.2 Intake induced drag and lift

Intake induced drag Many authors refer to an intake drag which makes up for the difference between a particular definition of gross thrust and some net thrust acting upon the hull. Although the intake drag is addressed several times, for example by Mossman et al. [19481, Arcand et al. [1968] and Hoshino et al. [1984], little attention is paid to its definition. An exception to this rule is the contribution by Etter et al. [1980].

The intake drag is defined as the difference between the gross thrust and the net thrust acting upon the hull (Section 2.2.3). The control volume representing the hydrodynamic jet model is selected to be volume D (Fig. 2.1) in Section 2.1.1. The definition of intake drag does not refer to the bare hull resistance, so it does not include a change in hull resistance due to the jet action.

The jet system's thrust deduction fraction t1, as introduced in Chapter 2, represents the non-dimensional intake drag D.:

t. (4.6) J - Tg

It has been demonstrated in Chapter 2 that the intake drag equals zero for a potential flow in free stream conditions.

As a step further, let us consider the isolated waterjet operating in a viscous flow. This condition is less accessible to the simple arguments used in Chapter 2. To get a proper idea of the viscous intake drag, a wake survey analysis of experimental data was considered to be one of the most accurate methods. To this end, detailed velocity measurements in plane VT3 (Fig. 4.1) were obtained from the LDV experiments in the MARIN large cavitation tunnel. The experimental set-up is described in Appendix 7. The operational condition of the intake, governing its drag, is characterized by the intake velocity ratio in the intake throat IVRE, by the ratio of ingested flow rate to flow rate ingested from the boundary layer Q'QbI and by the Reynolds number of the intake throat Rn. The test conditions are specified in Fig. 4.18.

The same two operational conditions have been used as in the preceding analysis, representative for modern jet system operations, viz. IVRE values of 0.62 and 0.94.

189 Chapter 4 Computational analysis

0.6

0.4 -- IVRt=0.62 e- IVR=0.94 0.2

-0.2

-0.4 2 -0.6 Rn 5 *1O -0.8 o 0.5 1.5 2

yI½w [-]

CDj=+l.9 1Ofor IVR=0.62 CDj=-3.l 1Ofor IVR= 0.94

Fig. 4.18 Momentum thickness distribution in plane VT3

Noting that there is no viscous contribution to FB, the intake drag can be written as (see also Section 2.2.3):

FXBC+FCD (4.7)

The forces FXBC and FXCD act upon the protruding streamtube of the jet system.

The viscous component of the intake drag can be obtained from a momentum consideration of Control Volume iin Fig. 4.19. The momentum balance in x-. direction reads:

JJp u(u-Uo)dA = -FXDJ-FXcD-Fxßc-FJ ¡B (4.8) A2

It is noted with the above equation that there is no net contribution of the ambient pressure p0 over the control volume. The force contributions in the right- hand term are reactions on the action forces acting on the bottom plating (positive drag) and the streamtube (positive intake drag).

190 4.1 Free stream intake analysis

.4 pump X F' I,z

A J

U0 cv i

Fig. 4.19Control volumes used for derivation of intake drag and lift

Using the definitions of the boundary layer displacement thickness2(Appen- dix 2) and the intake drag eq. (4.7), eq. (4.8) can be rewritten into

-- (4.9) D1 = 2pU fô2dy-FXJIB-FXDJ y=o where w,, =width of the wake survey plane = displacement thickness of boundary layer.

The viscous force FXDJ will be neglected in the following because of the small distance DJ in the test set-up. The force FJB equals zero when the dividing streamline is outside the boundary layer. When it gets within the boundary layer, its value increases up to a maximum value at the bottom plane IA. An estimate for the frictional force term when the streamline I'B is completely attached to the wall of the tunnel can be obtained from the boundary layer momentum thickness outside the intake affected flow region. For this purpose, the most outward boundary layer thickness value was selected and designated

191 Chapter 4 Computational analysis A non-dimensional intake drag coefficient can now be defined as the ratio between intake drag and ingested momentum flux:

D CD'= (4.10) pQU0

Using eq. (4.9) and (4.10), we find the following expression for the intake drag coefficient:

CD = AVR (4.11) Çv) =o forylw

= 2(w)fory>±w where =displacement thickness with active intake mounted (y) =displacement thickness caused by frictional force FXJB. It should be noted that there is a gradual transition in 6from O to S2(w). Because the form of this transition is not known, an abrupt change in is imposed at the lateral y-position of the geometric intake edge. Hence, the original displacement thickness öis set zero over the width of the intake, and is set equal to the most outward 2value for the other points. The difference in measured displacement thicknesses (2-6) is presented as a function of the transverse y-coordinate in Fig. 4.18, which also lists the drag coefficients. It can be concluded from these values and the uncertainty in S near the intake lateral edge, that the viscous intake drag iseffectively zero.

Mossman and Randall [1948] do not account for the change in FX1B with lateral position. Instead, they take the full displacement thickness measured without intake. Their intake drag coefficients consist consequently largely from the frictional drag coefficient of the tunnel wall.

192 4. 1 Free stream intake analysis Intake induced lift

An intake induced lift force on the stern of a vessel with an active waterjet has been suggested by Svensson [1989]. It has also been demonstrated in Section 2.2.4 that there is no intake induced lift for a jet operating in freestream conditions. Consequently, if an intake induced lift does exist, it must be caused by the limited bottom plating about the intake.

To study the above paradox, we will consider an intake operating in freestream conditions. To model the operational condition, part of the bottom plating aft of the intake is removed. The flow about the intake is left unchanged however. An estimate of the intake induced lift can thus be obtained from the freestream flow, by simply adding the geometric condition imposed by the hull.

The results from the HESM flow computations about the intake have been used to assess the lift effect. As demonstrated in the preceding section.a potential flow model provides a realistic flow outside the intake, provided the boundary layer at the hull is thin. This is a valid assumption for most hull forms fitted with waterjets. Because we focus on the induced lift production by the intake, the jet is considered to be discharged horizontally.

An estimate of the lift has been obtained by integration ofpressures over the bottom area, starting at the most aftward point on the plate and heading toward the intake lip. The thus obtained cumulative lift L(x) givesan indication of the force that is absent when the hull ends ata short distance behind the intake lip.

Typical transverse pressure distributions behind the lipare presented in Fig. 4.20. lt is seen here that the pressure at the lateral edge of the plating hasnot fully converged to zero pressure. This is considered to be partly caused by the asymptotic behaviour of the pressure with increasing distance from the intake, partly with the accuracy of the panel method. To get rid of this boundary effect, all pressures c(xy) have been reduced with thepressure at the lateral edge C1(x, ½w1,).

The cumulative lift force L(x) has been non-dimensionalized with the ingested momentum flux in the following way (see Fig. 4.21):

L(x) CL(x) (4.12) pQU0

193 Chapter 4 Computational analysis

0.15 x =0 (lip TE) X = 0.16 i X = 0.33 Ii 0.1 x = 3.06 I

0.05

o 2 3 4

transverse coordinate yI½w[-J

Fig. 4.20 Transverse pressure distributions behind an intake

3 ii

Intake Lip L (X) y

Cp(x,w) y = ½ Wp

Fig. 4.21Geometry and nomenclature used in lift deficit computation

194 4.1 Free stream intake analysis The lift coefficient CL(x) could subsequently be obtained from:

WJ) y x 2 (4.13) CL(X) J J Cp(x,y)-C(x,)}dydx IVRA vø where C(xv) = bottom pressure coefficient dependent on position w = width bottom plating used in HESM free stream model.

The results are presented in Fig. 4.22 for two distinct IVRE values, viz. 0.6 and 0.9. It is seen that the lift L(x) only amounts to approx. 2% of the ingested momentum flux in x-direction. This only provides a lift force of 0(0. 1 %) of the hull's displacement. The corresponding trimming moment would result in a change in running trim of 0(0.01) deg for the Hamilton test boat. This result is not in agreement with the lift reported by Svensson and not in agreement with the experimentally observed trim and sinkage (Chapter 3).

0.06

IVR=0.63 0.04 - - IVR=0.94

0.02

-0.02

-0.04 width width intakenel -0.06 O 3 Aftward distance from intake trailing edge I intake length[- I

Fig. 4.22Transverse pressure distributions behind an intake

195 Chapter 4 Computational analysis

Conclusions The following conclusions are drawn from the presented study on intake induced drag and lift:

The tested intake has no intake drag for the definition used here. Some authors refer to the ingested momentum as intake drag. This ingested momentum is regarded as part of the propulsor action throughout this work however, and is therefore incorporated in the thrust. A significant net lifting force induced by the intake can not be discerned from an intake in a free stream flow, matched with a geometric hull condition. Although it is demonstrated that missing lift due to a limited bottom area behind the intake lip occurs, which changes sign with IVRE, its magnitude is too small to give a noticeable contribution to the change in hull equilibrium position. As a result, the change in hull equilibrium must be caused by interaction effects in the local flow.

4.2 Computational prediction of interaction

A computed prediction of the interaction effects is desirable when its magnitude is uncertain. On the other hand, a computational prediction often improves the understanding of the phenomena involved and can be used for a further analysis of propulsion test data. This section deals with the predictive power of a few selected tools. Section 4.3 deals with a further analysis of propulsion test data.

A complete prediction of waterjet-hull interaction effects on the powering characteristics includes a prediction of the hull's resistance increment r and the jet system's interaction efficiencies Ti,711 and 11e1Relations for the jet system's interaction efficiencies are given in Chapter 2. For a given flow rate, these interaction parameters are determined by the boundary layer characteristics and the nozzle sinkage. Many relations are available for a prediction of the boundary layer characteristics in terms of thickness and velocity profile (see e.g. Schlichting [197911). We will concentrate in this section on a prediction of the resistance increment r and the nozzle sinkage.

For the evaluation of tools, we will use the case with the Hamilton Test Boat (see Section 3.4). The resistance increment will be discussed for two distinct speeds, corresponding to Froude numbers of 0.50 and 1.19 respectively. This case is selected because of the representative shape of the thrust deduction fraction with speed and because of the amount of information available.

196 4.2 Computational prediction of interaction Based on the discussion on results in Chapter 3, it is deemed important that the selected code should be able to compute the equilibrium position of the hull for a successful prediction of the resistance increment. It is furthermore deemed important that the code be able to compute the effect of ingested flow rate on the pressure distribution and hence the wavemaking resistance. This latter criterion is assumed to be particularly important in the lower speed range (FnL < approx. 1). The hypothesis on the potential flow character of the resistance increment (Section 3.4.1) is used here in the selection process.

The available programs that met the above constraints are the MARIN programs DAWSON/RAPID and PLANE. Descriptions of these programs are given in the Appendices 5 and 6 respectively.

4.2.1 Resistance increment for hump speed

Selection of code

The hump speed regime is particularly suitable for analysis with a free surface potential flow code such as e.g. DAWSON with linearized free surface conditions. An improved method is implemented in RAPID where the non-linear free surface conditions are solved. The RAPID code furthermore has the advantage that the equilibrium position of the hull is iteratively determined, which is not the case in DAWSON. Because of convergence problems with the RAPID code for the present case however, the results that are presented here have been produced by DAWSON. The intermediate RAPID results that became available indicated nonetheless similar values of the integral quantities (such as e.g. the resistance components).

It is noted here that viscous phenomena such as occur in breaking bow waves and in the separated flow behind the stern before it gets ventilated, are not accounted for in either method.

Modelling of problem

The modelling of the waterjet intake was done in a simple but representative way. Contrary to the work by Kim et al. [1994] and Latorre et al. [1995], the internal flow in the waterjet was not modelled. Instead, when a suitable condition in a boundary plane between external and internal flow is imposed, the problem is considered to be sufficiently well modelled for a study of interaction phenomena. For the boundary plane, the projected intake plane A'D can be used (see Fig. 4.23).

197 Chapter 4 Computational analysis The proper boundary condition in this plane was obtained by specifying the total required flow rate Q flowing through this projected intake area. In addition, the normal velocity distribution should be representative for an intake operating at the corresponding IVR1. 4x 2V pLi flip VP Zy

A A

B B 4 UI,

D A3 Suitable waterjet control volumes: CV A:II'CFF'I CVB: A'DCFF'A' CVC: A'B'CFF'A' CV D: ABCFF'A

A3 projected intake area

Fig. 4.23Control volume representing the waterjet system in the DAWSON/PLANE computations

The vertical velocity distribution in the projected intake area was obtained from the LDV measurements in the horizontal plane Hl (see Fig. 4.1), for the IVRE of 0.94. The IVRE obtained for the test boat from the propulsion tests at this Froude number was 0.89, sufficiently close to the LDV condition. The normal velocity distribution from the LDV tests is presented in Fig. 4.24 for 3 longitudinal cuts. This velocity profile has been represented in DAWSON by a constant normal velocity over the projected intake area AD' (see Fig. 4.25).

In modelling the intake this way, care should be taken that the resulting lift force due to the ingested vertical momentum flux is cancelled by an equal but opposite lift force within the jet (see Section 2.2.4). This neutralizing internal force is not modelled in the panel model, but should be accounted for in the obtained results, as will be demonstrated later in the discussion on trim and sinkage.

198 4.2 Computational prediction of interaction

1.4- yI½w=0 . y/½w = 0.58 1.2 .*- y/½w=O.8

1.0

N 0.8 N 0.6_r 0.4 A" =intakeLE in DAWSONmodel ______D'=intakeTE (lip) inDAWSONmodel 02 la 02 O -0.2 -0.4 -0.6 -0.8 -1.0 -1.2

D' xiii[-J A"

Fig. 4.24 Normal velocity distribution in projected intake area for an IVR=0.94 obtained from LDV measurements

transom

50 Q shaft ____._.l_ --p* F Qofship A" ord. O ord. I

Fig. 4.25Relation between actual waterjet intake and projected intake area A'' D' as used in the DAWSON computations

Results pressure distribution

To check the results of the rather coarse DAWSON model we will first study the computed pressure distribution. Fig. 4.26 shows the C1 distribution over the centreline of the intake. This distribution is compared with those obtained from

199 Chapter 4 Computational analysis the LDV measurements and the corresponding HESM computations. It is noted that the first pressure distribution belongs to an operational condition, whereas the latter two distributions belong to an intake in free stream conditions.

0.8 . DAWSON wjet IVRt = 0.89 . LDV wjet IVRt = 0.94 0.4 .*- HESMwjetIVRt=0.90

-0.4

-0.8 o -2

Fig. 4.26Comparison of computed and measured C distribution over centrehne intake

The pressure distribution from the DAWSON results has been deduced from the pressure distributions of the bare hull and the combined jet-hull system. To this end, the velocity field pertinent to the bare hull is subtracted from the field of the combined jet-hull system:

t7jet) = i(hull+jet)-(hul1) at any position (4.14)

It is observed from Fig. 4.26, that there is qualitative correlation. It is also seen that the DAWSON model does not follow the higher frequency peaks in G. This effect is ascribed to the relatively coarse panel distribution used.

Centreline Gdistributions for the bare hull (free stream condition) and the hull-jet combination (operational condition) are plotted in Fig. 4.27. A comparison of the C distribution over the complete aftbody is presented in Fig. 4.28. It can be observed from these comparisons that significant differences in pressure distribution occur in the intake region, due to the jet action.It can also be

200 4.2 Computational prediction of interaction observed however that the influence of the intake on the C,distribution is limited to an area which roughly extends between approximately one intake length ahead of the ramp tangency point and aft of the intake lip, and one intake width next to each lateral edge of the intake. Due to the nature of the potential function of sinks and sources, the influence of the intake on the pressure distribution decays asymptotically withhr2for non-zero hull speeds, wherer isthe distance between the point considered and the centre of gravity of the sink distribution modelling the intake.

0.6

0.4 -ca- aftbody- DAWSON waterjetIVR = 0.9 - LDV .,, -*-hull-jet- DAWSON 0.2 LwerJetDAWiJ

-0.2

-0.4_WI -0.6 -r O -2 -4 -6 -8

x/I1[-1

Fig. 4.27Comparison of computed C distributions over centreline aftbody for the isolated hull and the hull-jet combination

Fig. 4.29 shows that the wave profile that is generated by the hull with active waterjet resembles closely the wave profile without jet. Relative to the profile of the bare hull, the water level slightly falls along the aftbody, to subsequently give a slightly higher stern wave. It is to be noted that both computations are made at an equal equilibrium position of the hull, so that only the local suction effect of the intake on the profile is visualized.

201 Chapter 4 Computational analysis

Fig. 4.28 C distribution over complete hull with and without waterjet intake for FnL=O.5O and IVR=O.9

202 4.2 Computational prediction of interaction

0.4 ¡ I J J J J

0.3- AP FP fr. -1 fr. 8 ' 0.2-

-0.1

without waterjet -0.2- - - -with waterjet

-03 J I J J I I J 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 x/L

Fig. 4.29Comparisonofwave profile along the hull with and without waterjet

Results resistance computation

An important objective of the DAWSON computations is to predict the resistance increment of the hull due to the jet action. The relation for the resistance increment given in Chapter 2 (eq. 2.97) shows that the r is basically built up from two contributions. One is due to a change in frictional drag, caused by the missing part of the projected intake area A3 in the wetted surface. The other is due to a change in hull resistance, caused by a change in tangential stresses and normal pressures over the remaining wetted area (S-A3).

Let us first consider the contribution in frictional drag due to the missing intake area A3. A first estimate is made by assuming that the same frictional coefficient can be used for the total wetted area S as for the intake area A3. The contribution to the resistance increment r can then be written as:

A3 CF r = -- (4.15) SCT

where S =total wetted surface of the hull (excluding transom area) C1 = mean frictional drag coefficient =total drag coefficient.

203 Chapter 4 Computational analysis For the present case (hull form and speed), it appears that the frictional contribution of the missing area A3 to r is approx. 0.002. Itcan consequently be neglected here.

The hull frictional resistanceisfurthermore assumed to remain effectively unchanged and is left out of the following discussion.

The normal pressure drag R that is provided by DAWSON is computed from:

R =jf(PPo)ndA (4.16) where p= pressure p0 ambient pressure S= wetted surface up to undisturbed waterplane = x-component of unit normal vector at wetted surface S.

The pressure p can be rewritten with Bernoulli's theorem into:

P-P0 p(U_u2)+pgz (4.17)

The first term on the right-hand side is referred to as the dynamic pressurePdvn' the second term is the hydrostatic pressure. The normal pressure drag R can now be broken down into a component due to the hydrodynamic pressure, and a component due to a hydrostatic pressure. For conventional ships without ventilated stern or flow separation, the hydrostatic pressure does not exert a net force in x-direction. In case of a ventilated stern, it does exert a force however. This contribution is referred to as transom drag, and in the fully ventilated case, is obtained from:

Rr =JjpgzdA (4.18) ATr where ATr =ventilated transom area up to the undisturbed free surface.

The remaining pressure drag component due to the hydrodynamic pressure is referred to as wavemaking resistance' R. The residual resistance as obtained from resistance tests can directly be compared to the totalpressure drag obtained from DAWSON.

204 4.2 Computational prediction of interaction The computed resistance results in their non-dimensional form are summarized in the table below and compared with the experimental resistance values:

Table 4.2 Comparison of computed resistance with experimental data

Resistance DAWSON Resistance test component hull Hull HulI+jet

C lO 215 187 CTrlO 1688 1944 CReslO 2306 CF 267 267 267 CT l0 2170 2398 2573

All tgures refer to full scale. The above resistance coefficients all refer to the experimental wetted surface area S=l3.3 m2.

Itis important to note with the above table that the DAWSON results were obtained for the experimental trim and sinkage data. These data have been used because thehullequilibrium was notsufficientlyaccurate computed by DAWSON, whereas its importance for the final results was recognized.

We will now express the computed resistance increment in a fraction tr for a comparison with the total thrust deduction t as obtained from the experiments. The resistance increment t, (Section 3.4) can be expressed in CT, according to:

CT(hulljet)-Cl(hulI) (4.19) r - C-(hul1+Iet)

The tr fraction can now be computed with the data from Table 4.2.

Table 4.3 shows a comparison between the resistance increment tr and the total thrust deduction t. The resistance increment value obtained from the series of resistance tests (Section 3.4) is added for completeness.

205 Chapter 4 Computational analysis

Table 4.3 Comparison of computed resistance incrementtr with total thrust deductiontfrom experiments

Source oft t t,. tít [-1 [-1 [1 Propulsion/resistance tests 0.143 100 DAWSON computations 0.095 66 Resistance test regression 0.057 44

The following observations can be made on the thrust deduction fractiontr: Almost the complete contribution to the computed tr consists of a change in transom drag (110% oftr). The wavemaking drag furnishes a negative contribution to ç.

The importance of the transom drag contribution to the resistance increment is confirmed bythefindingthatthethrustdeductionfractiontforlow Length/Beam ratio hulls is usually significantly higher than the values for slender hull forms.

It is to be noted with Table 4.3 that the DAWSON predicted transom drag is too high, when the transom is not yet fully ventilated in reality. This is because it is assumed in the calculations that the transom is completely ventilated. This may partly explain the discrepancy in computed tr with that obtained from the systematic resistance tests. The resistance increment from these tests only explainsabout 45% oftheexperimentalthrustdeduction,whereasthe DAWSON results explain about 65%. If however, the transom is not yet fully ventilated,which can be concluded from Photo3.2,thetrueresistance increment will have a somewhat lower value than the DAWSON prediction. lt is concluded that a reasonable agreement exists between the computed resistance increment fraction and the experimental value for t,..It is also concluded that a significant gap between the total thrust deduction and the resistance increment still exists. One should note however, that the total thrust deduction is composed from the resistance increment contribution t,., and the jet system's thrust deductiont1.The effect of thïs latter contribution is discussed in Section 4.3.2.

206 4.2 Computational prediction of interaction

Results trimand sinkage

As demonstrated in the preceding discussion on the resistance increment, an accurate prediction of trim and sinkage is of paramount importance. This section will first provide the relations in the computational model that govern the equilibrium of thehull. Subsequently, the results that were obtained with DAWSON are discussed.

As mentioned in the discussion on the modelling of the problem, the waterjet is represented by control volume D in Fig. 4.23.

In order to find the change in trim and sinkage due to the jet action, we need to know the change in hull lift and trimming moment. The relations determining the vertical and pitch equilibrium are found from similar considerations as used in the derivation of the resistance increment in Chapter 2.

In the next discussion, we will use the earth-fixed coordinate system x',y',z'.

The hydromechanic force acting upon the hull in vertical direction (z') can now be written as:

Fo =jJG..odA +jjcYodA (4.20) S A3 whereF:,0=vertical force acting upon bare hull (including weight of jet system) s =wetted surface of hull excluding the projected waterjet intake area A3 A3 =projected waterjet intake area (see Fig. 4.23) G..' =total stress acting in z'-direction (see Section 2.2.1).

The hull'sverticalequilibrium positionisfound by matching the above hydromechanic force (including both hydrostatic and hydrodynamic pressures) with the combined weight of the jet-hull combination.

During the propulsion test (operational condition), the jet intake is open and the weight of the jet system is not part of the hull displacement any more. To find the total hydromechanic force acting upon the hull, we consequently have to consider the hull and the jet system separately. The total vertical force is then obtained by adding the vertical forces on both systems.

207 Chapter 4 Computational analysis The hydromechanic vertical force on the jet system can be obtained from the momentum balance for control volume D in vertical direction:

+JjJpgdV mnz'miz'= z'netJ J (4.21) A3+A8 V whereFnet = net vertical force acting upon the hull.

It is to be noted with the above equation that the net vertical force F.,net has been given a negative sign. This is because it represents the force acting upon the hull. Its reaction force (equal magnitude but opposite sign) acts upon the streamtube for which the momentum balance is constructed.

The hydromechanic force acting directly upon the hull system in the operational condition subsequently reads:

JJcdA (4.22)

The total vertical hydromechanic force acting upon the hull system in the operational condition consequently reads:

F +F, =J(L'dA dAJ"Jjg7dV (4.23) mnz' miz'+ J S A3+A8 V

Again, the vertical equilibrium position of the hull is found by matching the vertical hydromechanic force with the weight of the hull system. It should be noted that the weight of the entrained water in the jet system should not be used again to balance the hydromechanic force, as the jet system force (including entrained water) is already accounted for by Fznej

Similar relations can be found for the momentum moment balance, determining the pitch equilibrium.

From an analysis of the difference in resulting equilibrium position of the hull between the resistance test and the corresponding DAWSON computation, a reasonable correspondence occurs. The deviations in trim and sinkage are listed in the Table 4.4:

208 4.2 Computational prediction of interaction

Table 4.4 Deviation in computed hull equilibrium position relative to resistance test result (computation-experiment, full scale values)

- Error in transom sinkage (z [m], positive downward) 0.01 - Error in trim (&r [degi positive bow up) 0.15

The DAWSON results relative to the change in hull equilibrium caused by the jet action, are listed in the table below:

Table 4.5 Change in trim and sinkage due to the waterjet action relative to the resistance test condition (full scale values)

Experiments DAWSON Error Resulting sinkage at transom (dz [ml, 0.03 0.01 0.02 positive downward) Resulting trim (dt [degi, positive bow -0.57 -0.11 -0.46 down)

Table 4.5 shows the agreement in the trends for transom sinkage and trim. The computed values however, are only some 30 and 20% respectively of the experimental values for sinkage and trim. Although the computed values are still too low, they are much closer to the experimental values than the trim and sinkage prediction from the free stream jet consideration in Section 4.1.2. These values appeared to be an order of magnitude smaller.

From a comparison of the errors presented in the Tables 4.4 and 4.5, it is noted that they are of the same order of magnitude. Although the errors in hull equi- libriuin for the resistance condition are small in absolute terms, they are too big when used for a prediction of the resistance increment caused by the jet action.

Conclusions ltis concluded from the above results, that the DAWSON program provides a suitable tool for the analysis of the physical mechanisms involved in the change of hull behaviour due to the jet action. The prediction of the equilibrium posi-

209 Chapter 4 Computational analysis tion of the hullisnot sufficiently accurate for a prediction of resistance increment. The error with the experimental data causes a large error in the calculated resistance increment.

Possible reasons for the error in hull equilibrium position are:

The inadequacy of the flow model describing the transom clearance. The steepness of the wake is underestimated, causing a computed pressure at the transom that is relatively too high. The neglect of viscous effects in transom clearing. The coarseness of the panel distribution and the corresponding inac- curacy in the lift force obtained from pressure integration.

4.2.2 Resistance increment for design speed

Selection of code

For a study of the resistance increment at high Froude numbers (FnL>l), the Savitsky method is used. This popular resistance prediction method is recommended in a review paper by Altmeter [1993] for typical high speed monohulls.

The Savitsky method is implemented in the MARIN program PLANE. This program has been adapted to allow for the free stream forces and moments introduced with waterjet propulsion. No allowance is consequently made for possible interaction effects in the pressure distribution about the intake, such as computed in DAWSON.

Modelling of problem

The same control volume as applied in the DAWSON model can be effectively used here to determine the jet system's net forces and moments (see Fig 4.23). As derived in Section 2.3.1, the net thrust of a jet system on a flat plate is approximated by:

Tg = cosOn-pQcmUo (3.9)

where O,, =nozzle inclination relative to hull-fixed coordinate system.

Because the net force on the protruding streamtube plus external part of the intake lip equals zero, we can derive:

210 4.2 Computational prediction of interaction

,n3x =pQc,U0 (4.25)

The point of application of the ingested momentum follows from a momentum moment balance. Without detailed elaboration of this balance, this point is assumed to be in the centroid of the intake area.

As demonstrated in Section 2.2.4, the jet system in free stream conditions does not exert an intake induced lift force upon the hull.

Fig. 4.30 shows the forces that are modelled in the PLANE program. Resistance tests can be modelled by applying the pulling force in the actual towing point during the tests. The equilibrium position of the hull is obtained by solving the force and moment balance for each speed and condition.

7 CoB =Centre of Buoyancy CoF =Centre of Flotation CoG =Centre of Gravity FT= Towing force RT =Total drag A =Displacement weight V = Displacement volume

Fig. 4.30Forces acting on the hull-jet system as modelled in the computer program PLANE

Results

To check the validity of the computed results, they were compared with the experimental results. Both the resistance and propulsion test conditions were computed, to find the resistance increment and the change in trim and sinkage.

211 Chapter 4 Computational analysis A comparison of the measured and the computed resistance is presented in Fig. 4.31. It can be observed that the trend in computed resistance corresponds well with that of the measured resistance. Taking the limitations of the resistance prediction algorithm into account, the absolute values of the resistance in the lower speed range correspond surprisingly well with the measured values. For the higher speed range however, a discrepancy of some 10% with the measured resistance occurs.

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 FnL [1

Fig. 4.31Comparison of computed and measured resistance data

Fig. 4.32 shows a comparison of trim and sinkage data. Significant discrepancies in trim data occur over almost the entire speed range (up to 1.3 deg difference in trim angle). The correspondence in sinkage of the Centre of Grav- ity is satisfactory.

A computed resistance increment factor t,. could be derived from the resistance and propulsion computations, according to:

RBH (4.26) r T net

212 4.2 Computational prediction of interaction

0.3 lo

8 0.2

0.1 4 / . / o I. - tPLANE 2 _A I A riseCGexp 4AAAA -- riseCGPLANE -0.1 o

0.2 0.4 0.6 0.8 I 1.2 1.4 .6 FflL [1

Fig. 4.32 Comparison of computed and measured trim and sinkage data

This resistance increment factor tr is compared to the total thrust deduction fraction t in Fig. 4.33. It is to be noted that the thrust deduction fraction from the experiments consists essentially from a hull resistance increment, except at the point where the transom clears. This issue will be discussed in Section 4.3.2.

It is shown that the level of the thrust deduction fraction and the resistance increment factor roughly correspond for FnL 1. For increasing speeds however, the thrust deduction fraction t increases more rapidly than the computed resistance increment factor. A strong discrepancy occurs for the lower speed region as could be expected.

To investigate whether the discrepancy between t and computed t,. would mainly be caused by a discrepancy inhull equilibrium position, the relations between running trim and thrust deduction were compared (Fig. 4.34). Despite the fact that the level of computed Ir-values roughly corresponds with the experimental values for the higher speed regime, large discrepancies occur in corresponding change in running trim dt.

213 Chapter 4 Computational analysis

0.2 Experiment PLANE

0.1

u u u 0 U. .

-0.1

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 FflL []

Fig. 4.33Comparison of computed and measured thrast deduction fraction

0.04

0.02

-0.02 -0.04 /Experiment - PLANE -0.06 -0.6 -0.4 -0.2 O 0.2

dt (prop-res) [deg]

Fig. 4.34 Comparison of computed and measured thrust deduction fraction as a function of change in trim angle

A similar exercise was conducted to check whether the agreement in measured and computed resistance would improve if the computed running trim angle was brought in correspondence with the measured trim angle. This was achieved by adjusting the LCG value so as to obtain approximately equal running trim

214 4.2 Computational prediction of interaction angles at FnL' 1. Although the computed resistance at this speed more closely approached the experimental value, there isstill some 6% discrepancy. More- over. the trend of both resistance and running trim with speed, which closely resembled the experimental trend for the uncorrected LCG position, clearly differed from the experimental trend for this case. Adjusting the running trim angle therefore does not seem to improve the predictive power of PLANEover a certain speed range.

Conclusions

It is concluded from the above study that the Savitsky method, extended with a jet model consisting of free stream forces and moments, does not give a good correlation with the model tests. The trends in hull equilibrium and resistance increment are weakly shown, but the quantitative correspondence is poor.

4.3 Analysis of propulsion test procedure

In the data reduction applied in Chapter 3, a few assumptions and neglects have been made. This section will review the consequences of these simplifications and assess their importance.

In the determination of the ingested momentum and energy fluxes by the intake, it has been assumed that the imaginary intake area featured a rectangularcross section with a width that is 30% wider than the geometric width of the intake. The consequences of this assumption will be studied in Section 4.3.1.

In the derivation of the net thrust from the gross thrust, necessary to find the resistance increment of the hull, all integral terms in the relation for the thrust deduction t1 have been neglected. As a consequence, this thrust deductionwas equal to zero. Part of this simplification was already justified for a potential flow in Section 2.3.1.

The magnitude of the other contributions can now be assessed, as detailed information on both the integral quantities obtained from the propulsion tests, as well as detailed information from the flow field about the hull-jet system is available. The following contributions are addressed in Section 4.3.2:

Effect of free surface induced pressure gradient over protruding part of streamtube BCD (Fig. 2.1). Effect of a clearing transom stern. Effect of a running trim angle.

215 Chapter 4 Computational analysis 4.3.1 Effect of intake geometry on interaction efficiency

The geometry of the imaginary intake area is important in the determination of the ingested momentum and energy fluxes for a given flow rate Q, as is discussed in the Chapters 2 and 3. In the reduction of experimental powering data, many authors use a rectangular cross section with an effective width that is slightly wider than the geometric width of the projected intake area (see e.g. ITTC [1987]). An effective width factor ffor this cross section is often defined as:

We (4.27) Jw w wherewe= effective width of imaginary intake cross section (AB in Fig. 2.1) w, = geometric width of projected intake area.

It is easily seen that an increase of the effective width factor leads to a decrease in flow rate ratio Q'Qbl' consequently leading to an increase in the viscous contribution to the interaction efficiency TÌINT This effect is explained in Sec- tion 2.3.3.

The value of the flow rate ratio Q'Qbl depends on the shape of the imaginary intake area, as do the momentum and energy coefficients c,71 and c. Therefore an attempt is made here to obtain more knowledge about the true shapeof the intake. Subsequently the effect of the assumption of a rectangular intake shape on interaction data is studied. This is done through a comparisonof interaction efficiencies for the most likely intake shape and a simplified shape with rectangular cross section. Information on the shape of the imaginary intake area can be found in e.g. Spannhake [1951] and Alexander et al. [1994]. Spannhake concludes from data by Hewins and Reilly [1940] that the imaginary intake area for flush intakes of condensers resembles a half ellipsoid. It is to be noted that condenser inlet scoops have a similar geometry as flush waterjetintakes, but that their operational condition is typically at much lower flow rate ratios Q'Qhl This ellipsoi- dal shape of the imaginary intake is confirmed for flush waterjet intakes by Alexander et al.[1994]. These authors state that the width of the imaginary intake was found to be approximately 50% greater than the width of the waterjet intake. They furthermore report that the width was largely independent of the craft speed over the range investigated. The change in non-dimensional flow rate was effectuated through a change in height of the semi-ellipsoid.

216 4.3 Analysis of propulsion test procedure The data from Alexander et al. [1994] are plotted in Fig. 4.35, together with the profile that is inferred from the HESM results by the traced dividing streamlines. It is seen from this figure that both the experimental data from Alexander et al. and the computed data by HESM are close to a semi-ellipsoid with a maximum width equal to about 1 .5 times the geometric intake width.

1.2 oHESM IVRt = 0.6 .0 -Elliptic profile HESM IVRt = 0.9 0.8 o oAlexander etal ['941 ' 0.6

0.4

0.2 n 0 O 0.5 1.5 2 y/(½ w) [-1

Fig. 4.35Comparison of elliptic intake profile with HESM results

The effect of using an ellipsoid intake with a width factor f=l .5 instead of using a rectangular intake cross section with f,=l.3 will now be investigated. To this end, the momentum and energy coefficients c,77 and care numerically evaluated for both intake geometries. General expressions for these coefficients in their integral form are given in Appendix 2.

The shape of the imaginary intake geometry is not only determined by the aforementioned width factor but also by the power r of the following general geometrical relation:

= ( (4.28) max W2e

where We = maximum width of imaginary intake area = maximum height of imaginary intake area.

A value for r of 2 corresponds to a semi-ellipsoid streamtube cross section, a value of 1000 corresponds to a rectangular section.

217 Chapter 4 Computational analysis Other non-dimensional parameters determining the amount of ingested boundary layer are a non-dimensional height of the imaginary intake hmi and a non- dimensional boundary layer thickness 5/w.

A non-dimensional flow rate can now be defined that is related to hull speed and intake width, according to:

-Q (4.29) 2 U0w

The effect of the shape of the imaginary intake area is now studied for equal ingested flow rate, or equal flow rate coefficient C0. The results are plotted in Fig. 4.36. The variations in CQ have been obtainedby variations in non-dimensional height of the intake The non-dimensional boundary layer thickness ö/w was fixed at a value of 0.5, which is considered to be a relatively large value. In other words, the effect of ingested boundary layer is relatively large.

1.5 I i I NVR=1.7 1mmT / rectangle = 1.3 (rect), 1.5 (ellips) - 1.4 lumi / ellips öI = 0.5 11INT / rectangle 1.3 = 9 - - r = 1000 (rect), 2 (ellips) °lINT' chips

1.2

-c - - o

0.9 0 2 3 Cq (Q/(UoW2) []

Fig. 4.36Effect of imaginary intake geometry on interaction.

Fig. 4.36 shows, however, that the effect of the intake shape on total interaction efficiency rl/NT is within 0.5% over the complete range of flow rates. The effect is most pronounced at values of CQ around 0.75. corresponding to flow rate

218 4.3 Analysis of propulsion test procedure ratios Q'QhI of approx. 1.2. For decreasing flow rate ratios, the effect of intake shape diminishes again.

The effect of intake shape on thrust, expressed in momentum interaction effi- ciency1L is seen to amount to a maximum of approx. 1.5%. The effect is most pronounced around CQvalues of 0.75 again.

It is concluded from this sensitivity study that an imaginary intake of rectangular shape with a width factor f=1.3 gives a good approximation in the reduction of propulsion test data. Maximum bias errors in power due to the actual shape of the intake geometry are expected to be within 0.5%. Bias errors in net thrust due to the intake geometry are not expected to exceed 1.5%. These errors can be avoided by taking into account the best estimate for the intake area, being a semi-ellipsoid with a width factorf=1.5.

4.3.2 Effect of hull and free surface effects on t3 assumption

The relation between the gross thrust that is derived from propulsion tests or computations, and the net thrust, acting upon the hull is discussed in Section 2.2.3. The effect of jet-hull interaction on this relation is discussed subsequently in Section 2.3.1. The present section deals with a quantitative assessment of the terms and conditions derived in the above sections.

A total thrust deduction fraction t is obtained from propulsion tests in a straightforward manner. This thrust deduction links the gross thrust Tg to the bare hull resistance REH in the following way:

Tgoo(l_t) =RBH (3.39)

This total thrust deduction contains consequently a jet system thrust deduction t, to convert gross thrust to net thrust, and a hull resistance increment r. To rinkup with the existing nomenclature in propeller hydrodynamics, we may refer to the resistance increment as the hull's thrust deduction fraction tr A corresponding thrust deduction factor may subsequently be defined as:

T,iet(ltr) =RBH (4.31) so that

ltr = (4.32) 1+r

219 Chapter 4 Computational analysis

Consistent with the definitions introduced in Chapter 2, we may writeeq. (4.31) as:

Tgoo(ltj)(Itr) RBH (4.33)

Neglecting second order terms, we may write the total thrust deduction t as the sum of the jet system thrust deduction t1 and the hull's resistance increment tr:

t = tjt/ (4.34)

It is seen that, in order to derive the hull's resistance increment from propulsion tests, an estimate on t should be made.

The jet system's thrust deduction fraction t1 was derived to read (eq. 2.39):

ti = JJ G/IA+JJ(-a 0)dA+JJJpgdv) (4.35) A1+A2-A4 V

The first integral term on the right-hand side is the force acting on the protruding part of the intake (see also Fig. 2.1). The second integral term is a contribution over the nozzle areaA8, and the third integral term is a contribution of the entrained water weight when the jet is positioned under an angle. These three contributions will be addressed separately in the following.

Free surface induced pressure gradient over protruding streaintube

The first integral term on the right-hand side is the force acting on the protruding part of the jet system, defined by A1+A2+A4 (see Fig. 2.1). This force was derived to equal zero in a potential flow with free surface (see Section 2.3.1). In this derivation, the assumption is necessary that the contribution of the free surface induced pressure gradient in x-direction acting over BCD (Fig. 2.1) is negligible. This assumption will be validated here.

The additional force FXABCD due to the free surface pressure gradient would however affect the relation between bare hull resistance and gross thrust. Let us designate the contribution tot1 that is considered here as t.

The value of the thrust deduction component t» can be obtained after the dividing stream surface and the local pressure gradient are known:

220 4.3 Analysis of propulsion test procedure

ti1 -_ Pfl (4.36) g°°ABCDf

Information on the shape of the protruding part of the waterjet streamtube is presented in the preceding Section 4.2.1. The pressure gradient due to the bare hull (without waterjet) and free surface effects is computed by DAWSON for the Hamilton test boat at a Froude number FnL=O.5 (see also Section 4.2). The pressure distribution over the aftbody together with the position and the shape of the dividing streamline of the waterjet on its centreline, discussed in the previous section, is given in Fig. 4.37 Although the waterjet geometry used for the computation of the dividing streamline is not the one actually mounted in the test boat, the operational condition of the intake is equal to that measured during the propulsion test during this speed (IVR=O.9).

AFTBODY GEOMETRY

A /Q of ship fr. -1 fr. i

0.1

-0.1

-0.2

-0.3

-0.4

-0.5

Fig. 4.37Representative dividing streamline in aftbody induced pressure field of the Hamil- ton Test Boat (Fn=0.5)

221 Chapter 4 Computational analysis The strongest pressure gradient over the intake is preferably selected for an indication of its effect on thrust deduction. This condition will occur at the point where the flow about the transom stem gets fully ventilated. Pressure gradients in an unbounded flow occur where the streamlines are curved. The stronger the curvature, the higher the pressure gradient. The flowlines off the transom show only a weak curvature at low speeds, where a dead- water zone is entrained. This dead water zone is bounded by the transom stem and the continuous streamlines. At higher speeds, when the transom stern is fully ventilated, the curvature decreases with increasing speed. This effect is observed as the smoothing of the rooster tail occurring behind the transom with increasing speed. In the transition regime, where the actual clearing of the transom occurs, a strong curvature of the streamlines occurs.

Littleis known about this transition regime, probably caused by the strong interaction between the viscous dominated dead-water zone and the potential dominated streamlines. Also wave breaking mechanisms are expected to affect transom clearing (see e.g. Raven [1993]).

Although the pressure distribution on the aftbody is difficult to compute, the absolute value of the pressure is given by the condition that the static pressure at the transom edge cannot be lower than atmospheric pressure. It thus solely depends on the sinkage of the transom.

Because we consider a hull running at FnL=O.S, in the speed regime where the transom is clearing (observed from model tests, see Section 3.4.1) and where transom sinkage is about maximum, the situation considered is close to a worst case regarding the additional pressure force on the waterjet streamtube.

An estimate of the magnitude of the thrust deduction t» can now be obtained from a 2D consideration of the known dividing streamlines. Neglecting the contribution on the outer part of the intake lip CD, the 2D version of eq. (4.36) is found to read:

1 ph -Cph(A))nxds (4.37) =21 VR 0h (NVR - IJ AC where CPh = hull induced pressure coefficient A designates the longitudinal position of the imaginary intake AB ¡VR0 = intake velocity ratio in imaginary intake area AB (see Fig. 2.1) h. = height of ingested streamtube at imaginary intake area AB.

222 4.3 Analysis of propulsion test procedure The viscous momentum deficit in the intake area, expressed byCm has been neglected.

To convert eq. (4.36) to its 2D counterpart, the required 2D flow rate has been written as:

Q = U0! VR 0h (4.38)

The results obtained for the three longitudinal planes considered (Fig. 4.1) are summarized in Table 4.6.

Table 4.6 Results of 2D estimates of thrust deduction induced by free surface effects in hump speed region (FnL=O.5) at an /VR=0.9

JVR [-1 0.90 IVR0 [-j 1.03 NVR [-1 4.51 I/wi [-j 2.85 Plane VL1 Plane VL2 Plane VL3

ìii 102 [] 17.2 12.6 1.60 1II/c1nds l0 [-] 12.3 8.07 0.84

t.1102 [1 0.99 0.88 0.73

It is inferred from the above table thatthe 3D thrust deduction fraction t» due to the aftbody induced pressure fieldis within 1% for the present case.It should be noticed that this contributionmay increase up to a few percent when the NVR value is decreased at equalIVRr Such condition will for instance occur when a bigger nozzle diameteris used in combination with a smaller intake throat area.

If a bigger jet system is used to produce the same thrust, both the NVR and the IVRE value will decrease. These effects counteract each other in t11. An indication of their possible net effect is given in Table 4.7.

223 Chapter 4 Computational analysis

Table 4.7 Resultsof2D estimates of thrust deductiontinducedbyfree surface effects in the hump speed region at an IVR1=0.6 and an NVR=3

IVRE [-1 0.60 IVR0 [-1 1.03 NVR [-1 3.00 l/w1 [-1 2.85 Plane VL1 Plane VL2 Plane VL3

h1/!102 [I 12.0 9.90 1.00 I/1/CPhnXds [-1 6.81 5.32 0.47

t»102 [] 1.38 1.30 1.12

lt is concluded from the above table that the magnitude of the thrust deduction t» is not very sensitive to the size of the jetunit. Contributions to t» of 0(0.01) are computed for the present case.

If however, a non-zero external force would exist, it would not have an effect on overall efficiency nor would it have an effect on required power. This is understood when one takes into consideration that the pressure force acts perpendicular to the internal flow in the jet system. Hence no energy is exchanged between external and internal flow.

Clearing effect of transom stern

The second term in the right-hand side of eq. (4.35) is zero by definition in free stream conditions. It equals zero in operational conditions if the ambient pressure about the nozzle and the corresponding height at the transom stern of the hull are identical. This is a valid assumption if the transom stern and the waterjet nozzle are both ventilated (acting in air). The assumption is no longer valid when the projected nozzle position at the transom is ventilated, whereas the nozzle itself is still submerged. This condition occurs during the clearing of the transom stern, when the nozzle still protrudes in the following stern wave.

Let us designate the contribution to the thrust deduction that is considered here as t». This component can be obtained from the following relation: 4.3 Analysis of propulsion test procedure

i t12 TgJJA (4.39) A8

It can be seen from this relation, that whenever the nozzle protrudes in the following stern wave whereas the projected nozzle position at the transom is already ventilated, a positive contribution to t12 occurs (both the integral term and Tg are negative, see Section 2.2.1).

To study the character of t12 and to obtain an indication of the contribution to the total thrust deduction t, a simple model of the falling water level behind the stern is made. Before the simple model will be explained, one should bear in mind that the Froude number can be written as:

IX (4.40) FnL = 2ic L where A. = wave length of transverse wave L = characteristic length for the generation of transverse waves.

It is thus seen that the Froude number can be interpreted as a non-dimensional wave length, as well as a non-dimensional ship speed. We will use this interpretation in the assessment of the difference in Froude number between transom and nozzle ventilation, and in a judgement of the wave steepness just behind the transom. The latter is adjusted so as to bridge the gap between the experimental t-value and the computed t,. from Section 4.2.1.

The height from the nozzle centre to the free surface at the Froude number FnL=O.5O is used to compute the pressure at the nozzle before ventilation. Fig. 4.38 shows that the nozzle position at the stern becomes ventilated ata lower Froude number than the nozzle discharge centre, because of the smallerwave length required. This consideration neglects the effect of the transom stern on the local wave. The difference in FflL at which ventilation occurs can thus be estimated from the length of the protruding nozzle AX, the characteristic hull length and the Froude number of the hull. The difference in ventilation is estimated from:

AX AFnL = (4.41) L4f

225 Chapter 4 Computational analysis

z=0'

½A L

= stern wave length 0.03 L 0.07 L

Hamilton test boat at FflL = 0.5

Fig. 4.38 Waves relevant in the model for clearing of stern and nozzle

The falling rate of the water with increasing Froude number is supposed to follow a sinusoidal function (sinusoidal wave). Because of the transom stem, the wave behind the transom will be much steeper than the dominant transverse wave pertinent to FnL=O.S. The wave steepness during clearingis determined by both potential flow and viscous flow effects (see e.g. Raven [1993]). To the knowledge of the author, there is no proper model available to describe this clearing process. Observations of the breaking stern wave behind the transom do indeed indicate a much larger steepness.

The wave length coming off the transom stem is determined iteratively, so as to fill the gap between the computed tr and the measuredtas discussed in Section 4.2.1. The wave length at which a requiredt12of approx. 0.05 was found is indicated in Fig. 4.38. It is noted that when the height of the transom stem wave is increased, which is a realistic thought, the contributionoft1 will increase.

The relation betweent1 and FnL that results from this model is presented in Fig. 4.39. The sharp peaked character oft1 corresponds remarkably well with that of the experimental thrust deductiont,as found from the propulsion tests (see Figs. 3.25 and 3.26).

Apart from the aforementioned effect on thrust deduction fraction (or on the dead- water zone behind the transom also affects the parametric relation for

226 4.3 Analysis of propulsion test procedure the energy interaction efficiency r. This is because viscous energy losses occur in the dead- water zone behind the stern. Because of these viscous losses, the Bernoulli equation for a potential flow is not valid any more. This equation has been used in the derivation of the parametric relation for the energy interaction efficiency (Section 2.3.2). A correction for viscous effects is thus needed.

0.06 0.12 E

o . 0.08 004 N u N li transom - -nozzle 0.04 -*- tj2 computed

O o 0.35 04 0.45 0.5 0.55 FflL []

Fig. 4.39 Effect of transom clearing on thrust deduction fractionj2

Trim effect on entrained water weight

A third contribution to the thrust deduction fraction t1 is given by the third term in the right-hand side of eq. (4.35). lt is referred to as tß. Analogous to the value of t12 in free stream conditions, this term equals zero by definition in such conditions. When the hull operates at a running trim angle and the ingested water weight is not negligible compared to the vessel's overall resistance, this term cannot be neg'ected beforehand.

The value of tfrom the experiments with the Hamilton test boat amounted to maximum values of approx. -0.01.

Conclusion on t1

The effects discussed in this section are quantified for the Hamilton test boat operating at a Froude number Fn L=0 .5. The results are listed in the Table 4.8. It

227 Chapter 4 Computational analysis is to be noted that the most important contribution to t1 has not been obtained from measurements, but has been quantified so as to close the gap between the totalthrust deduction and the resistance increment as obtained from the DAWSON computations.

Table 4.8 Comparison of computed and measured contributions to the thrust deduction fraction r

Source of r t. tr t rit [-1f [-1 [-1 ¡1%] Contribution protr. streamtube r» 0(0.01) 7 Contribution clearing stern 0(0.04) 28 Contribution by entrained water t» 0(-0.01) -7

DAWSON computations 0.095 66 Resistance test regression 0.057 44

Propulsion/ resistance tests 0.143 100

It is concluded from the above study of the jet system's thrust deduction frac- tiont1,that deviations from zero may especially occur around the speed where the transom isclearing. For higher speeds, this fraction is practically zero (Tg,=Tnet). Hence, the experimentally derived thrust deductiontis a good measure for the hull's resistance increment for the higher speeds, but may need correctionatspeeds around transom clearing.Such corrections could be obtained from resistance and propulsion experiments when the static pressure at the projected position at the transom (resistance test) and in the nozzle discharge (propulsion test) are measured.

If the information to break the total thrust deduction fraction t down into atr and at.component is lacking, the contribution oft1to the momentum interaction effticiency rl,can be incorporated in the total thrust deduction fraction r. The total interaction efficiency TIJNT subsequently follows from:

el fl/NT =(1-t) (4.42)

wheretis obtained from the propulsion and resistance tests (eq. (3.39)), and the momentum and energy interaction efficiencies are obtained from the equations (2.79) and (2.86) respectively.

228 Chapter 5

5Conclusions and recommendations

This chapter issplit into three parts. The introduction summarizes the main conclusions, followed by recommendations for future work. Section 5.1 lists the more detailed conclusions that were drawn from the development and validation work on tools for the analysis of waterjet-hull interaction. Section 5.2 lists the conclusions on the physical mechanisms governing waterjet-hull interaction that were revealed in passing.

The following main conclusions are drawn from this work:

A parametric model for the description of the powering characteristics of a hull-waterjet system is proposed, allowing for a separate identification of the complete waterjet-hull interaction terms. This model has resulted in a better insight in the physical mechanism governing interaction. 0 An experimental procedure is proposed and validated to determine the complete waterjet-hull interaction terms. This method offers a higher accuracy (high precision) and robustness (little risk for bias errors) than methods that can hitherto be found in the existing literature. The resolution of the computational tools studied is not sufficient to give a meaningful estimate of the waterjet-hull interaction terms. The main asset of the computational analysis is that it enhances the understanding of interaction mechanisms.

229 Chapter 5 Conclusions and recommendations As a result, the following recommendations are proposed:

Because of the complex flow phenomena that determine the interaction effects (especially the hull's resistance increment and nozzle sinkage), it is likely that interaction effects are most accurately determined through model propulsion tests for the next decade or longer. A computational prediction method for interaction effects that can be used in preliminary design stages is therefore best based on an empirical approach. Based on the insight gained in the mechanisms of interaction and based on collected data on a wide variety of jet-hull combinations, an empirical prediction model can be derived. The data supplied in this work form a first step to arrive at such a prediction model. The accuracy of model propulsion results should be improved by ascertaining and possibly reducing the bias error in the experimental results. This is effectively done through the collection and analysis of carefully conducted propulsion tests.

5.1Methods and tools

Parametric model

1. A systematic separation between waterjet and hull appears to be possible, leading to a set of parametric relations that describe the free stream characteristics and their interaction effects explicitly. (Chapter 2)

A thrust deduction t is introduced that not only accounts for the hull's resistance increment, such as in propeller hydrodynamics, but also for the difference between gross thrust and net thrust. This latter component is expressed in the jet system's thrust deduction t3 and is also prone to interaction. (Chapter 2)

The powering characteristics of the overall hull-jet system are essentially independent on the choice of control volume modelling the jet system. A skilful selection of control volume does however allow for an accurate quantification of both theindividual and the combined powering characteristics. (Chapter 2)

4. To represent the hydrodynamic model of the jet system, control Volume D (Fig. 2.1) meets the constraints that should be imposed to allow for a separation of jet system and hull characteristics. For the computation of gross and net thrust in a potential flow with free surface effects however,

230 5.1 Methods and tools control volume A (Fig. 2.1) appears to yield simpler relations. This volume has its (imaginary) intake situated in the free stream. In a viscous flow, simple corrections on net thrust and power are necessary to account for the viscous stresses exerted by the hull on part of the streamtube. (Chapter 2)

Experiin entai procedure

The velocity profile and the swirl in any place in the jet system may change with model speed. A reference flowmeter should therefore show a low sensitivity to changes in flow pattern. An 'averaging static pitot tube' meets this criterion. It has proven to be a reliable transducer during many propulsion tests. (Chapter 3)

Calibration of the reference fiowmeter with flow rate easily leads to uncertaintiesthat render the meaning of propulsion tests doubtful. Calibrating it with model pulling force during bollard pull conditions yields both a better uncertainty in calibration input signal, but also provides a much weaker, or at most an equal propagation of all relevant error sources into the final thrust and power prediction. (Chapter 3)

Applying the above thrust calibration procedure, the errors in jet thrust (momentum flux from the nozzle) and ingested momentum flux or cause the biggest errors. Their relative contributions are quantified in Section 3.3. Based on the experimental trends observed in the hull's resistance increment and an experimental and computational study on a possible mechanism, itis concluded that the resistance increment of the hull largely consists of a potential flow contribution. The viscous effects in the momentum and energy interaction efficiencies are quantified. These findings confirm the assumptions made in the ITTC'87 extrapolation method. (Section 3.5)

It has been proven that it is essentially the viscous momentum and energy loss in the imaginary intake that affect the thrust and power characteristics of the jet-hull combination. These viscous losses can be determined during resistance tests. (Chapters 2 and 3)

231 Chapter5Conclusions and recommendations

Computational tools

Free stream characteristics

10. Potential flow methods, including higher order methods, do not give satisfactory predictions of the flow field within the intake. Deviations in computed C with experimental data of0(0.5)occur. Potential flow methods do give satisfactory predictions for flow fields outside the intake however. Maximum deviations in Cp along the dividing streamline were found to be approx. 0.1. (Section 4.1.1)

Computational prediction of interaction li. The DAWSON potential flow panel code provides a suitable means for analysis of the physical mechanisms involved in the change of hull behaviour due to the jet action. The prediction of the equilibrium position of the hull is not sufficiently accurate for a prediction of the resistance increment. The resulting deviation with the experimental data causes a large error in the resistance increment. (Section 4.2.1)

The 'Savitsky' resistance prediction method, extended with a jet model representing the free stream jet forces and moments, does not give a good correlation with the experimental results. The trends in hull equilibrium andresistanceincrement areweakly shown, but thequantitative correspondence is poor. (Section 4.2.2)

Analysis of propulsion test procedure

The imaginary intake area AB (Fig. 2.1) is adequately represented by a rectangular shape with a width of 1.3 times the geometrical width of the intake area, for the derivation of ingested momentum and energy fluxes. Maximum bias errors in power due to the actual shape of the intake geometry are demonstrated to be within 0.5%. These errors can be avoided by using the best estimate for the intake area, being a semi- ellipsoid with a width of approx.1.5times the geometrical width. (Section 4.3.1)

4. The pressure gradient over the protruding part of the streamtube (BD of Control Volume D in Fig. 2.1) may cause a contribution to the jet thrust deduction of 0(1%) of the thrust. This effect is quantified by t11. It shows a maximum in the hump speed region. (Section 4.3.2) 5.2 Physical mechanisms 5.2Physical mechanisms

The results of a selected set of waterjet-hull combinations, incorporating monohulls and catamarans from 7 up till 80 m length, show that the total interaction efficiency rl!NT may reach values between 0.75 and 1.15. The lower values occur in the hump speed region, around FnL=O.S. For slightly higher Froude numbers, the interaction efficiencies adopt values in between 1.0 and 1.15 (see also Fig. 3.24). (Section 3.4)

The resistance increment of the hull due to the jet action is dominated by pressure drag. For Froude numbers below approx. 1, this pressure drag is largely governed by the transom sinkage. For higher Froude numbers the trim angle becomes more important. The increasing importance of the forward sinkage is likely to be caused by the growing importance of spray drag from the forebody. (Section 4.2)

There is no intake drag for a flush type intake operating in a potential tiow. The viscous drag of a representative intake appears to be negligible from wake survey measurements.It can thus be concluded that a reasonably designed waterjet intake does not experience a drag force. (Sections 2.2 and 4.1.2)

There is no net contribution by the intake induced flow on the total lift force acting on the jet-hull system, provided the area around the flush intake opening is sufficiently large. (Section 2.2.4)

The net induced lift force that is obtained from free stream considerations by integrating the loss of lift due to the absence of plate area behind the intake lip, does not explain the experimentally observed trim and sinkage. As a consequence, the pressure distribution of the combined waterjet-hull system is not adequately represented by the sum of pressures of both individual systems in their free stream condition. (Section 4.1.2)

The sharp peak in thrust deduction fraction t as a function of Froude number is caused by the clearing of the transom stem. This is caused by the difference in water column present at the nozzle and the projected nozzle positionat the stern. The effectisquantified by t1. This contribution is also noticeable in the overall efficiency. If this contribution is to be obtained explicitly from propulsion tests, average static pressures should be measured in the nozzle discharge and at the projected nozzle area at the transom during the propulsion and resistance tests respectively. (Section 4.3.2)

233 Chapter 5 Conclusions and recommendations

21. The gravity acceleration typicallyincreasesthenet thrust with a contribution of 0(1%) for a given flow rate. Consequently, it reduces the power requirement by the same amount. The effect is quantified by t. (Section 4.3.2)

234 Appendix i Al Derivation of relations for ideal efficiency

In the derivation of relations for the ideal efficiency î, we will consider a waterjet unit operating in a free stream condition. This condition is defined as the condition where the jet system operates in an undisturbed flow with uniform velocity U0 in x-direction. The centre of the nozzle area is situated on the free surface. The intake plane AD is situated in the horizontal x-y plane (see Fig. 2.1).

We will consider Control Volume D, defined by the points ABCFF'A as a model of the jet system. The part CD of the intake lip, exposed to the external flow is included in the jet system. A possible force in x-direction, acting upon CD, contributes therefore to the net thrust production by the jet system.

The ideal efficiency is generally defined as the ratio of the work done by the jet's thrust per unit time (effective thrust powerTE) and the required hydraulic power JSEin a potential flow: T0U0 -t10) (All) - JSE0

where Tg =gross thrust t1 =jet system's thrust deduction fraction

235 Appendix 1

U0 =free stream velocity JsE =effective jet system power (hydraulic power) subscript O indicates free stream conditions.

This definition corresponds tothe similar rdefinition used inpropeller hydrodynamics.

It is demonstrated in Chapter 2 that the effective thrust power in free stream conditions for control volume D is identical to the thrust power for control volume A (II'CFF'I in Fig. 2.1). The same holds for the effective jet system power JSE The ideal efficiency can consequently be written as: TgooUo (Al.2) - D ' iSEO

where Tg =gross thrust for control volume A.

It is also demonstrated in Chapter 2 that the gross thrust Tgis identical to the net thrust Tnet delivered by the jet system.

The gross thrust Tgcan be found from a momentum consideration on control volume A: Tgoo = pQ(u-U0) (Al.3)

where p = mass density of fluid Q = flow rate through jet system u = mean velocity in nozzle discharge area FF'.

It is hereby assumed that the nozzle is completely effective in converting the pressure energy into kinetic energy, so that the pressure at the nozzle area equals the ambient pressure p0, provided the jet is discharged in air. Should this not be the case, the mean nozzle velocity should be replaced by the mean jet velocity that occurs in the vena contracta. Consequently, the jet area in this vena contracta should be used instead of the nozzle area.

The effective jet system powerJ5E canbe found from an energy consideration on control volume A:

236 Derivation of relations for ideal efficiency

JSE=Q±p(u,U) (Al.4)

If we define the nozzle velocity ratio as: u NVR = _-- (Al.5) U0

we can rewrite eq. Al.2 into its often quoted form:

2 nl = (A1.6)

The disadvantage of this form is that the NVR value needs to be computed from the required net thrust Tnet and the nozzle discharge area A. A direct relation between the ideal efficiency and these geometrical parameters is found by defining a thrust loading coefficient CTfl, according to:

Tgoo n (Al.7) -p UA,1

The relation between this thrust loading coefficient CT and the nozzle velocity ratio NVR is given through the momentum balance over control volume A (eq. Al.3). In addition, the conservation law of mass provides a relation between flow rate Q and nozzle velocity u: Q = uA (A1.8)

Substituting eq. Al.8 into Al.3 yields:

NVR = !+!/l+2CT (Al.9) 22

The ideal efficiency expressed in the thrust loading coefficient is now obtained by substituting eq. AL9 into eq. A 1.6:

237 Appendix i 4 Tli = (A 1.10) 3 +/i +2cm

23 Appendix 2 A2 Expressions for the computation ofCmandCe

The momentum and energy coefficientsC,17and Ce have a simple relation with the generally used displacement, momentum andenergy thicknesses in boundary layer theory. Provided the intake height exceeds the boundary layer thickness O (h>O), the following relations can be found:

02 Cm forhO (A2. 1) h-01 and

2 03 c (A2.2) e = 1-forh0 where the displacement thickness is defined as

= (A2.3) o the momentum thickness O as

239 Appendix 2

=J(l-)_dz (A2.4) - o and the energy thickness Eas

= (A2.5)

If the boundary layer velocity profile can be represented by the n-tb power law, simple expressions for c,and Ce can be found as a function of the power n, and the flow rate ratio QIQ111. The flow rate Qbl denotes the flow rate that can be absorbed from the complete boundary layer. The flow rate ratio shows the following relation with the height over which the flow is absorbed by the intake:

17 h for h (A2.6) Qbl and

h n for h (A2.7)

The boundary layer flow rate can be obtained from

Qbl =Uw(6-1) (A2.8) where

= (A2.9) n+i

The following relations for cm can be derived:

(A2. 10) Cm for h6 ?2±2Qbl

240 Expressions for the computation of C1 and and

(A2.1l) Cm=i -__(.) forh n+2 Q

Similarly, the following relations for Ce are found:

2 2 n+lQ)fl+1 (A2.12) C for h e n+3Qbl and

c2 =i for h (A2.13) flThj ?

241 This page intentionally left blank Appendix 3

A3 Outline of uncertainty analysis A3-1 Introduction

This appendix provides a summary of the uncertainty analysis, as used in the validation of experimental or numerical procedures throughout this work. The contents are based on the report of the Validation Panel of the 19th ITTC (Lin et al. [19901), to which frequent reference will be made.

The following concepts are of importance for a good understanding of uncertainty:

'Accuracy' is the qualitative expression for the closeness of a measured value to the true value. The quantitative expression of accuracy should be in terms of uncertainty. Good accuracy implies small uncertainty. 'Uncertainty analysis' is the means of quantifying and expressing 'how valid' the method (measurement, calculation etc.) is in estimating the required true value. A complete uncertainty analysis would define the probability distribution that the error (true value - estimate produced by the method) could take. Inevitably, it will often be necessary to deal with 'partial' validation and uncertainty analysis applied to only parts of the total method. Such activities may be perfectly acceptable, providing the basis and assumptions are clearly defined. 'Repeatability of a measurement' is the quantitative expression of the closeness of agreement between successive measurements of the same value of the same quantity carried out by the same method with the same measuring instrument at the same location at appropriately short intervals

243 Appendix 3

of time. s 'Repeatabilityof a measuringinstrument'isthequantitywhich characterizes the ability of a measuring instrument to give identical indications or responses for repeated applications of the same value of the quantity measured under stated conditions of use. s 'Linearity of a meter'isthe deviation (within preset limits) of a flowmeter's performance from the ideal straight line relationship between meter output and flow rate. s 'Validation' refers to the total process of confirming that the estimate (modeltest,numerical calculation,full-scale measurement, test-rig measurement, data base prediction, etc.) is properly related to the true value of the parameter in question. Validation includes all aspects from modelling assumptions, through measurement techniques and numerical methods to the production of the final estimate. s 'Verification' is to be used in a specific way to describe checking that a particular requirement inthe method is implemented correctly.In computational methods its use is to be confined to checking that the code correctly performs the solution of the chosen equation by the chosen technique. (Lin et al. [19901).

The above definitions were adopted from the BSI Guide [19911 and Kline [19851. A review of literature in the field of uncertainty analysis is presented by Lin et al. [19901. The recommendations of the validation panel to the 19th ITTC follow the lines of the ISO/ANSI standard. Abernethy and Ringhiser [19851 give further background information relativetothe development of aninternationally acceptable methodology.

A3-2 Guidelinesforuncertaintyanalysisof measurements

The objective of uncertainty analysis, is to construct an uncertainty interval for any measurement, within which the true value (by definition unknown) will lie with a chosen confidence (usually 95%, which is also adopted here).

A3-2.1 Types of error

'Only two types of error exist in a well-controlled activity: precision errors (random or repeatability), and bias errors (systematic or fixed). (The relation of these errors to the true value is illustrated in Fig. A3.1.) We need only add to the discussion that, in general, it is presumed that major mistakes and malfunctions are

244 Outline of uncertainty analysis absent from data subject to such scrutiny. If such errors do exist, they may of course contribute grossly to the two types of error and may well render the exercise meaningless. Monitoring of data and engineering judgement may be necessary to eliminate such errors, but this must be done by rational and not just careless discarding of 'rogue' or 'outlying' data points. Care is needed under the second type if it is known that the limits of bias error are not symmetric.' (Lin et al. [19901).

true true value average (JI)

measurement population bias error (B)

tota] error precision error

measured value (x)

Fig. A3. I Designation of errors

A3-2.2 Outline of methodology

The following stages are proposed by Lin et al. [19901:

- Identify all error sources. - Determine the individual precision (statistically) and bias errors (by judgement) for each source from 1. - Determine the sensitivity of each error source (from 2) to the end result. - Create the total precision uncertainty interval from 2 and 3. - Create the total bias uncertainty interval from 2 and 3. - Combine the tota! precision and bias uncertainty intervals from4and 5 respective!y

It is stressed by Lin et al. [19901 that the results of step4, 5and 6 should be declared separately.

245 I Appendix 3 A3-2.3 Calculation methods

A3-2.3.1 Elemental precision estimates (step 2)

'The object is to determine the precision index S of a particular elemental error source. S is an estimate of the standard deviation of the scatter that would be obtained if the measurement x were repeated a number of times. If an end result is influenced by k elemental measurements, x.(i_-1,k), then at this point, the object is to estimate the value S, that accompanies x Combining the k error sources follows later. If the basic measurementcan be repeated N times, then an estimate of the true' standard deviation (only obtainable from an infinite set of measurements) is available, usually called the 'experimental' standard deviation:

(x-i (A3.l) si = j=1 (N-l)

wherei,= average value of the N measurements.

The larger the value of N, the more accurate S. will be.' (Lin et al. [19901.

The precision index S. of the average value ï of a set of measurements is always less than that of an individual measurement, according to:

s s-xiv = _±. (A3.2)

A3-2.3.2 Elemental bias estimates (step 2)

The basic independent measurements x discussed in the previous section, may have a bias error in addition to the precision errors. Unfortunately, this error type is not amenable to statistical analysis. Remember that all known offsets and corrections that can be applied are assumed to have been implemented, so only residual unknown bias errors remain. Examples might include: the accuracy to which calibration coefficients can be calculated and applied; thepreci- sion with which zero settings can be made; perhaps the knowledge that a mean measurement (say force or pressure) may be biased by the intensity of fluctu-

246 Outline of uncertainty analysis ation (but having no direct measurement of the intensity); and, straying intoa computational area, perhaps the knowledge that a particular integrationor grid- based calculation tends to consistently underestimate or overestimate the 'true' value.

The limits to this bias error should be estimated with a 'confidence' level that is equivalent to 95 percent. (Note- the literature stresses that a normal human failing is to underestimate the size of these errors).' (Lin et al. [19901).

A3-2.3.3 Propagation of errors (step 3)

The parameters x that can be regarded as error sources, were already introduced in Section A3-2.3.1. The final result R of a test or prediction can be written as a function of the k independent variables x:

R = R(xl,x2,...xk) (A3.3)

For a small deviation Axt, a Taylor expansion about the point x can be written as:

2 2R R(x+Ax) = R(x)+Ax 3) (A3.4) 7?-2 x1 -.dx

The error in the result can therefore be approximated for small deviations of Ax. by:

R(x+Ax)-R(x) (A3.5)

Analogous to this result for one value of the parameterx, a similar result can be derived for the precision error of the result:

k (A3.6) result = (O1S)2 i- J where O =sensitivity

247 Appendix 3

Similarly, we can write for the bias errors:

k (A3 .7) Bresuit= (OB N i=1

If unsymmetric bias limits occur, upper and lower values for Bresultwill have to be calculated.

Instead of using the dimensional sensitivity as introduced above, itis often more convenient to use a non-dimensional sensitivity 0, relating the non- dimensional error in the result to the non-dimensional deviation in the source parameter x. Non-dimesionalizing eq. A3.6, we find:

S'it = (A3.8)

where s =non-dimensional precisionerror; Sj/i, and

(A3.9) o¡ =Löxj

A similar result is found when eq. A3.7 is non-dimensionalized.

The usefulness of the non-dimensional sensitivity 0isillustrated with the following example. Consider two transducers, giving a linear relation through the origin between the result R and the signal x

R = (A3.1O)

The coefficient a1 of transduceriis smaller than a2 of transducer 2. The dimensional sensitivity O of x for both transducers reads:

O = a (A3.11)

248 Outline of uncertainty analysis

Transducer 2 consequently shows the greater sensitivity for deviations inx, thus increasing the error in R. When we consider the non-dimensional sensitivity e; however, we find this to equal unity. This implies that both transducers show the same percentage deviation in the result for equal deviation in x, despite the differences in dimensional sensitivity 01. The non-dimensional sensitivity e; will be referred to as relative sensitivity in the following. Calculation of the sensitivity can either be done analytically or numerically.

It is emphasized that only factors with uncorrelated errors can be introduced in equations A3.6 and A3.8.

A3-2.3.4 Total uncertainty interval for precision and bias errors (steps 5 and 6)

'The random uncertainty interval is now given by:

±95t (A3.12) where M is the number of times the test is repeated and t95 is the Student's t distribution associated with 95% probability. If Sreuit is based on reliable S. values (large degree of freedom v, where v=N-1), then t95 can be approximated by 2. If relatively few samples (<30) contributed to the individual S. estimates, t95 may be larger than 2 as a result of the limited degree of freedom for each estimate. But as t95 is an overall value, requiring an 'average' degree of freedom to be attached to the final result, it needs to be weighted by the magnitude of the S values and their individual degrees of freedom v. This is done by the Welch-Satterthwaite approximation:

4 SR V result = (0S)'4 (A3.13)

in V1

The bias uncertainty interval is such that the true value of the result Rtrue lies within

R±BR (A3.14)

249 Appendix 3 or, if unsymmetric bias errors are identified:'

R BR

(Lin et aL [1990]).

A3-2.3.5 Total uncertainty (step 6)

'If a single number U is needed to express a reasonable limit of error for a given parameter, then some model for combining the bias and precision errors must be adopted, where the interval x±U (A3. 16)

represents a band within which the true value of the parameter is expected to lie for a specified coverage.

While no rigorous confidence level can be associated with the uncertainty U, coverages analogous to 95 percent and 99 percent confidence levels can be given for two recommended uncertainty models respectively: (A3.17) = URRSS /B+(tSR)2@ 95%

or URADD =BR+rSR@ 99% (A3.18)

Note that upper and lower limits should be constructed using B and Bjif these are different.'

A3-3 List of symbols

B - bias error of parameter x M - number of repeat tests N - number of measurements of parameter x R - result of a test or calculation S. - precision error (or index) or 'experimental' standard deviation of parameter x

250 Outline of uncertainty analysis s non-dimensional precision error (or index) or experimental standard deviation of parameter x U - uncertainty limit pertinent to a chosen uncertainty level (mostly 95 or 99%) - average value of parameter x- x, - j-th value of parameter x- O sensitivity for error in result due to error in x non-dimensional or relative sensitivity

251 This page intentionally left blank

252 Appendix 4 A4 Description of facilities and models used for experiments

253 Appendix 4 A4-1 Deep Water Towing Tank

Basin Towing carriage Drive wheels Harbour Passage to workshop

105m

DIMENSIONS 250 mx 10.5 m, 5.5 m deep. CARRIAGE Manned, motor driven, four drive wheels, four pairs of horizontal guide wheels. TYPE OF DRIVE SYSTEM AND TOTAL POWER Thyrister controlled power Supply. 4x 46kW. MAXIMUM CARRIAGE SPEED Bm/o. OTHER CAPABILITIES VerricaI/horzontal PMM. wind-force dynarnorrreter set-up.

INSTRUMENTATION Dynamometers with strain gauge transducers in propeller hub. wind-force dynamometer, 6-component force balance dynamometer, 5-hole pitot tube, laser doppler velocity scanner, underwater photographic and video tape Systems, pressure transducer for wave cut experiments. MODEL SIZE RANGE 1.5- 10m.

251 Description of facilities and models used for experiments A4-2 HAMILTON Jet Test Boat

The following table presents the main particulars of the full scale test boat at the parent condition LCG:

Description Symbol Magnitude Unit

Length between perpendiculars (Fr-i - 8) 7.27 m Length on waterline LWL 6.27 m Hull beam at draught moulded at midship B 2.226 m Draught moulded on FP TF 0.386 ni Draught moulded on AP TA 0.424 m Displacement volume moulded y 2.798 m3 Displacement mass in sea water 2.868 t Wetted surface area bare hull at rest S 13.264 m2 LCB position aft of frame 8 LCB 4.58 m Slenderness ratio L1v"3 5.16 - Length-beam ratio LJIB 3.27 - Beam-draught ratio B/TM 5.50 -

Fig. A4. I presents the hull's body plan and stem and stern contours. The jet model configuration as built in the hull model is presented in Fig. A4.2. The asp position as used in the first propulsion test (Test No. 48820) is presented in Fig. A4.3. Finally, the block marker distribution used for a precise determination of the wetted surface at speed is presented in Fig. A4.4.

A plywood model has been manufactured according to a scale factor of 3.00. The model was designated model No. 7386.

255 Appendix 4

FR. -1= AP FR. 8 = FP

Fig. A4. i Body plan, stem and stern profiles and sectional area curve of model

ofship

A B fr. O C fr .1

A B fr.O

Fig. A4.2 Waterjet intake opening i for model Dimensions are given in mm for ship

256 Description of facilities and models used for experiments

q N

Fig. A4.3 Position of ASP for ship model No. 7386 Dimensions are given in mm for ship ra w-r

Fig. A4.4 Block marker distribution of ship model No. 7386

257 Appendix 5

AS Description of potential flow panel codes 'HESM' and 'DAWSON' A5-1 Introduction

The MARIN computer codes 'HESM' and 'DAWSON' solve the potential flow problem for an arbitrary 3D body. HESM solves the potential flow equations for a fluid without free surface. DAWSON can be regarded as an extension of the former code, including free surface conditions. The methods are based on work by Hess and Smith [1964] and Dawson [1977] respectively.

A5-2 HESM

Mathematical statement of problem

The first problem considered is that of a steady flow of an unbounded perfect fluid about a 3D body. The state parameters describing the flow (V and p for an incompressible potential flow) can be obtained once the potential function cIin the fluid domain R' is known. The fluid velocity vector V at any point can then be expressed as: (A5.l)

259 Appendix 5 The unknown potential function ct must satisfy three conditions in an unbounded flow. It must satisfy Laplace's equation in the external fluid domain R' (outside the body), it must have a zero normal derivative on the body surface S, and it must approach the uniform stream potential at infinity. Symbolically:

A0 mR' (A5.2) =0 onS (A5.3)

- (A5.4)

The above equations are conveniently solved when the total potential function cI is written as the sum of the free stream potential pand the perturbation potential due to the body :

= (p00+(p (A5.5)

In order to solve the perturbation potential (p, it will be represented as the potential of a source density distribution over the surface S. The potential at a point P in space with coordinates x,y,z due to a unit point source located at a point q on the surface S is 1/r(P,q), where r(P,q) is the distance between the points P and q. Accordingly, the perturbation potential at P due to the complete source distribution over the body S is: (q) (p(x,y,z) = dS (A5.6) r(P,q)

It can be demonstrated that the above equation satisfies the conditions given by eq. (A5.2) and (A5.4) for any source distribution. The source distribution(q) is consequently determined from the normal derivative boundary condition eq. (AS .3). An expression for the normal derivative of the potential function is found from the limit where the point P in the fluid approaches the point p on the surface. Careful evaluation of this limit is required because the integrand in the right-hand side term becomes singular if the surface is approached. The limit of the normal derivative is found to consist of two terms:

260 Description of potential flow panel codes HESMand DAWSON

I = )(q)dS (A5.7) òn r(p,q)

The first term on the right-hand side is the contribution to the normal derivative of the portion of S in the immediate neighbourhood ofp, the second term is the contribution of the remainder of S. Substituting the above equation in eq. (3), yields an integral equation forthat needs to be solved:

2TccY(p)-( )(q)dS = -(p).V (A5.8) r(p,q)

Numerical method of solution

The basic problem in the method is the numerical solution of eq. A5.8. This requires an approximate evaluation of the relevant integral and an approximate representation of the body surface. Of several solutions possible Hess and Smith [1964] choose a method that consists of an approximation of the body surface by a large number of plane quadrilateral elements. The source density over each element is assumed constant. Eq. A5.8 can now be replaced by a set of linear algebraic equations from which the value of each source element is to be solved.

On each element one point is selected where the fluid velocity normal to the element is required to vanish and where tangential velocity and pressure are eventually evaluated. This point is taken as the point where the element itself has no effect on the tangential velocity, i.e. the point where the element gives rise to no velocity in its own plane. This point is designated the 'null point' of the element.

Once the values of the source density on the quadrilateral elements have been obtained, the fluid velocities at points away from the body surface may also be calculated. The velocities at points on the body surface other than the null points cannot be calculated directly, but must be obtained by interpolation of the velocities at the null points. A similar strategy is required for points just off the body surface. This restriction is imposed by the form of the approximation of the body surface. For example, direct calculation by summing the contributions of the quadrilateral elements gives an infinite velocity at a point on an edge of one of the elements.

261 Appendix 5

Algebraic equations can also be derived for the velocity induced by a quadrilateral source element in an arbitrary point in the fluid domain. Because of the complex character of these equations, Hess and Smith approximate the induced velocities with a multipole expansion through the second order if the point P is sufficiently far from the relevant source element. Such an expansion is known to converge if the point P is farther from the centroid of the source element than any point of the quadrilateral is. The designation 'multipole expansion' arises from the fact that the various terms in this expansion may be interpreted as the potentials of point singularities of various orders, located at the elements centroid.

By applying the above approximation only for points that are farther from the surface than a given criterion, Hess and Smith demonstrate that the additional loss of accuracy is negligible compared to the basic approximation of the body surface by plane quadrilateral elements with constant values of source density.

A5-3 DAWSON and RAPID

If the fluid is bounded by a free surface, a wave pattern on this surface occurs when the body under consideration translates through or in the vicinity of this surface. This problem gives rise to additional 'free surface conditions' (FSC's), that need to be fulfilled apart from the conditions for an unbounded potential flow (see Section A5-2).

On the free surface, a kinematic boundary condition is to be satisfied, requiring that the flow is tangential to the wave surface:

= O on free suiface y=T (A5.9)

The dynamic boundary condition ensures that the pressure in the flow at the free surface equals the atmospheric pressure:

= O (A5.lO)

The most important difference between the DAWSON and RAPID code is the way in which the free surface conditions are modelled. In linearized methods, such as applied in DAWSON, the boundary conditions are applied at the undisturbed free surface. In the non-linear method applied in RAPID, the boundary conditions are satisfied on the actual free surface. Additionally, the boundary conditions on the hull form are satisfied also above the undisturbed free surface.

262 Appendix 6

A6 Description of performance prediction code 'PLANE' A6-1 Introduction

The MARIN computer code 'PLANE' determines the equilibrium position of the hull and corresponding drag, lift and thrust forces fora prismatic planing hull form. The method is based on the work by Savitsky [1964].

A6-2 Statement of problem

To determine the required power or thrust ofa prismatic planing hull form for a given speed, the equations of motion in three degrees of freedomare solved, so that equilibrium is attained in vertical, horizontal and pitch motion. The relevant forces and their points of application are identified in Fig. A6. 1.

From a systematic series of tests on various prismatic hull forms, Savitsky has derived empirical relations for lift, drag, wetted area, centre ofpressure and porpoising stability limits as a function of speed, trim angle, deadrise angle and loading.

With these empirical relations, the three equations of motioncan be solved, rendering the hull's trim angle. Once the trim angle is known, the totaldrag and the hull's sinkage can be determined.

263 Appendix 6

CoB =Centre of Buoyancy CoF =Centre of Flotation CoG =Centre of Gravity FT =Towing force R1=Total drag A =Displacement weight V =Displacement volume

Fig. A6.1 Force acting on the hull-jet system as modelled in the computerprogram PLANE

A6-3 Limitations

It is to be emphasized that the empirical planing equations are only for hull forms having a constant deadrise, constant beam and constant trim angle over the entire wetted planing area. Most practical planing hull designs do have some longitudinal variation in these dimensions. According to Savitsky, deadrise angle and beam should in these cases be taken as the average in the stagnation line area of the hull. The trim angle should be taken as the average of the keel and chine buttock lines. It should also be noted that the empirical relations are not applicable to the lower speed range, where the forward pulled-up bow sections of the hull become wetted. In this situation, strong variations in deadrise and buttock lines with length occur.

To extend the prediction model to the lower speed range (below FnL 0.9), an empirical correction proposed by Blount and Fox has been added to the program (Blount [1976]). This so-called M-factor is a simple correction factor to force the resistance curve at the experimental curve in the hump speed region (FnL 0.5- 0.9).

264 Appendix 7

A7 Description of LDV experiments in the MARIN large cavitation tunnel

The objective of the LDV experiments on a waterjet intake was to obtain a better knowledge about the free stream characteristics of an intake, and to obtain validation materialfor CFD computations on anintake. To thisend, a representative intake geometry was mounted to the sidewall of the tunnel. The LDV measurements were conducted for two operational conditions. One being representative for design conditions (IVR1=OE6), the other being representative for off-design conditions, such as occur in the hump speed region (IVR=O.9).

Description of model

A geometric description of the intake model is given in Fig. A7.l. The flush intake is characterized by sharp edged and parallel side walls in the bottom plane. Furthermore relatively small radii of curvature are used for the intake lip and the transition from bottom plane into intake ramp.

Description of test set-up

The intake was mounted on the sidewall of the MARIN large cavitation tunnel. A waterjet pump was fitted to the intake, followed by a retour conduit, leading the ingested flow back into the tunnel. A calibrated asp was used to measure the flow rate through the retour conduit.

265 Appendix 7 Fig. A7.2 shows a sketch of the LDV head, mounted on top of the tunnel. The laser beams were transmitted under a fixed angle of approx. 30 deg. Variations in transverse position of the measuring volume were obtained through vertical translations of the laser head. The measuring volume that could be covered in this way is indicated in the figure.

Prior to the tests, the boundary layer velocity profile was measured at three longitudinal positions ahead of the intake Leading Edge LE (see Fig. A7.3). At the two foremost positions, measurements were done in three transverse sta- tions. The boundary layer profile measurements were done both with and without turbulence stimulation strip (Fig. A7.4). This strip had a width of 3 times the geometrical intake width, and was situated 1.5 times the intake length ahead of the intake Leading Edge. Based on these measurements, it was decided to do the actual LDV tests with the turbulence stimulation strip mounted. The resulting velocity profile at 70% of the intake length ahead of the intake LE is presented in Fig. A7.5 for three transverse positions. It appears that the boundary layer at the centreline of the intake is consequently thicker than at the other two locations. This phenomenon is ascribed to the wake of one of the guiding vanes of the tunnel, upstream of the intake.

Review of tests

The velocity distribution has been measured in a number of 2D planes, indicated in Fig. A7. 1. The velocity distribution has been measured for two operational conditions of the intake, viz. IVR0.62 and 0.94. The first condition is representative for design speeds, the second for conditions where the propulsor is more heavily loaded, such as for instance occurs around hump speeds (FnL=O.S). Apart from these LDV measurements, the pressures in the initial part of the intake were measured at the centreline intake. The positions of the pressure transducers are also indicated in Fig. A7.1.

266 Description of LDV experiments in the MARIN large cavitation tunnel

S I // * I-II _44all/li-> > llviIIIIlI1 VIlT4'uir-tiiiiiJ1 aiIir >

u o E

E L E > = LU o o uo E /ÏIIt m'ii -o

Fig. A7. I Intake geometry analysed by HESM computations and LDV measurements

267 Appendix 7

A = 150.0 B = 94.0 optical head

window 300

176.0

,'1aser beams

z yJ

Fig. A7.2Limitations in the measuring volume Dimensions are given in rum

268 Description of LDV experiments in the MARIN large cavitation tunnel

U J- reference point

GL...Bj

GL...A_1 GL..B_1 E Q GL. B 2 GL...A_2 GE. .B 3 Q - GL...A_3

l(A'Dfig.2.1) = 339 mm Fig. A7.3 Designation of strips for boundary layer measurements LE. intake

518mm

40 mm

30mm

Fig. A7.4 Position and geometry of turbulence stimulation strips

269 Appendix 7

Strip GL3AG-1 Strip GL3AG-2

1.0 1.0

0.9 0.9

0.8 0.8 I

0.7 0.7 0 2040 60 80100 0 2040 60 80100 z [mm] z [mm]

Strip GL3AG-3

1.0 bi. parameters

0.9 n=9 Cvp = 1.02 0.8/

0.7 0 2040 6080100 z [mm]

Fig. A7.5Boundary layer velocity profiles Uo = 3 m/s, stimulated turbulence position X = -667.5 mro

270 References

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ROY, S.M.; "The evolution of the modern waterjet marine propulsor unit", International Symposium on Waterjet Propulsion, RINA, Dec. 1994, London.

SAVITSKY, D. et al., "Status of hydrodvnamic technology as related to model tests of high-speed marine vehicles", David Taylor Naval Ship R&D Center Report DTNSRDC-81/026, AD A102 717, July 1981.

SCHMIECHEN, M.;"Performancecriteriaof puise-jetpropellers",7th Symposium on Naval Hydrodynamics, Rome, August 25-30, 1968.

SCHM LECHEN, M.; "Uber die Bewertung hydromechanischer Propulsions- systeme", Schiffstechnik, Band 17, Heft 89, 1970.

275 References SHERMAN, P.M. and LINCOLN, F.W.; "Ram inlet systems for waterjet propulsors", AIAA 2nd Advanced Marine Vehicles and Propulsion Meeting, Paper No. 69-418, May 21-23, 1969, Seattle.

SPANNHAKE, W.; "Comments and calculations on the problem of the condenser scoop", David Taylor Model Basin Report No. 790, Washington, Oct. 1951.

SVENSSON, R.; "Experience with the KaMeWa waterjet propulsion system", AIAA Conference, Paper No. 89-1440-CP, Arlington, June 1989.

TASAKI, R., SUGAWARA, K., MORI, H. and SATO, R.;"Peifor,nance prediction and design of duct systems for MHDS Yamato-]",1991, source unknown.

TERWISGA, T. VAN; "The effect of waterjet-hull interaction on thrust and propulsiveefficiency",Proceedings of theFAST'91Conference,Vol.2, Trondheim, June 1991.

TERWISGA, T. VAN; "A theoretical model for the description of the powering characteristics of waterjet-hull systems", MARIN Report No. 52227-2-SRD, Dec. 1992.

TOOGOOD, T. and HAYES, J.; "Forceing Water by Bellowes ....., English Patent No. 132, 1661.

WILSON, M .B.; "A sun'ey of propulsion-vehicle interactions on high-peiformance marine craft", Proceedings of 18th ATTC, Aug. 23-25, 1977.

References of Chapter 2

ALEXANDER, K.V. and TERWISGA, T. VAN; "Recent work on waterjet-hull interaction effects", 9th International High Speed Surface Craft Conference, Singapore, March 1993.

BOWEN, G.L.; "The net thrust relationship for waterjet-propelled craft", Hovering Craft Hydrofoil 10, Jan. 1971, pp.14-15.

DYNE, G. and LINDELL, P.; "Waterjet testing in the SSPA towing tank", RINA International Symposium on Waterjet Propulsion - Latest Developments, London, Dec. 1994.

276 Chapter 2/3 ETTER, R.J., KRISHNAMOORTHY, V. and SCHERER, J.O.; "Model testing of waterjet propelled craft", Proceedings of the 19th ATTC, 1980.

GENT, W. VAN; "Pressure distribution and cumulative force on streamline contour in sink flow", MARIN Internal Note, May 1993.

HAMILTON, J.O.F.; Verbal Communications, June 1994.

ITTC 1987; Report of the High Speed Marine Vehicle Committee, 18th Interna- tional Towing Tank Conference 1987, pp. 304-313.

MILLER. E.R. jr.; "Waterjet propulsion system peiformance analysis", Proceed- ings of the 18th ATTC, 1977.

MOSS MAN, E.A. and RANDALL, L.M.; "An experimental investigation of the design variables for NACA RM No. A7130", Jan. 1948.

SVENSSON, R.; "Experience with the KaMeWa waterjet propulsion system", AIAA Conference, Paper No. 89-1440-CP. Arlington, June 1989.

TERWISGA, T. VAN; "A theoretical model for the powering characteristics of waterjet-hull systems", FAST'93 Conference, Yokohama, Dec. 1993.

WEINBLUM, G.P.; "The thrust deduction", American Society of Naval Engin- eers, Vol. 63, 1951.

WILSON, M.B.: "A survey of propulsion-vehicle interactions on high-pe,formance marine craft", Proceedings of 18th ATTC, Aug. 23-25, 1977.

References of Chapter 3

ABERNETHY, RB.. BENEDICT, R.P.and DOWDELL, R.B. "ASME measurement uncertainty", Journal of Fluids Engineering, Vol. 107, June 1985.

ALEXANDER, K.V., COOP, H. and TERWISGA, T. VAN; "Waterjet-hull interaction:Recent experimental results", SNAME Annual Meeting, New Orleans, Nov. 1994.

B ARFORD, N.C.; "Experimental measurements: Precision, error and truth ", 2nd edition, John Wiley and Sons, 1987.

277 References

BOS, M.G.; "Discharge measurement structures", third edition, ILRI Publication No. 20, 1990.

BRENNEN, CE.; "Hydrodynamics of pumps", Concepts ETI, Inc. and Oxford University Press, 1994.

BSI Guide BS7405: "Guide to selection and application of jlowmeters for the measurement of fluid flow in closed conduits", 1991.

DYNE, G. and LINDELL, P.;"Waterjet testing in the SSPA towing tank", International Symposium on Waterjet Propulsion, Royal Institution of Naval Architects, London, Dec. 1994.

ENGLISH, J.W.;"Ship model propulsion experiments analysis and random uncertainly", preprint published for written discussion, The Institute of Marine Engineers, Jan. 1995.

FURNESS, R. A.;"Modern flowmeter applications ",KIVI/NIRIA studiedag 'Flowmeting nu en morgen', Amsterdam, Oct. 31, 1990.

HOERNER, S.F.; "Fluid dynamic drag", published by the author, 1965.

ITTC 1978; Report of the Peiforinance Committee, 15th International Towing Tank Conference, The Hague, The Netherlands.

ITTC 1987; Report of the High Speed Marine Vehicle Committee,18th International Towing Tank Conference 1987, pp. 304-313.

ITTC 1993; Report of the High Speed Marine Vehicles Committee, 20th International Towing Tank Conference, San Francisco, 1993.

LIN, W.C. et al.; "Report of the panel on validation procedures", 19th ITTC, Madrid, Sept. 1990.

WILLEMSEN, H. and TERWISGA, T. VAN; "liking van de Thomson goot als instrument voor het meten van debieten", MARIN Report No. 52227-1-SRD, Dec. 1992 (proprietary, in Dutch).

278 Chapter 4 References of Chapter 4

ALEXANDER, K.V., COOP, H. and TERWISGA, T. VAN; "Waterjet-hull interaction: Recent experimental results", SNAME Annual Meeting, New Orleans, Nov. 1994.

ALTMETER, iM.; "Resistance prediction of planing hulls: State of the art", Marine Technology, Vol. 30, No. 4, Oct. 1993.

ARCAND, L. and COMOLLI, C.R.; "Waterjet propulsion for high speed ships", Proceedings of the AIAA/SNAME Advance Marine Vehicles Meeting, Paper No. 67-350, Norfolk, Virginia.

ETTER, R.J., KRISHNAMOORTHY, V. and SCHERER, JO.; "Model testing of waterjet propelled craft", Proceedings of the 19th ATTC, 1980.

HESS, J.L. and SMITH, A.M.O.; "Calculation of potential flow about arbitrary bodies", Progress in Aeronautical Sciences, Vol. 8, Pergamon Press, 1966.

HEWINS, E.F. and REILLY, J.R.; "Condenser scoop design", Transactions SNAME, 1940, pp. 277-304.

HOSHINO, T. and BABA, E.; "Self propulsion test of a se,ni-displacement craft model with a waterjet propulsor", Journal of the Society of Naval Architects of Japan, Vol. 155, June 1984.

ITTC1987; Report of the High Speed Marine Vehicle Committee,18th International Towing Tank Conference 1987.

KASHIWADANI, T.; "The study on the configuration of waterjet inlet (ist Report)", Journal of the Society of Naval Architects of Japan, Vol. 157, 1985.

KASHIWADANI, T.; "The study on the configuration of waterjet inlet (2nd Report)", Journal of the Society of Naval Architects of Japan, Vol. 159, 1986.

KIM, K.S., HONG, S.Y. and CHOI, H.S.; "Analysis of the wate rjet-propelled ship .tlow by a higher order boundary element method", NAV'94 International Conference on Ship and Marine Research, Rome, Oct. 1994.

LATORRE. R. and KAWAMURA, T.; "CFD investigation of trim influence on waterjet pressure distribution and cavitation ",International Symposium on Cavitation CAV95, Deauville, May 1995.

279 References

MOSSMAN, E.A. and RANDALL, L.M.; "An experimental investigation of the design variables for NACA RM No. A7]30", Jan. 1948.

RAVEN, H.C.; "Nonlinear ship wave calculations using the RAPID method", 6th International Conference on Numerical Ship Hydrodynamics, Iowa City, August 1993.

SCHLICHTING, H.; "Boundary layer theory", 7th edition, McGraw-Hill Book Company, 1979.

SPANNHAKE, W.; "Comments and calculations on the problem of the condenser scoop", David Taylor Model Basin Report No. 790, Washington, Oct. 1951.

SVENSSON, R.; "Experience with the KaMeWa waterjet propulsion system", AIAA Conference, Paper No. 89-1440-CP, Arlington, June 1989.

References of Appendix 3

ABERNETHY, R.B.,BENEDICT,R.P.and DOWDELL, R.B.;"ASME measurement uncertainty", Journal of Fluids Engineering, Vol. 107, June 1985.

ABERNETHY, R.B.and RINGHISER,B.;"TheHistory andstatistical developmentofthenew ASME-SAE-AIAA-ISO measurementuncertainty methodology", AIAA-85- 1403, 1985.

BSI Guide to "Selection and application offlowmeters for the measurement offluid flow in closed conduits", British Standard 7405, 1991.

BOS, M.G. et al.; "Discharge measurement structures", 3rd revised edition, ILRI publication 20, Wageningen 1989.

LIN, W.C. et al.; "Report of the panel on validation procedures", 19th ITTC, Madrid, Sept. 1990.

KLINE,S.J.;"The purposes of uncertaintyanalysis",Journalof Fluids Engineering, Vol. 107, pp. 153-160, 1985.

280 Appendix 5/6 References of Appendix 5

HESS J.L. and SMITH, A.M.O.; "Calculation of nonlifting potential flow about arbitrary three-dimensional bodies", Journal of Ship Research, Sept. 1964.

RAVEN, H.C.; "Adequacy of free suiface conditions for the wave resistance problem", 18th Symposium on Naval Hydrodynamics, Washington, 1991.

RAVEN, H.C.; "Nonlinear ship wave calculations using the RAPID method", 6th International Conference on Numerical Ship Hydrodynamics', Iowa City, August 1993.

DAWSON, C.W.; A practical computer method for solving ship-wave problems". Second International Conference on Ship Hydrodynamics, Berkeley, 1977.

References of Appendix 6

BLOUNT, D.L.; "Small-craft power prediction", Marine Technology, Vol. 13, No. 1, Jan. 1976.

SAVITSKY, D.; "Hydrodvnamic design of planing hulls ", Marine Technology, Oct. 1964.

281 This page intentionally left blank

282 Nomenclature

A control surface

A intake area (default: area lin Fig. 2.1)

A1 intake throat area (area 5 in Fig. 2.1)

A,1 nozzle area (area 8 in Fig. 2.1) Ap propeller disk area

AT1 transom area below undisturbed free surface A3 projected intake area in bottom plane (Fig. 2.1) B. bias error of parameter x (Appendix 3) b non-dimensional bias error of parameter x (Appendix 3)

CDj intake drag coefficient; CDj=D/(pQU0) CF mean frictional drag coefficient

CL lift coefficient; CL=II(pQU0) pressure coefficient; C13 = I

CPh hull induced pressure coefficient CQ flow rate coefficient; CQ=Q/(U0w)

GRey residual drag coefficient; GR=RR/(½p U)

CT total drag coefficient; CT=Rl/('½pUS)

283 Nomenclature

CTfl thrust loading coefficient; CTfl=T/(½PUAfl) CT propeller thrust loading coefficient;CTp=Tpropelle/(½PUAp) CTr transom drag coefficient; CTr=RT/(½PUS) C wavemaking drag coefficient; Cw=Rv/('/2pUS) ce energy velocity coefficient due to boundary layer velocity distribution (Appendix 2)

Cm momentum velocity coefficient due to boundary layer velocity distribution (Appendix 2)

Cmn momentum velocity coefficient in nozzle discharge area potential flow velocity coefficient; cV/)= U/U0

Cweir calibrated weir coefficient D diameter or impeller diameter D. intake drag D nozzle diameter Dp differential pressure dz change in rise of hull due to waterjet action dz change in trim angle of hull due to waterjet action e total energy per unit mass e1 internal energy per unit mass ekfl kinetic energy per unit mass; ekfl=½u2 e0 potential energy per unit mass; e0=W F force

FD residual pulling force on model to compensate for scale effect in hull resistance during propulsion test F pressure force

FXbp pulling force experienced by hull-jet system in bollard pull condition (acting in x-direction) FT towing force applied to model during propulsion or resistance test

284 Nomenclature

Fxmeas measured pulling force acting in x-direction

Fxpiate measured force on 'stern' plate acting in x-direction

Fznet net force in z-direction acting on hull-jet system FnL Froude number based on waterline length f effective width factor intake; f=w/w g gravity acceleration component in i-direction waterjet system head H pump head

Ii height over which the flow is ingested h1 geometric height of intake throat cross section

Ii, maximum height of imaginary intake area

IVR Intake Velocity Ratio at some intake; default IVR=i71/U0 (see Fig.

2.1)

JVR1 Intake Velocity Ratio in intake throat (area 5 in Fig. 2.1)

KH head coefficient; KH=H/(pn2D2)

KM impeller torque coefficient; KM=M/(pn2D5) KQ flow rate coeffient; KQ=Q/(nD3) L lift geometric intake length (AD in Fig. 2.1) M impeller torque

NVR Nozzle Velocity Ratio; NVR=u/U0 n impeller rotation rate n value of power law describing boundary layer velocity profile n unit normal vector component in i-direction delivered power to pump impeller effective power; PE=RBHVS P, power input

285 Nomenclature

JsE effective jet system power; PJSE=QHJS

loss power loss soute effective power output

PE effective pump power; PPE=QHP thrust power; P7_TgUo

TE effective thrust power; TETnetV p pressure (time averaged)

Q flow rate

Qbl maximum flow rate that can be obtained from the boundary layer q rate of external energy exchange per unit mass q source point

RAPP appendage drag

RBH bare hull resistance RE effective or actual hull resistance R pressure drag

RRES residual drag

RT total drag

RTR transom drag Rw wavemaking drag Rn Reynolds number of intake; Rn=UoJVRVA/v r resistance increment fraction; RBH(]+r)=T,let S total wetted surface of the hull (excluding transom area) S. precision error of parameter x (Appendix 3)

S11 rate of strain tensor (time averaged) s girth coordinate s non-dimensional precision error of parameter x- (Appendix 3) s,, distance from nozzle discharge to 'stern' plate TgT gross thrust

286 Nomenclature

Tgoo gross thrust for a control volume with the imaginary intake area infinitely far upstream, corrected for viscous losses (eq. (2.78))

Tjetx thrust from nozzle in x-direction; Tjetx_,n,.

Tm net thrust in self propulsion point model

Tnet net thrust, passed through to the hull net thrust in self propulsion point ship tbp bollard pull thrust deduction fraction; Tietx(Jtbp)'xmeas t total thrust deduction fraction; Tg(lt)=RßH jet system thrust deduction fraction; Tg(ltj)=Tnet t» jet thrust deduction accounting for force on protruding streamtube ABCD (Fig. 2.1) tj2 jet thrust deduction accounting for force acting on nozzle area A8 (Fig. 2.1) tj3 jet thrust deduction accounting for gravity force tr resistance increment fraction; Tflet(ltr)=RßH U local potential flow velocity in x-direction

URRSS uncertainty limit for 95% confidence level in result R (Appendix 3) U0 free stream velocity in x-direction or hull speed u magnitude of velocity u1,u2,u3 mean velocity components in x,y,z direction mean energy velocity in i-direction

mean momentum velocity in i-direction

mean volumetric nozzle velocity

V control volume

V, ship model speed

V ship speed w volumetric wake fraction

287 Nomenclature

We effective width of imaginary intake AB (Fig. 2.1) w geometric intake width w width bottom plating or wake survey plane

WT Taylor wake fraction used in propeller hydrodynamics x,y,z Cartesian hull-fixed coordinates x1,x2,x3 Cartesian hull-fixed coordinates (identical to x,y,z) z, sinkage of the nozzle centre relative to free stream conditions

A displacement weight of hull or hull-jet system AR change in hull resistance due to waterjet action; RE=RBH+AR

6 boundary layer thickness Kronecker delta deviation in computed sinkage relative to experimental value deviation in computed trim angle relative to experimental value boundary layer displacement thickness

62 boundary layer momentum thickness 63 boundary layer energy thickness flduct ducting efficiency; lduct= JSF/PE leí energy interaction efficiency;JSEYJSE ideal jet system efficiency; 11/=Tgo(]tjo)U/PJsEo flINT interaction efficiency; rIJNTr/((I +r)flmj) RiET jet efficiency; 1JETTg'(/PJSE jet system efficiency; lJs=JsFY'D

TlmI momentum interaction efficiency; n, first order momentum interaction efficiency; fl,7j=Tgc/Tg second order momentum interaction efficiency; loA overall efficiency; loA =F/D pump efficiency; 11 PP PP/PD

288 Nomenclature

free stream efficiency;flo=flpfldt1]J weir V-notch angle nozzle centreline inclination to x-ordinate B. sensitivity of result R for an error in dependent parameter x (Appen- dix 3) non-dimensional sensitivity or relative sensitivity (Appendix 3) p dynamic viscosity of fluid p hull speed! nozzle velocity ratio; p=U-/u

V kinematic viscosity

E.r1. Ç Cartesian material bound coordinates p specific mass of fluid standard deviation total mean stress tensor; t hull trim angle total shear stress tensor; viscous stress; Reynolds stress tensor

eki kinetic energy flux through area i momentum flux through area i in j-direction total velocity potential disturbance velocity potential potential force field w stream function

Wiliss rate of change of internal energy through dissipation

289 Nomenclature subscripts:

sequence of subscripts with flow state parameters: e.g.Uabcd where a denotes type of flux; volumetric (-), momentum (m) or energy (e) b denotes area to which it refers

C. component (e.g. x,y or z) d conditions (e.g. O for free stream) bp bollard pull condition i intake i,j,k tensor indices denoting the ordinate m model n nozzle s full scale (ship) t intake throat (area 5 in Fig. 2.1) x,y,z vector indices denoting the ordinate, hull-fixed coordinate system x',y',z' vector indices denoting the ordinate, space-fixed coordinate system vector indices denoting the ordinate, material-bound coordinate system

O free stream conditions

290 Summary

The main objective of this work is to develop and validate tools for the analysis of interaction effects in the powering characteristics of jet propelled vessels.

Despite our knowledge about the hull and the waterjet in isolated conditions, a lack in knowledge with regard to the interference between hull system and jet system seems to exist. Many discrepancies between computed and actually measured power-speed relation of the prototype vessel are ascribed to interaction. Little knowledge is available on the mechanisms and the magnitude of these effects however.

Misunderstandings in the field of jet propulsion are believed to often originate from a lack of clear definitions of concepts. It is demonstrated in Chapter 1 that a great deal of confusion can be found in the existing literature on definition and description of jet-hull interaction. Hence, this work starts with a theoretical model describing the complete waterjet-hull interaction. The effect of interaction on the hull is expressed in a hull resistance increment. The effect of interaction on the jet performance is expressed in a thrust deduction and so-called momentum and energy interaction efficiencies. The latter efficiencies account for the change in ingested momentum and energy flux due to the presence of the hull.

Although a rough procedure for model propulsion tests was provided by the ITTC in1987, this procedure was found to easily lead to large systematic errors, rendering the results of the tests doubtful. In addition, the data reduction procedure was based on an incomplete theoretical model. An improved experimental procedure based on thrust calibration through bollard pull tests is developed, together with a data reduction procedure that allows for quantification of the interaction parameters.

291 Summary Detailed computations and LDV measurements were made on the flow in the intake and aftbody region. They give insight into the validity of assumptions made in the experimental data reduction procedure. They show that a rectangular cross section of the imaginary streamtube upstream of the intake with an effective width of 1.3 times the geometric width, provides an adequate representation of the ingested flow. They also indicate that the jet system's thrust deduction fraction is not negligible in the speed range where the transom clears.

Computations were conducted with a potential flow code and a Savitsky method, aimed at a direct computation of interaction. These computations did not show a satisfactory agreement with the experimental results. An empirical prediction model based on testresultsis recommended for preliminary power-speed computations.

The present work provides a consistent set of definitions for a complete description of both the powering characteristics of the isolated hull system and jet system, and their interaction. An experimental procedure with a lower uncertainty level than hitherto published in the open literature is proposed for their quantification. The results of this work are hoped to contribute to a wider acceptation of the waterjet system and to smoother contractual negotiations, as the final performance of the hull-jet system is better predictable.

292 Acknowledgement

The more comprehensive our knowledge gets, the more teamwork is required to advance this knowledge. The present work could only be achieved through the contributionsof numerous people.Contributions whicharegratefullyac- knowledged.

I would like to thank my promotor Prof. Gert Kuiper, who has enthusiastically supported this work from the beginning. Furthermore, I am indebted to the MARIN Management Team for their permission to undertake this work and to publish the results in the form of a thesis.

Other people as well have made decisive contributions. Jouke van der Baan's enthusiasm for the subject has played a key role in the early hours of this study. Do Ligtelijn and Ubald Nienhuis have contributed greatly by allowing me the time required, despite the work load for our department they often had to negotiate. This appreciation is extended to my colleagues, whose work load will have been increased from timeto time because of this work. Harry Willemsenis acknowledged for his contribution in tediously analysing the heaps of experimental data.

Special mention is due to the contributions of various people at Hamilton Jets of New Zealand. The numerous discussions with them have greatly contributed to my understanding of the jet-hull interaction mechanism. I am furthermore indebted to their permission to use data on their test boat for this thesis. A special word of thanks is extended to Mr. Jon Hamilton. I will always remember his brain energizing thought-experiments.

A personal word of appreciation goes to the trio that prepared the manuscript for printing. The illustrations by Gerrit Radstaat and the text processing and layout work by Manette Drinóczy-Jansen and Gerard Trouerbach have made ita presentable piece of work.

Finally, I warmly thank Jacintha for keeping up with me and my frequent absent- mindedness. She did a great job in timely pulling me out of the attic. Her contribution is not only indirectly reflected in the contents of this work, but also physically present in the front cover.

293 Curriculum Vitae

Tom van Terwisga was born on October 16, 1959 in Sneek in The Netherlands. He attended secondary school at the RSG in Heerenveen, from 1972-1978. He started studying Naval Architecture at Deift University of Technology in 1978. In 1985, he finished his studies in hydrodynamics on the development of a powering prediction model for SES craft. After obtaining his master's degree, he was employed bytheMaritimeResearchInstituteNetherlands (MARIN)in Wageningen, where he worked in the R&D Department on developments in hydrodynamic tools and designs for special vessels. In 1990 he moved to the Ship Research Department where he conducted projects on high speed vessels and their propulsion.Heiscurrentlyinvolvedinresearchprojectsonpropulsor hydrodynamics.

295 X pump 7 Vp 4 z I. fixed (material) boundaries 4 Ij A intake leading edge (imaginary) variable (imaginary) boundaries in the flow EE'DCI'BCA' = lower dividing streamline = ramp= intakestagnation tangency trailingthroat point pointarea edge or outer lip tangency point Area 2 1 = A2A = dividing stream surface = imaginary intake area VolumeArea 8764 P = Vp = pump control volume = A6A7A4 = internalboudaryouter lip material area surface of pumpjet boudary control volume8 = nozzle discharge area CVB:CVA:Suitable A'DCFF'A'II'CFF'I waterjet control volumes: CVCVC: D: A'B'CFF'A'ABCFF'A Definition of jet system's control volume