Recent Developments in Marine Propeller Hydrodynamics Ddfl Ú/: # - /2.B40 /R

Lab.y.Schepbcwwkun Tecimsche hoy';scíioo Recent develoPments in marine propeller hydrodynamics DdfL ú/: # - /2.B40 /r. /:_I 7f4/ 3e.- / I97 Dr Jr \V. C. Oosierveld and Ir P. van Oossanen ¡ Netherlands Ship Model Basin, \Vageningen ¿4 1q73.

Introduction complete integration of the design willi the wake at the propeller position is obtained. A short exposition of the On looking back on a 40 year period of work in the principles of this method is given. field of ship hydrodynamics at the Netherlands Ship odcl Basin (NSMB) a number of memorable highlichts Experimental projlIer characteristics such as open- çn he discerned. Anumber of these highflghls are noted water test results are increasingly used in preliminary c!cwhere in this book. Most of these memorable propeller design and parameter studies by means of jtivities vere the result of seif-sponsoced research with high speed computers. For this purpose it is veryad- the aim to promote the efficient designing of ships. vantageous to have these experimental propeller charac- :riicuiarly intensive research has constantly been devot- teristics in the forni of polynomials or formulas. Among cd to the various aspects of ship prcpulsion, the results the well-known screw series developed by Schaifran, of which were nearly always published in well-known Gawn artd ailiers, the Wageningen B-screw series of the maeaziiies and periodicals. Netherlands Ship Model Basin are perhaps the most used. This screw series has through the years been ex- li, not the intention of this paper to review past tended and now comprises some 120 models with blade activities in the field of ship propulsion, but rather to numbers ranging from 2 to 7 and binde ai-ca ratios from rc.nsider more recent work in this field, carried out or 0.3 to 1.05. The cross-fairing of the open-water test data Fing carried out, in particular at the NSMB. by means of the computer for a Reynolds number of 2 x lO& has now been completed, and it was considered

' his paper is divided into the following four main topics: appropriate that these results should be pubhshed for the I. Theoretical propeiJer theory. first time in this paper. The thrust and torque polyrio- 2. Experimental (conventioria i) p opcller characteristics. mials given incorporate the results of some 40 years of .3. Characteristics of non-conventional propulsion open-water testing at the NSMB. ices. 4. Propdlcr testing techniques and facilities. In the chapter on non-conventional propulsion devices, particular attention is given to the characteristics of the i he state-of-the-art of sub-cavitating optimum propeller various propulsion devices. The application of non-con- theory has progressed to a stage ensuring the highest ventional propulsion devices is increasing due to the fact possible efficiency in both the free-running and wake- that modern ships sometimes demand specific propulsion ndaptcd cases. A short review of past developments in requirements which can not be obtained with the con- theoretical propeller theory particularly concerned with ventional screw propeller. The propulsion devices con- ub-cavitating optimum propellers is included in this sidered are the following: p.per.With the unmistakable trend towards higher ship - ducted propellers, sreeds and larger displacements, howcver. non-optimum - contra-rotating propellers, propl1er design in connection with securing the best - overlapping propellers, psib1e cavitation properties is becoming relativelymore - controllable pitch propellers, important. As a consequence, many research institutes - vertical axis propellers. have recently intensified workon this aspect of propeller c-:the above mentioned. ducted propellers are being theory. At the Netherlands ShipModel Basin a method increasingly applied behind large tankers. Ducted h.tbeen developed to determine overall and local propellers are therefore considered in more detail. PrOpeller geometry in accordance with obtaining maxi- Accelerating, decelerating and non-axisymetrieal nozzles mum latitude to the angle of attack. In this method are regarded.

51 Lastly, this paper deals with some recent developments Propeller Theory in the cavitation testing of propellers, both from the viewpoints of techniques and facilities. Rev/en' of past developments

Model tests are often employed to determine the best Before considering some recent progress made in propeller-afterbody configuration. The main reason for propeller theory, a survey of past developments is this is the difficulty involved in the theoretical determina- appropriate. In 1865, Rankine [3] developed the fore- tion of unsteady propeller action, cavitation, and propel- runner of momentum theory as it is known today. This ler-afterbody interaction effects when the propeller opera- theory is based on the change of momentum and the tes in a wake. related axial motion of the fluid passing through an With modern propeller theory the determination of actuator or propeller disk. [n 1889, R.E. Froude [1] unsteady propeller forces in the non-uniform velocity considerably extended this theory and it has subsequent- field can, to a certain extent, be realized. Theoretical ly become known as the Rankine - Fronde axialmornen- assessment of the cavitation properties and, in turn, the turn theory. The effects of the rotational motion of the influence of propeller cavitation on propeller action and slipstream were included by Betz [5] in 1920. This interaction effects, has not progressed that far. In conse- theory is today used in various propeller problems. The quence, model testing is particularly employed to deter- fact that it gives no indications of the geometry of the mine propeller cavitation properties, induced vibrations propeller causing the changes in the flow is a large and other adverse effects of cavitating ship screws. The drawback, and in fact the reason for it not being used in tests to determine propeller-induced vibratory forces general design problems. acting on the afterbody of a ship vere up till now performed in conventional towing tanks. In this ship The first to attempt to formulate the relation between model testing facility the effect of propeller cavitation is propeller geometry and the associated propeller thrust not taken into account. It has recently been established, and torque was W. Froude [6] in 1878. His crude blade that the effect of cavitation on the vibratory forces on element theory was the forerunner of all theories relating the ship's afterbody and appendages and on the the lift and drag of an clement of a blade to its geome- propeller itself is considerable [1, 2]. Complementary try. Later, Drzewiecki [7] considerably extended this tests with model propellers in cavitation tunnels in theory and suggested performing tests to determine the wake-simulated flows are therefore often necessary to lift and drag forces experienced by blade section forms obtain an impression of the cavitation properties of the at various angles of attack when he found that he could propeller. Actual interaction effects between propeller not calculate them. The uncertainty as to the character- and afterbody are, however, not taken into account in istics which must be assumed for such sections was, and this way, while it is found extremely difficult to simulate to a certain extent still is, an unsatisfactory feature of the required distribution of the axial and tangential such theories. Furthermore, early workers in this field wake components. These and other difficulties have led failed to recognise finite aspect ratio effects, causing the the Netherlands Ship Model Basin to construct a depres- arithmetical results obtained with this theory to be surizcd towing tank, in which the air pressure can be far from satisfactory. lowered to such an extent that ship model testing can be In consequence of the large discrepancies between the performed a the correct cavitation index. The climens- momentum theory and the blade element theory, at- ions of this towing basin are such that ship and propel- tempts were made to combine the two, and to use ler models are of a size with which it is possible to the induced velocities as determined by the momentum avoid unpredictable scale effects. theory to reduce the angle of attack in the blade element theory. In this way large differences between experiment Besides a short description of this facility, this part of and theory were avoided but duc to the still unaccount- the paper includes a review of the many problems as- ed finite aspect ratio and chordwise effects, and the still sociated with ship model testing including such subjects unknown variation of blade section characteristics with as scale effects and cavitation scaling. Reynolds number, these differences remained unacceptable, in particular for broad bladed marine propellers.

In 1907, Lanchester [8] put forward a new theory which accounted the lift of an aeroplane wing duc to the 52 development of circulation around each section in the difficulty inherent to the finite blade nunìbcrcase lies span direction. He postulated that the vortex movement in the complexity of calculating the induced velocities around such an aeroloil is continued in the fluid in the caused by the system of trailing vortices constituting a forni of vortices trailing from the ends, and in the case finite number of vortex sheets. Particular credit must be of propeller blades, passing downstrean in approxinia- paid to J3etz's paper, not only for determining the op- tely helical paths from the tips. This concept of the timum radial load distribution from the viewpoint of shedding of vortices from the tips of propeller blades efficiency, but also for being the first to successfully was shown to be true by Flamm [9] in 1909 by means of apply the Prandil vortex theory to propellers and to photographs of the wake of a propeller. Many scientists define the mathematical model concerned. subsequently endeavoured to calculate the induced velocity associated with this system of trailing vortices, With these new vortex conceptions, which in fact con- and in this regard the work of Joukowski [10] in 1912, stituted an important break-through in propeller theory, Grammel [11] in 1917 and Wood and Glauert,[12] in various importanit propeller theories were developed in 1918 should be noted. In 1918, Prandtl [13] succeeded, the years that followed. Amongst the most important is and the concept of trailing vortices became fully accept- tIte work of Glauert [15] in 1926, Pistolesi [16] in 1922 ed. Prandtl concluded to state that the behaviour of an and particularly, the work of Kawada in 1933, 1936 and element of an aerofoil of finite span can only be consid- 1939 [17, 18, 19]. Bienen and Von Karman [20] in 1924 ered the same as in two-dimensional flow when proper extended Betz's 1919 paper and performed the addit- allowance is made for the induced velocities caused by ional calculations for the case that the effects of profile the shedding of vortices from such ari aerofoil. This first drag arc included. In 1927 Betz [21] extended his work vortex theory is often referred to as a lifting line theory to the heavily loaded, free-running case. In the case of a due to the fact that a wing of finite span is replaced by heavily loadòd propeller the influence of the induced a vortex line. In this way it was possible to account for velocities on the shape of the helical vortex sheets is spanwise variations in the circulation distribution, the taken into account as well as the effects of centrifugal circulation of the vortex line at each section being put forces and of the contraction of the induced velocity equal to the chordwise integrated circulation at that components. Only in the case of the lightly loaded section. This theory is therefore not able to calculate propeller are the vortex sheets true helical surfaces. subsequent effects of the fact that the circulation around a section of a propeller blade or a wing is not concen- In 1929, Goldstein [22] successfully considered the flo\v trated at the position of the line vortex, but distributed past a finite number of true helical vortex sheets and along the chord. For moderate aspect ratios it was found obtained an expression for the ratio between the mean that the Prandtl lifting line theory was very satisfactory, circulation taken around an annulas and the circulation and this very soon led to the standard procedure in at the helical surfaces for a 2 and a 4 bladed propeller. airscrew design to use two-dimensional lift and drag From these values the ratio between the mean inflow characteristics (so-called profile characteristics) at an velocity taken around any annulas and the corres- angle of incidence corrected for the induced velocities. ponding larger inflow velocity in way of the helical For the broad bladed propeller this theory was still not vortex sheets at the position of the propeller blades was satisfactory, however. derived. The values of this ratio for various values of the propeller radius, the hydrodynaniic pitch angle and the On assuming that the trailing vortices behind a propel- number of blades have since been designated as Gold- ler blade follow helical paths with a constant angle of stein factors. A large number of these values ware advance (implying a uniform propeller inflow and that calculated by Lock and Yeatman [23] in 1935, in 1941 by the induced velocities are small, i.e. that the propeller Kramer [24], and very accurately in 1950 by Tach- is lightly loaded), and on neglecting the profile drag of mindji and Milam [25]. The Tachmindji and Milarn the blade sections, Betz [14] in 1919 succeeded in esta- values arc valid for the case of zero circulation at the blishing the best load or thrust distribution along the hub, which case is now considered as correct. blades for minimum induced drag. Due to the involved Today these Goldstein factors are extensively used, and mathematical difficulties, Betz had to assume that the often in cases where they are not applicable. They are propeller had an infinite number of blades. In an appen- strictly only valid for uniform propeller-inflow (so-called dix to Betz's paper, Prandtl establishedan approximate free running propellers), having a constant radial virtual correction to account for a finite number of blades. The pitch, i.e. the Betz optimum radial circulation distribu-

53 tion. Furthermore, none of the devised marine propeller dynamic pitch angle are a result. design methods based on the Goldstein factors are suitable for heavy screw loading. Very few recognize slip- Ludwieg and Ginzel [34] in 1944 were the first to stream contraction and the influence of the radial recognize this influence and they actually calculated pressure gradient. The most used marine propeller some correction factors with which the amount of blade design methods based on the lifting line procedure section camber could be corrected for the induced incorporating Goldstein factors are those due to Burrill curvature of the flow. These camber corrections were [26, 27] in 1943 and 1955, Lerbs [28] in 1945, Hill given in the form of a ratio between the effective camber [29] in 1949, Van Manen [30] in 1952 and Eckhardt and the geometric camber of the blade sections as a and Morgan [31] in 1955. function of propeller radius, blade area, blade number and hydrodynarnic pitch. These particular correction When Lerbs [32] in 1952 published his lifting line factors were, however, only strictly valid for the opti- method bascd on induction factors as defined by Kawa- mum radial circulation distribution, uniform chordwise da in 1933, it was a timely introduction of a method loading (circular arc rncanhines) and a uniform propeller suitable for a radially varying wake and a non-optimum inflow. Due to the large amount of work involved in circulation distribution. In 1958, Van Manen [33] show- calculating such correction factors, the Ludwieg and ed that important differences occur between the results Ginzel camber factors were used for a large number of of the induction factor method and the Goldstein factor years following 1945. Very often they were applied in method when applied to so-called wake adapted propel- cases where they were unsuitable, resulting in fact in lers. larger errors than caused by the correction factors based on experiments with profiles in cascades which they As mentioned above, lifting line procedures were found replaced. to be very suitable for the design of propellers and wings of moderate aspect ratios as low as 3. This was Prior to the work performed by Ludwieg and Ginzel, contrary to the case with wide bladed propellers having all lifting line procedures for the design or analysis of lower aspect ratios. Soon after lifting line procedures marine propellers incorporated correction factors based were introduced it was found necessary to supplement on previous experience or theoretical or experimental design procedures based on the lifting line concepts for vork on cascade effects. The opinion, that the differen- wide bladed marine propellers with emporicalor theore- ces occurring between theory and the results of experi- tical correction factors. lt is now known that this is due ments with marine propellers are due to so-called casca- to the fact that in the case of wide propeller blades it is de effects, was then a general one, and many efforts rio longer correct to calculate the induced velocity at the were made at developing reliable theories and at ob- position of the vortex line representing the blade and to taining relative experimental information in the 50-year neglect the variation of the induced velocity along the period following the first suggestion to rioso by Drze- chord. A distribution in the induced velocityor down- wiecki in 1892. Drzewiecki first found that the lift and wash along the chord results in a specific curvature of drag forces appeared to depend considerablyon the ratio the flow over the blade which, amongst other effects, of length to breadth of the propeller blades. The changes the effective camber of the blade setons. Such experimenta! investigatious eventually culminated in effects remain unaccounted fer in lilting line procedures. the work of Gutsche in 1933 [35] and 1938 [36] who In the case of moderate aspect ratios it is moreor less tested a series of cascades of aerofoils and propeller correct to consider the induced velocity at the lifting blade sections at different pitch angles and variousgap line as a correction to be applied to the geometric ratios. angle of incidence in determining an effective angle of Particularly good theoretical work on cascadeswas incidence to which the corresponding blade section performed by Weinig in 1932 [37]. reacts as if it were in a two-dimensional flow. In the case of low aspect ratios, however, the decrease in After the J.udwieg and Ginzel paper, the application effective camber and, in general, the way in which the of cascade corrections in marine propeller problems blade sections react to the curved flow, must also be continued. The reason for this is best reproduced by accounted for. Changes in the ideal angle of attack Burrill in the discussion of his 1955 paperon the op- and, in the case of non-symmetric chordwise loading of timum diameter of marine propellers [27]. Toquote the meanline about the midchord position, in the hydro- from t he relative passage: 54 For myself, I am noiconvinced that (the Ludwieg- 1950 [46] an.d 1955 [47], by Kerwin in 1961 [48]. Ginzel theory is the right one for correcting the vortex 1963 [49] and 1964 [50], and by English in 1962 [Sl] line into a vortexsheet theory) this is corrcct, despite was based on the vortex-lattice representation of a the correction factors and otherdevices which have been propeller blade. Then in 1959 Sparenberg [52] derived introduced recently to enable the correct pitches to be the three-dimensional integral lifting surface equation obtained, as the centrelinc camber corrections suggested for a screw propeller in a steady flow. This theory in- by this method lead to very high cambers indeed at the corporated a continuous vortex sheet representation of tip of the blades and much lower canibers at the root. the lifting surface, i.e. without physical or mathema- One of the deficiencies of the Ludwieg-Ginzel corree- tical assumptions and models for the arrangement of the lions is that they have been worked out for wide-tipped lattice. Such a formulation for a lifting surface (a wing) outlines arid another is that the basic aerofoil section was first given by Garner in 1948 [53] and 1949 [54] and characteristics obtained from wind tunnel work must be by Multhopp [55] in 1955. In 1962 Hanaoka [56] extend- corrected by similar lifting surface curvature effects ed Sparenherg's work to the case of unsteady flow. This in order that they may be applied to propeller design theory was then further developed by Pien [57], Nishiya- work. nia and Nakajima [58], Yamazaki [59] and others. In The use of the Gutsche cascade corrections may seem obtaining numerical results with this theory, various to he out-of-date, but they have the merit of simplicity different numerical procedures have evolved to solve and they do seem to be of the right order and to give the integral equation. In this connection the work done satisfactory integrated values of thrust, torque and effi- by Cheng [40], Tsakonas et al. [60, 61, 62, 631, Brown ciency.' [64, 65], Greenberg [66] and Verhrugh [67] should be particularly mentioned. The necessary approximations With the advent of high speed computers, gradually and linearizations necessary for the solution must be proper and more accurate lifting surface calculations carefully chosen in order not to cause appreciable errors were made, and now most propeller design procedures in the numerical results. incorporate lilting surface correction factors, in 1961 Cox [38] derived a set of camber corrections valid for 4 In 1965, Harley [68] carried out a comparison between different types of blade shapes, with 3, 4 and 5 blades, the results of Kerwin's vortex lattice program and applicable to the case of constant chordwise loading at Cheng's program for the continuous voi-tex theory of shock-free entry of the flow. In the last 10 years, lifting Pien. He found that the differences were small. It should surface corrections have been derived for various types be mentioned, however, that Cheng's numerical proce- of propeller designs. Of these, the correction factors of dure is essentially a vortex lattice representation of Morgan, Silovic and Denny [39] for a family of non- Pi.ens theory. skewed and skewed propellers, should be mentioned. These correction factors were derived from the lifting Recen! developments surface programs developed by Cheng [40] for blade loading and Kerwin [41] for blade thickness. They are Application of lifting surface theory to propeller design valid for the NACA a = 0.8 meanline and the NACA 66 has as yet not been carried out to a large extent. Fur- thickness distribution. The number of blades for which ther refinements to the numerical procedures are yet to (liese corrections are given are 4,5 and 6. For the res- be iiiade in order to perform the necessary calculations pective 3-bladed propellers of this series, the correc- faster and more efficient. For the analysis of propeller tion factors were derived by Minsaas and Slattelid [42] performance, however, lifting surface theory has already by means of the sanie programs. proven invaluable. In 1967 and 196S Tsakonas etui [69, 70] performed a comparison of vibratory thrust and Lilting surface theory for marine propellers has develop- torque calculations with experimental values obtained ed basically along two different paths. 'The first calcula- at the isssn by Wereldsmna [71] in 1966. The results lions and theories were really extended lifting-line showed the same agreement in trends of vibratory thrust methods. These evcitually developed into so-called vor- and torque bui relative large discrepancies in magnitude. tex lattice methods, in which the lifting surface is re- This has been ascribed to the insufficient number of presented by a descrete lattice of vortices. After the readings in the wake survey. Ludwieg and Ginzel theory, the work done by Guillo- ton in 1949 [43] and 1955 [44, 45] by Strecheletzky in Another result of lifting surface theory application has

55 been the development of propellers having large skew. 'With lifting surface theory it is possible to determine the desired radial load distribution and the associated necessary ideal angle correction to the hydrodynarnic V1 pitch angle. Lifting surface calculations and measure- o ments show that propellers with a large skew experience substantial reductions in propeller force and moment fluctuations [72, 73]. Recent work by Boswel and others at theNSRDC[74] has also shown that the cavitation t performance of skewed propellers can be superior to the cavitation performance of the comparative propellers 0 without skew. o 02 0,6 03 "o '2 4 116 Fig. IAngular variations in effective propeller inilow at Due to the importance of designing propellers with various propeller radii and ship speeds for a destroyer type cavitation properties, research into non- acceptabl vessel. optimum propeller design has recently received a great deal of attention. At the NSMB, a method has been developed to account for the peripheral inequality of the wake in the design process [75]. The necessary cal- than the blade thicknesses resulting from current stan- culations and iterations, performed on an electronic dard design practices. This is particularly the case for computer, have been found to give good results, Pro- the outer propeller radii. It is therefore often necessary peller pitch, blade thickness and camber are calculated to specify a maximum blade section thickness to avoid in accordance with obtaining maximum latitude to bubble cavitation and unacceptable high drag coefficients. variations in the angle of attack. From 5-hole pitot-tube \Vhen relative high values occur at low values for measurements, an accurate survey of the axial, tangen- the cavitation number, it is impossible to design prop- tial and radial wake components is made. These eller blades free of sheet cavitation. In that case this components determine the geometric inflow conditions. design process can be applied, e.g., to avoid cavitation By assuming a specific blade section geometry, the on the face. effective propeller inflow at a large number of' points in the screw disk is calculated. Together with the calcula- Besides the aspects of propeller pitch, blade thickness tion of the cavitation index over the screw disk, it and camber, recent studies have also shown that a becomes possible to select a new blade section geometry carefull selection of propeller diameter, rotative speed, at each radius having the necessary cavitation-free angle direction of rotation and the number of blades should of attack range and the required average lift. With this be made.Unloading of the blade at the tip and at the second geometric configuration, the associated induced hub by means of a carefully selected radial load distribu- velocities are again calculated, the blade section geome- tion should be seriously considered and more often try determined, etc. initiating an iteration procedure applied, particularly in view of the fact that the prop- which is continued until the effective propeller ipflow eller efficiency is not seriously cifected. When in particul- at the various points in the screw disk no longer chang- ar hub vortex cavitation is a problem, use of a diver- es. gent fairwater has been found to be very successful [761. Calling the total variation in the effective inflow at a certain screw radius and ship speed it is possible Experimental propeller characteristics: to construct a diagram showing the variation tile Wageningen B-screw series with ship speed and screw radius on a base of cavitation number. in Fig. i these results arc given for a twin- An important method of screw design is that based on screw destroyer type vessel. A figure of this nature the results4 of open-water tests with systematically varied illustrates th necessary cavitation-free angle of attack series of screw models. Among the well-known screw or lift coefficient range the blade sections must have to series developed by Schaifran, Taylor Gawn and others, be free of cavitation at a specific ship speed. the B-screw series of the Netherlands Ship Model Basin, This procedure for the determination of blade section often designated as the 'Wageningen B-Screw Series', geometry very often leads to higher blade thicknesses take an importuni place. The B-series screw type is

56 frequentlY used due to its satisfactory efficiency and Table 2aDimensions of four five, six and seven bladed adequate cavitation properties. Wagcningcn B-screw series.

Cr. Z Sr/D = ArBrZ The first tests with systematic series of screw propellers nR--.----- ar/Cr br/Cr at the Netherlands Ship Modcl Basin were performed D. A1;/A0 Ar Br

¡ 1936. From model experiments carried out by Baker and Riddle [77] and Baker [78] it had become evident 0.2 1.662 0.617 0.350 0.0526 0.0040 that screws with circular-back blade sections and ellipti- 0.3 1.882 0.613 0.350 0.0464 0.0035 cal blade outline such as the Taylor and Schaifran series 0.4 2.050 0.601 0.350 0.0402 0.0030 were inferior as regards efficiency to propellers with aero- 0.5 2.152 0.586 0.350 0.0340 0.0025 foil sections. At the Netherlands Ship Model Basin these 0.6 2.187 0.561 0.389 0.027$ 0.0020 0.7 2.144 0.524 0.443 0.0216 conclusions were verified. These results led to the devel- 0.0015 0.8 1.970 0.463 0.479 0.0154 0.0010 opment of a series of model propellers having acrofoil 0.9 1.582 0.351 0.500 0.0092 0.0005 sections. This series was called the A4-.40 series as itvas 1.0 - O - 0.0030 0 a series having 4 blades and a blade area ratio of 0.40. The results of the open-water tests with this series were given by Troost [79]. Table 2bDimensions of three bladed \Vageningen B-screw series. Later, it was found that the A4-40 screw series were C, z Sr/Dr ArBrZ only suitable for use in cases where no cavitation danger r/R at/Cr br/Cr was prcsnt. This was found to be due to the fact that D.AE/AO Ar 1r3r the narrow blade tips and the aerofoil shaped blade sections gave rise to very unfavourable pressure distribu- 0.2 1.633 0.616 0.350 0.0526 0.0040 lions on the blades. In addition, the A4-40 screw series 0.3 1.832 0.611 0.350 0.0464 0.0035 possessed unfavourable hacking characteristics. It was 0.4 2.000 0.599 0.350 0.0402 0.0030 therefore decided to design a new screw series having 0.5 2.120 0.583 0.355 0.0340 0.0025 wider blade tips, circular blade sections near the tips 0.6 2.186 0.558 0.389 0.0278 0.0020 and aerofoil blade sections ilear the hub. This new prop- 0.7 2.168 0.526 0.442 0.0216 0.0015 eller series was designated as the B-series. The first B- 0.8 2.127 0.481 0.478 0.0154 0.0010 screw series to be designed was the B4-40 series and due 0.9 1.657 0.400 0.500 0.0092 0.0005 1.0 - to great popularity this screw series was gradually ex- - - 0.0030 0 tended to other blade numbers and blade area ratios. The results of the first open-water tests were given by Troost [80] and others [81, 82]. Table Ilists the available B- screw series. The geometry of the B-screw series is given in Table 2. At present, about 120 model propellers of the B-series have been manufactured and tested at theNSMB.The results of the open-water tests are given in the form

Table ITable of existing Wagcningcn B-screw series.

l3tade number z Blade al-ea ratio AL/Ao 2 0.30 3 0.35 0.50 0.65 0.80 4 0.40 0.55 0.70 0.85 1.00 5 0.45 0.60 0.75 1.05 6 0.50 0.65 0.80 7 0.55 0.70 0.85

57 of the thrust and torque coefficients KT and KQ express- the blade section at 0.75 R is equivalent for the whole ed as a function of the advance coefficient J and the blade. At a specific value of the advance coefficient pitch ratio P/D, where: the lift and drag coefficients and the corresponding profile angle of attack is deduced from the KT- and KQ T K values from the open-water test. In this way the polar pn2D4 curves for C0 and CL on a basis of a is calculated from the known propeller characteristics KT and KQ on a K basis off. Reynolds number effects are only considered and to influence the drag coefficient of the equivalent profile. It is furthermore assumed that the influence of Reynolds number on the drag coefficient is n accordance with a J= (3) nD vertical shift of the C0 curve equal to the change in the minimum value of the drag coefficient. This mini- in which mum value is for thin profiles composed of mainly T = propeller thrust, frictional resistance, the effect of the pressure gradient p = fluid density, being small. n = revolutions of propeller per second, According to Hoerner [89] the minimum drag coefficient D = propeller diameter, of the profile is: VA velocity of advance.

CDni n= 2Cf(i+2()O75R) Some years ago it was decided to cross-fair the B-screw series open-water test results by means of a regression in which analysis. in this way the existing small errors in the Cf = 0.075 diagrams would be eliminated and the resulting analyti- [043429ln(R0 _2]2 cal expressions for the thrust and torque would be very 75R where welcome for use in preliminary design calculations by means of high speed computers. One reason for the CO7SR/v4 2 +(0.75 rnD)2 R,, - small errors in the diagrams was the inconsistancy of O.75R D the Reynolds number during open-water tests. The early open-water tests were carried out at a lower rotational Cf is the drag coefficient of a flat plate in a turbulent propeller speed than the more recent tests. For the correction of the test results for Reynolds number flow and the term (I + 2(O.75R)represents the effect effects the method developed by Lerbs [83] was applied. This method is a so-called 'equivalent profile method', of the pressure gradient. consisting of replacing the propeller by one of its profiles, the equivalent profile, and deducing the prop- On setting out the minimum value of the drag coefficient erties of the propeller at other scale and roughness as obtained from the polar curve for each propeller on values from the known properties of this profile Titis a base of Reynolds number,large scatter was appas- idea was first considered by Lock [84] and Von Doepp ant as shown in Fig. 2. \Vhen this mimimum value of [85] and was previously apphed by Driggs [86] and Kramer [87]. the drag coefficient ¡s set out against for each

Tite cross-fairing of the B-series was first attempted pitch-diameter ratio, it is seen that below a specific value for each blade number separately. The results of the of the blade area-blade number ratio an increase in the investigations for the four and five bladed 13-series CD,fl;fl value occurs. For a pitch-diameter ratio equal were given by Van Lammeren etal [88] in 1969. It was to 1.0, this i's shown in Fig. 3. The existance of such a later decided to include the blade number as an inde- correlation of the CD,,jn value with propeller geometry pendent variable in the cross-fairing and also to include points to the fact that the scatter in Fig. 2 is not the Reynolds number as an independent variable in the entirely due to Reynolds number effects and experimen- polynomials for K and KQ. tal errors. It is obvious that the drag coefficient is influen- In the Lerbs equivalent profile method it is shown that ced by a three-dimensional effect. it is necessary, there-

58 The lift and drag coefficients oblained in this way were o0:4 each expressed as a function of blade number, blade area ratio, pitch-diameter ratio and angle of attack by means of a multiple regression analysis method. By

O 020 applying this process in reverse, thrust and torque coefficient values were next calculated. The basis for this reverse process was formed by calculating CL and

Dcoefficients from the CL and C, olynomials for colo specific combinalions of z, AE/Ao, P/e' and R3. The resulting values formed the input for the development ola th-ust coefficient and a torque coefficient polynomial. Foc R8 = 2 x 106 the polynomials obtained in this way are given in Table 3. The choice of choosing a Reynolds number value of 2 x 106 for the characteristics on the model scale followed from the fact that the O 003 corresponding1D;njo value is an average of all model values. With the aid of a tape-controlled drawing machine a new set of open water diagrams has been prepared. o00: Figs. 4, 5, 6, 7 and 8 show the results for the B3.65, B4-70, B5-75, B6-80 and B7-85 propellers for the Reynolds number value of 2 x 106. in formulating the

TlO minimum value of the drag coefficient as a function of the Reynolds number, it is possible to cale ilate thrust Fig. 2Uncorrected value of the minimum drag coefficient and torque values valid for the full-scale by correcting of equivalent proflle of B-series propellers. the CD-values as described above. lt is therefore possibl to calculate a nev set of coefficients in the KT and KQ polynomials alie-ady obtained foi R0 = 2 X l0'. The

¿D n O FOR ALL POINTS necessary calculations can be performed by a least squares method. By correlating the values of the respective coefficicnts with the value of the Reynolds number, a

.0008AGE PELArION 04-RO - 00.80 final KT and a final KQ polynomial is to be developed FOR P/O lO 04.100 07-30 having as independent variables the number of blades, 07-85 the blade area ratio, the pitch-diameter ratio, the advance coefficient and the Reynolds number.

A program ha also been started to include the thick- TOREE - 1010005101ML ness of the propeller blades at a characteristic radius in these polynomials. The ultimate aim is to determine the following relations:

AR/AO KT = f1 (J, P/D, AE!AO,; R,,,

Fig. 3Three-dimensional effect on minimum drag coefficient and (7) of equivalent profile of B-series propellers. , KQ = f2 (J, P/D, AE/Ao, "721 C fore, before correcting for Reynolds number according With these relations it will be possible to perform to equations 4, 5 and 6to subtract this three-dimensional preliminary design calculations to determine the op- effect from the CD20I,2-value. An estimation of this effect timum propeller geometry parameters in connection was obtained by applying regression analysis. with obtaining a specific ship speed, the required strength

59 .1

Table 3Coefficients and terms of the KT and KQ polynomials for the Wageningen B-screw series for R = 2 X 106 KT = .Z (J)S(p/D)t(A/A)U(zV) - K0 = L (J).(P/D)t.(AE/AO)u.(zv)

KT: C. S t u y K0: Cs.1.uV s t u y (J) (P/D)(AE/Ao) (z) (J) (P/D) (AE/Ao)(z)

±0.00880496 0 0 0 0 -rO.00379368 O O O O -0.204554 1 0 0 0 +0.00886523 2 0 0 0 +0.166351 0 1 0 0 -0.032241 1 1 0 0 ±0.158114 0 2 0 0 +0.00344778 0 2 0 0 -0.147581 2 0 1 0 -0.0408811 0 1 1 0

-0.4S1497 I i 1 0 -0.108009 1 1 i O ±0.415437 0 2 1 0 -0.0885381 2 J I O

± 0.0144043 0 0 0 1 + 0.188561 0 2 1 0 -0.0530054 2 0 0 1 -0.00370871 1 0 0 1

+0.0143481 0 1 1 0 +0.00513696 0 1 0

± 0.0606826 1 1 0 1 -F 0.0209449 1 1 0 1 -0.0125894 0 0 1 1 ±0.00474319 2 1 0 1

+0.0109689 0 1 1 -0.00723408 2 0 1 I -0.133698 0 3 0 0 ±0.00438388 i i 1 1 +0.00638407 0 6 0 0 -0.0269403 0 2 I -0.00132718 2 6 0 0 +0.0558082 3 0 1 0 ±0.168496 3 0 1 0 ±0.0161886 0 3 i O -0.0507214 0 0 2 0 +0.00318086 1 3 1 0 ±0.0854559 2 0 2 0 ±0.015896 0 0 2 0 -0.0504475 3 0 2 0 ±0.0471729 I 0 2 0 ±0.010465 I 6 2 0 ±0.0196283 3 0 2 0 -0.00648272 2 6 2 0 --0.0502782 0 I 2 0 -0.00841728 0 3 0 1 -0.030055 3 1 2 0 +0.0168424 1 3 0 1 ±0.0417122 2 2 2 0 -0.00102296 3 3 0 1 -0.0397722 0 3 2 0

-0.0317791 0 3 1 1 -0.00350024 0 6 2 0 ±0.018604 1 0 2 1 -0.0106854 3 0 0 i -0.00410798 0 2 2 i +0.00110903 3 3 0 1 -0.000606848 0 0 0 2 -0.000313912 0 6 0 1 -0.0049819 1 0 0 2 +0.0035985 3 0 1 1 -F00025983 2 0 0 2 -0.00142121 0 6 I -0.000560528 3 0 0 2 --0.00383637 1 0 2 1 -0.00163652 I 2 0 2 +0.0126803 0 2 2 -0.000328787 I 6 0 2 -0.00318278 2 3 2 1 +0.000116502 2 6 0 2 +0.00334268 0 6 2 i ±0.000690904 0 0 1 2 --0.00183491 1 1 0 2 +0.00421749 1 0 3 2 ±0.000112451 3 2 0 2 + 0.0000565229 3 6 1 2 -0.0000297228 3 6 0 2 -0.00146564 0 3 2 2 ±0.000269551 1 0 1 2

-j- 0.00083265 2 0 1 2

+0.00155334 0 2 1 2

+0.00030283 0 6 1 2 -0.0001843 0 0 2 2 -0.000425399 0 3 2 2 R,, = 2 x 106 +0.0000869243 3 3 2 2 -0.0004659 0 6 2 2

+0.0000554194 1 6 2 2 60 8365

uailiiii:i!I:,!ii

misi4. LN14uI

qo K, /4 -. LL - . Ii IiL!IIi!!' o Fig. 4Cross-fai red open-water test results for B3-65 propellers 09 io i-' 12 13 for R,, = 2 x 10e. UUNNR ì.i!iiUIi..::::::::.a

10KIP,:i ::::u::::IE I!1hìp!PiirIiR I1i KoF1It1 01 Fig. 5Cross-faired open-water test results for 134-70 propellers 06 o, ii i) i' ¶3 16 for R = 2 x 1O.

61 13 uaaaaua ua. aaa aaaaaaaaaaua uasaa1 aaaa ti:::::... ioauuaauuiuaaauauu.:IIIi.!Iiiiu uauuua :1 cguuuuuu aiuauu 10k0 08 auuuuuuauiva i 07 au4PII.iu

0. iir :u 00 iuuuuuuu

b.. 'I0.6 0.8 uu uui Fig. 6Cross-faircd open-water test results for135.75propellers 02 03 09 07 06 09 15 for R9 = 2 x

i. uu.uuuilinuI uuuu .fllLululiïUuuuUuuuuuuau ::uuauuuuuuu ti ..¡Ii,.i.:uu# .uuuuuuuluuuuuuuuu 09¡uiIJ11I uuuauuuu IO k aiIPLuuuuau o,iI:uIIiIiuIa 'tu!.

Fig. 7Cross-faired open-water test results for136-80 400 propellers 02 03 00 05 06 07 08 09 12 i' 15 for R9 = 2X106. 62 '3 : F: Ji: li!:I.'i1l' N 101:111 PII'. .111:

oe IlL:1! N o, -r p 06.iiIuÏ..

o' aun. I i uiVIvri4iiI ìui rnu 03 K, - j---N :i OC '-r 0' Fig. 8Cross-faired open-water test results for B7-85 propellers

03 00 05 06 for J,, = 2 x 106. t'áVIiÁL!07 08 09 lo Is

and acceptable cavitation properties.

For design purposes, the B,, diagrams at the Reynolds number of 2 x 106 for the propellers for which the open-water diagrams are given are shown in Figs. 9, ifi, II, 12 and 13. The Taylor variable B,, is related to the various dimensionless variables by the equation:

B = 33.07KQ'1/f512 = NP'1/V512 (8) 'hcre N = number of revolutions per minute, P = power in hp, VA speed of advance in knots. The speed ratiois defined as: = 101.27/f = ND/VA (9)

Curves, showing the efficiency ,defined as KTJ 11e (IO) 2IrKQ' the speed ratio, and the pitch ratio P/D corresponding to the optimum diameter, are given in Figs. 14, 15, 16, 17, and 18. Each figure is for one blade number.

S I!:'4 t%ÒS$ $$4Yv44'444A,

20 25 90 ¿D so 60 70 BD 90 lOO lID 120 I lOO ISO 167 170 180 199 200

Fig. 12Bp-ö diagram of B6-80 propellers based on cross-faired open-water lest results foi R= 2X1O.

Fig. 13Bp-ó diagrams of B7-85 propellers based on cross-faired open-water test results forR0 = 2 x 106. 33o i/ /P

65 84 - 40 83 - 35 84 - 55 8 3 - 50 84-70 B 3 - 65 0.7 84-85 07 8 3 - 80 84 - 100 83 - 95 500 500

06 0,6 14 14 - 400 400

'10

05 1.2 05 1.2 300 300

5 5 1.0 to 04- 0.4 PIO 200 P/D 200 08 0.8 03 0.3 100 100 06 06

i i 04 i I i___.J_._....__. ii I 04 r i i i i i o 4 6 8 10 20 3040 50 100 200 300 4 6 8 10 20 30 4050 100 200300 B B 33.08 f7jc

Fig. 14Curves for optimum diameter of thrcc-bladcd Fig. 15Curves for optimum diameter of four-bladed B-

B-series propellers at R = 2 x 106. , series propellers at R = 2 z 106.

66 85 - 30 136 - 35 135 - 45 8 6 - 50 65 - 60 136 - 65 07 85 - 75 07 13G - 80 135 - 90 500 f36 - 95 50G 55 - 105 (36 -110

06 06 14 400 14 400 10

05 1.2 05- 1.2 300 300

o o 10 1.0 04 P/S 200 200

08 08

0.3 03 roo 100 0.6 0.6

04 ii r O 04 i r r r ir o 4 6 8 10 20 30 4050 100 200 300 4 6 6 10 20 30 40 50 100 200300 /k/j 33,0g Fig. 16Curves for optimum diameter of five-bladed B- Fig. 17Curves for optimum diamcter of six-bladed B-series series propellers at R = 2X106. propellers al R,, = 2 x 106.

67 6 7 - 40 In the designof recent-day ships such as high speed 87 - 55 87 - 70 cargo ships and very large tankers with full hull forms, 07 67 - 85 special attention has lo be given to the growing danger 67 - 100 °° of vibrations generated by the ship propeller. Recently, it was found that cavitation has a substantial effect on the vibratory forces acting at the stern of the ship and 06 on the bending moments acting on the propeller shaft 14 400 [91, 2]. There is also a growing demand for thruster systems which are able to improve the manoeuvrability and position-keeping ability of vessels, especially those vessels used for ocean exploration. These new trends in 05-12 ship design demand a well balanced compromise be- 300 tween the main requirements for a ship propeller as already mentioned. Non-conventional propulsion devices 5 10 which may have advantageous properties over the 04 conventional ship propeller due to these new trends in

e/O 200 ship design are: - ducted propellers, 08 - overlapping propellers, - controllable pitch propellers, 0.3 - contra-rotating propellers, 100 - vertical axis propellers. - 0.5 0f these propulsion devices the ducted propeller is by far the most important and therefore discussed in more detail in the section on ducted propellers. In the case 0.11 1 I t I of heavy screw loads (all types of towing vessels) the 4 6 8 lO 2030 40 50 100 200 300 attractiveness, with regard to propulsion efficiency, of the application of accelerating nozzles has been Fig. 18Curves for optimum diameter of seven-bladed B- demonstrated in practice in the course of the past series propellers at R = 2 x 1O. thirty years. Recently, the field of application of ducted propellers was extended tQ large tankers.

Other propulsion devices, which may be of use for high Characteristics of non-conventional propulsion devices speed craft, are the fully-cavitating or super-cavitating propeller [92, 93, 94], the waterjet propulsion system Gai¡eral considerations with internal pumps [95], the water-air ramjet [96, 97], and the airscrew and ducted airscrew. For high speed The mair. requirerrens for a ship propeller aie, as craft the selection of the propeller type has a dominat- summarized by Van Manen [90]: ing effect on the whole design configuration. - high efficiency, - no adverse effects of cavitation, viz, erosion, Controllable pitch propellers - minimum vibration-exciting load fluctuations, - good stopping abilities, Overlapping and controllable pitch propellers are two - favourable interaction with the rudder to improve special configurations of the conventional screw propel- manoe uvrabi li ty, ler. The controllable pitch propeller can be used succes- - reliability and invulnerability, fully when good accelerating, stopping and manoeuvr- low initial and maintenance costs. ing qualities are desired or when in the operation of the Due to its advantageous properties with respect to these ship widely diverging speeds or widely varying degrees requirements, the conventional ship propeller has of loading occur [98, 99]. The attractiveness of applying dominated for more than a century among Ihe modes controllable pitch propellers lias already been demon- of ship propulsion. strated in practice for tugs, fishing vessels, incebreakers, 68 ferry boats etc. The sblution of various mechanical and cchnological difficulties and the development of suitable control systems has recently led to the application to frigates and oilier warships and to various types of merchant ships. Shaft horsepowers of up to 30000 are flow being installed. The supreme stopping and accelerating properties of controllable pitch propellers promise continuing application of this propeller type.

Overlajpiitg prope/Icis

The overlapping twin screw propeller arrangement, see Fig. 19, may soon find application in cases of high powered ships where the single screw soluiio«has to ha left out of consideration. From the results of various model tests [100, 101] it cati be concluded that the reductions in DHP which cati be obtained with this propeller configuration are of the order of 5 to 8 percent compared to the conventional single screw propeller and 20 to 25 percent compared to the conventional twin screw arrangement. The hull excitation ievel appears lo be somewhat higher than that of the conventional twin screw arrangement, but comparable lo that of the regular single screw configuration. The cavitation properties of each of the propellers also appear to be comparable to those of the respective conventional single screw configurations. Unfavourable interaction of cavitating tip vortices, as shown in Fig. 20, can occur however.

Fig. 20Sketch of observed interference of tip vortices of overlapping propellers.

Fig. 19Drawing of overlapping twin-screw arrangement.

69 Vertical axis propellers variations in the effective angle of attack, however, cavitation may set a bound to such high speeds [102, The group of propulsion devices in which a number 103]. of perpendicular mounted blades rotate around a vertic- cal axis are specified as Cycloidal Propellers', see Fig. Contra-rotating propellers 21. By means ola special mounting mechanism, each blade is given a movemeCt whereby a thrust is created. The contra-rotating propeller arrangement may form a The vertical axis propeller is a propeller type with out- serious competitor of the conventional ship screw on standing manoeuvring capabilities. Ferries, tugs and fast and large container ships where the required power supply vessles are examples of ship types where succes- cannot be installed on one screw. However, applications full application of the vertical axis propeller is frequent- have not been realized up to date due to problems involv- ly realized. Recent applications include ships and float- ed with the shafting system. Contra-rotating propellers ing structures in the field of ocean engineering, where consist of two co-axial screw propellers situated a dynamic positioning capabilities must be high. Future short distance apart having opposite directions of rota- prospects may be hidden in developing the vertical axis tions, see Fig. 22. The aim of such a propeller con- propeller for very high speeds, in which case the blade figuration is to reduce the rotational losses in the screw motion ressembles the motion of a fish. Very high race. Results of open-water tests with this propeller type efficiencies are then possible. Due to the peripheral show that in the case of light loads higher efficiencies can indeed be obtained. Fig. 23 shows curves for the efficiency .,, the pitch-diameter ratio P/D and the speed ratiofor the optimum diameter of a conventional screw propeller series (B4-70 series), an accelerating d acted-propeller and a decelerating-ducted propeller series (Ka 4-70 inNSMBnozzle no. 19A and Kd 5-100 inNSMBnozzle no. 33 respectively) and a contra-rotating propeller series, on a base of B. This contra-rotating propeller series has a 4-blade forward screw and a 5-bladed screw aft having a smaller diameter so as to avoid that the tip vortices of the forward screw interfere with the blades of the aft screw [104]. With such a contra-rotating propeller series, low propeller induced vibratory forces can be obtained. With respect to

Fig. 21Photo of model ship fitted with vertical-axispro- Fig. 22Photo of contra-rotating propeller arrangement pellers. behind a model ship. 70 (loe rotation of the fluid are then zero. The influence of 1.3 friction is neglected. With momentum ihcory the follow- P/c ¡ng expressions for the ideal efficiency ijand the ratio 08 1.1 between the velocity V, at the impeller llane and the 07600 09 undisturbed stream velocity VA can be derived:

00500 2

B L-70 serien fo 05400 Ka 4-70 in 19A s -- Kd5-lOOïn 33 CRP series 04300 V/I'4 = CT (12) 2 03200 E- i +/'i+

02100 where

0.) 0 T 20 3040 50 70 100 200 300 LOO (13) Olp PVA2 D2 Fig. 23Curves for optimum diameter of different types of propellers. and

t=Tp (14) cavitation and stopping abilities, no marked advantages T or disadvantages with respect to the conventional screw propeller appear to exist [99, 105). T and T denote the total thrust and the impeller thrust respectively; D is the propeller diameter. These formulas Ductc'd piopellers are graphically represented in Fig. 25. From this diagram it can be seen that due to the nozzle action the Insight into the working principle of a ducted propeller inflow velocity of the impeller can b either less or can be gained by the application of fundamental mo- greater than the inflow velocity of an open propeller mentum relationships. Fig. 24 shows the simplified under equal condii ions. For a thrust ratio -r cua1 to system by which the ducted propeller can be replaced. 1.0, no force acts on the nozzle and the flow pattern is Here the screw propeller is represented by an actuator comparable with that of an open screw. With decreasing disk rotating at infinite angular velocity. The tangential valves of -r, the nozzle produces a positive thrust, the induced velocities and consequently, the losses due to inflow velocity of the impeller is increased, and an

240.90 L/2

1.6070

VA ,tI VP/VA

VP Pl Os 050

O - 030 0.25 0.5 2 c1 ' 6

Fig. 24Control for volume momentum considerations of Fig. 25Efficiency and mean axial velocity of a ducted dueled propeller. propeller.

71 improvement in ¡deal efficiency ¡s found. For thrust Although the idea of surrounding a propeller by a ratios greater than 1.0, a negative thrust or drag force nozzle is very old, it was not until the early 1930's acts on the nozzle, the inflow velocity of the impeller before the ductcd propeller came into praëtical use. decreases and the ideal efficiency ¡s lower. Luisa Stipa and later Kort [106] experimentally proved the advantages which can be obtained by application of Insight into the shape of the nozzle profile of a ducted the accelerating nozzle. These investigations clearly propeller can be gained by means of Fig. 26. Here the showed that an increase in efficiency can be obtained flow through different types of ducted propellers is with this nozzle when applied in the case of heavy screw superimposed on the flow through an open propeller. loads. Primarily due to the work done by Kort, the Both the open- and the ducted propellers are designed application of ducted propellers behind certain ship for the same mass flow rate and velocity in the ultimate types (tugs, pushboats, supply vessels, trawlers) has wake. Consequently the thrust and ideal efficiency of become common practice. This may be the reason that these systems are equal. the accelerating ducted propeller is frequently referred to as the Kort' nozzle.

Many studies on ducted propellers have been made during the last 40 years. An extensive sum mary of this work was made by Sacks and Burnell [107] in 1960. A DECELERATING ELE PATIN G NOZZLE NOZZLE general review of the more recent theoretical studies on ducted propellers has been given by Weissinger and Maass [108]. Among the theoretical studies on ducted propellers the investigations of Horn and Amtsbcrg [109], Kücheman and Weber [I IO], and Dickman and Weissinger [1111 may be mentioned in particular. Especially, the work of Dickmann and Weissinger was a first step to develope a more refined theory for ductcd propellers. This paper was the basis for the work which has been performed at Karlsruhe by Dickmann, Weissinger, Wiedemcr, Boliheimer, Brakhage, Maass and Rautmann. Some of the basic ideas used at Karlsruhe were also used by other investigators such as Ordwy, Ritter, Greenberg, Rough, Kaskel, !.o. Sluytcr, Sonnerup, Morgan, Caster, Chaplin, Voight, Nielsen, Krievel, t Mendenhall, Sacks, Spangler etc. Fig. 26Streamline forms induced by diffircnt nozzle types. Most of the theoretical investigations on ducted propellers were concentrated to a large extent on the lineariz- ed theory and on axisymmetrical nozzles in a uniform The ducted propeller with the accelerating flow type of flow. These theories do not give data about the danger of nozzle is now used extensively in cases where the ship flow separation on the nozzle. 1f flow separation occurs, screw is heavely loaded or where the screw is limited in which may happen if the nozzle is very heavily loaded, diameter. The accelerating nozzle offers a means of the drag of the nozzle will increase sharply. The efficien- increasing tl:e efficiency of heavely loaded propellers. cy of the system will decrease and the propeller will The nozzle itself produces a positive thrust. In the case operate in a highly irregular flow. Flow separation on of the decelerating flow type of nozzle, the nozzle is the nozzle surface should be avoided. For the design used to increase the static pressure at the impeller. This of a ducted propeller it is therefore necessary to have ducted propeller system is the so-called pumpjet. The available a sound theoretical method supported by the duct will produce a negative thrust. This nozzle may be results of carefully seiected systematic experiments. used if retardation of propeller cavitation is desired. A comparison of theory and experiments on ducted For naval ships a reduction in noise level cari be ob- propellers has been made by Morgan and Caster [112]. tained, which may be of importance for tactical reasons. Tests on ducted propellers are scarce, however, and 72

- most of these tests arc restricted to isolatcd applica- lions. By far the most extensive systematic experiments on dueled propellers for application on ships have been -1 performed at the NSMB over the last 20 years. These investigations included nozzles of bolli the accelerating ¡111.: [113, 114, 115, 116, 17] and decelerating [118, 119] flow type. Ka h S S

Accelerating nozzles

The investigations on accelerating nozzles have led to the development of a standard nozzle (nozzle no. l9A) for application in the case of heavy screw Iqads. This nozzle has, from the structural point of view, a simple shape. The inner side of the nozzle at the location of the screw lias an axial cylindrical form. The outside of the nozzle profile is straight and the trailing edge of the Fig. 28Blade planlorm of the Ka-series propellers. nozzle is relatively thick. The profile of nozzle no. I 9A is shown in Fig. 27.

rather puer. For towing vessels (espeia1ly pushboats). the thrust which can be developed at bollard pii11 condition either with the propeller running ahead or astern is of the utmost importance. In such cases it is attractive to tise a nozzle with a relative thick trailing edge. Therefore, a new type of nozzle, especially suited for astern operation was developed. The profile of this. nozzle is given in Fig. 29. In comparison with nozzle Fig. 27Profile of nozzle no. l9A of the NSMR. no. 19A, this nozzle (designated as nozzle no. 37) lias a well-rounded and relatively thick trailing-edge. This prevents flow separation in reversed condition. Open-water tests were performed with all these nozzles For use in nozzle no. I 9A, special screw series (the in combination with the Ka 4-70 screw series. The fair- so-called Ka-screw series) were designed. Screws of ing of the open-water test results was performed by these series have relatively wide blade tips which niake theni less susceptable to blade tip cavitation Extensive investigations performed at the NSNI}3 have led to the design of these series having uniform pitch and fiat face sections. The results of the experiments mentioned show that this type of screw has no drawbacks with respect to efficiency and cavitation. The particulars of these screw models are given in Table 4 and Fig. 28. .1-w) Nozzle No. 19A has a length-diameter ratio LID equal to 0.5 For application on pushboats and tugs, nozzles with larger length-diameter ratios may he attractive. Therefore two other nozzles were designed of which the basic form is equal to the shape of nozzle no. l9A, possessing length-diameter ratios LID of 0.8 and 1.0. These nozzles were designated as No. 22 and 24. The backing characteristics of these nozzle types are Fig. 29Profile of nozzle no. 37 of the ss,t.

73 Table 4Dimensions of the Ka-screw series. nR 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

56.44 Length of blade Length of the blade from centre line 30.2136.1741.45 45.9949.87 52.93 55.04 56.33 section at 0.6 R = sections in percentagesto trailing edge of the maximum length 56.44 = 1.969±AE/Ao of the blade section froni centre line 36.94 40.4243.74 47.0250.13 52.93 55.04 56.33 at 0.6 R to leading edge total length 67.15 76.5985.19 93.01100.00 105.86 110.08112.66122.88

Max. blade thickness in percentages of Maximum thickness 0.50 at centre of shaft = the diameter 4.00 3.52 3.00 2.45 1.90 1.38 0.92 0.61 0.049 D

Distance of maximum thickness from 34.98 39.7646.02 49.13 49.98 leading edge in percentage of the length of the sections

Distance of the ordinates from the maximum thickness From maximum thickness to trailing edge From maximum thickness to leading edge 90% 95% 100% rlR 100% 80% 60% 40% 20% 20% 40% 60% 80%

Ordinates for the back 27.40 0.2 - 38.23 63.65 82.40 95.00 97.92 90.83 77.19 55.00 38.75 37.37 27.57 0.3 - 39.05 66.63 84.14 95.86 97.63 90.06 75.62 53.02 25.83 0.4 40.56 66.94 85.69 96.25 97.22 88.89 73.61 50.00 34.72 45.84 30.22 22.24 0.5 - 41.77 68.59 86.42 96.60 96.77 87.10 7;.46 20.44 0.6 - 43.58 68.26 85.89 96.47 96.47 85.89 68.26 43.58 28.59 30.79 22.88 0.7 - 45.31 69.24 86.33 96.58 96.58 86.33 69.24 45.31 26.90 0.8 - 48.16 70.84 87.04 96.76 96.76 87.04 70.84 48.16 34.39 31.87 0.9 - 51.75 72.94 88.09 97.17 97.17 88.09 72.94 51.75 38.87 39.25 32.31 1.0 - 52.00 73.00 88.00 97.00 97.00 88.00 73.00 52.00

Ordinates for the face 33.33 0.2 20.21 7.29 1.77 0.1 - 0.21 1.46 4.37 10.52 16.04 20.62 10.30 21.18 0.3 13.85 4.62 1.07 - - 0.12 0.83 2.72 6.15 8.28 4.44 13.47 0.4 9.7 2.36 0.56 - - - 0.4.1 1.39 2.92 3.89 7.81 0.5 6.62 0.68 0.17 - - - 0.17 0.51 1.02 1.36 1.53 Note: The percentages of the ordinates relate to the maximum thickness of the correspondingsection.

means of regression analysis and the polynomials together with the coefficients are given in Tables Sa and Sb. The open-water diagrams are given in Figs. 30, 31, 32 and 33.

74 Table SaCocílìcienis and terms of the K.,-, K.,-and K0 polynomials of the Ka 4-70 screw series in nozzles nos. 19A and 22. Nozzle no. 19A Nozzle no. 22

x y Ax)' Bxy Ccy Axy Ax)' Cx)'

o o o 0.030550+0.076594±0.006735+0.008043+0.001317±0.032079

1 1 -0.148687 ± 0.075223 2 2 -0.061881 -0.016306-0.208843 -0.020219 3 3-0.391137-0.138094 -0.902650 -0.021294 4 4 -0.007244 -0.937036 5 5 -0.370620 -0.369317 6 6 +0.323447 -30.682898

7 1 0 -0.271337 -0.102805 8 1 -0.432612-0.687921 -0.661804 0.559885 9 2 -1-0.225189 -0.024012+0.752246 10 3 +0.951865 11 4 -0.376616 12 5 -0.159272 13 6 -0.081101 14 2 0 +0.667657+0.666028 -3-0.720632+0.371000±0.140281 15 1 16 2 ±0.285100H-0.734285 +0.005193 17 3 18 4 19 5 20 6 21 3 0 -0.172529-0.202467±0.046605-0.202075-0.096038-0.026416 22 1 +0.011043 23 2 -0.542490 24 3 25 4 26 5 27 6 -0.016149 28 4 0 -0.007366

29 1 30 2 31 3 +0.099819 32 - 4 33 5 34 6 35 5 0

36 1 +0.030084 -0.008516 37 2 38 3 -0.093449 39 4 40 5 41 6 42 6 0 -0.001730 43 1 -0.017283 -0.000337 + 0.005229 44 2 -0.001876+0.000861 45 3 + 0.045373 46 4 -0.000 195 47 5 48 6 49 0 7 -0.244550+0.001334 Table 5bCoefficients and ternis of theKT, KTNand KQ polynomials of the Ka 4-70 screw series in nozzles nos. 24 and 37. Nozzle no. 24 Nozzle no. 37

X y Axy Bxy Cxy Axy Bxy Cxy

0 0 0-0.068666-0.026195+0.023557 --0.162557-0.0l6S06 0.016729 i i ± 0.098268 2 2 -0.483300 -0.016989 3 3-1.190490-0.838832 4554 -0.077387 6 6 + 1.005980±0.555129 0.082386 -0.099544 ±0.030559 7 1 0 +0.242630±0.109624+0.072021-0.598107 0.048424 8 1 -0.781923-0.681638 -1.009030-0.548253 -0.011118 9 2 ± 1.136930---0.773230 ±0.230675-0.056199 10 3 -0.037596 11 4 -0.034871 12 5 13 6 14 2 0 ±470803 ±0.259217+0.103364+0.085087+0.460206±0.083476 15 1 +0.425585 16 2 +0.045637 17 3 -0.042003 iS 4 -0.131615 19 5-0.276362 20 6 21 3 0--0.121062-0.058287-0.013447 .-0.216246-0.008652 22 1 23 2 24 3 25 4 26 5 -0.021044 27 6 ±0.013180 28 4 0 -f-0042997

29 1 30 2 -0.012173 31 3 +0.046464 32 4 -0.035041 33 5 34 6 35 5 0

36 1 --0.038383 37 2 38 3 -0.044629 39 4 40 41 6 42 6 0 43 1 -0.001176 44 2 -0.014992 ± 0.002441 45 3 + 0.026228 46 4 47 5 48 6 ±0.009323

49 0 7 -0.239044-0.049039+0.036998+0.051753 - 0.012160 -- K LQ SCREWSERIES uINNOZZLEN2.IRA

O O !UIiiIJu u

uiu 7 i! 4iui u.. u

02 L Fig. 30Open-water test results of Ka 4-70 O' 02 O) Oh 00 06 Ql 08 00 QQ ...12 screw series in nozzle no. 19A.

K.'., u.... K 0.10 SCEW SERIES - IIIii . uuuuiuiuI IN NOZZLE 10022 -u uuuuuu.. u uu uu :riL I! 1Ui1ii:uuiIII i.0I. 03 ifrÀI&

O' uuuuu u um sR Fig. 31Open-water test results of Ka 4-70 02 03 0L 02 06 OB 09 uuuuBO 12 sciew series in nozzle no. 22. w w ti J 77 - - u -I]U j kL-76 SCREW SOPlES IN N0ZZE NOiE 'iIì0 ti aI11!!iuIiIiIi!1' U ' ,fr ¼ U MU 1UU iIÌ IIIÍEI!HH' o Fig. 32Open-water test results of Ka 4-70 Ift0. fl screw series in nozzle no. 24. J Ijil IIIIIIIIIIIIIIlin600105 UUUUUUUUUUUUUUUUUUUU1;!JHIIHIIHHIII UUUUUUUUUUUU1I1IIIHIIIHIHHIII UUUUU UUUuUuUUmaUUUUUUUUUUU UUUUUU .UUNIUU..UU.LIUUU U!UUUUUUUUUU1UUU

n.0 j_u. Fig. 33Open-water test results of Ka 4-70 0UUU I GO screw series in nozzle no. 37. 03 as ìU06 j 07 03 78 Important factors ithe selection ol' a propulsion device From Fig. 34 it can be seen that for ducted propellers for tugs, pushboats etc. are: the efficiency coefficient qj is much higher than for - the forward static bollard pull, conventional screws. Further, it can he seen that the - the astern static bollard pull, effect of nozzle leiìgtli on 17d is small. With increasing - the free-running speed. length-diameter ratio of the system a slight increase in A comparison between the forward static bollard pull the efficiency factor ?/j has been found. of nozzles nos. 24, 22, 19A and 37 and a conventional screw series (the B4-70 series) can be made with the aid A comparison between the astern static bollard pull of of Fig. 34. In this diagram the thrust coefficient KT, nozzles nos.I 9A and 37 and the 134-70 screw series the torque coefficient KQ, the impeller thrust-total thrust can be made with the aid of Fig. 35. From this diagram ratio T and the efficiency coefficient of the different it can be scen that the efficiency factor tid for nozzle no. propulsion devices are given on a base of the pitch 37 is much higher than for nozzle no. 19A. This can ratio F/D. The efficiency coefficient 11d is defined as: be explained by the fact that nozzle no. 19A suffers from flow separation when operating astern. The efficiency (Kr/2t)3"2 factor Jd of nozzle no. I 9A is still higher than the value '/a= (15) KQ of this factor for the B4-70 screw series.

This efficiency can he used as a direct measure for the effectiveness of different propulsion devices at the static 1,8 condition, if systems with the same diameter and power 17 are considered. However, this coefficient must not be

used if there are restrictions in choosing the RPM of the 1.5 different prol)UISiOfl devices. 1.5 10

K1 1.2 10K0

0.5

o 05 08 10 12 1.4 1.6 19

Fig. 35Characteristics of different propulsion devices at astern static bollard condition.

For the method of selecting the propulsion device based o 06 1.0 1.2 14 16 19 on the free-running speed of the vessel, more practical P/ information can be derived from the KTKQ--.J diagram. Fig. 34Characteristics of different propulsion devices at The most widely encountered design problem for the forward static bollard condition. screws of cargo ships is that where the speed of advance

79 of the screw V4, the power to be absorbed by thescrew rs P and the nuniber of revolutions n are given. The diameter D is to be chosen such that the greatest efficiency can be obtained. Pushboats often operate in restricted 02 water. This means that the ship must be limited in draft

and have small propellers or tunnelsterns. In such cases 117. 7, 00 it is more convenient to start the propeller design from given V4, T and D or V4, P and D. The problem of es 08 determining the optimum diameter or the optimum os / number of revolutions can be solved by plotting and 1/j J as functions of: '70 noAi' 0.4 4 :: KQIJ5 if V4, P and n are given, 37 KT/J4 if V4, T and ri are given, 3 3 KQ!J3 if V4, P and D arc given, (16) Vi KT/J2 if V4, Tand D are given. 0.2 For the Ka4-70 screw series in nozzles nos. 24, 22, 19A and 37 and for the B4-70 screw series, the curves 0.1

for optimum diameter (on base of (KQ/J)1 and (KT/J4)) O and for optimum number of revolutions (on base of 050.7 2 345 7 10 20 30 4050 (KT/J2) and (KQ/J3)) are given in Figs. 36, 37, 38 and 39. 5' Fig. 36Curves for the determination of the optimum diam- On comparing the characteristics of ducted propellers eter of various ducted propellers if V4, P and n are given. with the B4-70 screw series, it may be concluded that ducted propellers give a higher efficiency than conventional scre\vs at larger screw loads. The differences

between the different ducted propellers are small. 1.6 Nozzles nos. 19A. 22 and 24 have about a 2 percent higher efficiency than nozzle no. 37. Nozzle no. 37 ira 1.4 IuuuII comparison with nozzles nos. l9A, 22 and 24 presents, p/U however, a very attractive solution when both ahead 02 RI astern operation are of interest. 0.7 7 l.a I From these results it can be concluded that ducted 0.6 io I-/ I propellers are to be recommended for heavy screw loads such as occur on towing vessels, trawlers etc. En addi- 0.5 . I 10 tion, the ditctcd propeller lends itself very well to restrict- vi nozzle nolSA 01. / ed water applications as the nozzle protects theprop- II eller blades from striking fixed objects sLichas the bot- ::I 03 3 tom or banks. Furthermore the nozzle may protect the

propeller from damage by ice. Q2

Finally, it must be noted that the flow velocity at the 0.1

impeller disk of a ducted propeller is far less sensitive o os 0.7 to variations in ship speed than in the case of acon- al-ii.2 3 4 5 7 10 20 304050 ventional screw propeller. Consequently thepower ab- sorption of a ducted propeller is relatively less sensitive Fig. 37Cures for the determination of the optimum diam- to variations in the ship speed. This feature has also eter of various clucted propellers if V4, T and ri are given. been important in the choice of ducted propellers behind tugs, pusliboats and trawlers. Ail these ships must operate satisfactoraly at different loadings (towing and free-running) of the screw. 80 16 For single screw tugs spending an appreciable percentage of their service life to nianoeuvring, the ducted 14 pl0 propeller configuration must include backing rudders forward of the propeller besides the traditional steering 1.2 i rudder located aft of the propeller. Without backing or 07 7 1.0 flanking rudders a fixcd nozzle does not provide direct- iona.l control'hcn backing. A twin-screw tug has 06 0.8 I enough manocuvri ng qual ¡tics.

0,5 River pushhoats can not operate safely without flanking 1?o 1/j i no'zle nolOA rudders. Even on multi-screw pushboats, flanking rudders iii: are to be used to provide satisfactory directional con- 02 3 I trol when backing. In Fig. 40 a typical dueted propeller configuration for a pushboat is shown. 02 2

01 '-..'i>iii

o 0.05 007 01 02 030,4 06 07 2 345

Fig. 38Curves for the determination of the optimum number of revolutions of variuus ducted propellers if J, P and D arc given.

1.6

1h Io

12 Fig. 40Photo model push boat showing the ducted propel- 07 7 1.0 ler configuration.

06 0,8

0.5 7o Investigations have also been carried out to determine 1/, 70 nozzLe the effect on performance of various ducted propeller- 4 0ìrI;,,'___ rudder systems when applied to pushboats and tugs. For instance the effect of the flanking rudder angle o on 03 performance was investigated for a ducted propeller

02 2 arrangement as shown in Fig. 41. The results of these tests are given in Fig. 42. From this diagram it can be 0.1 seen that the flanking rudder angle has a marked effect on the characteristics of the system. With increased Q OES 07 3 45 lO 20 304050 loading of the ducted propeller system a larger flanking rudder S becomes attractive. This is due to the relatively larger slipstream contraction at larger screw loads. Fig. 39. Curves for the determination of the optimum number of revolutions of various dueled propellers if VA, T and A flanking rudder angle O of 15 to 20 degrees gives the D are given. best characteristics.

81 gain in static pressure at least compensates the unfavourable effect of the increased screw loading. The result of an analysis of the minimum pressures which may occur at the blades of a ducted propeller is given in Fig. 43.

0.2

-0.4

Fig. 41Ducoed propeller configuration with single rudder arrangement for a pushboat. a

C Pmin

e o - e a e.,o - O 15

2 a.

-6

-12:3

-2 -.

N 16

- -al -5.2- 0-, 03 05 0K 0.7 O.K 0.6 0.8 LO 12 1.4 Fig. 42Eflect of flanking rudder angle O on open-water Fig. 43Minimum static pressure at impeller blades of a characteristics of ducted propeller configuration for a push- ductcd propeller. boat.

This diagram shows that iniproved cavitation properties Decelerating nozzles for the particular screw considered (blade-area ratio AE/AO = 1.0 and number of blades z = 5) only occurs As already mentioned, the application of the flow for low values of the thrust coefficient CT. If ducted decelerating nozzle may be attractive if retardation of propellers with larger blade-area ratios of the inipeller propel!er cavitation phenomena is desired. The reduc- or with more rotor- (and eventually niore stator-) rows tion of the flow rate inside the dccelerating type of arc considered, the decelerating nozzle may favourably nozzle results in an increase of the static pressure at the affect the4cavitation properties of the screw for larger impeller. However, the duct itself will produce a negative values of Ci.. thrust (r > 1). Tn order to compensate for this thrust loss (induced nozzle drag), the impeller loading must Application of the decelerating nozzle results, further- be increased. An improvement of the cavitation proper- more, in a reduction of the pressure at the exterior ties of the impeller will therefore only be obtained if the surface of the nozzle. From a comparison between the

82 mi nimuni pressures which occur at the exterior surface Table 7Cocfficients and terms of theKT,Ár and KQ of the nozzle and at the .inipcllcr blades, it can be con- polynomials of the Kd 5--100 screw series in nozzle no. 33. cluded that except in the case of very short nozzles or very Kd 5-100 series inozzlc no. 33 low loaded systems, impeller cavitation is niore critical. Systematic series of model tests with decelerating ducted xy C>. propellers have also been performed. The design of the O 00 -0.347562 --0.0077894 +0.083142 nozzles was based on the vortex theory as described in i 0 1 --0.321224 -0.0224240 -0.332286 [119]. The variation of the design parameters 2 0 2 -f- 0.075277 +0.305926 considered is shown in Table 6. The experiments 303 -0.0090870 -0.1132106 450504 -0.009560 Table 6Design parameters of decelerating nozzle series 606 -0.013948 7 1 0 -f-0.963261 Nozzle number C.-0 t0 LID alL $/L diD 8 1 1 -0.215803 9 12 -0.0104923 -0.349298

30 0.95 1.00 0.6 0.5 0.15 0.20 10 1 3 31 0.95 1.15 0.6 0.5 0.15 0.20 11 i 4

32 0.95 1.30 0.6 0.5 0.15 0.20 12 1 5

33 1.0 1.2 0.6 0.5 0.15 0.20 13 1 6 -0.000031 34 1.0 1.2 0.6 0.5 0.09 0.20 14 20 -1- 0.0824632 35 1.0 1.2 0.9 0.5 0.10 0.20 15 2 1 36 1.0 1.2 1.2 0.5 0.075 0.20 16 22 -I- 0.0261933 17 2 3 -0.0095845 + 0.038469 18 2 4 with these nozzles were all carried out with a series 19 25 +0.0010293 of five bladed Kaplan type screws (Kd5-100 series). 20 2 6 The Kd 5-100 series screws were designed in 21 3 0 +0.119965 22 3 i - 0.007 6923 combination withNSMBnozzle no. 33. The pitch clistribu- 23 3 2 +0.013402 lion of the screws depend on the velocities induced by 24 3 3 the nozzle at the impeller plane and on the radial load 25 3 4 distribution. For the design, use was made of [117]. 26 3 5 Particulars of the screw models are given in Table 8 27 3 6 -0.0000935 and in Fig. 44. The screws were located in the nozzle 28 40 -0.016882 -0.0031955 -0.043816 wit h a uniform tip clearance of 1 mm. The fairing of the 29 4 1 open-water test results was performed by means of 30 4 2 regression analysis. The polynomials toet1ier with the 31 4 3 coefficients arc given in Table 7. The K-K0-J diagram 32 44 -0.000 1172 of nozzle no. 33 with the Kd 5-100 screw series is given 33 45 in Fig. 45. 34 46 35 50

36 5 1 + 0.001752 37 5 2 Table 8Typical Bp and CT values for different ship types. 38 5 3 C- 39 54 40 5 5 Torpedo's <10 <0.5 41 5 6 Twin-screw ships 10-15 0.5-1.0 42 60 Fast warships (frigates, destroyers) 10-25 0.5-1.5 43 6 1 Single Screw cargo ships 15-35 1.0-2.5 44 62 Coasters 35-60 2.5-4.0 45 63 Tankers 35-70 2.5-5.0 + 0.000 1523 46 64 Trawlers 60-100 4.0-8.0 47 6 5 Towing vessels (tugs, pushboats) >80 >6.0 48 66 -0.000028 49 0 7 J 0.003691 ua3933 i3etad btede li. PasS dbatQ: ___ .___

no 3931 003934 p pressure Side .0 back side .52

Particulars All screws 0.240 nyc z . 0167 A,A10

no 3932 Screw ro3930 P110.10 (at OiR) no3931 .12 nu3932 - .14 Fig. 44Particulars of Kd5-lOOmodel propellers. no.3933 - .16 no.3934 - -IB -.

10 10 2 j.. 09 ______

08 07 IUIIUÌ1HJHIIr

05lo

04 -'i

O-

02O I.15'

s 02 TU!!IL!!I 06 08 10 12 14 IO 52 o' 2 t8 2)2 02 24 26

Fig. 45Open-water test results of Kd5-100propellers ¡n nozzle 610.33.

84 From all the model tests performed with accelerating Optimum curves for open-water efficiency i, diameter and decelerating nozzles at theNSMBit can be deduced coefficient 6 and thrust ratioîof the Ka 4-70 screw that the relation between the thrust coefficient CT and series in nozzle no. 19A, the Kd 5-100 screw series in the thrust ratiotof a ducted propeller system is nozzle no. 33 and the B 4-70 screw series are presented approximately independent of the pitch ratio P/D of in Fig. 47. Typical Ba-values for different ship types arc the impeller. Furthermore, it was found that for the indicated in Table 8. The lightly loaded screws of fast considered nozzles there exists a fixed relation between ships arc on the left side of Fig. 47 while the heavily the impeller disk area-nozzle exit area ratioAO/AEX. loaded propellers of towing vessels are on the right. It This result is shown in Fig. 46. In Fig. 46 the optimum efficiency which can be obtained with the different ductcd propeller systems is also given. Furthermore it can 400 be seen that with decreasing value of the area ratio 360: I Ao/AEX, the thrust ratio r decreases and the efficiency noZL,0033. n000Ie no 196 .... / - 'io of the dueled propeller system increases. Thus with 320080 i n0o increasing positive loading of the nozzle, the efficiency 780020 of the dueled propeller system increases. The loading of the nozzle, however, is limited by the risk of flow 240 separation on the nozzle. 700 .;w, 160 : ; 20 070 ,.,zot,f033t t I 80020 6 -.. nolgA.t---0g aso

010 07 aso I. es 040 .5 2 3 46 IO 20 30 4050 70 00

ajo Fig. 47Optimum relationship between q, (5 and Bp of the

620 Ka 4-70 screw series in nozzle no. 19A, the B4-70 screw 080 0.90 1.30 10 series and the Kd 5-100 screw series in nozzle no. 33. 06 -

1.5 can be seen from Fig. 47 that the accelerating nozzle 1h (nozzle no. 19A), when compared with a conventional u cv' screw (B 4-70 series), gives rise to an improvement in u open-water efficiency 910 in the case of heavy screw loads. The decelerating nozzle (nozzle no. 33) has a low open- j water efficiency 'Jo The curves of the diameter coefficient w 6 of the accelerating and the decelerating nozzle almost coincide; the B 4-70 series has a larger optimum screw 09 diameter. It is interesting to note that the curves for the diameter coefficient c5* based on the maximum diameter of the system of both the accelerating and the decelerating nozzle and the B 4-70 screw series almost coincide.

as Wake adapted nozzles 0h 680 WO A0/A 1.10 120 130 1.40 EX Usually the variations of the velocity field at the screw Fig. 46Relations between impeller disc area-nozzle exit behind a ship can be split up into two components: area ratio, thrust coefficient C and efficiency of a duct- 1 The radial variation, especially of the axial velocities. ed propeller system. This variation does not lead to unsteady phenomena at

85 the screw. A propeller working in such a velocity field has a steady flow-and force-pattern. Moreover, the propeller can be adjusted to this radially non-uniform flow by an appropriate distribution of pitch and camber, and optimum efficiency and cavitation properties may be expected. 2 The circumferential (at a given radius) variation of both the axial and tangential velocities. This non- uniformity is the origin of the periodically fluctuating pressure distributions along the blade chords and leads to the unsteady force pattern at the screw and at the stern of the ship. These periodically fluctuating pressure distributions also lead to unsteady cavitation phenomena which may be serious from a viewpoint of erosion and noise radiation. In addition, these unsteady pressure distributions lead to propeller induced vibrations. The inflow to the screw can be made more constant over the screw disk by surrounding the propeller by a non- axisymmetrical nozzle which is adapted to the wake Fig. 48View of stern of tanker fitted with non-axisyrnmetri- distribution and the flow direction behind the ship. cal ducted propeller.

Based on results, as presented in Fig. 47, propulsion tests have been performed at the NSMB with a large number of tanker models equipped with ducted pro- Table 9Reduction in DHPof tanker fitted with vai-ious pellers [I 19J. The results of these tests generally confirm nozzles with respect to tanker with conventional stern and the conclusion that an increase in propulsive efficiency propeller. can be obtained by application of a ducted propeller Configuration Loaded Ballast for this ship type. In the case of a single screw ship the condition condition intake velocity will be lower in the upper part of the Ship with conventional stern and screw disk than in the lower part. Consequently, the axisymruet neal ducted propeller.2-6 % propeller is more heavily loaded in the upper part of Ship with conventional stern and the screw disk. By applying a non-axisymetrical nozzle non-axisymmetrical ducted reductions which is adapted to the wake distribution as occurs propeller. 6-9 % about 230/ behind the ship, acceleration of the flow in the upper larger part of the screw disk (by increasing the exit area of the Ship with cigar-shaped stern and nozzle) and deceleration of the flow in the lower part axisymmetrical ducted propeller. 5-8% of the screw disk (by decreasing the exit area of the nozzle) can be realized. A view of a tanker wth a conventional stern and equippcd with a non-axisymmetrical nozzle is given in Fig. 48. In Table 9 the results velocity of the impeller that the non-axisymmetnical of a large number of model self-propulsion tests, ducted propeller offers a means of mininhizirig propeller performed with tankers with conventional and cigar- induced vibration and cavitation problems. shaped stern arrangements and fitted with conventional screws, ducted propellers a rid non-axisymmetrical duct- For naval ships it is of importance that the cavitation ed propellers, are compared. From this lable it can be inception speed, or the lowest speed at which cavita- seen that the conventional stern with the non-axisyrn- tion phenorjcna at the screw occurs, should be as high metrical ducted propeller gives a reduction in DHP as possible. For tactical reasons a minimum radiation which is still larger than can be obtained by application of propeller noise is necessary. In the case of twin screw- of a cigar-shaped stern with axisymmetxical nozzle. In ships, the propellers operate in a varying inflow primarily addition, it may be expected from the homogenizing due to the shaft inclination. This inclination is a conse- effect of the non-axisymmetrical nozzle on the inflow quence of the fact that the propeller shaft usually has a 86 sizeable inclination to both the horizontal and the Propeller testing techniques and facilities buttock lines in way of the propeller. Wake data indic- ate that the flow follows the buttock linesclosely. From Introduction the viewpoint of retardation of propellercavitation, the application of a non-axisymnietrical nozzle may be. As already mentioned, the Netherlands ShipModel attractive here also. This nozzlc must be designedin Basin has recently completed the building of adepres- such a way that the actual effective incidence changes surized towing tank. The decision to build such afacility of the blade sections of the impeller will be as low as was for a large part a consequenceof the fact that possible during a revolution. A part of the stern of a conventional cavitation testing facilities such as cavita- twin-screw ship fitted with non-axisymmetrical n ozzles tion tunnels very often supply insufficient and unrealistic is shown in Fig. 49. This nozzle (the starboardnozzle) experimental information regarding cavitation on the accelerates the flow velocity with respect to the mean propeller and associated interaction effects between flow velocity at the starboard side (q =900) by in- propeller and ship aítcrbody. This is primarily caused creasing the exit area of the nozzle and decelrates the by the absence of the ship's hull in the cavitation tunnel flow at the port side ( = 270°) by decreasing the exit in front of the propeller. Elsewhere, other research area of the nozzle. The nozzle iscylindrical at the trailS- facilities have recently built large cavitation tunnels in ing edge. Th leading edge of the nozzle is adapted to order to be able to build the ship model into the test the flow direction. The velocity diagrams of a screw section. In order to evaluate these new developments in blade-element at a radius of 0.7R are given in the same propellr and ship model testing, an evaluation of con- figure for the different angular positions of the blade. ventional techniques and facilities is necessary.

Tc generaf p, obleni of obicining ca"ilat fon s0inilarity i'; jiiode! testing HULL BUTTOCK LS WAY OR PROPILCER CESTFRÇI( Detrimental cavitation effects have their origin in the interference of the cavitation zone with the fluid flow. lt is therefore necessary, in studying cavitation and its effects on a model scale, to ensure geometric and flow similarity. Any deviation from geometric and so-called kinematic similarity will cause a scale effect. Two geo-

Vt metric figures are similarifthe ratios of all the corres- DIRECTIOu OF \H O TK IO 0G K R O UK A) pondi ng lengths are identical, while kinematic similarity

LOOKING FORWARD is complied with when the flow velocities around model and true object have the same direction. Dynamic similarity is obtained when the specific forces on the model ..sa. and thefullscale object are similar. To obtain dynamic or physical similarity the effects of gravitation,viscosity, - 0KWH O, surface tension, vaporization, temperature, etc., must be accounted for. That is, the scaling factors must be Fig. 49Hull of twin-screw vessel fitted with non-axisym- known in order to accomplish the conversion. Sedov metrical nozzles. [120] defines dynamic similarity as follows: Two phenomena are similar if the characteristics of one can be obtained from the assigned characteristics of the These diagrams show that the angle of incidence of the other by a simple conversion analogous to the trans- flow with respect to the blade element can be made formation from one system of units of measurements constant during a revolution. However, the incidence to another'. velocity of the blade element will vary. Results of tests In the case of dynamic similarity, therefore, all the performed with a non-axisymmetrical nozzle at different nondi mensional variables (nondimensional combina- shaft inclinations in a cavitation tunnel of the NSlR tions of dimensional quantities) have the same numerical have shown that an improvement in the cavitation values. This statement leads to the following important characteristicsofthe screw can be obtained. axiom in the modelling of physical phenomena: 87 'The necessary and sufficient conditions for two pheno- - F, implies that Vm =V/.J) mena to be similar, are that the numerical values of the - R,, implies that V,,, V..) nondimensional coefficients forming the basic system - W, implies that Vm = V..J are constant. These conditions are called similarity (18) criteria'. -oimplies that Vm = The physical similarity problem is thus reduced to the - J implies that Vm = V.nm/n) problem of finding this set of nondimensional coeffi- - ir7 implies that V,,, = V.) cients. where it is assumed that for prototype and model g,,, = This is possible with the aid of dimensional analysis g, p = p, q,, = q, a,, = a, Pg,, = Pg, dm = dand as shown in [121]. There are 9 important independent Cm = e. Here ? is the model scale and the subscript m nondi mensional coefficients. These are: refers to the value for the model. It follows that when the properties of sea water and the water used in V2 pVD P laboratories are considered identical, simultaneous ir1= ir2= ; ir3= gD q pV2 identity can only be obtained for the following groups: - F,,, a0 and J when the pressure and rotativepropeller Pg. p V2D Pv speed can be freely chosen; ir4 its= ir6= (17) pV2' a pV2 - R,. a0, .1 and ir7 (the gas diffusion number) when again the pressure and rotative propeller speed can be d V. C freely chosen and the required high flow speeds for R,, it7 ir8 = ir9 = VD' nD p offers no problems; - W,, a0 and J when once again the pressure and in which rotative propeller speed can be freely chosen. -

flow velocity (LT-1), Tn a cavitation tunnel, model testing with marine g= acceleration due to gravity (LT-2), propellers is usually performed in accordance with the static pressure (L-1 MT-2), cavitation number and the coefficient of advance (or '1= dynamic viscosity of fluid (L-MT-'), so-called KT-idcntity) only. Simultaneous identity of p-r- fluid density (L3M), F, and R, is impossible in water. if model propellers a = surface tension of licuid-gas interface (MT2), are run at the correct Froude number this would imply e = gas concentration in fluid (L-3M), low water speeds and therefore under-critical flows. vapour pressure (L-1 MT-2), Water speeds are therefore chosen as high as possible P9 = gas pressure in cavity (L'MT2), to minimize R, differences occurring between prototype d = diffusion coefficient of gas (L2T-2), and model. The scale effects associated with not com- D = propeller diameter (L), plying to the various nondimensional similarity criteria n = rotative propeller speed (T-i) derived above is discussed in one of the following sec- Tt is readily seen that tions. ir1 = Froude number F,, Present methods employed ¡n 1/ic study of ca rit allan on ir2 = Reynolds number R, marine propellers ir5 = Weber number W ir3 = Advance ratio J Historical development From the combination of ir3 and irthe cavitation number o-can be formed. The gas diffusion number ir7 To study cavitation on a model scale, it is necessary to and the gas (air) content number ir9 have as such have at one's disposal a facility in which the water never been used in model testing. Simultaneous identity pressure can be varied. The need for suc.h a facility of these 9 nondijuensional coefficients for prototype was first realized by Parsons. He constructed the fore- and model is hardly feasible. For instance in water: runner of the modern cavitation tunnel in 1895. A photo of this historical tunnel is shown in Fig. 50. In 1910 Parsons constructed a larger tunnel in \Vallsend, England, with which he was able to test 12 inch cavitat-

88 lion was controlled by varying the circulating pump speed. The test section included devices for measuring thrust, torque and model propeller speed. The propeller vas illuminated by a large searchlight through a system of revolving mirrors directly into the propeller plane.

In 1929 a 12-inch propeller testing tunnel vías built at the David Taylor Model Basin. In the years that followed, cavitation tunnels vere built in Hamburg at the Hamburg Model Basin, at the National Physical Labor- atory in Feltham England, at the Masachusetts Institute of Technology and at the Netherlands Ship Model Basin. By ibis time man)' refinements and improvements over Parson's tunnel and been developed.

Description of some cavitation tunnels suited for propeller testing and their characteristics.

The large cavitation tunnel of the Netherlands Ship Model Basin, see Fig.52,was designed and built in the period between 1938 and 1940. Between1962and1966 Fig. 50.Parson's first cavitation tunnel(1895). lIte test scction, downstream bend ard difusor vere modified to improve its cavitation and noise characteristics. This tunnel is a very large unit, having an octagonal test section shape of0.9ni by0.9ni, and is suited for propeller models up to a diameter of 500 mm (20 inches). The maximum waler speed in the test section is about 11 rn/see, the maximum poss'er absorbed by the impeller is 300 hp, that by the propeller model 250hp, whilst the maximum propeller speed is 3200 r.p.m. Recording of propeller thrust and torque is by means of strain gauge dynamometers. The minimum obtainable cavitation number is about 0.3. The cavitation phenomena is observed by means of stroboscopic lighting. This tunnel is used for noise measurements on cavitating propeller models and for investigating various propellers and propeller configurations (contra-rotating propellers, vertical axis propellers, overlapping prop-

Fig.51 Parson's second cavitation tunnel (1910). ing propeller models. This tunnel consisted of a closed circuit with a flow path of about20metres, see Fig. 51. The test section was about 0.7 metres by0.76metres with glass windows in the sides. Distilled water was circulated from a4.25metre diameter and 3.5 metre high stilling tank through the test section down to a low level where the circulating pump was situated, and back to the stilling tank. The flow rate in the test sec- Fig. 52Large cavitation tunnel of the NSMB.

89 ellers, etc). Special arrangements have been made for type of cavitation tunnel arc its complexity and its low testing propellers in inclined flows and behind built-in hydraulic efficiency due to increased flow resistance. ship afterbody models. A more detailed description of this tunnel is given by Witte and Esveldt [122]. The fact that variable throttling over the upstream flow This cavitation tunnel is representative for a whole cross section by means of a screan or flow regulator class of cavitation tunnels specifically built for research does not reproduce the basic three-dimensionality of of propeller cavitation. Typical characteristics of these the flow behind the ship's hull, has been the reason to tunnels is their large size (in connection with the desire construct tunnel working sections in which upstream a to test at high Reynolds number and to reduce wall model of the adjacent portion of the ship can be built- effects) and their moderate flow velocity in the test in. At the Netherlands Ship Model Basin this method of section. constructing in the tunnel working section, upstream of the propeller, a model of the ship's afterbody is used From the viewpoint of marine propeller research, a in cases where the tangential wake components are second type of cavitation tunnel was introduced in 1955. relatively important. The large cavitation tunnel, already At that time experimentors were becoming aware of described, was adapted for this purpose, the upper the fact that the differences occurring between the portion of the working section being removable and erosion patterns on screw blades obtained in the cavita- suitable for models of 2,5 m length. The difficulty of tion tunnel and those of the ship were due to imperfec- providing enough of a ship model to produce a satis- tions regarding the correspondence of the velocity factory approach to the influence that the real ship has fields in which the model propeller was tested. The use on the flow remains however. A problem inherent in of solids of revolution in front of the propeller in the this approach is the choice of model scale, since the cavitation tunnel to imitate the radial distribution of the amount of hull surface that must be modelled to obtain velocity field was in this regard found to be unsatis- a satisfactory velocity distribution for the propeller factory. The same applied to the placing of roughened requires a relatively small-scale model. planks or wire mesh in iront of the propeller. Attemps The propeller diameter should not be too small, how- to eliminate the effects of these imperfections by testing ever, in connection with manufacturing difficulties of at a cavitation number 10 to 20 percent less than that the leading edges and in connection with avoiding large of the full-size propeller vas found to be only a very Reynolds scale effects. Figs. 53 and 54 show built-in rough correction. The NSMB decided, therefore, to build afterbody models in the large cavitation tunnel of the a new cavitation tLlnnel in which the flow could be Netherlands Ship Model Basin for simulation of the regulated in accordance with the required distribution non-uniform flow for respectively a twin-screw vessel of the axial velocities. This flow regulator divides the and a single-screw vessel. cross section into a large number of elementary sections. The amount of fluid passing through each sec- These difficult facets of model testing in cavitation tun- tion can be adjusted by means of a valve. The valve nels have led various laboratories to build larger cavita- rods are adjustable from the outside. This tunnel was tion tunnels with or without a free water surface. Tite built in 1955 and came into usc in 1956. It is suited Swedish State Shipbuilding Experimental Tank has for testing propeller models with a diameter up to 250 recently built a large cavitation tunnel especially suited mm (10 inches). The maximum r.p.m. of the propeller for ship models of a length between 6.5 in and 8m. This model is 3500, the maximum torque is 4 kgm, the cavitation tunnel has a length between the centre lines maximum thrust is 100 kg and the average speed in the of the vertical parts of 20 m and a height between the test section is 4.5m/sec when the flow regulator is in horizontal parts of 12 ni. Large cavitation tunnels of operation. The minimum cavitation number in this this type, with or without a free surface, may be classi- condition is about 2.0. The maximum power absorbed fied as the third type of cavitation tunnel suited for by the propeller model is 13.5 hp. propeller testing. The KrylofY Shipbuilding Institute and The velocity field in way of the screw can be measured the Nethelands Ship Model Basin have selected the by means of a rotating pitot-rake which can also be alternative to this type of cavitation tunnel; the depres- moved longitudinally. The test section of the tunnel is surized towing tank. Mention should also be made of circular and at the propeller position provided with a the existance of many other cavitation tunnels of a slotted val1 to reduce tunnel wall effects whereby rela- multy-purpose nature, used for the testing of turbines tively larger models can be tested. The drawbacks of this and other hydraulic devices, and of a special nature 90 such as high speed cavitation t unnels of which the Netherlands Ship Model Basin also possesses one. A description of a large variety of cavitation research facilities is given in [123].

Factors prevenhi/ig precise simulation in cavitation tunnel testing

From the previous sections it shall have become appar- ent that a number of difficulties exist preventing precise simulation of full-scale behaviour in the cavitation tunnel. The factors involved arc the impossibility of simultaneous identity of the 9 similarity criteria already discussed, wall effects, and the difficulty involved in the simulation of the irregular flow behind the ship.

Scale effects and cavitation scaling

The impossibility of simultaneous identity of the various similarity criteria discussed earlier, introduces so-called scale effects. To account for these scale effects ii is necessary to devise corrections. This is termed scaling. Normal cavitation tunnel testing with marine propellers is usually performed in accordance with a nominal 1ig. 53Photo of built-in model aflerbody of a twin-screw cavitation number and the ratio of advance only, the vessel in the large cavitation tunnel of the NSMB. water velocity in the test section being adjusted as high as possible. This implies that neither the Froude number nor the Reynolds number is obeyed. This is in consequence of the fact that were the Froudc number obeyed, the water velocity in the test section would be low and as such prescribe low pressures. A further consequence would be that the Reynolds scale effect would be larger than it already is. Identity of Reynolds number on the other hand prescribes extremely high vvater velocities in the test section. The scale effect resulting from not obeying the Froude number is probably the most serious. lt implies that the local cavitation number at a particular propeller radius x (= nR) and angular blade position ço will not be the same for model and ship propeller. This follows from the fact that when, e.g., at the centre line of the shaft ut,,, = the nondimensional pressure head difference in the model at a point (x,) can only have the same value as for the prototype when: pgR, pgR (I 9) 4-pi';,,2 -4pV2 i.e. when Vm = V/%/Â

Fig. 54Photo of built-in model afterbody of a single-screw vessel in the large cavitation tunnel of theNSMB.

91 When the Froude number is not obyed, therefore, cavitation parameter encountered within the prototype'. equal values for the cavitation number for model and prototype can only be obtained in one point. In that This last view would be true were it not for the necessity case this point is usually taken to be at the centre line in propeller testing to take into account the influence of of the shaft, in this way securing a nominal cavitation the wake on the cavitation properties: these are not number. The argument that in this way cavitation prop- 'easily and accurately calculated'. In a homogeneous erties are effected least, due to the fact that the average propeller inflow this method would indeed seem to be value of the local cavitation number at (x, ç) during a the best. The variation in the angle of attack during a propeller revolution is the same, is not correct however. propeller revolution in the wake, however, leads to This is due to the fact that the conditions for cavitation instationary cavitation phenomena and in consequence inception are not the same as those for cavitation once different effects on performance, erosion, propeller- it has been formed. Hence it is important to secure induced vibrations, etc. can be expected from case to identity of the local cavitation number. Newton [124J case, depending on the ship's afterbody and appendages. gives an example of the influence of the effect of These effects can only be ascertained when the develop- Froude number on the onset of tip vortex cavitation. ment of cavitation on the model propeller is similar. There is a marked difference between the value of the nominal cavitation number for onset of this cavitation At this stage it is difficult to determine the influence of form at different Froude numbers. When determining Reynolds number on the onset of cavitation. Various the ship speeds at which cavitation inception on the test results show an increase of the value of the cavita- propeller occurs, it is therefore important to perform tian number with increase of the Reynolds number. in the tests at the correct Froude number. general it is assumed that as long as the flow is super- critical large scale effects will not occur. In this regard The importance of performing experiments at the cor- it should be noted that the flow in most cavitation rect local cavitation number also follows from the tunnels is rather turbulent. A Reynolds number of large influence of Froude number on propeller perfor- approximately 3 x 10to 5 x l0for the chord length mance. This is to be expected since this influence is at 0.75R should be sufficient in most cases. For a large largely an influence on the extent of cavitation on the tunnel the R,, influence can to a certain degree be propeller during a revolution. To improve the simula- obtained explicitly by conducting tests on a geosim tion of the pressure field over the propeller, Newton propeller series at the same F,,. But then again, the suggests using as a nominal cavitation number the local difference in wall effect on the different propellers ¡s a cavitation number for x 0.7 for the upright blade disturbing factor, as are also the physical properties of position. He goes further to state that: 'The low water the fluid when extrapolating to full-scale values. speeds needed to run a model propeller at the correct Fraude number will mean a low Reynolds number and The scale effects associated with the physical properties introduce a larger error in viscous scaling effects, but as of the fluid are also largely undetermined. An important the author pointed out to the 9th I.T.T.C. ¡t should be physical property of the fluid is the gas or air content. easier to correct for one larger error than for two smaller The air content, as measured by the Winkler or Van and interrelated errors'. Slijkc method, is the total air content of both dissolved and undissolvcd air. It is the undissolved air content, On the other hand Knapp et al [125] suggest that: however, which influences cavitation inception. Various 'The variation ¡t cavitation characteristics of an individ- tests at different laboratories have shown that the in- ual liquid is governed by properties of the liquid ii fluence of air content on cavitation inception and cavita- ways which are not clearly understood. On the other ating propeller performance can be large. The precise hand, the variation in cavitation parameter due to the scale effect and scaling rules can only be detbrmined variation in depth during a revolution of a propeller or when the undissolved air (gas)contcnt and the size of the turbine runner is easily and accurately cidculated. There- bubbles (bubble-spectrum) in which it is present can be fore, it would seem wise to make model tests of large accurately determined. At the Netherlands Ship Model low-Froude number equipment by using prototype or Basin such fundamental cavitation studies are under- higher velocities in the model and to explore the differ- way. The determination of this bubble spectrum in the ences in cavitation characteristics by making tests at cavitation tunnel is to be attempted by holographic various system pressures to cover the range in the means. In the meantime it is important to keep the 92 total a ir conten t constant du ri ng t un nel testi ng. This In a dcpressurized towing tank, a method of model can be done by either a standard cavitator or frequent testing far in advance of contemporary testing methods measurements. lt is also important to ensure that read- is possible. Testing can be carried out in accor- ings are not rnadc untill sufficient time has passed after dancerith t he Froudc iìumbcr, the cavitation number every velocity or pressure changc in the tunnel, so that and the coefficient of advance. This means that identity stability between the amount of dissolved and uudissolv- of the local cavitation number is obtained. Furthermore, ed air is obtained. To conclude this section it miehi be the problem pf correct simulation of the propeller stated that it is of little or no avail to consider surface inflow is no longer present. The correct effect of cavita- tension, gas diffusion and other cavitation scale effects tion in propeller performance, propeller-induced vibra- in model testing when one does not possess the means tions on the afterbody, etc, can easily he obtained. In to measure the undissolved gas or air content and the addition, the dimensions of the tank have been chosen way this is present in the fluid. As already mentioned, such that propeller and ship models can be large enough this physical property of the fluid is perhaps the most to avoid unpredictable Reynolds number effects with important in modelling cavity flows. - respect to propeller cavitation, perlormance, flow separation phenomena on the ship's hull, etc. Tunnel wall effect List of symbols The presence of boundaries, in the form of tunnel walls, influence the flow conditions in the test section. Cor- a axial distance between leading edge of nozzle rections for the effect of tunnel walls for non-cavitating and impeller plane. propcllnrs in the screw race can be calculated by a expanded blade area of screw. method given by Wood and Harris [126] when the exit area afozzle. propeller is considered as an actuator disk. The extra A0 disk area of screw wall effect due to the finite number of blades and the Ar constant in equation for Sr/D for Wageningen B-series propellers. presence of tangential induced velocities has been shown distance between leading edge and generator by Van Manen [127] to be negligible for ratios of line at radius r of Wageningen B-series propellers. propeller disc area to tunnel cross section normally coefficients in KT polynomial of ducted propellers employed. For cavitating propellers in a cavitation tun- B loading coefficient, Bp = 33.07 KtQ.j_5/2 nel no adequate method for determining the effect of B constant in equation for Sr/D for \Vagningcn tunnel walls on performance and on the cavitation pat- B-series propellers. tern has as yet been devised. br distance between leading edge and maximum thickness of blade section at r of \Vageningen Simulation of irregular propeller inflow in the cavitation B-series propellers. tunnel coefficients in KTN polynomial of ducted propellers. C chord length of blade section of propeller and gas concentration in fluid. The difficulties involved in the correct simulation of the C0 7 55 chord length of blade section of propeller at irregular propeller inflow in cavitation tunnels has al- 0.75R. ready been commented upon. Due to the fact that CD drag coefficient of propeller blade section, cavitation patterns on propellers are very much depen- D dent on the varying angle of attack during the propeller C revolution it will be obvious that propeller performance = 1/2pV02c is also appreciably affected. Nowadays everyone is CD",in minimum value of the drag coefficient. convinced about the importance of correct simulation CF skin friction drag coefficient. of the ship wake at the propeller position; the problem CL lift coefficient of propeller blade section, now is how to obtain the best possible simulation. The L CL Netherlands Ship Model Basin believes that this can be 112P V02c adequately done rnly by including the ship's hull in propeller testing. This has been one of the reasons for P-P0 CP pressure coefficient, Cp = the Netherlands Ship Model Basin to build a depressur- '/2P V02 ized towing tank. Cprn in minimum pressure coefficient.

93 VA speed of advance of open-water propeller CQ torque coefficient, CQ Va axial propeller inflow velocity component ''/2,0V2A4D2 VP average velocity at propeller disk. cl. chord length of Wageningen B-series propellers Vs ship speed. at radius r. Vt tangential propeller inflow velocitycomponent. c,t.. coefficients in KT and KQ polynomials of Wage- axial induced velocity at a specific propeller. fingen B-scries propellers. radius and angular blade position. T Wi tangential induced velocity at a specific propeller CT thrust coefficient, C,- radius and angular blade position. 'I2PV2AD2 pV2D CT,, design thrust coefficient. w,, Weber number, W,, - cxy coellìcients in KQ polynomial of ducted propellers. a D propeller diameter and drag force. (based on propeller diameter), d diffusion coefficient of gas. X dimensionless propeller radius, x= nR f caniber of propeller blade and nozzle section. X power of P/D in KT, KTN and K polynomials for V2 ducted propellers. F,, Froude number, F,, = gD y power of J in K,-, KTN and KQ polynomials for ducted propellers. g acceleration due to gravity. z number of propeller blades. A E/Ao blade al-ea ratio of screw. J advance coefficient, J VA uD Ao/Aix ratio between impeller diskarea and exit area of nozzle. T fiL camber ratio of nozzle. thrust coefficient. K= pn2D4 P/D pitch ratio of screw. L/D nozzle length-diameter ratio SIL TN maximum thickness ratio of nozzle. KTN nozzle thrust coefficient, KTN tic -pn2D4 thickness to chord length ratio of profileor propeller blade section. o thickness to chord length ratio of propeller blade KQ torque coefficient, KQ = pn2D5 section at 0.75R. angle of attack of flow relative to nose-tail line L nozzle length. of propeller blade section. ii, N number of revolutions per second and per effective hydrodynamic inflow angle relative minute. to P nose-tail line of propeller blade section ata pressure, propeller pitch and power. specific radius and angular blade position, PO static pressure. Pg gas pressure in cavity p p,, vapour pressure xm,iD+ Ve-o',, torque Q maximum value of effective hydrodynarnic in- R propeller radius flow angle at a specific propeller radius and ship local propeller radius speed. p VD fil minimum value of effective hydrodynanic inflow R,, Reynolds number, R,, =- (based on angle at a specific propeller radius arid ship 11 speed. propeller diameter). z1ß1 angular variation in the effective hydrodyiiamic R,0.75 R Reynolds number based on chord length of inflow angle at a specific propeller radius and propeller blade section at 0.75R (see equation 6) ship speed. S maximum thickness of nozzle section. Sr propeller blade section thickness at radius 101.27 r of ¿5 diameter coefficient or speed ratio, ¿5- Wageningen 13-series propellers. J T thrust ¿5* iamcter coefficient or speed ratio basedon the propeller blade section thickness. maximum diameter of ducted propellersystem. thrust of impeller of ducted propeller. efficiency. V flow velocity. open \vater efficiency of propeller in the static Vo undisturbed flow velocity. bollard condition (see equation 15).

94 ideal efficiency. 1 I R. C,rammcl, Die hydrodynamischen Grundlagen des Fiuges. Brau oschweig, F. Vieweg, I 917. KT.J lo open-water efficiency, = 12 R. Mck. Wood. and H. Glaucri. R & M. 620, 1918, 2irKQ Aeronautical Research Council. o flanking rudder angle. 13 L. Prandil. Turgflächentheorie I und II, Göttingcr À scale ratio of prototype to model. Nachrichten, 19 1 8 and I 9 I 9. Reprinted in L. Prandtl, and V kinematic viscosity of valer. A. Betr.: Vier Abhandlungen zur 1-Jydro- und Aerodynamik, 7t1.9 dimensionless dynamic similarity coefficients. Göttingen, 1927. p fluid density. 14A. Betr. Screw Propellers with minimum Loss of Kinetic ci cavi tat ion number based on vapour pressure, Energy. reprinted in Vier Abhandlungen zur Hydro- und Aerodynamik. by L. Prandil and A. Betz. 1927. Po-Pv 15H. Glauert. Elcmenls of Aerofoil and Airscrew Theory. 1/2p V02 Ca mbridge University Press, I 926. G surface tension of liquid-gas interface. 16E. Pistolesi. Neue Anstitze und Ausführungen zur nominal cavitation number Theorie der Luftschrauben. Berlin, 1924. 17S. Kawada. On the Fundamentals of the Vortex Theory T impeller thrust-total thrust ratio, T = - of Airscrevs. International Congress, Rome, 1928. T 18S. Kawada. On the induced Velocity and Characteristics T0 design thrust-total thrust ratio. of a propeller. Journal of the Faculty of Engineering, Tokyo, angular blade position relative to the top Imperial University, Vo!. 20, 1933. (12«clock) blade position. 19S. Kawada. Induced Velocity by Helical \'ortices. 0) angular velocity. Journal of the Aeronautical Sciences, vol. 3, 1936. Also Report of the Aeronautical Pesearch Institute, Tokyo, Imperial University, no. 172, 1939. References 20Th. Bienen, and Tu, von Karman. Zeitschrift des Vereins Deutscher Ingenieure, 68, 1237; 1924. I J. D. van Manen. The Effect of Cavitation on the 21 A. Betz. Traguiugel und Hydraulische Machinen. Hand- interaction Between Propeller and Ships Hull. Paper presen- buch der Physik, 1927. ed at the IUTAM Symposium on Non-Steady Flow of \Vater 22S. Goldstein. On the Vortex Theory of Screw Propellers. at High Speeds, Leningrad, June 22-26, 1971. isp, January Proceedings of the Royal Society (London), Series A, Vol. 1972. 63, 1929. 2 P. van Oossanen and J. van der Kooy. Vibratory Hull 23C. N. H. Lock and D. Yeatman. Tables for use ¡n an Forces Induced by Cavitating Propellers. Paper presented Improved Method of Airscrcw Strip Theory Calculation. at the Spring Meatings of the Royal Institution of Naval R & M 1674. A.R.C.HMSO,London, 1935. Architects, April 1972. 24K. N. Kramer. Weiterführung von Goldsteins Lösung 3 W. J. M. Rankine. On the Mechanical Principles of the des optirnalprob!enìs für Schraubeupropeller. Deutsche Action of Prepellers. Trans. Institution of Naval Architects, Versuchsanstalt für Luftfahrt, 1941. 1865, Vol. 6. 25A. J. Tachmindji. and A. B. Milam. The Calculation 4R. E. Froude. On the Part Played in the Operation of of Goldstein Factors for Three, Four, Five, and Six Blades. Propulsion by Differences in Fluid Pressure. Trans. Institu- DTMBReport No. 1934; 1956. tion of Naval Architects, 1889, vol. 30. 26L. C. Burril. Calculation of Marine Propeller Perform- 5 A. Betz. Eine Erweiterung der Schrauben Theorie. Zeits. ance Characteristics. NEd, Vol, 60, March 1944. Fiugtechn., 1920. 27L. C. Burri!. The optimum Diameter of Marine Prop- 6 W. Froude. On the Elementary Relation between Pitch, ellers; A New Design Method. NEd, Vol. 72, Nov. 1955. Slip and Propulsive Efficiency. Trans. Institution of Naval 28. H. \V. Lerbs, Applied Theory of Free Running Ship Architects, 1878, vol 19. Propellers. AEW Report No. 42/48. 7 S. Drzewiccki. Des Hélicès Propulsives. Bulletin de 29J. G. Hill. The Design of Propellers. SNAME, Vol. 57, L'Assoc. Technique Maritime, 1900, vol. lI. 1949. 8 F. W. Lanchester. Aerodynamics. Constable & Co., 30J. D. van Manen. Fundamentals of Ship Resistance and London, 1907. Propulsion, Part B. Publication No. l32a of the NSMR, 9 Flamm. Die Schiffschraube. Berlin, 1909. is1952. 10N. E. Joukowski. Théorie Tourbillonnaire de l'hélice 31 M. K. Eckhardt and W. B. Morgan. A Propeller Design Propulsive. Paris 1929. Reprinted from Soc. Math. Moscow, Method. SNAME, Vol. 63, 1955. 1912.

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