Master's Thesis

MASTER'S THESIS

Performance Prediction of a Microjet Engine Run on Alternative Fuels

Maja Nylén 2013

Master of Science in Engineering Technology Space Engineering

Luleå University of Technology Department of Computer Science, Electrical and Space Engineering

- To Hedvig - 10 May 2013

iii

Abstract

Microjet engines have gone from being developed in private workshops meant for the RC model aircraft world to become a common feature in various military and commercial applications. Modern microjets emulates the full-sized engines in function and sophistication but have documented major fuel efficient problems. The engines are mostly run on aviation kerosene, which is rather expensive, but a swap to a cheaper or more environmental friendly fuel may result in costly redesigns of the entire fuel delivery system and a reduced power output. The solution is to blend the alternative fuel with the regular fuel to maintain engine functionality to a lower cost and/or increased fuel availability. This project aims to determine whether the performance of the Merlin VT80 microjet engine run on different blends may be predicted by using a gas turbine model entirely based on simple aero-thermodynamic equations. The fuels tested were blends of Jet A-1 and standard diesel and biodiesel. Performance parameters for each blend where collected during experimental runs for every 10th throttle setting using different monitors and readers. An intake horn with an elliptical profile and bell-mouth geometry was designed to enable air mass flow rate calculations using a pressure sensor attached to the intake to measure the dynamic pressure of the air flow which will give the flow velocity. Basic gas turbine thermodynamic equations where used to describe the different processes at each stage throughout the engine based on relevant input parameters. The equations were used to determine the unknown compressor pressure ratio at different speeds by testing different compressor pressure ratio values in the equations to generate a thrust output which was compared to the experimentally found result until a satisfying vale was reached. The compressor map of another microjet of similar size was researched to give reasonable values for the different efficiencies needed in the equations. The results show that most of the data collected at the experimental rig may be derived from the measured pump voltage which mathematical relationships are being used in the gas turbine model. When the compressor pressure ratios and efficiencies found are used as input parameters, the model can predict the microjet engine’s thrust output with very small deviations from the true value regardless of what fuel blend is used. Impeller analysis suggested that the compressor geometry is too complicated to be described with simple equations which means the compressor pressure ratio cannot be derived and thus must remain an input parameter. This concludes that simple thermodynamic equations alone cannot completely predict the performance of the Merlin VT80.

Contents

1 Introduction 1 1.1 Performance prediction ...... 1 1.2 Use of alternative fuels ...... 3 1.3 Biofuels ...... 4 1.4 Gas Turbine Evolution ...... 4 1.4.1 The First Jet Engine ...... 4 1.4.2 Microjet Engines ...... 5 1.5 Engine Theory ...... 6 1.5.1 Gas Turbines ...... 6 1.5.2 The compressor ...... 7 1.5.3 The combustion chamber ...... 7 1.5.4 The turbine ...... 8 1.6 The Project ...... 9 1.6.1 Purpose of the project ...... 9 1.6.2 Problem description ...... 9 1.6.3 Project process ...... 10

2 Theory 11 2.1 Basic physical concepts ...... 11 2.2 Fuel properties ...... 13 2.3 Error analysis ...... 14 2.4 The Vena Contracta Eﬀect ...... 14 2.5 Thermodynamic calculations in gas turbines ...... 16

3 Method 20 3.1 The Engine ...... 20 3.2 Fuels ...... 20 3.3 The experimental rig set-up ...... 20 3.4 Designing the air intake ...... 22 3.5 Calibrating the thrust load cell ...... 26 3.6 Calculating the air mass ﬂow rate ...... 26 3.7 Fuel blends ...... 28

vii 3.7.1 Solubility test ...... 28 3.7.2 Density determinations ...... 28 3.7.3 Blend properties ...... 28 3.8 Performance characteristics measurements ...... 30 3.8.1 Starting the engine ...... 30 3.8.2 Collecting data ...... 30 3.8.3 Engine shut down procedure ...... 31 3.9 Compressor map analysis ...... 31 3.10 Compressor pressure ratio investigation ...... 35 3.10.1 Impeller theory ...... 35

4 Results 37 4.1 Model parameters ...... 37 4.2 Performance characteristics ...... 38 4.3 Parameter relationships ...... 40

5 Discussion 43 5.1 Model parameters ...... 43 5.2 Performance characteristics ...... 43 5.3 Parameter relationships ...... 45 5.4 The computer model ...... 46

6 Conclusions 47 6.1 Conclusions ...... 47 6.2 Future work ...... 47

A Extra ﬁgures 49

B MATLAB code 52

C Test run results 56

viii Preface

This thesis is the ﬁnal project for a Master of Science in Engineering degree fo- cusing in Aerospace Engineering at the Department of Computer Science, Elec- trical and Space Engineering (SRT) at Lule˚aUniversity of Technology (LTU) in Lule˚a,Sweden. The project was conducted at the Department of Mechanical and Aerospace Engineering at Monash University in Melbourne, Australia under the supervision of Associate Professor Damon Honnery. The examiner at LTU was Associate Professor Lars-G¨oranWesterberg.

I would like to thank A/Prof. Damon Honnery for the opportunity to carrying out my project at Monash University and for all the help and guidance he has given me. I give extra thanks to Edward Kuo for his invaluable help and support at the rig and for always being there. I also want to thank all postdoctoral and postgraduate students at the LTRAC lab for their support and kindness. Fur- thermore I would like to thank Angpannef¨oreningensForskningsstiftelse,˚ Sven Molin for all the help with accommodations and Helen Fox at Monash HR Im- migration for help getting the visa approved in time.

Finally, I would like to thank my family and friends for their support and encour- agement; without it I would not have made this far. Special thanks to Daniel, who chose to accompany me on my journey and made the experience, not just mine, but our adventure.

Maja Nyl´en Melbourne, Australia

List of Figures

1.1 The team behind the first jet driven RC Air plane in 1983 (Photo: RC Universe)...... 5 1.2 The first microjet was 340mm long, had a diameter of 120mm and weighed 1.7kg. It run on propane and produced ∼ 40N of thrust at 85, 000rpm [2]...... 6 1.3 Simple gas turbine system [1]...... 6 1.4 (a) An axial flow compressor with multiple stages (Photo: Gary Brossett, 2003). (b) Centrifugal compressors; an impeller with radially tipped blades and an impeller with slightly retro-curved blades [11]...... 7 1.5 Diagram of a combustion chamber [11]...... 8 1.6 An axial turbine blade [11]...... 9

2.1 Streamline patterns and contraction coefficients for a (a): sharp edge orifice and (b): a well-rounded orifice. Cc is the contraction coefficient [15]...... 15 2.2 The velocity flow profile into a plain pipe (a) and a radius pipe (b) - the vena contracta effect is evident by the regions of higher Mach number at the entry in (a) but the effect has reduced significantly in (b) due to the well-rounded intake [14]...... 16 2.3 A simple turbojet engine with station numbering[1]...... 16

3.1 The MERLIN VT80 microjet engine produces ∼ 85N of thrust at 150, 000rpm...... 21 3.2 The experimental rig set-up; 1) The microjet 2) Fuel mass indicator 3) Thrust indicator 4) Fuel tank 5) 5kg load cell 6) Battery 7) 30kg load cell...... 23 3.3 (a) Nomenclature and design guide lines for the bell-mouth used in the project [14]. The finished bell-mouth got the characteristics: ELL-70-70-150-12. (b) The bell-mouth’s velocity profile shows almost no vena contracta effect present at all.[14]...... 24 3.4 The elliptical profile expressed mathematically in MATLAB ...... 25 3.5 (a) The ready intake horn and (b) The intake mounted to the engine. 26

xi 3.6 Calibrating the load cell using weights...... 27 3.7 The pressure sensor collar...... 28 3.8 Pycnometer with biodiesel (V olume = 51.233cm3 )...... 29 3.9 Compressor map used to deﬁne a typical polytropic eﬃciency range for the VT80 [22]...... 32 3.10 Nomenclature for a radial impeller and corresponding velocity triangles [1]...... 35

4.1 The predicted thrust compared to the experimental results for a pure Jet A-1 fuel run. The results coincide well over the span of throttle settings...... 37 4.2 The blends perform consistently throughout the entire span of throttle settings...... 39 4.3 The thrust load cell is not consistent...... 39 4.4 The EGT lowers as more air is pumped through the engine but at higher throttle setting the air mass flow decreases and hence the temperature rises...... 40 4.5 The TSFC is not consistent for the different blends at lower throttle settings...... 41 4.6 Curve fitting for different sets of measured data...... 42

A.1 The intake horn drawing...... 50 A.2 The discharge coeﬃcient for ASME ﬂow nozzle [12]...... 51

xii List of Tables

3.1 The microjet’s engine specifications [17]...... 21 3.2 Fuel properties [18] [19] [20]...... 22 3.3 ASME Long-Radius nozzle standards [12]...... 23 3.4 Intake measurements...... 25 3.5 Measured properties for the different fuels...... 29 3.6 The 80/20% and the 50/50% blend weight distribution...... 30 3.7 The energy content and the density of different blends...... 30 3.8 Measured and calculated values for the five points chosen in Figure 3.9...... 34 3.9 Pressure ratios and efficiencies for the VT80’s compressor. πc lies within the expected 1-4 range and ηc within the 0.65 − 0.78 range. . 34

4.1 Technical parameters for the VT80 run on diﬀerent fuel blends. .. 38 4.2 Slip factor and pressure value investigation ...... 38

xiii Nomenclature

Abbreviations AFR Air-Fuel Ratio ASME American Society of Mechanical Engineers CFD Computational Fluid Dynamics CO Carbon monoxide ECU Electronic Control Unit EGT Exhaust Gas Temperature ELL Elliptical profile bell-mouth FAR Fuel-Air Ratio HHV Higher Heating Value (Gross calorific value) LHV Lower Heating Value (Net calorific value) LTRAC Laboratory for Turbulence Research in Aerospace and Combustion LTU Lule˚aUniversity of Technology MAV Micro Air Vehicles NOx Nitrogen Oxides PP Plain pipe (sharp-edged) RAD Simple radius pipe RC Radio Controlled RPM Revolutions Per Minute SOx Sulphur Oxides SRT Department of Computer Science, Electrical and Space Engineering TIT Turbine inlet temperature TSFC Thrust Specific Fuel Consumption UVA Unmanned Aerial Vehicles

xiv Commonly used symbols

β Intake diameter ratio, De/Di - c Speed of sound [m/s] ca Ambient velocity [m/s] c5 Nozzle exit velocity [m/s] Cc Contraction coefficient - F Thrust [N] M Mach number - m˙ Air mass flow rate [kg/s] m˙ f Fuel mass flow rate [kg/s] p Static pressure [Pa] π Pressure ratio - R Specific gas constant (air) [J/kgK] Rg Specific gas constant (hot gas) [J/kgK] Re Reynolds number - ρ Density [kg/m3] Tc Critical temperature [K] V Flow velocity [m/s] z Relative height [m]

Indexes a Ambient B Combustor c Compressor i Intake j Propelling nozzle jc Critical propelling nozzle t Turbine 01 Compressor inlet 02 Compressor outlet 03 Turbine inlet 04 Turbine outlet 5 Nozzle exit

Constants

cpa 1005 [J/kgK] cpg 1145 [J/kgK] γa = γair 1.4 - γg = γgas 1.333 - R 286.9 [J/kgK]

xv Chapter 1

Introduction

1.1 Performance prediction

Gas turbines are currently used all over the world; in land based industries, on oceans and especially in the air. They are power eﬃcient with low fuel consumption, deliver eﬀective power well beyond the limitations of piston engines and they provide considerable improvements in emissions compared to diesel engines. Due to these performance capabilities, the gas turbine has been denoted one of the most important inventions of the 20th century [1].

Micro gas turbines, or microjet engines, have over 30 years developed from being an appreciated constituent in the Radio Controlled (RC) model aircraft world to become a common feature in various military and commercial applications. Some of these applications currently include cruise missiles, Unmanned Aerial Vehicles (UVA’s) and Micro Air Vehicles (MAV’s). These vehicles are designed to carry out missions such as real-time reconnaissance, laser marking of targets, surveillance and even analysing the air for potential chemical or biological warfare agents [2]. The microjet engine’s high thrust-to-weight ratio makes them highly suitable for these types of missions. Modern microjets emulates the large engines in function and sophistication with the advantages of compact size, light-weight, small number of moving parts, low energy costs and emissions and multi-fuel ca- pacity. This means microjets can be mounted on scaled airframes to support the ﬂight test program of the ﬁll-sized aircraft to a much lower cost, without risking a pilot and the ability to perform manoeuvres that are not easily simulated in a wind tunnel.

Unfortunately the downsizing of gas turbines does result in major fuel eﬃciency problems and reduced overall engine performance. For instance, current micro

1 turbine powered military target drones may only fly at desired altitude and loca- tions for a few minutes at a time before returning to base for refuelling [3]. This means large amounts of costly petroleum based fuels are being consumed at a high rate, which is not economically beneficial nor particularly environmentally friendly. Hence research on alternative fuels to be used as substitutes has become a highly current topic as the demands and field of applications increases for the microjet industry. Tan & Liou [4] demonstrated the performance characteristics for the MW54 microjet engine when run on various blends of a B100 1 biofuel and Jet A-1 kerosene. They showed that the microjet could operate and perform in a consistent manner and that various blends produced the same amount of thrust at the same engine speed. The Thrust Specific Fuel Consumption (TSFC)2 was found to be significantly lower for the pure biofuel than kerosene at the 50% throttle setting. Also, they concluded that the more efficient combustion of the biofuel indicated a possible reduction in greenhouse gas emissions. Later, Tan & Liou [5] also demonstrated the engine performance and emission for the MW54 microjet when run on kerosene, B100 biodiesel, HJ and JP-83 fuels. Results show that the engine performed consistently well in the wide range of fuel and it was found that the B100 fuel produced the least nitrogen oxides (NOx) but produced the most carbon monoxide (CO) and carbon dioxide (CO2).

The ability to predict an engine’s performance when run on a certain fuel not only minimize the number of costly tests but it also has great time reduction benefits as well. Computational fluid dynamics (CFD) analyses or computer programs based on simple aero-thermodynamic equations are usually used to calculate specific performance parameters. Jones [3] sought to optimize the performance of the AMT Olympus HP microjet engine after alterations to individual components using the GasTurb performance simulation software. The engine was deconstructed and the individual components were precision scanned to produce CAD models which were used in a CFD simulation to predict their individual performances. Due to time restrains, the model was however not capable of fully simulating the performance when the report was published. Despite the current and relevant topic is the amount of articles regarding computer model predictions for microjet engines run on alternative fuels limited. Performance prediction research have however been conducted on individual components such as the compressor and combustion chamber. Eftari et al. [6] investigated the performance characteristics of an two-stage axial flow compressor using 1-D modelling. The intended performance features were reached with corresponding compressor map features outlined. Prior models on various compressor components had been used to pre-

1The number after the B indicates the % of biofuel in the blend. 2Described in Chapter 2 3The military equivalent of Jet A-1

2 pare a comprehensive model which up until this research had not been found in the open literature. Gieras & Stankowski [7] performed 3-D numerical CFD simulations studies of aerodynamic flow inside the GTM-120 micro turbine combustion chamber. Since knowledge of combustion processes in micro turbines is mostly derived from full-scale testing of large turbine engines, the authors intend to describe what effects miniaturization of engine construction has on the air flow and heat transfer in the engine. The results showed that the total pressure drop for this miniature combustor (cold flow) is approximately 10%. The study also concluded that the amount of air mass flow through the combustor affects the total loss of total pressure, i.e. increased air mass flow gives distinct increase in total pressure loss. An optimization of the whole combustion chamber was hence concluded to be necessary to obtain smaller pressure losses.

Any advanced gas turbine model capable of determining engine performance base their algorithms on simple aero-thermodynamic equations. None of the studies mentioned above have discussed at any deeper level the possibility of using a computer model entirely based on simple, 1-D aero-thermodynamic equations to predict the engine performance. This project thus aims to investigate whether a self-written computer model of this simple sort is capable of determining the engine performance when run on alternative fuels.

1.2 Use of alternative fuels

Engines of any sort are most often designed to run on one specific fuel only. Gas turbines are no exception. This is to make sure the functionality of the fuel delivery system is not jeopardized, since another fuel of other characteristics may block or harm vital engine parts. Most engines would need a complete redesign of the fuel delivery system if a different fuel is to be used. A swap to a more environmentally friendly fuel, such as biofuels, might also have the effect of a lowered power output in the engine due to the lower energy content. A costly complete redesign and a decreased power output is not what most engine oper- ators long for, but the regular fuel may however be blended with another fuel of similar characteristics. At certain blend concentrations may a lower energy content be compensated for by other distinguish characteristics in the alternative fuel, such as density and viscosity, and the power output therefore remains unchanged. Since only a portion of the new, so called ’drop-in fuel’, is added to the regular fuel the blend may still fully compatible with the engine and the fuel delivery system. A fuel blend of desired properties may therefore help avoid unnecessary waste of expensive and non-environmental friendly fuels.

3 Microjet engines are designed to run on aviation kerosene4, mostly Jet A-1. Un- fortunately aviation kerosene is rather expensive and the microjet’s apparent major fuel eﬃcient problems makes the search for alternative fuels an interesting topic from an economical point of view. If price is the only consideration the alternative fuel does not necessarily need to be a biofuel; a cheaper fuel like diesel might be appropriate to use as a drop-in fuel. Also, if the accessibility to the kerosene becomes limited the use of alternative fuels is a reassurance that the engine still may be able to fully operate. The later is a real necessity in military applications.

1.3 Biofuels

Biofuels are fuels produced from diﬀerent renewable biological resources such as plant material that absorbs CO2 and uses sunlight to grow. Studies suggest that biofuels are anticipated to provide an estimated 80% reduction in overall CO2 life cycle emissions compared to fossile fuels [8]. Fuels made from sustainable, non- food biomass sources that do not impact the food supply chain or fresh water resources, or causes deforestation are known as next-generation or sustainable biofuels and examples of feedstocks, i.e. raw material frow which the fuels are produced, include camelina, jatropha, halophytes and algae. Biodiesel is a ﬁrst generation biofuel which is made from e.g. vegetable oils and animal fats.

1.4 Gas Turbine Evolution

1.4.1 The First Jet Engine The first really important application for the gas turbine was the military jet engine developed during the end of World War II in which technology practically exploded and reformed the entire aviation industry. The success lies in the gas turbine’s ability to deliver practical high speed aircraft at a much lower engine weight and size at higher altitudes - something the piston engine is incapable of. The world’s first flight of a turbojet propelled aircraft, the Heinkel He 178, was realized on 27 August 1939 in Germany and a British parallel, the Gloster E28/39 was airborne on 15 May 1941 [9]. Even though the early jet engines were fuel inefficient, unreliable and extremely noisy the development needed only less than 20 years to mature and become the standard form of propulsion for civil aircraft. 4Kerosene, gasoline and diesel oils are all product extracted from crude oil (petroleum).

4 1.4.2 Microjet Engines The microjet engine first evolved from model aircraft devotees longing for miniature replicas of the full-sized engine. This evolved into home-build prototypes that were innovated and developed over time in private workshops. On 20 March 1983, a British team lead by Jerry Jackman, performed the world’s first turbine powered model flight when their RC model aircraft Barjay took off from the Greenham common airfield, UK and accomplished a three minute flight. A photo of Barjay and the whole team on the day of the premier flight is presented in Figure 1.1. Jackman’s engine, seen in Figure 1.2, had a diameter of 120mm, was 340mm long and weighed 1.7kg. Running on propane it produced over 40N at 85,000rpm and had a top speed of 97,000rpm [2]. It is easy to presume that micro turbines are merely scaled down versions of the operating large engines, but the fact is that air does not scale! A miniaturization of components will result in major changes in the air flow parameters and the heat transfer in the engine [10] along with greater demands on the bearings and the material used due to the high operating speeds (rpm). Also, the models operate in low speeds at low altitudes for short durations with thrust being the aim and with low priority of the fuel efficiency. Complete redesign is hence required when developing micro turbines and much of the innovation actually continues to be among home-builders. Ever smaller turbojets are constantly being developed as design techniques and material knowledge increases. For instance, the American company M-Dot Aerospace has designed a mini-micro-turbojet that fits inside an egg and produces 6.2N of thrust [2].

Figure 1.1: The team behind the ﬁrst jet driven RC Air plane in 1983 (Photo: RC Universe).

5 Figure 1.2: The ﬁrst microjet was 340mm long, had a diameter of 120mm and weighed 1.7kg. It run on propane and produced ∼ 40N of thrust at 85, 000rpm [2].

1.5 Engine Theory

1.5.1 Gas Turbines A gas turbine, or internal combustion turbine, in its simplest form consists of three main components; an upstream compressor, a combustion chamber in the middle and a downstream turbine connected together as shown diagrammatically in Figure 1.3. The compressor uses a pressure ratio to provide the turbine with energy which in turn is used to run the compressor and so the gas turbine work cycle is in progress.

Figure 1.3: Simple gas turbine system [1].

The process for a shaft gas turbine is as follows: the working ﬂuid, e.g. air, is compressed in the compressor and then expanded through the turbine which generates power output. If combustion of fuel is performed in the compressed air the temperature will rise in the gas and an even greater pressure ratio can be obtained. This is clearly shown when looking at the Ideal Gas Law

pV = nRT (1.1) where, for an ideal gas, p is the pressure, V is the volume, n is the number of moles, R is the universal gas constant (R = 8.314J/molK) and T is the temperature. The now hot and more compressed air will enhance the expansion through the turbine which generates an increased power output in addition to driving the

6 compressor. Turbojet engines has a similar mechanical layout and work process to the simple gas turbine but the turbine is now designed to produce just enough power to run the compressor. A high velocity jet is then produced when the working ﬂuid leaves the turbine at high pressure and temperature and expands to atmospheric pressure in a propelling nozzle.

1.5.2 The compressor Large engines with high power requirements use axial flow compressors in which the gas is being compressed in a series of stages. However, the large number of stages involves great constructional complexity and as the engines get smaller the concept no longer remains suitable. The small sizes and low Reynolds numbers also diminish the level of efficiency as the engines becomes smaller and that is why micro turbine almost exclusively use the centrifugal compressor instead [11]. Images of both compressor models are presented in Figure 1.4. The centrifugal compressor is extremely robust and straightforward in its construction and consists of a stationary casing containing a rotating impeller. The air is drawn into the impeller eye and whirled around by the blade ducts and thus accelerates the flow. The air then flows outwards at high speed in the radial direction under the influence of centrifugal force and once outside the impeller the air is slowed in the compressor diffuser system. This action will then convert the kinetic energy of the air into pressure.

(a) (b) Figure 1.4: (a) An axial ﬂow compressor with multiple stages (Photo: Gary Brossett, 2003). (b) Centrifugal compressors; an impeller with radially tipped blades and an impeller with slightly retro-curved blades [11].

1.5.3 The combustion chamber With no moving parts, the design of the combustion chamber seems fairly easy but it is actually highly critical and a good design is essential for an operational engine. If the combustion is uneven it will result in portions of inﬂow air that is not heated to full temperature and consequently does little work when ﬂowing

7 Figure 1.5: Diagram of a combustion chamber [11].

through the turbine. A diagram of a combustion chamber is presented in Figure 1.5. To get a stable combustion a stoichiometric fuel-air mixture ratio is needed i.e. the mixture contains enough oxygen to enable complete combustion. The stoichiometric mixture is burned in the primary zone of the chamber, where the major part of the fuel combustion process occurs, and the hot gases are then cooled with supplementary air in the secondary zone via air holes. The cooling is necessary to give the hot gases a temperature which the turbine can withstand. For model jet engines the combustion chamber cooling is not a problem since the temperature rise is fairly low due to the low pressure ratio. However, the smaller the engine the smaller the chamber gets and optimizing design problems occur. The air spends an extremely short period of time in the combustion chamber, 1 only about 500 of a second [11], and within this period the air and fuel have to mix, burn, and be cooled. Since combustion only can occur when a combustible mixture is formed, a too short chamber will result in only a proportion of fuel being burnt in the chamber, and the excess fuel will leave the engine unburned. Not only will this result in lower engine efficiency but it will also cause flames to continue into the turbine and then blow out of the exhaust. Poor combustion hence has an unfavourable effect on the turbine efficiency and its life span since the turbine is being exposed to overheating. This, in turn, might cause some heating of the air during the compression process which will result in diminished effect of the combustion and thus lower the turbine efficiency further. Therefore it is extremely critical to restrict the combustion process to the confines of the combustion chamber.

1.5.4 The turbine The turbine’s method of working is the opposite of the compressor i.e. the pressure is reduced and then converted to kinetic energy. The hot gases from the combustion chamber are deﬂected in the turbine blades and are forced out in the direction opposite to rotation at high speed. Each ﬂow duct hence form a

8 Figure 1.6: An axial turbine blade [11].

small jet that produces a thrust which is acting upon the turbine blades and the sum of the thrust forces generates a peripheral force i.e. torque. Though axial turbines are the standard for full-sized jet engines, both axial and centrifugal turbines can, in theory, be used on model engines [11]. However the centrifugal turbine have issues of mechanical nature rather than thermodynamic e.g. the rotor might weigh up to 0.4kg which means a high moment of inertia and hence a poor accelerating ability. Therefore, axial turbines are more likely to be chosen in model engine context as well. A picture of an axial turbine for microjet engines is presented in Figure 1.6.

1.6 The Project

1.6.1 Purpose of the project The purpose of the project was to undertake a series of experiments measuring the performance characteristics of a microjet engine operating on a range of alternative fuels for the purpose of validating a 1-D aero-thermodynamics based gas turbine model. The aim was to determine whether these relatively simple gas turbine codes can be used to predict engine performance when operating on alternative fuels. To be able to achieve this, a primary thorough investigation of the microjet engine’s performance had to be conducted.

1.6.2 Problem description The project had three major problems to address and try to ﬁnd solutions to:

• All parameters needed to create a working gas turbine model can be found from the experimental rig except for the air mass flow rate through the engine. To calculate this data, an intake needed to be designed where a pressure sensor attached to the intake enables calculations on the flow velocity. The intake had to be made robust, light and long enough to enable measurements of the flow before it got disturbed by the engine’s electrical starter mounted in front of the compressor intake.

9 • When collecting the microjet engine’s performance characteristics, several parameters are documented both manually and in a computer program. To save time, and thus fuel, when performing test at the rig an investigation on parameter relationships were to be conducted. If a mathematical expression could be linked from one easily measured parameter to several others with low errors, calibrations and documentations of chosen sensors could be eliminated.

• The experimentally found performance characteristics were to be implemented in thermal analysis calculations to derive further parameters and help determine engine specifications, such as compressor pressure ratio and isentropic efficiencies. The complete set of parameters were to be used to create a simple gas turbine model that is able to describe the engine performance at different speeds when run on pure Jet A-1. By conducting further tests with higher percentage of alternative fuel blends, the results could be compared in the working model to determine similar behaviours and deviations characteristic to a certain blend. If only minor deviations occur between the results, then the model has verified that the thermodynamic codes can still predict the engine performance when operating on different blend concentrations of alternative fuels.

1.6.3 Project process The project was to be conducted in three diﬀerent stages:

Stage 1 Preliminary work such as literature and fuel research, become an approved trained operator for the microjet, and designing the intake.

Stage 2 The testing phase where all performance characteristics were collected.

Stage 3 Modifying data to determine the microjet engine performance and development of a workable gas turbine model to be used when validating the ﬁnal results.

10 Chapter 2

Theory

2.1 Basic physical concepts

The Reynolds number is a dimensionless parameter commonly used in the field of fluid mechanics. It is a measure of the ratio of inertia to viscous forces on an element of fluid and is thus defined as ρvL vL Re = = (2.1) µ ν where v is the mean velocity of the fluid, L a characteristic length, µ the dy- µ namic viscosity, ρ the density and ν the kinematic viscosity of the fluid (ν = ρ ). Reynolds number combines the effects of viscosity, density and velocity of a moving fluid and can be used as a criterion to distinguish between laminar (Re ≤ 2000) and turbulent (Re ≥ 4000) flow [12].

The Mach number is the ratio of the speed of the moving ﬂuid to the speed of sound in that ﬂuid: V M = (2.2) c The speed of sound can be calculated using

c = pγRT (2.3) where γ = cp/cv, R is the speciﬁc gas constant and T is the temperature of the ﬂuid.

The Bernoulli’s equation for steady, inviscid, incompressible ﬂows states that 1 p + ρV 2 + ρgz = constant along a stream line (2.4) 2

11 The first term p is the static pressure which is the actual thermodynamic pressure 1 2 of the air as it flows. The second term 2 ρV is the dynamic pressure which depends on the flow density ρ and flow velocity V . The third term ρgz is the hydrostatic pressure which depends on the specific weight γ = ρg and on the relative height z. If the flow between two points (1 and 2) is assumed to be horizontal (z1 = z2) then Equation 2.4 becomes 1 1 p + ρV 2 = p + ρV 2 (2.5) 1 2 1 2 2 2 When the cross-sectional area of the intake is much smaller than that of the room containing the air, it is valid to assume that the air velocity in the room is equal to zero [13], hence V1 = 0 in Equation 2.5. The difference between the static pressure of the flow and the atmospheric, ambient pressure thus gives the dynamic pressure which the flow velocity can be extracted from: s 2(p − p ) V = 1 2 (2.6) 2 ρ

The pressure diﬀerence is easily measured using a pressure sensor attached to the air intake.

The continuity equation states that the air mass ﬂow rate (m ˙ ) throughout a system is constant. It is deﬁnes as

m˙ = ρA1V1 = ρA2V2 (2.7) where ρ is the density of the air, A the cross-sectional area of the ﬂow and V the ﬂow speed.

The Thrust Specific Fuel Consumption (TSFC) is the ”mass of fuel burned by an engine in one time unit divided by the thrust that the engine produces”. It is thus expressed as m˙ TSFC = f (2.8) F wherem ˙ f is the fuel mass flow rate and F is the net thrust. The lower the TSFC is, the more fuel efficient the engine is considered to be. The word specific means ”divided by mass or weight, or int his case: force” and the word thrust in TSFC indicates that a gas turbine is being considered (Engines that produce shaft power uses Brake Specific Fuel Consumption (BSFC))

12 The Air-Fuel Ratio (AFR) is a common reference term used for mixtures in gas turbines and is deﬁnes as the ratio between the mass of air and the mass of fuel in the fuel-air mixture at any given moment: m AF R = air (2.9) mfuel

Even more used in the gas turbine industry is the Fuel-Air Ratio (FAR) which is the reciprocal of the AFR: 1 F AR = (2.10) AF R Isentropic eﬃciency (η) is a parameter that compares the actual performance of a device to the performance that would be achieved under idealized circum- stances for the same inlet and exit conditions. It is hence a measure of the energy degradation occurring in steady-ﬂow devices and is commonly used in aero-thermodynamic calculations.

Polytropic efficiency (η∞), or small-stage efficiency, is defined as the isentropic efficiency of an elemental stage in the process such that it is constant throughout the whole process [1]. It is related to the compressor pressure ratio (πc) and the compressor isentropic efficiency (ηc) according to the equation

(p /p )(γ−1/γ) − 1 η = 02 01 (2.11) c (γ−1)/(γη ) (p02/p01) ∞ − 1

Unlike the isentropic efficiencies in the compressor and turbine (ηt), that tend to vary with changes in the corresponding pressure ratio, is it reasonable to assume constant polytropic efficiency for the same process [1]. This assumption does not only automatically allow for the variations of the isentropic efficiencies to take place in the background but since the isentropic and polytropic efficiencies actually presents the same information but in different forms, only a minor change in the thermodynamic equations is required to replace ηc and ηt with the corresponding polytropic value.

2.2 Fuel properties

The Energy content (heating value) of a fuel describes the amount of heat produced by combustion of a unit quantity of a fuel. This value can be divided into two categories, a lower and a higher heating value based on the heat of water vaporization:

13 The Lower heating value (LHV) or Net caloriﬁc value is the amount of heat released by combusting a speciﬁed quantity (initially at 25◦C) and returning the temperature of the combustion products to 150◦C which assumes the latent heat of vaporization of water in the reaction products is not recovered.

The Higher heating value (HHV) or Gross caloriﬁc value is the amount of heat released by a speciﬁed quantity (initially at 25◦C) once it is combusted and the products have returned to a temperature of 25◦C, which takes into account the latent heat of vaporization of water in the combustion products. The HHV are derived only under laboratory conditions.

Since the microjet engine in this project is not recovering any heat through con- densation of water vapour in the exhaust, the LHV will be used when determining the energy content of the various fuels and blends.

2.3 Error analysis

Error is the diﬀerence between a measured and a true value of the measurement:

Error = E = XT − Xm (2.12)

Uncertainty is the estimation of an error and is usually expressed within limits of conﬁdence; a 95% conﬁdence limit is most used

The standard deviation (s) for a trend line over a set of data is calculated according to the equation v u n u 1 X s = t 2 (2.13) n − 1 k k=1 where k is the deviation of a measurement Xk from the mean X of the sample given by k = Xk − X (2.14)

2.4 The Vena Contracta Eﬀect

The shape of an air intake has an impact on the diameter of the jet at the intake entrance which has to be accounted for when performing nozzle calculations. For a sharp-edged intake, the ﬂow will not be able to make a complete 90◦ turn and a jet with a diameter smaller than the diameter of the intake oriﬁce occurs at the

14 Figure 2.1: Streamline patterns and contraction coefficients for a (a): sharp edge orifice and (b): a well-rounded orifice. Cc is the contraction coefficient [15].

entrance. This is known as the vena contracta effect and is illustrated in Figure 2.1(a). If the intake is gradually rounded, this effect will diminish and be almost completely gone for some ideal design parameters. The degree of contraction, also known as the effectiveness of the flow, is given by a contraction coefficient Cc based on the ratio of the jet to intake orifice areas according to

Aj Cc = (2.15) Ah

In Figure 2.1(b) the intake is well rounded and since Cc = 1.0 the jet and the intake diameter coincide and the effectiveness of the flow is at its maximum for this case. Studies performed on different nozzle geometries demonstrate the vena contracta effect through CFD simulations [14]. In Figure 2.2(a) a sharp-edged plain pipe (PP) shows a high particle velocity (Mach 0.3) close to the entry surrounding by a still region (Mach 0) and a reduction of velocity towards the pipe exit (Mach 0.225). Interpretation of this result using the continuity equation (Equation 2.7) shows that a higher velocity only occurs if the cross-sectional area of the jet is reduced in size (sincem ˙ is constant). This combined with the reduced Mach number towards the exit which shows that the cross-sectional area of the jet increases along the pipe, demonstrates the existence of a vena contracta effect close to the nozzle entry. The reduced effect by a well-rounded, simple radius pipe (RAD) is clearly demonstrated in Figure 2.2(b). The particle velocity is practically constant along the pipe, i.e. no changes in the cross-sectional area, and only a small region of a slightly higher Mach number occurs at the very edge of the entry.

15 Figure 2.2: The velocity flow profile into a plain pipe (a) and a radius pipe (b) - the vena contracta effect is evident by the regions of higher Mach number at the entry in (a) but the effect has reduced significantly in (b) due to the well- rounded intake [14].

Figure 2.3: A simple turbojet engine with station numbering[1].

2.5 Thermodynamic calculations in gas turbines

Aero-thermodynamic calculations for gas turbines can quite easily describe the diﬀerent processes at each stage throughout the entire the engine. Figure 2.3 shows the layout for a turbojet engine with a classic station numbering which are used as indexes in the equations described in this section. The index 0 indicates that stagnation1 properties are used.

Intake (a → 01) The intake (or ram) pressure ratio (πi) is deﬁned as p01 γa − 1 2 πi = = ηi M + 1 (2.16) pa γa

where ηi is the intake eﬃciency, γa = 1.4 and M is the Mach number in the intake. 1The value the static parameter would retain when brought to rest adiabatically and isen- tropically

16 Compressor (01 → 02) The inlet pressure for the compressor (p01) is deﬁned as

p01 = πi pa (2.17)

The temperature rise (T02 − T01) in the compressor is determined from h i (γa−1)/γaη∞ T02 − T01 = T01 πc − 1 (2.18)

where T01 is the intake temperature, πc = p02/p01 is the compressor ratio and η∞ is the polytropic eﬃciency. The pressure at the compressor outlet (p02) is deﬁned as p02 = πc p01 (2.19)

The work required to drive the compressor (WC ) is expressed as

WC = cpa(T02 − T01) (2.20)

where cpa = 1005J/kgK.

Combustor (02 → 03) Due to pressure losses in the combustion chamber, the pressure at the turbine inlet (p03) can be determined using

p03 = πB p02 (2.21)

where πB = p03/p02.

Turbine (03 → 04) The work extracted from the turbine (WT ) in a single spool engine is equal to the compressor work value with an adjustment for spool mechanical losses and is hence deﬁned as

cpa(T02 − T01) WT = cpg(T03 − T04) = (2.22) ηm

where ηm is the mechanical eﬃciency and cpg = 1148J/kgK. An expression for the temperature loss in the turbine can then be found using Equation 2.22 cpa(T02 − T01) T03 − T04 = (2.23) cpg ηm

The turbine inlet temperature (TIT) (T03) is found by adding the EGT to the turbine temperature rise since T04 = EGT

T03 = (T03 − T04) + EGT (2.24)

17 The turbine pressure ratio is deﬁned as

γg p04 T03 − T04 (γg−1)η∞ πt = = 1 − (2.25) p03 T03

where γg = 1.333. The pressure at the turbine outlet (p04) is deﬁned as

p04 = πt p03 (2.26)

Propelling nozzle (04 → 05) The propelling nozzle needs to be checked for critical ﬂow conditions in which a Mach number of 1 is reached at the minimum area along the duct. This means that any further reduction in downstream pressure provides no increase in mass ﬂow and the duct is said to be choked. To determine the critical conditions, the nozzle ratio πj = pa/p04 is compared to the critical nozzle ratio (πjc)

Choked duct if πjc > πj → p5 = pc (2.27)

Non − choked duct if πjc < πj → p5 = pa (2.28) (2.29)

where πjc is deﬁned as

γg pc 1 γg − 1 γg−1 πjc = = 1 − (2.30) p04 ηj γg + 1

ηj is the nozzle eﬃciency. For a choked ﬂow the duct exit temperature (T5), exit pressure (p5) and exit velocity (c5) is calculated as follows:

2 T5 = Tc = T04 (2.31) γg + 1

p5 = pc = P04 πjc (2.32) p c5 = γgRgTc (2.33)

For a non-choked ﬂow the temperature reduction in the nozzle (T04 − T5) and the duct exit velocity (c5) is calculated as follows:

" γg−1 # γg T04 − T5 = ηjT04 1 − πj (2.34)

q c5 = 2cpg(T04 − T5) (2.35)

18 The net engine thrust (F ) is deﬁnes as

F =m ˙ [(1 + F AR)(c5 − ca)] + Aj(p5 − pa) (2.36) where the ﬁrst term is called the momentum thrust and the second term the pressure thrust. Since the engine is stationary (ca = 0) and it is assumed thatm ˙f << m˙ (F AR ≈ 0) the net thrust for a non-choked ﬂow (p5 = pa) will become F =mc ˙ 5 (2.37)

19 Chapter 3

Method

3.1 The Engine

The engine used in this project is the MERLIN VT80, a single shaft, microjet gas turbine produced by Jets-Munt Turbines in Spain, presented in Figure 3.1. It is specifically designed to power RC model aircraft and uses an electric starter situated in the front to ensure an automatic start. Almost all vital components, such as the Engine Control Unit (ECU) and rpm sensor, are integrated inside the engine and the only external components are the fuel pump and filter. The engine specifications are presented in Table 3.1. At maximum throttle it was measured that the engine produces approximately 132 dB which is practically the same level as for a full sized jet engine which means dual protection (plugs + earmuffs) must be worn at all time! [16]

3.2 Fuels

The fuels available for the project were Jet A-1, standard diesel and BioMaxTM Biodiesel (B100). They have similar characteristics and are hence suitable for blends. Some main fuel properties are listed in Table 3.2.

3.3 The experimental rig set-up

A photo of the experimental rig set-up is presented in Figure 3.2. The engine is suspended between two metal plates which are mounted onto a baseplate. A 30kg load cell is placed right in front of the baseplate to register the thrust produced from the engine when the baseplate pushes against the load cell during runs. A thrust indicator next to the engine registers the load cell values. A fuel tank is placed on-top of a 5kg load cell and a fuel mass indicator registers its weight. A software program is linked to the indicator and documents how the weight

20 Figure 3.1: The MERLIN VT80 microjet engine produces ∼ 85N of thrust at 150, 000rpm.

Table 3.1: The microjet’s engine speciﬁcations [17].

Merlin VT80 engine speciﬁcations Guaranteed thrust in ISA conditions 80N Max. rpm 150,000 Idle rpm 45,000 Idle thrust 4.5N Diameter 90.5mm Length 217mm Engine weight 950g Installed weight 1075g EGT at Max. rpm 550 − 650◦C Fuel Kerosene =4% oil Fuel consumption at 80N 220 g/min or 0.29 l/min ECU processing 500 times/s

21 Table 3.2: Fuel properties [18] [19] [20].

Properties Jet A-1 Diesel Biodiesel Appearance Colourless Pale straw Green Boiling point 150 − 300◦C 170 − 390◦C > 200◦C Freezing point < −47◦C Not available1 Not available1 Flash point 38 − 55◦C ∼ 63◦C > 120◦C Auto-ignition temp. > 220◦C > 220◦C > 200◦C Density (at 15◦C) 775 − 840 ∼ 840 860 − 890 kg/m3 kg/m3 kg/m3 Kinematic viscosity 1 − 2mm2/s 2 − 4.5mm2/s 3.5 − 5mm2/s (at 40◦C)

1 Not well deﬁned because they are mixtures

changes during runs, i.e. the fuel mass ﬂow rate (m ˙ f ) can be calculated. The fuel tank is connected to an electrical fuel pump which supplies the engine with fuel. The full engine control settings are run either by a RC controller or using the software program LabView. The microjet is connected to a power switch and has an input port that receives commands, i.e. the throttle settings, from the computer and an output port that provides another software called Fadec with information of the engine’s properties. The parameters registered by Fadec are the throttle setting, duty cycle, (fuel) pump power, exhaust gas temperature (EGT), thrust and rpm. A pressure sensor mounted to the intake horn will give information on the air mass ﬂow rate (m ˙ ) through the engine and a volt meter measures the voltage over the pump as the throttle settings changes during runs. The entire rig is placed right in-front of an exhaust fan venting duct to minimize the exhaust fumes inside the lab.

3.4 Designing the air intake

To be able to measure the air mass flow rate into the compressor, an air intake was to be designed. To reduce the vena contracta effect discussed in Chapter 2, an intake horn, or a cone, was concluded to be the most beneficial geometry for this application. Studies performed on different nozzle geometries have shown that a completely rounded edge in combination with a gradually decreasing nozzle will almost entirely eliminate the vena contracta effect [14]. This geometry, when the edge is completely round and wrapped towards the back, is called a bell-mouth. The flow results can be further improved by designing the bell-mouth as ”short and fat”, i.e. the length equal to the inner diameter according to the dimensions presented in Figure 3.3(a). This bell-mouth has an elliptical profile (ELL) and

22 Figure 3.2: The experimental rig set-up; 1) The microjet 2) Fuel mass indicator 3) Thrust indicator 4) Fuel tank 5) 5kg load cell 6) Battery 7) 30kg load cell.

the corresponding velocity profile is presented in Figure 3.3(b) which shows a smooth flow with almost no vena contracta effect present at all. Thus, an ELL- geometry based on these dimensions was chosen for the project. The American Society of Mechanical Engineering (ASME) provides some flow nozzle standards based on the so called β ratio where D β = e (3.1) Di is the ratio between the nozzle exit and inlet diameter. This ratio was used to determine the shape for the elliptical profile. The ASME standards for low respectively high β ratios are presented in Table 3.3. For this project, β = 0.47 which is right in the middle of the two β-series and hence any of the two can be chosen. The decision was made to use the low β-series dimensions to give the

Table 3.3: ASME Long-Radius nozzle standards [12].

β-ratio Series Major semi-axis (a) Minor semi-axis (b)

2 0.2 ≤ β ≤ 0.5 Low β-Series a = De b = 3 De,

Di Di−De 0.45 ≤ β ≤ 0.8 High β-Series a = 2 b = 2

23 (a) (b) Figure 3.3: (a) Nomenclature and design guide lines for the bell- mouth used in the project [14]. The finished bell-mouth got the characteristics: ELL-70-70-150-12. (b) The bell- mouth’s velocity profile shows almost no vena contracta effect present at all.[14].

intake the appearance of an horn rather than a cone. The wrap-round of the bell- mouth edge can be made to a full ”ball” radius, i.e. a 360◦ wrap-round, if wanted. However, it is considered unnecessary when compared to a ”half-radius” in terms of performance and is much more complicated from a construction perspective. Hence, a half-radius was primary the design approach but after consultations with the project supervisor the wrap-round concept was found not vital for the project so it was removed completely to save time during manufacturing.

It was possible to manufacture the desired elliptical proﬁle for the horn if it could be described by a mathematical function. However, since an ellipse is not a function the problem was solved by expressing only one quadrant of the ellipse for certain intervals. The equation for an (vertical) ellipse at origo

x 2 y 2 + = 1 (3.2) b2 a2 with a = 70 and b = 47, according to Table 3.4, will yield the expression r x 2 y = 70 1 − (3.3) 47 When run in MATLAB for −50 < x < 0 a mathematical expression for the elliptical proﬁle is achieved. The plot is presented in Figure 3.4.

Due to the electrical starter mounted in front of the compressor intake, the intake horn had to be elongated to permit air ﬂow measurements upstream from the starter. The elongation pipe was attached to a back piece which was designed to ﬁt like a hood on top of the engine front. All measurements for the three parts

24 Figure 3.4: The elliptical proﬁle expressed mathematically in MATLAB

are presented in Table 3.4 and the ﬁnal drawing can be seen in Appendix A. Alu- minium was chosen as the material for the entire intake to keep the construction strong and light weight to a low price. The ﬁnished intake is presented in Figure 3.5.

Table 3.4: Intake measurements.

Piece Symbol [mm] Horn: Exit inner diameter De 70 Inlet inner diamter Di 150 Length L 70 Corner radius RC 12 Wall thickness dh 2-5 Elliptical proﬁle: Major semi-axis a 70 Minor semi-axis b 47 Pipe: Length Lp 150 Wall thickness dp 3 Back piece: Inner diameter Dbp 90.45 Length Lbp 29 Wall thickness dbp 2

25 (a) (b) Figure 3.5: (a) The ready intake horn and (b) The intake mounted to the engine.

3.5 Calibrating the thrust load cell

Due to the extra weight of the intake horn, the thrust load cell needed to be recalibrated. By attaching a thin wire to the engine base plate and letting free hanging weights pull it through a pulley system, the gravitational force is easily calculated using Newton’s 2nd law F = ma (3.4) When calibrated correctly, the load cell will display a thrust equal to F . A picture of the set-up is presented in Figure 3.6. A linearizing method was used in which a few points where measured; the force at the minimum and maximum load and five arbitrary points in-between. The result for each point was programmed into the computer and the pulley system was then removed from the rig. A test run of the engine confirmed the quality of the calibration by looking at the thrust output at maximum throttle setting and compare the result to the engine specifications presented in Table 3.1.

3.6 Calculating the air mass ﬂow rate

One important parameter when predicting engine performance is the compressor throughput, i.e. the air mass ﬂow rate (m ˙ ), through the compressor. It is derived from the continuity equation (Equation 2.7) and is measured in kg air per second. m˙ is virtually constant at all points in a model jet engine [11] which means

m˙ intake =m ˙ compressor (3.5) Using Equation 2.6 thus gives an expression for the idealm ˙ in the compressor: s 2(p − p ) m˙ = ρA V = ρ πr2 atm static (3.6) compressor i i i ρ

26 Figure 3.6: Calibrating the load cell using weights.

To enable measurement of the pressure difference patm − pstatic, a ’collar’ was attached to the intake according to Figure 3.7. The collar is hollow and is connected to the air flow inside the intake via four holes in the intake wall. A pressure sensor that is externally attached to the collar via a tube is hence able to measure both the static pressure inside the intake and the atmospheric pressure in the room. The intake area (Ai) is known and the density of the air can be determined using p ρ = a (3.7) RTa where pa and Ta are the ambient conditions and R = 286.9 is the specific gas constant for air. However, the true flow rate is almost always less than the theoretically calculated value so a discharge coefficient (Cn) for a flow nozzle has to be included and yields the equation:

m˙ real = Cn m˙ compressor (3.8)

Cn accounts for viscous, secondary ﬂow separations and any vena contracta eﬀects and can be determined by calculating the Reynolds number using Equation 2.1 and reading of Figure A.2 found in Appendix A for β = 0.47.

27 Figure 3.7: The pressure sensor collar.

3.7 Fuel blends

3.7.1 Solubility test A solubility test to check the stability of the diﬀerent blends was conducted with arbitrary blend concentrations. Samples of a 60/40% diesel blend and a 75/25% biodiesel blend were prepared and left in sealed glass containers. The blends showed no indication of layering in neither case after 24 hours. Even 6 days later, the samples looked ﬁne but advice was still given to prepare the blends and perform the test on the same day to guarantee maximum stability during the tests.

3.7.2 Density determinations The densities for each fuel was measured using a pycnometer; a glass ﬂask with an accurately known volume which has a capillary tube through its stopper to allow air bubbles to escape. A photo of the pycnometer containing biodiesel is presented in Figure 3.8. The weight of a dry and empty pycnometer was subtracted from the weight of the ﬁlled equivalence and the result was divided by the pycnometer volume of 51.233cm3 to get the density for each fuel. The results are presented in Table 3.5 together with the LHV and the kinematic viscosity for each fuel.

3.7.3 Blend properties The measured densities were then used to determine a suitable blend that fulﬁlled the requirements for the fuel tank (max 5L), the engine rig (max 5kg) and the amount of oil needed (5%). The results for an 80/20% and a 50/50% blend, measured by weight, is presented in Table 3.6. The density of each fuel blend was then

28 Figure 3.8: Pycnometer with biodiesel (V olume = 51.233cm3 ).

Table 3.5: Measured properties for the diﬀerent fuels.

Component Density Energy Kinematic [kg/m3] content Viscosity at 20◦C (LHV) [mm2/s] [MJ/kg] at 40◦C Jet A1 789.0 42.82 1-24 Standard Diesel 835.6 45.53 2.33 B100 877.0 38.23 4.23 Jet oil 1003.51 - 27.61

1From Mobil Jet Oil II data sheet 3 From [21]

2 From ASTM D1655 4 From [18]

easily calculated by adding the weights and dividing by the total corresponding volume: P m + m ρ = fuel oil (3.9) blend P V A good approximation for the energy content in a fuel blend is to assume the heating value to be linear with blend fraction by mass. Hence the LHV for each blend can be found from the equation

LHVblend = m% × LHVfuel1 + m% × LHVfuel2 (3.10) where m% is the mass fraction of each fuel. The results for these calculated blend properties are presented in Table 3.7.

29 Table 3.6: The 80/20% and the 50/50% blend weight distribution.

Component Weight [kg] Weight [kg] (80/20%) (50/50%) Jet A1 2.8 1.8 Diesel/B100 0.7 1.8 Jet oil 0.1855 0.1908 Total values Weight 3.685 kg 3.791kg Volume ∼ 4.5L ∼ 4.5L % of oil 5 5

Table 3.7: The energy content and the density of diﬀerent blends.

Blend LHV Density with Jet A-1 [MJ/kg] [kg/m3] Diesel (20%) 43.3 806.3 Biodiesel (20%) 41.9 813.3 Diesel (50%) 44.2 819.5 Biodiesel (50%) 40.5 838.1

3.8 Performance characteristics measurements

3.8.1 Starting the engine The tests to determine diﬀerent performance characteristics of the microjet engine were conducted in the same way for each fuel and fuel blend. First, all sensors, exhaust fans and computer programs (LabView and Fadec) were turned on and the trim on the engine controller was set to ’idle’ (∼ 20% throttle setting.) Setting the controller to full throttle and back to idle again will begin the start-up sequence where the electrical starter ﬁrst will be powered up to have the rotor turning at slow speed. Once the rotor is at speed, the pump and solenoid valves will be energized and the fuel will ignite. When the ignition is detected, the fuel is routed to the main injectors and the rotor speed will progressively increase to idle rpm. At this stage the ECU will automatically disconnect power to the starter and once the speed has reached idle and stabilizes the engine is running.

3.8.2 Collecting data First a complete set of tests were conducted for the pure Jet A-1 fuel followed by the same procedure for each blend. Data from every 10th throttle setting, starting

30 with idle at 20% to max throttle at 100%, was collected for each test. Each test carried out three runs; the primary run, a repeatability run and a variability run. The first two runs (performed equally) begun measurements at idle and increased the throttle setting until max throttle was reached. The variability test started at max throttle and was decreased until idle was reached. A complete set of 1-3 runs was repeated on a different day for each fuel blend to see if changing ambient conditions had any effect on the results. Hence, atmospheric conditions were thoroughly documented before each test and individual run.

3.8.3 Engine shut down procedure To shut down the engine, the throttle setting and trim is lowered. It is recom- mended to leave the throttle setting at ∼ 25%, allowing temperatures to stabilizes for about ﬁve seconds, before carrying out the shut-down procedure. The engine shuts down when the throttle is completely set to zero.

3.9 Compressor map analysis

Some parameters for the microjet were not known in advance, such as the compressor pressure ratio at different speeds and the different component isentropic efficiencies. To determine theses, the thermodynamic calculations for a gas turbine explained in Section 2.5 were put into a MATLAB script to serve as a first draft of a performance prediction model. When basic conditions of the engine and ambient temperatures and pressures are known, the combination of equations will make it possible to calculate the thrust output. Compressor pressure ratio is however a crucial input parameter which is unknown here. Hence, an itera- tive process had to be performed where, for different throttle settings, a range of compressor ratios where tested to each generate a thrust output. This calculated thrust was then compared to the true thrust value, i.e. the error was analysed. The error was plotted against the range of pressure ratios used and where the error became zero, i.e. the calculated value equalled the true value, it showed at which pressure ratio the desired thrust would occur. This was repeated for every throttle setting until a complete set of pressure ratios represented the entire span from 20 − 100%. To get an idea of what pressure ratio ranges to expect, a compressor map of a similar engine size was analysed. That compressor map is presented in Figure 3.9 and is read like this: The axes show the compressor air mass flow rate (x-axis) and the compressor pressure ratio (y-axis). The slightly curved and tilted lines on the main part of the map are the speed lines. 1 They propagate, as the pressure ratio on the y-axis increases, over an area of dashed

1 The mass ﬂow rate and the speed is in their corrected values which is the value that√ corre- sponds to ambient conditions at sea level on a standard day (101.325kPa and 288.15K): m θ/δ = p √ p m T01/288.15/(p01/101325) and N/ θ = N/ T01/288.15 [1].

31 Figure 3.9: Compressor map used to deﬁne a typical polytropic eﬃ- ciency range for the VT80 [22].

32 circles which are called efficiency islands. Where a speed line at a certain mass flow rate and pressure ratio intersects (or closely intersects) one of the islands shows how efficient the compressor is at those conditions. The compressor efficiency (ηc) is denoted in percentage for each island in the map. The left hand boundary (dashed line) of the map is called the surge line. Compressor surge is a pulsating back flow of gas through the engine which is associated with a sudden drop in delivery pressure and operation to the left of this line represents a region of flow instability. There is also a right hand boundary called the choke points which is where the speed lines terminates. Beyond this point no further increase in mass flow can be obtained and choking is said to have occurred. Hence, this point represents the maximum mass flow rate obtainable at each particular rotational speed. A line drawn along the centre of the efficiency islands is called the peak efficiency line and represents the operating points for maximum efficiency. Ideally, it is desirable to operate the compressor close to this line [1]. This compressor map indicates that it is reasonable to assume compressor pressure ratios somewhere between 1 and 4.

When performing thermodynamic engine calculations, it is important to include fair values of the isentropic efficiencies for each component. As discussed in Sec- tion 2.1, ηc and ηt can be substituted by η∞ to decrease the number of unknowns in the equations. For full-sized jet engines, it is reasonable to find η∞ ≈ 0.85 but it is not well documented if that is suitable for microjets. The assumption of constant η∞ might not even be true for microjets due to the greater amount of losses experienced in them. By investigating the compressor map in Figure 3.9, η∞ could be determined for that particular engine and the results could give an idea what range to expect and if it can be assumed constant or not. A rearrangement of Equation 2.11 gives an expression for η∞: (γ−1)/γ log{(p02/p01) } η∞ = (γ−1)/γ (3.11) log{ (p02/p01) − 1 + 1} ηc ηc The peak efficiency line on the compressor map intersects the efficiency islands at five points where the isentropic efficiencies could be directly read. The pressure ratio and mass flow rate for each point were then also read directly of the map and all parameters were put into Equation 3.11. The values collected from the map and the corresponding calculated η∞ values are presented in Table 3.8. The result indicates that the polytropic efficiency in fact is not constant over a range of pressure ratios for a microjet of similar size to the VT80 η∞ seem to vary between 0.66 − 0.73. When running the model with the thermodynamic equations for pressure ratios between 1-4 it became obvious that a constant η∞ was not able to generate a thrust output equal to the measured value for all throttle setting in the entire span. This means a fair compressor ratio could not

33 Table 3.8: Measured and calculated values for the ﬁve points chosen in Figure 3.9.

πc m˙ corr ηc η∞ 1.20 0.047 0.65 0.66 1.32 0.054 0.68 0.69 1.56 0.072 0.70 0.72 2.18 0.104 0.70 0.73 2.77 0.126 0.68 0.72

be obtained for all throttle settings. Hence the conclusion is that η∞ has to vary for the VT80 microjet as well. A set of varying polytropic efficiencies with corresponding pressure ratios were then determined using the variations in Table 3.8 as a guideline. To check the plausibility of the results, Equation 2.11 were used to get the corresponding ηc values which for microjets varies within the range 0.65 − 0.78 [11]. The remaining critical efficiencies needed such as ηi, ηj, ηm and πB were investigated simultaneously in the model to find reasonable values for all of them. The results are presented in Table 3.9.

Table 3.9: Pressure ratios and eﬃciencies for the VT80’s compressor. πc lies within the expected 1-4 range and ηc within the 0.65 − 0.78 range.

Throttle πc η∞ ηc setting[%] 20 1.11 0.73 0.73 30 1.18 0.74 0.73 40 1.23 0.77 0.76 50 1.35 0.79 0.78 60 1.54 0.80 0.79 70 1.87 0.80 0.78 80 2.30 0.81 0.79 90 2.88 0.80 0.77 100 3.60 0.80 0.76 ηi = 0.95 ηj = 0.95 ηm = 0.98 πB = 0.98

34 3.10 Compressor pressure ratio investigation

The pressure is increased in the centrifugal compressor according to the theory discussed in Section 1.5.2. Hence it would be mathematically possible to determine the generated pressure ratio using knowledge of the impeller speed and geometry. One goal in this project was to investigate whether πc could be determined accurately for the VT80 using basic equations to be used in the computer model.

3.10.1 Impeller theory The impeller eye is where the air is being drawn into the compressor but the vanes stretches longer beyond the size of the eye, as can be seen in Figure 3.10. The velocity of the rotating air at the impeller tip can be calculated using velocity triangles. Figure 3.10 demonstrates graphically that the absolute velocity (C2) which the air leaves the impeller tip with has a tangential, or whirl component, (Cw2) and a comparatively smaller radial component (Cr2). The impeller tip speed (U) would be equal to the whirl component under ideal conditions but due to its inertia is the air trapped between the impeller vanes reluctant to move

Figure 3.10: Nomenclature for a radial impeller and corresponding velocity triangles [1].

35 round with the impeller. This prevents the air from acquiring Cw2 equal to U and the eﬀect is called slip. The slip factor (σ) for radial-vane impellers can be found from the equation 0.63π σ = 1 − (3.12) n where n is the number of vanes. The VT80 has n = 14 and thus σ = 0.86.

Due to friction between the casing and the air carried round by the vanes the applied torque, and therefore the actual work input, is greater than the theoret- ical value. To account for this, a dimensionless power input factor (ψ) can be introduced. Typical values for ψ lies in the region 1.035-1.04 for full-sized jet engines. πc can now be calculated using the equation

2 γa/(γa−1) ηcψσU πc = 1 + (3.13) cpaT01 where ψσU 2 = T02 − T01 (3.14) cpa The impeller tip speed is calculated according to

U = π × Ø × rpm/60 (3.15) where Ø is the overall diameter of the impeller. Ø for the VT80 was estimated to be 0.055m.

There is another equation valid for model jet engines that gives πc. It is de- ﬁned as ψU 2 3.5 πc = + 1 (3.16) 2cpaT where ψ now is denoted as a dimensionless unit called the pressure value. ψ = 0.98 is a typical value for microjet engines with slightly retro-curved blades [11] and ψ remains largely constant over a broad range of rotational speeds which makes it easy to calculate πc or U if the other parameter is known.

36 Chapter 4

Results

4.1 Model parameters

The results from using the eﬃciencies and pressure ratios found in Table 3.9 in the computer model to predict the thrust is presented in Figure 4.1. The MATLAB code to the model is presented in Appendix B.

Figure 4.1: The predicted thrust compared to the experimental results for a pure Jet A-1 fuel run. The results coincide well over the span of throttle settings.

37 4.2 Performance characteristics

Some typical performance parameters for the diﬀerent blends found from the engine tests are presented in Table 4.1.

Table 4.1: Technical parameters for the VT80 run on diﬀerent fuel blends.

Blend Speed range Thrust Air mass E.G.T with Jet A-1 [kRPM] [N] ﬂow rate [◦C] [g/s] Jet A-1 (100%) 45.2 − 150.3 3.9 − 85.6 41 − 191 500 − 604

Diesel (20%) 45.3 − 150.3 3.6 − 85.3 42 − 191 504 − 584

Biodiesel (20%) 45.2 − 150.2 3.6 − 83.8 42 − 190 504 − 596

Diesel (50%) 45.2 − 150.3 3.9 − 78.9 42 − 188 504 − 588

Biodiesel (50%) 45.2 − 150.4 3.8 − 80.3 42 − 188 500 − 596

Rearranging Equations 3.13 and 3.14 using the known values from Table 3.9 and the temperature difference generated by the computer model made it possible to calculate σ (when ψ = 1.04) for different throttle settings. A rearrangement of Equation 3.16 generates the pressure value ψ for different throttle settings. The results are presented in Table 4.2.

Table 4.2: Slip factor and pressure value investigation

Throttle T02 − T01 U rpm σ ψ [%] [K] [m/s] (ψ = 1.04) 20 12.3 130.7 45,400 0.69 1.05 30 19.4 167.6 58,200 0.67 1.02 40 23.5 202.7 70,400 0.55 0.88 50 33.8 244.5 84,900 0.55 0.89 60 49.2 282.2 98,000 0.60 0.98 70 74.0 320.2 111,200 0.70 1.13 80 101.0 360.0 125,000 0.75 1.23 90 136.1 395.7 137,400 0.84 1.33 100 172.3 432.5 150,200 0.89 1.40

38 The throttle setting vs. thrust for all blends and the same plot for a pure Jet A-1 test with all three runs documented are presented in Figure 4.2 and Figure 4.3 respectively.

Figure 4.2: The blends perform consistently throughout the entire span of throttle settings.

Figure 4.3: The thrust load cell is not consistent.

39 The throttle setting vs. EGT and the AFR is presented in Figure 4.4.

Figure 4.4: The EGT lowers as more air is pumped through the engine but at higher throttle setting the air mass ﬂow decreases and hence the temperature rises.

The throttle setting vs. the TSFC for all blends is presented in Figure 4.5.

4.3 Parameter relationships

From the speed (rpm) the pump voltage can be determined using the equation V (rpm) = 1.387 × 10−6rpm3 − 0.000276rpm2 + 0.03307rpm − 0.3208 (4.1) The standard deviation is 0.01 and the experimental results are presented in Fig- ure 4.6.

The air mass ﬂow rate can be determined from the pump voltage using m˙ (V ) = 0.0008643V 5 − 0.006199V 4 + 0.01088V 3 + 7.142 × 10−5V 2+ (4.2) + 0.06378V − 0.008007

The standard deviation is 2.81 × 10−4 and the experimental results are presented in Figure 4.6.

40 Figure 4.5: The TSFC is not consistent for the diﬀerent blends at lower throttle settings.

The fuel mass ﬂow rate can be determined from the pump voltage using

−6 m˙f (V ) = 0.00154V − 5.632 × 10 (4.3) The standard deviation is 3.6 × 10−5 and the experimental results are presented in Figure 4.6.

The EGT can be calculated from the pump voltage using the equation

EGT (V ) = −14.94V 5 + 140.7V 4 − 510V 3 + 939.5V 2 − 921.7V + 1175 (4.4)

The standard deviation is 0.93 and the experimental results are presented in Fig- ure 4.6.

The relationship between the speed (rpm) and the throttle setting is linear according to the equation

rpm(τ) = (1.3205τ + 18.626) × 103 (4.5)

The standard deviation is 0.51 and the result is implemented in the computer model to be used if the input parameter is the throttle setting instead of the speed.

41 Figure 4.6: Curve ﬁtting for diﬀerent sets of measured data. 42 Chapter 5

Discussion

5.1 Model parameters

Figure 4.1 shows that when using the parameter values found in Table 3.9 in the computer model, the predicted thrust will coincide well with the experimental results for a pure Jet A-1 run. The microjet engine’s performance may hence be predicted with only minor deviations from the true value and the compressor ratios and different efficiencies presented in Table 3.9 are thus considered to be valid. The computer model uses a combustor efficiency (πB) of 98% which, after the model was constructed, was discovered to maybe be too high. The investigation done by Gieras & Stankowski [7] suggested that the total pressure drop in a miniature combustor would be approximately 10% since microjets do experience greater losses than a full-size engine. A correction was meant to be done but the computer model was found to be quite sensitive to variations in the efficiency parameters and a changed value for πB would result in a complete change in the other parameters as well. This would be too time consuming to fit within the project’s time restrictions. However, since the other efficiencies and pressure ratios are within reasonable values and generates a predicted thrust with only minor deviations from the true value was it concluded that πB was to remain at 98% to save time.

5.2 Performance characteristics

The geometry for the impeller mounted in the VT80 is not known since the component is enclosed inside the engine body and hence is not accessible. The investigation on the slip factor was to give an idea of the geometry. Equation 3.12 says that, for a radial-vane impeller, the slip factor only depend on the number of vanes which generates a constant value for σ. However, table 4.2 shows a varying value for σ over the span of throttle settings. It is hence concluded that

43 the impeller for the VT80 is not purely radial. If this is the case, Equation 3.15 that gives the impeller tip sped U, might also be incorrect since a back-swept blade would result in a vector component to be used instead. The results from the pressure value investigation using the rearrangement of Equation 3.16, also presented in Table 4.2, suggest that ψ vary too much. It was expected for radial impellers that ψ only varies within narrow limits i.e. practically constant. This result suggest once more that the geometry of the impeller is not purely radial and that U has to be modiﬁed using a vector component based on the blade angle. In conclusion, the geometry for the VT80’s impeller seems to be far more complex than the simple equations can handle and thus πc cannot be derived exclusively from these equations.

Table 4.1 and Figure 4.2 both show that the microjet engine was able to operate and perform in a consistent manner throughout the throttle setting span for the various blends tested. This is in accordance to the results found by Tan & Liou [4] and was hence an expected result. Though the two 50% diesel and biodiesel blends generated a slightly lower maximum thrust output value compared to the others is the deviation approximately negligible. Hence, in conclusion: the model can predict the thrust output for each blend tested for without having to state which blend is currently being investigated since they all generate the same results.

Figure 4.3 demonstrates a problem discovered with the thrust load cell when conducting the performance tests on the engine. The load cell placed in front of the engine baseplate measures the thrust generated by the engine during runs as the baseplate pushes against the load cell. For the ﬁrst and the repeatability run, where the throttle setting is gradually increased, the load cell generates consistent results for the fuel/blend used at the current ambient conditions. A problem however occurs during the variability test, where the throttle setting is gradually decreased from maximum value. As seen in Figure 4.3 will the thrust output registered by the load cell be slightly higher than the other two runs for the lower throttle settings. This may be explained as follows: the load cell is experiencing the highest level of thrust ”pushing” against it for maximum throttle and as the setting is gradually decreased, i.e. lesser and lesser thrust is experienced, the load cell will fail to retract at the same pace as the decreasing thrust. Thus, the thrust output generated for lower throttle settings will result in a false, higher value than expected. This is a problem since the three diﬀerent runs made for each test are to give statistically supported results but an average of the lower throttle settings results will now produce an untrue value. This has to be considered when running tests and a solution to this problem would be of high importance in future works.

44 Figure 4.4 demonstrates the peculiar behaviour the EGT was discovered to have as the throttle setting increases: the temperature decreases up to about 70% throttle but then starts to increase as the throttle goes towards its maximum value. This decrease/increase in the EGT over the entire span of throttle settings can be explained by looking at the air-fuel ratio (AFR) for the same run. As the AFR increases, i.e. more air is being pumped through the engine, the working temperature lowers. However, the engine is not capable of maintaining the high AFR value as the highest throttle settings are set due to the increased amount of fuel mass ﬂow and the temperature hence begins to increase as the AFR decreases. This behaviour is consistent for all fuel blends used, as Figure 4.4 clearly shows.

Figure 4.5 demonstrates the TSFC for the different blends. Unlike the throttle setting vs. thrust plot in Figure 4.2 is the TSFC not consistent over the entire throttle setting span for the different blends. The difference between the blends is greater for lower settings but almost none for the top values which suggests that an added coefficient to the computer motel is not a solution to get a fair prediction for each fuel.

5.3 Parameter relationships

The fuel pump voltage is easily measured during engine tests using a volt meter. From this value a number of other important parameters can be derived with fair accuracy, such as the rpm,m ˙ ,m ˙ f and EGT according to the equations presented in Section 4.3. Figure 4.6 gives a graphic view over how well the parameters can be described mathematically. This means that only the pump voltage needs monitoring when performing tests which reduces the time spent performing the tests and may reduce the time the microjet engine is running and thus save expensive fuels. The pump voltage is also easily derived from the speed (rpm) using Equation 4.1 which was used in the computer model since the rpm may be in interesting parameter to predict engine performance from.

45 5.4 The computer model

The MATLAB code used for the computer model is based on the theory discussed in Section 2.5 where the number of input parameters have been reduced signiﬁcantly using the pump voltage’s mathematical relationship to other parameters. Due to the complexity of the compressor geometry is the compressor pressure ratio however not able to be determined using simple equations and thus is an unavoidable input parameter. η∞ also has to be included manually in the model according to the results presented in Table 3.9. Since not all performance characteristics seem to coincide amongst the diﬀerent fuel blend is the current model a pure Jet A-1 model. The performance of the microjet engine may now be determined by using the input parameters: throttle setting, πc, η∞ and the ambient conditions sought for. The model generates results close to the true values for all characteristics found in the experimental tests.

46 Chapter 6

Conclusions

6.1 Conclusions

Simple aero-thermodynamic gas turbine equations have shown to be able to predict some performance characteristics for the Merlin VT80 when run on pure Jet A-1 with good accuracy. An simple equation that describes the compressor pressure ratio is however not obtainable due to the found complexity in the compressor geometry. The computer model thus has to include both πc and η∞ as input parameters to function which is not a convenient model structure. The similarities for the diﬀerent blends when calculating the thrust output suggests that a future model may be able to exclude further, non-relevant information to simplify the input parameters needed. It was, for instance, found in this project that the knowledge of which fuel blend used in the test was not relevant to predict the engine thrust output. The amount of Jet A-1 fuel consumed in the progress of this project really stresses the need for a cheaper alternative fuel to be used in mirojet engines. The realisation that the pump voltage is almost the only parameter needed to be documented during tests has however given an opportunity to lower the fuel consumption since the tests time can be reduced. Due to time restrictions was the computer model only able to determine relevant parameters for the pure Jet A-1 case with good accuracy at the end of this project. Future work to address these shortcomings in the results are discussed in the next section.

6.2 Future work

To get a complete working model to describe the performance characteristics of diﬀerent fuel blends will some adjustments to existing data and more thorough

47 investigations of the engine’s diﬀerent components be needed.

• The problems with the not retracting thrust load cell is a major issue that needs to be addressed to be able to conduct thrust tests with realistic and dependable results.

• The compressor geometry may be further investigated to determine the true relationship between the impeller blade angles and the compressor pressure ratio.

• An investigation on the true pressure loss in the combustor and a more thorough denotation of the efficiencies used in the model may be vital to find more subtle variations in the different blends.

• An deeper investigation on the pump voltage relationship to the same parameters used in this project but for all the diﬀerent blends as well might be useful to get an idea of the possible varying blend’s properties.

• Sincem ˙ can be derived with minor deviations from the true value is the need for the intake reduced. The removal of it will increase accessibility to the engine but the microjet would start to experience other conditions which have to be investigated.

48 Appendix A

Extra ﬁgures

49 Figure A.1: The intake horn drawing.

50 Figure A.2: The discharge coeﬃcient for ASME ﬂow nozzle [12].

51 Appendix B

MATLAB code

52 % Microjet engine performance prediction model

Ts=50; %Throttle setting pa=1.0135; %Air pressure Ta=294; %Air temperature pi_c=1.35; %compressor pressure ratio % 20=1.11, 30=1.18, 40=1.23, 50=1.35, 60=1.54, %70=1.87, 80=2.3, 90=2.88, 100=3.6 n_p=0.79; %polytropic efficiency %20=0.73, 30=0.74, 40=0.77, 50=0.79, 60=0.8, %70=0.8, 80=0.81, 90=0.8, 100=0.8

%------Constants------cpa=1005; %[J/kg] cpg=1148; %[J/Kg] gamma_a=1.4; % air gamma_g=1.333; % hot gas R=286.9; % spec. gas constant (air) d=0.07; A=d^2*pi/4; %------fprintf('______\n') rpm=1.3205*Ts+18.626; rho_a=(pa*100000)/(R*Ta); fprintf('The air density is %g kg/m^3 \n',rho_a)

Ca=sqrt(gamma_a*R*Ta); fprintf('The speed of sound in air is C= %g m/s\n',Ca)

V=1.387*10^(-6)*rpm^3-0.000276*rpm^2+0.03307*rpm-0.3208; fprintf('The pump voltage is %g V\n',V) m_ff=0.0015*V-5.632*10^(-6);

EGT=-14.94*V^5+140.7*V^4-510*V^3+939.5*V^2-921.7*V+1175; mdot=0.0008643*V^5-0.006199*V^4+0.01088*V^3+7.142*10^(-5)*V^2+... 0.06378*V-0.008007; c_pipe=mdot/(rho_a*A); fprintf('The speed of air in the intake is C= %g m/s\n',c_pipe) delta_p=c_pipe^2*rho_a/2; fprintf('Delta p in the intake is %g Pa\n',delta_p)

M=c_pipe/Ca; fprintf('The Mach number in the horn M= %g\n',M)

T01=(delta_p+(pa*100000))/(R*rho_a); fprintf('The Temp in the intake is T01= %g K\n',T01) p01_pa=((0.95*M^2*0.2)+1)^3.5;

53 fprintf('p01/pa= %g\n',p01_pa) p01=(p01_pa)*pa; fprintf('p01= %g bar\n',p01)

T02_T01=T01*((pi_c^((gamma_a-1)/(gamma_a*n_p)))-1); fprintf('T02-T01= %g K (polytropic eff)\n',T02_T01)

T02=T02_T01+T01; fprintf('T02= %g K\n',T02)

T_ratio=T02/T01; fprintf('T02/T01= %g K\n',T_ratio) p02=pi_c*p01; fprintf('p02= %g bar\n',p02) p03=p02*0.98; fprintf('p03= %g bar\n',p03)

Wc=cpa*(T02_T01); fprintf('The work to drive the compressor is Wc= %g J/kg\n',Wc)

T03_T04=Wc/(cpg*0.98); fprintf('T03-T04= %g K\n',T03_T04)

T03=(T03_T04)+EGT; fprintf('T03= %g K\n',T03) pi_t=(1-((T03_T04)/T03))^(gamma_g/(n_p*(gamma_g-1))); fprintf('p04/p03= %g\n',pi_t) p04=p03*pi_t; fprintf('p04= %g bar\n',p04) pi_jc=(1-((gamma_g-1)/(gamma_g+1)*(1/0.95)))^4; fprintf('The critical nozzle p-ratio is pi_jc= %g\n',pi_jc) pi_j=pa/p04; fprintf('The p-ratio over the nozzel is Pa/p04= %g\n',pi_j)

EPR=1/(pi_j); fprintf('The engie p-ratio is EPR is p04/pa= %g\n',EPR) fprintf('If pi_jc= %g < pi_j=%g then p5=pa (non-choked flow)\n',pi_jc,pi_j)

T04_T5=0.95*EGT*(1-(pi_j^(1/4))); fprintf('T04-T5= %g K\n',T04_T5)

T5=EGT-(T04_T5); fprintf('T5= %g K\n',T5) c5=sqrt(2*cpg*(T04_T5));

54 fprintf('c5= %g m/s\n',c5)

F=mdot*c5;

TSFC=m_ff*3600/F;

fprintf('______\n') fprintf('rpm= %g \n',rpm) fprintf('EGT= %g K\n',EGT) fprintf('The air mass flow rate is %g kg/s\n',mdot) fprintf('The thrust is = %g N\n',F) fprintf('The fuel flow rate is %g kg/s\n',m_ff) fprintf('TSFC= %g kg/h\n',TSFC) fprintf('______\n')

55 Appendix C

Test run results

56 Jet A-1 K C kg/s kg/s kg/N.h % L/s Throttle rpm EGT EGT m_dot Ftrue m_fuel TSFC AFR FAR Volt. pump TSFCxLHV Vol. ff rate m_fuelxLHV 20 45400 837 564 0,0426 3,34 0,00110 1,161 38,70 0,026 0,75 6,1 49,7 0,00139 1,3078E-05 LHV[MJ/kg] 30 58200 813 539 0,0564 6,58 0,00143 0,734 39,46 0,025 0,93 7,0 31,4 0,00182 1,7041E-05 42,8 40 70400 800 527 0,0705 10,72 0,00170 0,550 41,46 0,024 1,12 8,6 23,5 0,00215 2,0211E-05 Density 50 84900 786 513 0,0879 17,29 0,00210 0,426 41,87 0,024 1,35 10,0 18,2 0,00266 2,4967E-05 789 60 98000 782 509 0,1065 26,05 0,00247 0,336 42,96 0,023 1,59 11,9 14,4 0,00313 2,9326E-05 [kg/m^3] 70 1E+05 779 506 0,1257 36,56 0,00287 0,280 43,78 0,023 1,85 14,0 12,0 0,00363 3,4081E-05 80 1E+05 790 517 0,1480 50,79 0,00343 0,241 43,15 0,023 2,21 17,3 10,3 0,00435 4,0819E-05 90 1E+05 820 547 0,1690 65,93 0,00393 0,211 42,79 0,023 2,60 20,9 9,0 0,00499 4,6763E-05 100 2E+05 872 599 0,1905 86,48 0,00480 0,201 39,69 0,025 3,13 26,7 8,6 0,00608 5,7067E-05 Diesel 20 K C kg/s kg/s kg/N.h % L/s Throttle rpm EGT EGT m_dot Ftrue m_fuel TSFC AFR FAR Volt. Pump TSFCxLHV Vol. ff rate m_fuelxLHV 20 45450 841 568 0,0427 3,91 0,0011 0,8446 38,82 0,0258 0,74 6,3 36,6 0,00136 1,3231E-05 LHV[MJ/kg] 30 58200 813 540 0,0565 7,22 0,0014 0,6199 40,32 0,0248 0,92 7,3 26,8 0,00174 1,6839E-05 43,3 40 73100 801 528 0,0713 12,11 0,0017 0,4749 41,31 0,0242 1,11 9,0 20,6 0,00214 2,0748E-05 Density 50 84500 788 515 0,0880 18,38 0,0021 0,3930 41,89 0,0239 1,31 10,0 17,0 0,00260 2,5258E-05 806,3 60 98000 782 509 0,1063 26,25 0,0024 0,3198 44,28 0,0226 1,53 12,0 13,8 0,00298 2,8867E-05 [kg/m^3] 70 1E+05 778 505 0,1257 36,30 0,0028 0,2761 44,51 0,0225 1,78 14,0 12,0 0,00350 3,3978E-05 80 1E+05 785 512 0,1480 49,80 0,0033 0,2373 44,51 0,0225 2,11 17,0 10,3 0,00412 3,9992E-05 90 1E+05 812 539 0,1711 67,40 0,0039 0,2093 43,59 0,0229 2,49 21,0 9,1 0,00487 4,7209E-05 100 2E+05 856 583 0,1913 85,20 0,0046 0,1958 41,37 0,0242 2,95 25,5 8,5 0,00574 5,5628E-05 B20 K C kg/s kg/s kg/N.h % L/s Throttle rpm EGT EGT m_dot Ftrue m_fuel TSFC AFR FAR Volt. Pump TSFCxLHV Vol. ff rate m_fuelxLHV 20 45300 859 586 0,0425 3,60 0,0011 0,9264 38,68 0,0259 0,74 7,0 38,8 0,00135 1,2803E-05 LHV[MJ/kg] 30 58300 824 551 0,0564 7,95 0,0014 0,6389 39,33 0,0254 0,92 7,3 26,8 0,00176 1,6682E-05 41,9 40 71100 805 532 0,0709 12,52 0,0018 0,4961 40,13 0,0249 1,10 9,0 20,8 0,00217 2,0562E-05 Density 50 84600 789 516 0,0874 17,94 0,0021 0,4083 41,63 0,0240 1,31 10,0 17,1 0,00258 2,4442E-05 813,3 60 98600 784 511 0,1064 25,92 0,0025 0,3341 43,13 0,0232 1,54 12,0 14,0 0,00303 2,8709E-05 [kg/m^3] 70 1E+05 779 506 0,1253 35,50 0,0029 0,2885 43,21 0,0231 1,78 14,0 12,1 0,00357 3,3753E-05 80 1E+05 785 512 0,1478 49,40 0,0034 0,2463 43,46 0,0230 2,11 18,0 10,3 0,00418 3,9572E-05 90 1E+05 809 536 0,1698 64,90 0,0039 0,2136 43,54 0,0230 2,50 21,0 8,9 0,00480 4,5392E-05 100 2E+05 842 569 0,1902 83,85 0,0047 0,2019 40,47 0,0247 2,97 26,7 8,5 0,00578 5,4703E-05 Diesel 50 K C kg/s kg/s kg/N.h % L/s Throttle rpm EGT EGT m_dot Ftrue m_fuel TSFC AFR FAR Volt. Pump TSFCxLHV Vol. ff rate m_fuelxLHV 20 45500 855 582 0,0423 4,27 0,0012 0,9787 36,76 0,0272 0,74 6,5 43,3 0,00140 1,4119E-05 LHV[MJ/kg] 30 58450 825 552 0,0576 7,20 0,0014 0,7017 41,16 0,0243 0,88 7,0 31,0 0,00171 1,7189E-05 44,2 40 71000 808 535 0,0701 10,97 0,0017 0,5579 41,25 0,0242 1,04 8,3 24,7 0,00207 2,0872E-05 Density 50 84500 789 516 0,0867 16,85 0,0020 0,4346 42,64 0,0235 1,24 10,0 19,2 0,00248 2,4965E-05 819,5 60 97800 781 508 0,1048 23,83 0,0024 0,3626 43,66 0,0229 1,44 11,0 16,0 0,00293 2,9467E-05 [kg/m^3] 70 1E+05 775 502 0,1241 33,80 0,0028 0,2929 45,12 0,0222 1,69 13,5 12,9 0,00336 3,3764E-05 80 1E+05 779 506 0,1465 46,73 0,0032 0,2466 45,78 0,0218 2,00 16,0 10,9 0,00390 3,9289E-05 90 1E+05 801 528 0,1667 60,05 0,0038 0,2278 43,88 0,0228 2,37 20,0 10,1 0,00464 4,6656E-05 100 2E+05 853 580 0,1880 78,90 0,0045 0,2053 41,78 0,0239 2,86 25,0 9,1 0,00549 5,5250E-05 B50 K C kg/s kg/s kg/N.h % L/s Throttle rpm EGT EGT m_dot Ftrue m_fuel TSFC AFR FAR Volt. Pump TSFCxLHV Vol. ff rate m_fuelxLHV 20 45300 863 590 0,0423 4,43 0,0012 0,9930 35,25 0,0284 0,75 7,0 40,2 0,00143 1,3500E-05 LHV[MJ/kg] 30 58000 828 555 0,0556 7,38 0,0015 0,7350 37,10 0,0270 0,91 7,7 29,8 0,00179 1,6875E-05 40,5 40 70600 808 535 0,0700 11,17 0,0018 0,5810 38,91 0,0257 1,08 9,0 23,5 0,00215 2,0250E-05 Density 50 84700 788 515 0,0870 16,93 0,0022 0,4614 40,14 0,0249 1,29 10,7 18,7 0,00259 2,4375E-05 838,1 60 98300 776 503 0,1055 24,50 0,0025 0,3675 42,22 0,0237 1,51 12,3 14,9 0,00298 2,8125E-05 [kg/m^3] 70 1E+05 773 500 0,1247 34,30 0,0030 0,3098 42,26 0,0237 1,76 16,0 12,5 0,00352 3,3188E-05 80 1E+05 781 508 0,1469 47,53 0,0035 0,2614 42,59 0,0235 2,09 18,0 10,6 0,00412 3,8813E-05 90 1E+05 805 532 0,1670 61,35 0,0040 0,2347 41,75 0,0240 2,47 22,5 9,5 0,00477 4,5000E-05 100 2E+05 853 580 0,1886 80,30 0,0048 0,2152 39,29 0,0255 3,00 29,0 8,7 0,00573 5,4000E-05

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