EFFICIENCY ANALYSIS OF A TURBOFAN ENGINE. GRADUATION PROJECT Yıldırım Burak KILINÇ. Department of Astronautical Engineering

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1 ISTANBUL TECHNICAL UNIVERSITY FACULTY OF AERONAUTICS AND ASTRONAUTICS EFFICIENCY ANALYSIS OF A TURBOFAN ENGINE GRADUATION PROJECT Yıldırım Burak KILINÇ Department of Astronautical Engineering Anabilim Dalı : Programı : Thesis Advisor: Prof. Dr. Ali KODAL JANUARY, 2019

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3 ISTANBUL TECHNICAL UNIVERSITY FACULTY OF AERONAUTICS AND ASTRONAUTICS EFFICIENCY ANALYSIS OF A TURBOFAN ENGINE GRADUATION PROJECT Yıldırım Burak KILINÇ Department of Astronautical Engineering Anabilim Dalı : Programı : Thesis Advisor: Prof. Dr. Ali KODAL JANUARY, 2019

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5 Yıldırım Burak KILINÇ, student of ITU Faculty of Aeronautics and Astronautics student ID , successfully defended the graduation entitled ANALYSIS OF A TURBOFAN ENGINE, which he/she prepared after fulfilling the requirements specified in the associated legislations, before the jury whose signatures are below. Thesis Advisor : Prof. Dr. Ali KODAL... İstanbul Technical University Jury Members : Prof. Dr. İbrahim ÖZKOL... İstanbul Technical University Assist. Prof. Dr. Hayri ACAR... İstanbul Technical University Date of Submission : 02 January 2019 Date of Defense : 15 January 2019 i

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7 To my family, and my loyal friends, iii

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9 FOREWORD Being a student in Istanbul Technical University, has been very difficult to me. Challenging with some situations and lectures makes me stronger and now, I am stepping to my future adventures with this thesis. I will be always proud of being a part of a huge family and I will never forget my memories which I lived in Istanbul Technical University. I would like to show my thanks and respects to my thesis advisor Prof. Dr. Ali Kodal. When I started to think about studying on engine design, I had many questions about it, however, with guidance of Prof. Dr. Ali Kodal, I answered my question and I had to chance to finish my graduation thesis. Prof. Dr. Ali Kodal made me believe myself again. I would like to thank to my family for encouraging and supporting me. Thanks to them, I have a chance to think and act freely and truly. I believe they would like to see me as a graduated more than me. My father has been always a friend, an advisor and an idol for me. Even we do not have same ideas, he always respects my ideas and supports them. I have to thank to my mother, indivually. Whenever I need love, compassion and speaking, she always stands side by me. I have to mention my little sister and brother, I will always work a better world for them and I am very happy to be their big brother. I gained many friends in Istanbul Technical University. I would like to show my respects and thanks to my loyal friends Alihan Tanrıkulu, Hüseyin Ataseven and Niyazi Abacıoğlu. Their fellowships, friendships and critisms made me better person and student. December 2018 Yıldırım Burak KILINÇ v

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11 TABLE OF CONTENTS Page FOREWORD... v TABLE OF CONTENTS... vii ABBREVIATIONS... ix LIST OF TABLES... xi LIST OF FIGURES... xiii SUMMARY... xv 1. INTRODUCTION Purpose of Thesis History and Development of The Turbofan Engine Working Principle of The Turbofan Methodology Engine Selection ANALYSIS A Brief Review of Thermodynamics Properties Internal Energy and Enthalpy First Law of Thermodynamics Entropy and The Second Law of Thermodynamics Isentropic Relations Aircraft Gas Turbine Thrust Propulsive Efficiency Gas Turbine Components The Inlet The Compressor The Combustor or Burner The Turbine The Exhaust Nozzle Brayton Cycle Aircraft Gas Turbine Engine Equations Notation Design Inputs Steps of Gas Turbine Engines Parametric Cycle Analysis Assumptions for Ideal Cycle Analysis Ideal Turbofan Engine Cycle Analysis Steps of Cycle Analysis Summary of Equations Definition of Flight Conditions Effects of Design Choices on Engine Performance Effects of Bypass Ratio Effects of The Fan Pressure Ratio Effects of The compressor Pressure Ratio Performance Analysis of IAE V2533-A RESULTS AND COMMENTS NEO Design Choices NEO Engine Performance Analysis and Comparing of IAE V2533-A Leading Advises Conclusion REFERENCES APPENDIX vii

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13 ABBREVIATIONS ARP AYT FR Ft Hp HPC IAE LPC MATLAB NEO SAW SL TSFC US VIE : Aerospace Recommended Practice : Antalya International Airport : Thrust Ratio : Feet : Horse Power : High Pressure Compressor : International Aeroengines : Low Pressure Compressor : Matrix Laboratory : New Engine Option : Sabiha Gökçen International Airport : Sea Level : Thrust Specific Fuel Consumption : United States : Vienna International Airport ix

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15 LIST OF TABLES Page Table 1.1 : The flights of TC-SOB at the 8 th December, 2018 taken from flightradar24.com Table 1.2 : Partly fleet informations for some airlines based on Turkey adopted websites of airlines Table 1.3 : IAE V2533-A5 Performance at SL [7] Table 1.4 : Pratt & Whitney Engine Characteristics [4] Table 2.1 : Temperature and pressure realations for all π and τ [6] Table 2.2 : Sea level and cruise conditions for selected engine Table 2.3 : Design inputs for IAE V2533-A Table 2.4 : Performance parameters output for IAE V2533-A Table 3.1 : NEO design choices Table 3.2 : Design inputs for NEOs Table 3.3 : Performance parameters output for NEOs Table 3.4 : Comparing of NEO v3 and IAE V2533-A5 at cruise xi

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17 LIST OF FIGURES Page Figure 1.1 : The TF39 Turbofan engine used on the Lockeed C5A [6] Figure 1.2 : Specific Thrust characteristics of typical engines [6] Figure 1.3 : Efficiency characteristics of typical aircraft engines [6] Figure 1.4 : JT3D-3B Turbofan Internal Pressures and Temperatures [6] Figure 2.1 : Gas turbine schema [6] Figure 2.2 : Schematic drawing of an engine installation showing the mechanical and thrust power [4] Figure 2.3 : A generic subsonic inlet [6] Figure 2.4 : Schematic drawing of different types of compressors in aircraft gas turbine engines [4] Figure 2.5 : Straight flow in combustor [6] Figure 2.6 : Axial flow turbine elements [6] Figure 2.7 : Convergent exhaust nozzle [6] Figure 2.8 : a) Brayton cycle graph. b) Brayton cycle schmatic [6] Figure 2.9 : Thermal effiency of brayton cycle [3] Figure 2.10 : Ideal brayton cycle for Ideal turbofan engine Figure 2.11 : Station numbering for gas turbine engines according to ARP 755A [6] Figure 2.12 : Station numbering for the tubofan engine [6] Figure 2.13 : The Brayton cycle for a turbofan engine with station numbers [6] Figure 2.14 : Bypass ratio effects on engine performance parameters at SL Figure 2.15 : Bypass ratio effects on engine performance parameters at cruise Figure 2.16 : Fan pressure ratio effects on engine performance parameters at SL Figure 2.17 : Fan pressure ratio effects on engine performance parameters at cruise Figure 2.18 : Compressor pressure effects on engine performance parameters at SL Figure 2.19 : Compressor pressure ratio effects on engine performance parameters at cruise xiii

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19 EFFICIENCY ANALYSIS OF A TURBOFAN ENGINE SUMMARY The importance of aircrafts and air transportation is increasing everyday. As an aerospace student, to improve and develop aircrafts, air transportation and etc. is my duty, interests and life goal. However, as in every fields of technology, it does not come without any problems. Every development and investment, brings a problem with it. For example, todays, number of aircrafts is getting larger and larger. If we think an average airlines or air force, we can see more than a hundred aircrafts. It means a large amount of fuel and cost for countries or airlines. Because of that, the meaning of efficiency is reshaping itself and getting more and more important, today. Increasing of efficiency can be provided by decreasing drag forces on aircraft, nowadays, many engineer are working on aerodynamics. However, shape of aircrafts is considered as almost the best. Therefore, we have to find another things to increase efficiency. Aircraft engine is coming to forefront if we think fuel consumption and costs. Engines also are studied by many engineers, to increase its efficiency. Today, the leaders of aviation, are working on new engine options. Airbus has been taking orders for its aircrafts with NEO (New Engine Option), also, Boeing has. Engine design are based on two main stages which are one dimensional and real engine. One dimensional stage consists of thermodynamics law, and real engine stage consists of thermodynamics and mechanics, both. This thesis will focus on one dimensional engine and will try to increase efficiency. At the beginning, this thesis will chose a turbofan engine which is still in operation for any aircraft. Turbofan engine is a version of gas turbine engine, in general. In simple words, gas turbine engines are working with cycle called as Brayton cycle. The history of aircraft engine starts with the first aircraft The Flyer which also is the first powered aircraft. Then, traditional piston engine were getting not enough for larger and weighter aircrafts. Late 1930 s, Whittle produced a gas turbine engine with brayton cycle, a turbojet. It was more suitable for aircraft because of huge amount of thrust. Todays, turbojets are used for mostly military, fighter aircrafts. Then, studies keep continue and different types of turbojets were built. Turbojets were more suitable for high speed aircrafts and it was consuming more fuel, also it was not able to achieve long range and subsonic operations. These reasons caused to built a new type engine like turbofans. Turbofan engine burns air which is entering with the fan and compressor, and fuel in combustor. The energy for driving fan and compressor, is provided by exhaust gas which drives turbine. Therefore, efficiency of turbofans is higher than turbojets. Compared to turbojets, exhaust velocity of turbofans is lower, however, the exhaust mass rate is more than turbojets. Low exhaust velocity causes that turbofan engines can not achive high speed flights as turbojets without large mount of fuel.so, for subsonic flights, turbofans are more suitable than turbojets. xv

20 At the beginning of thesis, thesis decided to focus commercial aircrafts because of its number and flight hours per day. Firstly, aircrafts were examined, then Airbus A was chosen. The engine of Airbus A , which is International Aeroengines V2533-A5, was chosen as base engine. IAE V2533-A5 was flied the first time at april, 1995 with Airbus A New engine options have same specifications as IAE V2533-A5 except design choices which are bypass ratio, fan pressure ratio and compressor pressure ratio. This thesis also focused on gas turbine equations which are based on thermodynamics. Therefore, a brief information about thermodynamics was given. And then, this thesis gave more information about gas turbine engines and its components. Also, flight conditions were defined.after perfomance equations were found, IAE V2533-A5 performance parameters were calculated. After that, effects of design choices on engine performance parameters are studied to determine NEO s design choices. Design choices which are bypass, fan pressure ratio and compressor pressure ratio, were determined accordingly engine equations and effects of its on engine performance parameters.three different design choices were determined for three NEOs. New engine option s performance parameters were calculated after determination of design choices. IAE V2533-A5 and NEOs were compared in terms of performance parameters. Each NEOs is more efficient than IAE V2533-A5. This means thesis achieved its own goal. Also, thesis gave leading advices for possible problems, and new design choices. xvi

21 1. INTRODUCTION 1.1 Purpose of Thesis This thesis aims to make performance analysis and develop a turbofan engine which is still in operation. If it is considered how much importance air transportation has today, the efficiency of aircraft engines is getting more crucial due to costs and environmental concerns. Aircraft engines efficiency can describe in three different valuables, the propulsive efficiency, thermal efficiency and overall efficiency. The ratio of the useful power output to the total power output of the propulsion system is called as the propulsive efficiency [6]. Also, thermal efficiency can be described as the net rate of organized energy out of the engine divided by the rate of thermal energy avaible from the fuel in the engine [6]. The thermal and propulsive efficiencies can be combined to give the overall efficiency of a propulsion system [6]. Overall efficiency and Thrust Specific Fuel Consumption will be considered at first. Calculations will be handled at MATLAB according to gas turbine performance equations which will be mentioned at Chapter 2. This thesis will increase overall efficiency of a turbofan engine which is still in operation for airlines. Aircrafts which are using for airlines will be focussed due to their flight frequency and flight hours. Table 1.1 helps us to know partly, how many hours a commercial aircraft flies at one day. Also, if it is considered that over 1,000 aircrafts are fliying at same time, to focusing on commercial aircraft is can be understandable. 17

22 Table 1.1 : The flights of TC-SOB at the 8 th December, 2018 taken from flightradar24.com. Date From To 8 Dec, Dec, Dec, Dec, 2018 Flight Number Flight Time STD STA VIE AYT XQ191 2:11 1:55 PM 6:35 PM AYT VIE XQ190 2:31 12:05 PM 1:05 PM SAW AYT XQ7527 0:48 9:50 AM 11:10 AM AYT SAW XQ7526 0:52 7:45 AM 9.05 AM If it is analyzed, it can be easiliy seen that the aircraft flies over than 6 hours as its scheduele. Therefore, the thesis will focus on commercial turbofan engines instead of military turbofan engines. Also the descriptions will be given at following chapters. 1.2 History and Development of The Turbofan Engine History of the turbofan engine should be known at the beginning of thesis. It goes until Wright Brothers and their aircraft. Wright Brothers started a new epoch when they designed, built and flew The Flyer in Carolina and also this was beginning of Powered Flight. Farohki says that 12-hp reciprocating intermittent combustion engine gave a life to The Flyer and until late 1930s, this type engine was used all manned aircraft then the history of aircraft gas engine started in January 1930 with Frank Whittle (2014). Brayton cycle is the fundamental of Whittle s turbojet engine. In 1936 a new turbojet engine was developed by von Ohain in Germany and it was the first engine which was flew. If modern era is considered, it can be easily seen that the developing of gas turbine engine is still last [4]. The early turbojets were used as propulsion systems for high-speed fighter and reconnaissance aircraft. For these applications, the turbojet was more suitable than traditional propeller engines however fuel economy, reliability and endurance were not characteristics of the turbojet. The first developments were about pressure ratios. Early 1950s, the turbojets achieved 10:1 18

23 pressure ratio after that it becomes 40:1 at 2000s. U.S Air Force asked for engine which had capability of long range subsonic speed operation. This means turbojets should be developed into more efficient engines. TF39 was the first turbofan engine which made by General Electric under the leadership of Gerhard Neumann in 1965 for Lockeed C5A [6]. Figure 1.1 : The TF39 Turbofan engine used on the Lockeed C5A [6]. Turbofan, turboprop and turboshaft engines which were made for needing of more thrust at low speeds are the versions of the turbojet engine. So, the turbojet engine was the first step to a Long Journey of Gas Turbine Engines. The turbofan engine came into existence with inlet fan, gas generator and nozzle. Turbojet engines are more expensive and not efficient at subsonic flight because of that the turbofan engines are preferred mostly. The reason of difference of efficiency is that the turbofan engine accelerates a larger mass of air to a lower velocity than the turbojet [6]. Increasing of fuel cost, environmental concerns and reliability push developer to improve more efficient engines. As mentioned in Figure 1.2 capability of thrust of engine depends on aircraft mach number. Also, Figure 1.3 shows that efficiency of engines is changing with its type. The turboprop is the most efficient engines according to Figure 1.3 however Figure 1.2 points that the turboprop cannot provide thrust at 19

24 M=0.8 which is generic cruise speed for commercial aircraft. For example, Boeing needs 24 lbf/lbm/sec specific thrust for cruise at feet according to manufacturer publish, in simple words, the turboprop is not suitable for commercial planes. Because of that, manufacturers of commercial aircraft prefer to use the turbofan engine. Figure 1.2 : Specific Thrust characteristics of typical engines [6]. 20

25 Figure 1.3 : Efficiency characteristics of typical aircraft engines [6]. 1.3 Working Principle of The Turbofan Brayton cycle is the basement of the turbofans as the turbojets. The air comes into with inlet fan and then compressor will pressurize it [5]. Pressurized air burns with fuel in combustion chamber and nozzle is the outer portion for exhaust gas. When exhaust gas is going through nozzle it passes the turbine and it produces energy for fan s and compressor s driving. It is easily seen it is just cycle mentioned at the beginning. Also, the fan portion is named as fan section, core section consists with combustion chamber. Ratio of mass flow which passes fan and core section is called as bypass ratio α. Fan, compressor ratios and bypass ratio which can be denoted as π f, π c, and α respectively, are the design parameters which affect engine performance. 21

26 Figure 1.4 : JT3D-3B Turbofan Internal Pressures and Temperatures [6]. 1.4 Methodology Any turbofan engine will be selected as base engine which is still in operation because this thesis aims to improve that engine with parameters which are supplied from manufacturer at off design stage. Equation will be emphasized at Chapter 2 and fuel type, combustion chamber temperature and materials which used to manufacture that engine stay same as its origin. So, parametric calculation will give possible range for bypass, fan and compressor ratios and at the end the new possible engines and base engine will compared with others and this thesis will focus on overall efficiencies of possible and base engine as off-design point. 22

27 1.5 Engine Selection To reach aim, engine should be in operation also if efficiency is considered, it is important that aircraft and engine should have more flight frequency than the others possibility aircraft and engine because literature research was made. Also, older engines are more avaible for this thesis due to new engine options are already worked and studied by engine manufacturers. If airlines which are based on Turkey, like Turkish Airlines, Onur Airlines, Atlas Global etc. is studied, some aircraft models and engines come to the forefront (Table 1.2). These aircrafts are Boeing B737, B777 and Airbus A320, A321. Table 1.2 : Partly fleet informations for some airlines based on Turkey adopted websites of airlines. Airlines # of B737 # of B777 # of A320 # of A321 Turkish Airlines Onur Airlines Atlas Global Pegasus Airlines Sun Express Airlines If it is considered that engine manufacturers already started to produce new engine options for B737 and A320, to focus on B777 and A321 engines make thesis to achieve its own goal. If Table 1.2 is examined, the engine of A321 comes to forefront as a suitable candidate. 23

28 Table 1.3 : IAE V2533-A5 Performance at SL [7]. Performance V2533-A5 Take Off Thrust, lbs 32,000 Bypass Ratio 4.8 Overall Pressure Ratio 33.4 Fan Ratio 1.8 Combustion Temperature, Celcius 1550 Take Off Mach 0.2 International Aeroengines which was founded in to develop an engine for the 150-seat single aisle segment. Some of leading aero engine companies which were Pratt&Whitney, Rolls-Royce, Japanese Aero Engine Corporation, MTU Aero Engines and FIAT, came together was focus on delivering the most technologically advanced engine solution for the industry. One of their productions was V2533-A5, has been used for Airbus since April, 1995 [7]. The V2533-A5 is a member of V2500 programme which were studied and produced for especially, Airbus A320 family. It standed out its 4.8 bypass ratio, and 1550 celcius degree combustion temperature and about 32,000 lbs thrust force [7]. Table 1.4 gives some information about V2533-A5 as experimental however this thesis will focus on off-design point of selected engine. Thesis will expect to gather approximate values compared of Table 1.4. The values will be mentioned at chapter 2. 24

29 Table 1.4 : Pratt & Whitney Engine Characteristics [4]. 25

30 2. ANALYSIS To understand how much thrust it can provide or how much fuel it can consume, also, to find its efficiencies, gas turbine equations should be known.this chapter will give brief information about thermodynamics law and aircraft gas turbines and performance equations, however, because of aims of this thesis, component efficiencies will be neglected.at the end of the chapter, IAE V2533-A5 engine will be studied according to performance equations and then parameters which will be also mentioned at this chapter, will be determined for producing new engine options. As mentioned at chapter 1.4, changes will be only bypass ratio α, fan pressure ratio πf and compressor pressure ratio πc which are going to be mentioned, therefore this thesis will focus on uninstalled engine which also will be mentioned. The law of mechanics and thermodynamics manages the operation of gas turbines. Solid and fluid are studied as field of mechanics, however proccess on fluids is examined as gas dynamics. Conservation of mass, energy, momentum and entropy has to be known to analyze gas turbine performance [6]. This thesis assumes the gas as a perfect gas and the flow as one-dimensional flow, and all the properties of fluid will be taken constant through the flow and only in axial direction [4]. 2.1 A Brief Review of Thermodynamics Properties In this chapter, thermodynamics law and compressible flow properties will be studied for reviewing and remembering. As mentioned before, fluid and flow will be modeled as a perfect gas. 26

31 2.1.1 Internal Energy and Enthalpy A gas consists of smaller particles which are molecules, atoms, electrons etc. Random motions and electronic structure of these particles make a field which can be described as intermolecular forces [1]. However, as known, particles in a gas are far away from each other because of that the intermolecular forces are small and can be neglected. The state which intermolecular forces are neglected is called a perfect gas for a gas and it can be described with pressure p, density ρ, temperature T, and specific gas constant R;! = #$% (2.1) If individual molecule of a gas is considered, it can be observed the molecule has energy due to motion of molecule, nuclei. Finite volume of a gas has energy which consists of translational, rotational, vibrational and electronic energy. Internal energy can be defined as to sum of all these energies. The specific internal energy denoted by e, is the internal energy per unit mass of gas, a related quantity is the specific entropy, denoted by h. It can be defined with specific volume v, pressure p, and specific internal energy as, For a perfect gas, e and h are functions of only temperature, h = - +!/ (2.2) - = - % (2.3a) h = h % (2.3b) Let de and dh represent differentials of e and h, respectively. Then equations (2.3a and 2.3b) become, 3- = 4 5 3% (2.4a) 3h = 4 7 3% (2.4b) 27

32 where c v and c p are the specific heats at constant volume and constant pressure respectively [1]. c v and c p can be taken as constant for intermediate temperatures (for air, for T<1000 K). If we combined equations (2.4a and 2.4b) as c v and c p are constants for a perfect gas, - = 4 5 % (2.5a) h = 4 7 % (2.5b) For a specific gas c v and c p are related through the equation, = $ (2.6) Define γ=c p / c v and dividing equation (2.6) by c p, we can obtain, 4 7 = ;$ ; 1 (<. =) Similarly, dividing equation (2.6) by c v, 4 5 = $ ; 1 <. > First Law of Thermodynamics Let consider a finite system which consists a gas, the outside of control volume is called surroundings. It can be energy transfer between system and surroundings, if piston system is considered, there can be work, also. The changes in work and energy transfer can be denoted by δw, and δq, respectively. The relation between work, energy transfer and internal energy can be defined as, 3- =?@ +?A <. B It can be also stated as conservation of energy which is empirical result confirmed by experience. Because of de is an exact differential, and its value depends only on the initial and final states [1]. 28

33 There are infinite number of processes however the three-main process are focussed, Adiabatic process, there is no heat transfer, not added or not taken to process. Reversible process, there is no dissipative effects or phenomena as viscosity, thermal conducvity, mass diffusion, etc. Isentropic process, both adiabatic and reversible process. For reversible proces, dw=-pdv where dv is an incremental change in the volüme due to a displacement of the boundary of the system. So, equation (2.9) becomes,?@!3/ = 3- <. CD Entropy and The Second Law of Thermodynamics Entropy can be explained as the thermal energy of system which can not be transform mechanical energy, also known as randomness and irregularity law. It is state variables and it can be described as, 3E =?@ FG5 % <. CC where entrophy of the system s, an incremental amount of heat added reversibly to the sytem δq rev, and system temperature as T. Also, equation (2.11) can be written as, 3E =?@ % + 3E HFFG5 <. C< In equation (2.12), δq is the actual amount of heat added to the system during an actual irreversible process and ds irrev is the generation of entrophy due to the irreversible, dissipative phenomenas wihtin system [1]. Dissipative phenomena increases the entropy, 3E HFFG5 0 <. CK 29

34 If there is no dissipative phenomenas during the process as reversible, combining equations (2.12 and 2.13), entropy changes for reversible process is, % <. CL Equation can be arranged for adiabatic process, δq=0, equation (2.14) becomes, 3E 0 <. CM Equations (2.14 and 2.15) are forms of the second law of thermodynamics for different process. These equations explain that for adiabatic and reversible process, enthropy of the system will increase or stay same. There is some practical combinations of enthalpy and entropy. Assume that in equation (2.10) heat is added reversibly, then the definition of entropy becomes, % 3E = 3- +!3/ <. CN From the definition of enthalpy (Equation 2.2), we have, 3h = 3- +!3/ + /3! <. C= If equations (2.16 and 2.17) are combining, % 3E = 3h /3! <. C> Equations (2.18 and 2.16) are different forms of the first law of thermodynamics in terms of entropy. For a perfect gas, remember equations (2.5 and 2.6). Combined equations (2.16 and 2.5), 3% 3E = 4 5 % +!3/ % <. CB And if we combined equations (2.18 and 2.6), 3% 3E = 4 7 % /3! % <. <D Remember equation of state, pv=rt, and substitute equation (2.20), 3% 3E = 4 7 % $ 3!! <. <C 30

35 Consider a thermodynamic process with initial and end states denoted 1 and 2 respectively, equation (2.21) integrated between states 1 and 2, becomes, Q R 7 R 3% 3! E O E P = 4 7 $ Q S % 7 S! (<. <<) For a perfect gas, c p and R can be taken as constants, so equation (2.22) becomes, E O E P = 4 7 TU % O % P $ TU! O! P <. <K Isentropic Relations Isentropic process was defined as combination of adiabatic and reversible process which means there is no heat added or taken from system and entrophy changes equals to zero. If isentropic process is wanted to write as equation, rearranging equation (2.23) for isentropic process, or, 0 = 4 7 TU % O % P $ TU! O! P TU! O! P = 4 7 $ TU % O % P (<. <LV)! O! P = % O % P W X /Z (<. <L[) If we combined equations (2.24b and 2.7), equation (2.24) can be written as,! O! P = % O % P \ \]S <. <M 31

36 2.2 Aircraft Gas Turbine This chapter will give information about aircraft gas turbine before the parametric and performance equations. This chapter includes thrust, propulsive efficiency, gas turbine components and brayton cycle Thrust Gas turbine propulsion system can be defined as a combination of some elements increases kinetic energy of fluid which is passing through it. Gas turbines are designed to produce thrust with using kinetic energy of fluids [4]. The propulsion system contains, an engine and housing about the engine (nacelle or duct). Also, there are two terms comes to up which are uninstalled engine thrust and installed engine thrust. Uninstalled engine thrust is the engine thrust which depends on the engine without nacelle or duct so it must be independent. The thrust which produced by engine with nacelle, is that installed engine thrust [6]. Figure 2.1 : Gas turbine schema [6]. 32

37 Definiton of thrust is the sum of difference between the inlet and exhaust momentum divided by gravitational acceleration and the difference of pressure difference multiplied by the exhaust area. If description of sections is made, the freestream, inlet, and exhaust can be numbered as 0, 1 and 9 respectively. So, thrust equation can be written as; Where, ^ = _`a` _ b a b c W + d` d b e` (2.26) ^ _ a c W e = Thrust = Mass Flow Rate = Velocity = Gravitational Acceleration = Area Propulsive Efficiency As mentioned, gas turbine engine provides to increase kinetic energy of fluid which passing thorugh it, propulsive efficiency is the fraction of the net mechanical output of engine which is transformed into thrust [4]. The net meachanical output is gh and the thrust power for the perfectly expanded nozzle is F.V inlet, therefore, propulsive efficiency can be defined as, i 7 = ^a HjkGl Δno (<. <=) 33

38 Figure 2.2 : Schematic drawing of an engine installation showing the mechanical and thrust power [4] Gas Turbine Components Gas turbine consists of the inlet, compressor, combustor, turbine and nozzle in basicly. The brief information will be given for knowledge The Inlet An inlet decreases the velocity of entered air to suitable speed for compressor. Compression helps to reduce the air velocity and it increases the air pressure. An inlet can be described according to efficiency of compression process, the external drag of the inlet, and the mass flow into the inlet [6]. It can be examined in two parts, subsonic and supersonic inlets. Figure 2.3 : A generic subsonic inlet [6]. 34

39 The Compressor Increasing of pressure of incoming air is the function of compressors because efficiency of combustion process and power extraction process after the combustion will increase if the incoming air is pressurized. Also, increasing of pressure of incoming air means that the specific volume of incoming air will be decreased, and it helps fuel/air ratio in the combustor will happen in smaller volume [6]. It can be studied in two parts as centrifugal compressors and axial compressors. Figure 2.4 : Schematic drawing of different types of compressors in aircraft gas turbine engines [4] The Combustor or Burner The combustor is designed to burn fuel/air mixture at steady temperature. As in see figure 2.5, fuel is enjected to the chamber and it makes a mixture of fuel and pressurized air. The efficiency of combustor must be high if it is considered how much energy storaged in fuel per mass. 35

40 Figure 2.5 : Straight flow in combustor [6] The Turbine The turbine is the power extractor which in the gas burnt in combustor. Energy which is gained a gas, is used for compressors and inlet fan driving. Figure 2.6 : Axial flow turbine elements [6]. 36

41 The Exhaust Nozzle To increase the velocity of exhaust gases, is the function of exhaust nozzle. The thrust can be calculated from Newton s second law of motion, therefore velocity of exhaust gasses should be more than velocity at the inlet or free stream air. The nozzles are controlling expand ratio, it means, it arranges pressure and velocity at the exhaust, however, performance analysis of an engine should be done for perfect expand ratio. Also, it can be examined in two main class, convergent nozzles and convergentdivergent nozzles [6]. Figure 2.7 : Convergent exhaust nozzle [6]. 37

42 2.2.4 Brayton Cycle The brayton cycle is the basis thermodynamics relation and model which used for ideal turbomachinery engines [4]. Figure 2.8 : a) Brayton cycle graph. b) Brayton cycle schmatic [6]. If figure 2.8 is studied, the brayton cycle is made by 4 main process at the inlet, compressor, combustor and turbine; 1. Isentropic compression (2 to 3) 2. Constan-pressure heat addiction (3 to 4) 3. Isentropic expansion (4 to 9) 4. Constant-pressure heat rejection (9 to 2) For a perfect gas, thermodynamic analysis of the ideal brayton cycle can give equations for the rate of energy transfer for each component, p Wqr7FGssqF = _4 7 % t % O p lufvhjg = _4 7 % w %` x Hj = _4 7 % w % t (<. <B) (<. KD) (<. KC) 38

43 x qul = _4 7 %` % O U-y p qul = p lufvzjg p Wqr7FGssqF (<. K<) (<. KK) Thermal efficiency of the cycle is, i l{gfr k = U-y p qul x zj (<. KL) And note that, d t d O (}~P)/} = % t % O = % w %` (<. KM) Combining equations (2.34 and 2.35), i l{gfr k = 1 1 d$ }~P /} (<. KN) PR is the pressure ratio as P 3 /P 2. So thermal efficiency can be plotted as figure 2.9 for two ratios of specific heats. It is easily seen until pressure ratio reaches about 10, thermal efficiency will increase immediately. Figure 2.9 : Thermal effiency of brayton cycle [3]. 39

44 Brayton cycle can be redefined for the turbofan which includes the fan, compressor, combustor and the turbine. For turbofans, compressors and turbines consist of two main parts due to its pressure; low pressure and high pressure. Figure 2.10 : Ideal brayton cycle for Ideal turbofan engine. If figure 2.10 is examined, it can be seen, the energy which is required for driving fan and compressor, is provided by high pressure turbine. Because of that, energy which is driving fan can be written as, p j = _4 7 % O % b and net work out for turbofans, can be rewritten as, U-y p qul = p lufvzjg p Wqr7FGssqF p j 40

45 2.3 Aircraft Gas Turbine Engine Equations Aircraft gas turbine engine equations can be examined in two main parts, parametric cycle analysis and performance analysis. These analsys can be defined as to study on thermodynamic changes on the fluid which passing through engine. Performance analysis can be called as off-design. Parametric analysis can be called as on-design [6]. Main difference between two analysis, parametric analysis is mostly used for finding many option for engine. Each points on the plots which are produced according to parametric cycle analysis, represent a different engine. However, performance analysis represents an engine which has parameters which are determined by parametric cycle analysis. Also, performance analysis is including components efficiencies but this thesis will neglect component efficiency because of original engine s unknown Notation The temperature reached when a flowing fluid is brought to rest adiabatically is the definiton of the total or stagnation temperature [6]. If T t shows total temperature, there is a relation between static temperature T and velocity of fluid V. If the first law of thermodynamics is considered, we have relation for a perfect gas about T t which can be described, % l = % + ao 2c W 4 7 <. K= Also the relation between mach number M, fluid velocity V and acoustic velocity a. This can be written as M=V/a (2.38), and we know that a=(γg c RT) (2.39), if equations (2.37 and 2.39) are combined, it becomes, 41

46 % l = % 1 + ; 1 2 ÄO (<. LD) The pressure reached when a flowing fluid is brought to rest isentropically is the definition of total or stagnation pressure P t [3]. Since, P t /P = (T t / T) γ/γ-1, then, d l = d 1 + ; 1 2 ÄO \ \]S <. LC Ratios of total temperatures and pressures will be used to calculate engine performance, so notation is made for these ratios, specially. π will be used for ratios of total pressures across the component with a subscript which is indicating components as f for fan, b for burner, c for compressor, t for turbine, n for nozzle and go on, Å = yçyét!ñ-eeöñ- T-É/ÜUc 4Ç_!ÇU-Uy É yçyét!ñ-eeöñ- -Uy-ÑÜUc 4Ç_!ÇU-Uy É <. L< Similarly, τ will be used for ratios of total temperatures across the components, á = yçyét y-_!-ñéyöñ- T-É/ÜUc 4Ç_!ÇU-Uy É yçyét y-_!-ñéyöñ- -Uy-ÑÜUc 4Ç_!ÇU-Uy É <. LK It can be defined these ratios for freestream (π r and τ r ) in terms of specific heat ratios γ, and the freestream mach number M 0, Å F = d lb d b = 1 + ; 1 2 Ä b O \ \]S <. LL á F = % lb % b = 1 + ; 1 2 Ä b O <. LM Also, τ λ can be defined as the ratio of the burner exit enthalpy to the ambient enthalpy, á à = h l vufjgf GâHl h b = 4 7% l vufjgf GâHl 4 7 % b <. LN 42

47 Figure 2.11 : Station numbering for gas turbine engines according to ARP 755A [6]. Station numbering is important to follow gas turbine engines equations. So, table 2.1 which can be seen below, will show us all ratio denotations which may be used for following chapters,. Table 2.1 : Temperature and pressure realations for all π and τ [6] 43

48 Note that, for table 2.1, station numbers are used for bypass stream and decimal numbers as 1.3 which are used to show for intermediate station Design Inputs The total temperature ratios and pressure ratios, etc. Can be classified into four main categories, 1. Flight conditions; P 0, T 0, M 0, c p, τ r, π r, 2. Design limits; (c p T t ) burner exit 3. Component performance; π d, π b, π n, etc. 4. Design choices; π c, π f, etc Steps of Gas Turbine Engines Parametric Cycle Analysis These chapter will be listed the steps of gas turbine engines parametric cycle analysis equations for a jet engine which has single inlet and single exhaust [6]. It is expected from parametric cycle analysis, to find how engine performance varies with changes in the flight conditions, design limits, design limits and design choices. As mentioned at chapter 1, this thesis will focus only design choices effects on engine performance. The analysis which will be made in this thesis, will assume that new engine options have flight conditions, design limits, and component performance same as a base engine IAE V2533-A5. 1. Starting with an uninstalled engine thrust equation (2.26), it will be rewritten in terms of flight conditions, ^ = _`a` _ b a b c W + d` d b e` ^ _ b = É b c W _` _ b a` É b Ä b + e`d` _ b 1 d b d` 2. Next, it should be expressed velocity ratios as V 9 /a 0 in terms of Mach numbers, temperatures and gas properties of states 0 and 9, 44

49 a` É b O = ÉÒÄÒ É b O = ;`$`c W %` ; b $ b c W % b ÄÒ 3. Find the exit mach number M 9. So, or, d l` = d` 1 + ; 1 2 ÄO` \ \]S ÄÒ = 2 ; 1 d l` d` (}~P)/} 1 where, d l` d` = d b d lb d lo d lt d lw d lä d lã d l` = d b d` d b d lb d lo d lt d lw d lä d lã d` 4. Find the temperature ratio T 9 / T 0, Å F Å å Å W Å v Å l Å çé Å j %` = % l`/% b = % b % l`/%` % l`/% b d l`/d` (}~P)/} where, % l` %` = % b % lb % lo % lt % lw % lä % lã % l` = á %` % b % lb % lo % lt % lw % lä % F á W á v á l á çé á j lã 5. Apply the first law of thermodynamics to the burner and then the fuel/air ratio z can be found in terms of t s, fuel heat capaticy h PR. _ b 4 7 % lt + _ è h êz = _ b 4 7 % lw 6. To find an expression for the total temperature ratio across the turbine, by relating turbine power output to the compressor and the fan and/or requirements. This allow us to find τ t in terms of other variables. 7. Evaluate the specific thrust, using the preceding results. 8. Evaluate the TSFC, using the specific thrust and fuel/air ratio, 45

50 %ë^í = ì î r ï 9. Develop expressions about thermal and propulsive efficiencies Assumptions for Ideal Cycle Analysis For analysis of ideal cycle, this thesis assumes that, 1. Compression and expansion processes in the inlet, compressor, fan, turbine, and nozzle, are according to isentropic conditions which are adiabatic and reversible. So, á å = á j = 1 Å å = Å j = 1 á W = Å W (}~P)/} á = Å (}~P)/} 2. Combustion chamber is designed for constant pressure and p b =1. The fuel flow rate can be taken as following, WqFG 1 ÉU3 _ + _ WqFG _ WqFG 3. The working fluid is air which behaves as a perfect gas with constant specific heats. 4. The engine exhaust is designed perfect expansion rate condition which means exhaust gas pressure should be equal environment pressure (P 9 = P 0 ) Ideal Turbofan Engine Cycle Analysis The turbofan is the version of the turbojet engine which mentioned in chapter 1. The main difference between them is the turbofan has a fan section which helps to increase propulsive efficiency [6]. The mass flow rate can be increased with the fan section and decreased exit velocity at the same thrust. If it is considered fuel flow rate helps to increase exit velocity, to decrease exit velocity means that the fuel flow rate will decrease with it [6]. However, decreasing of exit velocity causes aircraft velocity 46

51 to be limited. So, higher velocity are not preferable for the turbofan applications (M 0 >4). Station numbering for the turbofan is given at figure 2.12, between stations 2 and 13 are defining of the fan and stations 13 and 19 are for fan nozzle. Figure 2.12 : Station numbering for the tubofan engine [6]. We can write following four equations for the fan and the fan nozzle denoted by p f and p fn respectively, Å = d lpt d lo á = % lpt % lo Å j = d lp` d lpt ÉU3 á j = % lp` % lpt The gas flow is passing through the core engine is _ ò, and the gas flow is passing through the fan is _ î. The ratio of fan flow to the core flow is defined bypass ratio denoted as α, so, öõ!éee ÑÉyÜÇ ú = _ î _ ò <. L= The total gas flow can be expressed as 1 + ú _ ò. _ b can be used to definition of total gas flow, so, _ b = _ î + _ ò = 1 + ú _ ò (<. L>) 47

52 Figure 2.13 : The Brayton cycle for a turbofan engine with station numbers [6]. In the analysis of the turbofan engine, this thesis assumes that the core mass rate is much higher than the fuel mass rate [6]. Also, nozzles including the fan nozzle are designed for perfect expand, so it means d b = d` = d P` Steps of Cycle Analysis The turbofan which is represented in figure 2.13 and 2.12, will be analyzed in this section. The steps are, Step 1: The thrust equation for the turbofan engines is, so, ^ = _ ò c W a` a b + _ î c W a P` a b <. LB ^ _ b = É b c W É Step 2: a`/é b can be rewritten as, a` É b Ä b + ú a P` É b Ä b <. MD a` É b O = ÉÒÄÒ É b O = ;`$`c W %` ; b $ b c W % b ÄÒ <. MC 48

53 Step 3: Then, d l` = d` 1 + ; 1 2 ÄO` \ \]S (<. M<) and, d l` = d b d lb d b d lo d lb d lt d lo d lw d lt d lä d lw d l` d lä = d b Å F Å å Å W Å v Å l Å j (<. MK) However, for ideal gas turbine engine cycle Å å = Å v = Å j = 1 and so, d l` = d b Å F Å W Å l and so, ÄÒ = 2 ; 1 d l` d` \]S \ 1 <. ML where, d l` d` = d l`d b d b d` = d b d` Å F Å W Å l = Å F Å W Å l (<. MM) Then, equation (2.54) becomes, ÄÒ = 2 ; 1 Å FÅ W Å l \]S \ 1 (<. MN) However, as mentioned in table 2.1, á F = Å F (}~P)/}, and for ideal turbofan á W = Å W (}~P)/} and á l = Å l (}~P)/}. So, we can rewrite equation (2.56), Step 4: ÄÒ = O }~P á Fá W á l 1 <. M= then, % l` = % b % lb % b % lo % lb % lt % lo % lw % lt % lä % lw % l` % lä = % b á F á å á W á v á l á j = % b á F á W á v á l (<. M>) %` = % l`/% b = % b % l`/%` á F á W á v á l d l`/d` (}~P)/} = á Fá W á v á l \]S = á Fá W á v á l á Å F Å W Å \ F á W á l l (<. MB) thus, 49

54 %` % b = á v <. ND Step 5: Application of steady flow energy equation to the burner gives, _ b 4 7 % lt + _ è h êz = _ b 4 7 % lw (<. NC) For an ideal cycle, _ + _ WqFG _ WqFG and 4 7t = 4 7w = 4 7, if we arrange equation (2.61), it becomes, or, _ è h êz = _ b 4 7 % lw % lt = _ b 4 7 % b % lw % b % lt % b (<. NC) ù = _ è _ b = 4 7% b h êz % lw % b % lt % b (<. N<) However, á à = % lw % b = á F á W á v <. NK So, it can be rewritten equation (2.62) as, á F á W = % lt % b <. NL ù = _ è _ b = 4 7% b h êz á à á F á W <. NM Step 6: The power output of the turbine is, and it can be rewritten as, p l = _ + _ ò 4 7 % lw % lä _ ò 4 7 % lw % lä (<. NN) p l = _ ò 4 7 % lw 1 % lä % lw = _ ò 4 7 % lw 1 á l <. N= The power required to drive the compressor is, p W = _ ò 4 7 % lt % lo = _ ò 4 7 % lo % lt % lo 1 = _ ò 4 7 % lo á W 1 <. N> 50

55 The power required to drive the fan is, p = _ î 4 7 % lpt % lo = _ î 4 7 % lo á 1 <. NB Since p l = p W + p for the ideal turbofan, so, % lw 1 á l = % lo á W 1 + ú% lo á 1 á l = 1 % lo % lw á W 1 + ú á 1 á l = 1 á F á à á W 1 + ú á 1 <. =D Step 7: Equation (2.51) can be rewitten as, a` É b O = %` ÄÒ = 2 á à á % b ; 1 á F á F á W á l 1 W and according to equation (2.71), note that % P` = % b and the fan nozzle equation can be written as, a P` É b O = % P` Ä O % P` = 2 b ; 1 á Fá 1 <. =C Equations (2.70 and 2.71) can be combined as, a` É b O = 2 á à á ; 1 á F á F á W 1 á F á W á W 1 + ú á 1 1 (<. =<) à Equation (2.72) can be simplified as, a` É b O = 2 ; 1 á à á F á W 1 + ú á 1 á à á F á W <. =K The specific thrust for turbofan is given by equations (2.50, 2.71, and 2,72). Step 8: ë = _ ^ = ù ^/_ ò = ù (_ b /_ ò )(^/_ b ) = ù (1 + ú)(^/_ b ) (<. =L) Step 9: The thermal efficiency can be described as, i Q = 1 1 á F á W <. =M 51

56 Propulsive efficiency can be defined as, i ê = 2 a`/a b 1 + ú(a P`/a b 1) aò/a b O 1 + ú(a PÒ /a b O 1) (<. =N) Thrust ratio is also useful performance parameter for the turbofan engine is ratio of specific thrust per unit mass flow of the core stream to that of the fan stream. Thrust ratio is denoted by FR. It can be described as, It can be rewitten as, ^$ = ^ò/_ ò ^î/_ î (<. ==) ^$ = a`/é b Ä b a P`/É b Ä b (<. =>) Summary of Equations $ = ; 1 4 ; 7 (<. =BV) É b = ;c W $% b (<. =B[) á F = 1 + ; 1 2 Ä b O (<. =Bû) á à = % lw % b (<. =Bü) á W = Å W (}~P)/} á = Å (}~P)/} (<. =B ) (<. =B ) a` É b = 2 ; 1 á à á F á W 1 + ú á 1 á à á F á W <. =B a P` É b = 2 ; 1 á Fá 1 <. =B ^ _ b = É b c W É a` É b Ä b + ú a P` É b Ä b (<. =B ) 52

57 ù = 4 7% b h êz á à á F á W (<. =B ) ë = ù (1 + ú)(^/_ b ) i Q = 1 1 á F á W i ê = 2 a`/a b 1 + ú(a P`/a b 1) aò/a b O 1 + ú(a PÒ /a b O 1) i = i ê i Q ^$ = a`/é b Ä b a P`/É b Ä b (<. =B ) <. =Bß (<. =B ) (<. =B ) (<. =B ) 2.4 Definition of Flight Conditions To calculate performance of gas turbine engine flight conditions should be known. Earth atmosphere model will be used. Temperature T, and pressure P can be defined as [3] in term of altitude h, % = h <. >D d = % ä.oäø (<. >C) where, T = Temperature (oc), P = Pressure (kpa), h= Altitude (m). At the beginning, sea level is taken as zero and cruise level is taken 35 kft. Equations (2.80 and 2.81) can be used to calculate environmental temperature and pressure which can be seen at table 2.2. Take off and cruise mach number are taken from manufacturer s information [4]. 53

58 Table 2.2 : Sea level and cruise conditions for selected engine. Sea Level Cruise Altitude, ft Temperature, K Pressure, kpa Mach 0.2 (Take off) Effects of Design Choices on Engine Performance As mentioned before, only design choices will be considered for increasing efficiency therefore, the effects of design choices should be known. The bypass ratio, fan pressure ratio, and compressor pressure ratio will be examined in this chapter, and effects on the specific thrust, TSFC, overall efficiency and FR will be studied. The equations at chapter 2.3.5, were transformed into cycle with MATLAB. All codes which written for calculations in MATLAB, will be announced at appendix. MATLAB Codes need only design choices for calculating, the another inputs were already written as invariant. Sea level performance and cruise performance will be examined Effects of Bypass Ratio Bypass ratio is the most important design choice as mentioned so far. Thesis will study effecs of bypass ratio on engine performance parameters. As in figure 2.14 and 2.15, bypass ratio affects four main performance parameters. If figure 2.14a and 2.15a are examined, the specific thrust decreases with increasing of bypass ratio. And, it can be seen that, TSFC also decreases with increasing of bypass ratio at figure 2.14b and 2.15b. If equations (2.79j and 2.79l) are studied, decresing of the specific thrust and TSFC is expected almost linearly and it can be easily seen at figure 2.14 and However, unlike TSFC and the specific thrust, overall efficiency increases with bypass ratio, respectively. If there is willing to 54

59 increase overall efficiency, bypass ratio should be increased, as figure 2.14c and 2.15c, however, the specific thrust should be considered Effects of The Fan Pressure Ratio The fan pressure ratio can be defined as ratio of the total pressure of leaving to fan to the entering to fan. The fan is the specific component for only turbofan. The fan pressure ratio does not behave like bypass ratio. If figure 2.16 and 2.17 are examined, the specific thrust and overall efficiency increase at some point and then, it starts to decrease, with increasing of the fan pressure ratio. Also, figure 2.16a and 2.17b shows us that increasing the fan pressure ratio at some point, can help to increase the specific thrust, also, figure 2.16c and 2.17c, shows it for the overall efficiency. However, accordingly figure 2.16d and 2.17d, if fan pressure ratio is increased above 3, thrust ratio will decrease under zero. So that means, it does not make sense to increase fan pressure ratio above 3. For figure 2.16 and 2.17, the optimum value for the fan pressure ratio comes forefront as Effects of The compressor Pressure Ratio The compressor pressure ratio can be defined as ratio of the total pressure of leaving to compressor to the entering to compressor. If figure 2.18 and 2.19 are examined, overall efficiency icreases with increasing of compressor pressure ratio, however, as in figure 2.18a and 2.19a, the specific thrust can not be affected less than other parameters. If figure 2.18b and 2.19d are studied, TSFC and FR are increasing with increasing of compressor pressure ratio. Also, according to figure 2.18c and 2.19c, overall efficiency increases with increasing of compressor pressure ratio. 55