Pressure and Heat Recovery in High Altitude Supersonic Ejector of a Low Bypass Turbofan Engine Test Facility

Pressure and Heat Recovery in High Altitude Supersonic Ejector of a Low Bypass Turbofan Engine Test Facility

February, 2011.

Ph. D. Dissertation

Pressure and Heat Recovery in High Altitude Supersonic Ejector of a Low Bypass Turbofan Engine Test Facility

February 25, 2011

Pressure and Heat Recovery in High Altitude Supersonic Ejector of a Low Bypass Turbofan Engine Test Facility

Advisor : Professor ChangDuk Kong

February 25, 2011

Table of Contents

List of Figures ··· VI List of Tables ··· X Nomenclature ··· XI Abstract ··· XIII

Chapter 1

Fundamental Classifications

1.0 Introduction ··· 1

1.1 Wind Tunnel Theoretical Summary ··· 1

1.2 Wind Tunnel Classifications ··· 1

1.2.1 Closed Circuit Wind Tunnel ··· 2

1.2.2 Advantages of closed circuit wind tunnel ··· 2

1.2.3 Disadvantages of closed circuit wind tunnel ··· 2

1.2.4 Open Circuit Wind Tunnel ··· 2

1.2.5 Advantages open circuit wind tunnel ··· 3

1.2.6 Disadvantages open circuit wind tunnel ··· 3

1.3 Main Components of Wind Tunnel ··· 3

1.3.1 Application Areas of Wind Tunnel and Test Chambers ··· 3

1.3.2 Applications related to jet engine testing ··· 4

1.4 Summary ··· 5

List of papers publications related to this thesis ··· 8

Chapter 2 Research and Development of Wind Tunnels ··· 9

2.0 Literature review ··· 9

2.1 Introduction ··· 9

2.2 Wind tunnel diffuser ··· 9

2.3 Ramjet diffuser ··· 13

2.4 Ejectors ··· 15

2.5 Summary ··· 17

Chapter 3 Fundamental System Theories ··· 19

3.0 Principles of gas turbine engines ··· 19

3.1.1 Conservation Equations ··· 19

3.1.2 Conservation of mass ··· 20

3.1.3 Conservation of momentum ··· 20

3.1.4 Conservation of energy ··· 20

3.1.5 Zero heat addition with Ve>V0··· 21

3.1.6 Zero heat addition with Ve<V0 ··· 21

3.1.7 Zero heat addition with P =constant >0 ··· 22

3.2 Propulsive efficiency ··· 22

3.2.1 Heat addition, ΔQ>0 ··· 23

3.2.2 Constant heat addition, ΔQ=constant>0 ··· 24

3.3 Overall efficiency. ··· 24

3.3.1 Fuel Consumption efficiency ··· 25

3.4 The Force Field for Air breathing Engines ··· 26

3.5 Summary ··· 29

Chapter 4 Fluid Dynamics Principles of a Test Cell ··· 30

4.0 Test facility operation principals ··· 30

4.1 Quasi one dimensional flow equation ··· 30

4.1.1 Equation of State ··· 30

4.1.2 Speed of Sound ··· 31

4.1.3 Mach Number ··· 31

4.1.4 Conservation of Mass ··· 32

4.1.5 Conservation of Energy ··· 34

4.1.6 Conservation of Momentum ··· 34

4.2 The Equations of Motion in Standard Form ··· 35

4.3 Summary ··· 38

Chapter 5 Nozzles ··· 39

5.0 Intake nozzle ··· 39

5.1 Inlet ··· 39

5.1.1 Inlet Maximum Mass Flow ··· 39

5.1.2 Internal Compression Inlet ··· 41

5.1.3 External Compression Inlets ··· 45

5.2 Summary ··· 47

Chapter 6 Supersonic Diffuser ··· 48

6.0 Diffusers ··· 48

6.1 Elements of supersonic diffuser flow ··· 48

6.2 Summary ··· 53

Chapter 7 Pressure loss calculation in duct ··· 54

7.0 Duct Flow and Pressure Loss Calculations ··· 54

7.1.1 Laminar flow in a pipe ··· 54

7.1.2 Turbulent flow in a pipe ··· 54

7.1.3 Fanning Friction Factor for Laminar Flow ··· 57

7.1.4 Flow measurements ··· 57

7.1.5 Reynolds number calculation ··· 59

7.1.6 Pressure increase experiments of the Ejector ··· 59

7.1.7 Turbulence ··· 61

7.1.8 Experimental setup ··· 61

7.1.9 Pressure Calculation Procedure For High Speed Gas Flow ··· 62

7.2.1 Mach Number ··· 62

7.2.2 Total Pressure and Loss Coefficients. ··· 62

7.3 Straight Constant Area Ducts ··· 63

7.3.1 Area Change ··· 63

7.3.2 Abrupt Area Increase ··· 63

7.3.3 Diffusers ··· 64

7.3.4 Convergent Duct (Nozzles) ··· 65

7.4 Calculation Procedures ··· 66

7.4.1 Mach Number Calculations ··· 67

7.4.2 Straight Duct (intake) ··· 67

7.4.3 Abrupt area increase (intake) ··· 70

7.4.4 Abrupt area increase (exhaust) ··· 71

7.5 Sample Calculation ··· 74

7.6 Summary ··· 76

Chapter 8 F404-402 Engine Design Point Simulation ··· 77

8.0 Study Engine selection ··· 77

8.1.1 Selected Engine Characteristics ··· 78

8.1.2 Engine Design Point Analysis ··· 78

8.1.3 Design Point iteration Data ··· 79

8.1.4 Test Cell Schematic Layout ··· 83

8.1.5 Direct Connection Mode (DC) ··· 84

8.1.6 Free Jet Connection Mode (FJ) ··· 84

8.1.7 Steady State Simulation Mode ··· 84

8.1.8 Ground Test Simulation Mode (Altitude Testing) ··· 85

8.1.9 Left Side of Mach Number ··· 86

8.2 Right Side of Mach Number ··· 87

8.2.1 Engine Steady State Simulation Results ··· 103

8.3 Summary ··· 104

Chapter 9 2D Design of Altitude Test Chamber ··· 105

9.0 Test cell design and modelling ··· 105

9.1.1 Bell Mouth Nozzle ··· 106

9.1.2 Bell Mouth engine air mass flow ··· 106

9.1.3 Test Section ··· 107

9.1.4 Direct Connection ··· 108

9.1.5 Measurement Schemes ··· 108

9.1.6 Airflow metering method ··· 109

9.1.7 Engine Stand ··· 112

9.1.8 Full Schematics Altitude Testing Facility ··· 113

9.2 Analysis and Results ··· 116

9.3 Summary ··· 120

Chapter 10 Heat Recovery ··· 121

10.0 Heat Exchanger ··· 121

10.1.1 Classification of Heat Exchangers ··· 121

10.1.2 Introduction ··· 121

10.1.3 Classification according to transfer processes ··· 122

10.1.4 Indirect-Contact Heat Exchangers ··· 123

10.1.5 Direct Transfer Type Exchangers ··· 123

10.1.6 Heat Recovery ··· 123

10.1.7 Material Thermal Conductivity ··· 125

10.1.8 Convection from a fluid to wall and thickness of liquid (unknown) ··· 126

10.1.9 Turbulent flow through a shell and tube heat exchanger ··· 128

Chapter 11 Conclusion ··· 132

References

Appendix

Acknowledgemen

List of Figures

Fig. 1 Wind Tunnel Layout ··· 2

Fig. 2 Main Parts of Wind Tunnel ··· 3

Fig. 3 Test cell application areas ··· 4

Fig. 4 Engine testing chambers ··· 4

Fig. 5 Gas turbine engine ··· 19

Fig. 6 Schematic of idealized flow machine a ··· 19

Fig. 7 The specific thrust produced by a propeller ··· 22

Fig. 8 The efficiency of a propeller ··· 23

Fig. 9 The thrust of a turbojet engine as a function of flight speed ··· 24

Fig. 10 Specific fuel consumption as a function of average velocity for turbojet ··· 26

Fig. 11 Schematic diagram of the control volume for an air breathing engine ··· 26

Fig. 12 Control volume for one-dimensional analysis of an air-breathing engine ··· 27

Fig. 13 Schematic diagram of a simple inlet ··· 40

Fig. 14 Maximum mass flow of air passed by the inlet ··· 40

Fig. 15 Captured stream tube for maximum mass flow through an inlet ··· 41

Fig. 16 Internal compression under maximum mass flow conditions ··· 42

Fig. 17 Variation of captured stream tube area ··· 45

Fig. 18 Variation of total pressure recovery as a function of flight Mach number ··· 45

Fig. 19 Schematic diagram of an external compression ··· 46

Fig. 20 Adiabatic Inlet compression process ··· 46

Fig. 21 Shock pattern through supersonic diffuser ··· 49

Fig. 22 Force balance (macroscopic momentum balance) on straight pipe ··· 55

Fig. 23 Data correlation for friction factor (delta P) Versus Re(flow rate) in pipe ··· 56

Fig. 24 Re<2100 Laminar ··· 56

Fig. 25 2100 < Re <4000 Transitional ··· 56

Fig. 26 4000<Re Turbulent ··· 57

Fig. 27 Wind Velocity Measurement ··· 57

Fig. 28 Difference in Static and Total Pressure ··· 58

Fig. 29 Mixed ejector schematic arrangement ··· 60

Fig. 30 Ejector System Schematics ··· 61

Fig. 31 Abrupt Area Change ··· 63

Fig. 32 Diffuser Angle ··· 64

Fig. 33 Calculation Procedure ··· 66

Fig. 34 Pressure ratio calculation ··· 66

Fig. 35 Reynolds Calculation ··· 66

Fig. 36 Straight intake duct ··· 67

Fig. 37 Straight Duct (Intake) ··· 68

Fig. 38 Straight Duct (Exhaust) ··· 68

Fig. 39 Duct inlet with bellmouth entrance ··· 69

Fig. 40 Duct inlet length with sharp edged with or without screen ··· 69

Fig. 41 Sharp edged entrance with or without screen at entrance ··· 69

Fig. 42 Entrance with or without screen at entrance ··· 70

Fig. 43 Abrupt intake area increase ··· 70

Fig. 44 Abrupt intake area increase ··· 71

Fig. 45 Abrupt exhaust area increase ··· 71

Fig. 46 Abrupt intake area decrease ··· 72

Fig. 47 Abrupt exhaust area decrease ··· 72

Fig. 48 Exhaust Increase ··· 73

Fig. 49 Intake diffuser configuration ··· 73

Fig. 50 Intake diffuser calculation ··· 74

Fig. 51 Exhaust diffuser calculation ··· 74

Fig. 52 Propeller exhaust diffuser example ··· 74

Fig. 53 Intake pressure loss ··· 75

Fig. 54 F Series Engine Classification Courtesy of GE Aviation ··· 77

Fig. 55 Multi Spool mixed flow turbofan engine with Afterburner ··· 78

Fig. 56 Station Numbering and Bleed Points ··· 79

Fig. 57 Design Point Simulation Results @ Sea Level Static Condition ··· 80

Fig. 58 Low Pressure Compressor ··· 81

Fig. 59 High Pressure Compressor ··· 81

Fig. 60 High Pressure Turbine ··· 82

Fig. 61 Low Pressure Turbine ··· 82

Fig. 62 Test Cell layout ··· 83

Fig. 63 Enthalpy/entropy ··· 84

Fig. 64 Flight test Mode ··· 85

Fig. 65 Ground test Mode ··· 85

Fig. 66 Reheat on(afterburner) ··· 88

Fig. 67 DC 1 a/b on low ··· 89

Fig. 68 DC 2 a/b on low ··· 89

Fig. 69 DC 3 a/b on low ··· 90

Fig. 70 DC 5 a/b on low ··· 90

Fig. 71 DC 7 a/b on low ··· 91

Fig. 72 DC 9 a/b on low ··· 91

Fig. 73 FJ a/b on low ··· 92

Fig. 74 No Reheat (Afterburner off) ··· 92

Fig. 75 DC 1 a/b off low ··· 93

Fig. 76 AB off high working @ temp 449K ··· 93

Fig. 77 DC 2 a/b off low ··· 94

Fig. 78 DC 2 a/b off high@449K ··· 94

Fig. 79 DC 3 a/b off low ··· 95

Fig. 80 DC 3 a/b off High @440K ··· 95

Fig. 81 DC 4 a/b off High @440K ··· 96

Fig. 82 DC 5 a/b off low ··· 96

Fig. 83 DC 5 a/b off high@440K ··· 97

Fig. 84 DC 6 a/b off high@440K ··· 97

Fig. 85 DC 7 a/b off high@440K ··· 98

Fig. 86 DC 7 a/b off low ··· 98

Fig. 87 DC 8 a/b on low ··· 99

Fig. 88 DC 8 a/b off high ··· 99

Fig. 89 DC 9 a/b on high ··· 100

Fig. 90 DC 9 a/b off high ··· 100

Fig. 91 DC 10 a/b on high ··· 101

Fig. 92 DC 10 a/b off high ··· 101

Fig. 93 FJ a/b off low ··· 102

Fig. 94 Sterling Chamber ··· 105

Fig. 95 Bell Mouth Nozzle ··· 106

Fig. 96 Test Section Configuration ··· 108

Fig. 97 Flow metering devices ··· 109

Fig. 98 Traditional Ejector model ··· 110

Fig. 99 Proposed Model ··· 110

Fig. 100 Effect of mixed flow on shock wave ··· 111

Fig. 101 Engine Stand ··· 112

Fig. 102 Exhaust Ejector and Heat Exchanger ··· 112

Fig. 103 2D Autocad Modeling of The Test Facility ··· 113

Fig. 104 3D Solid works modeling ··· 113

Fig. 105 Ejector and heat exchanger 3D model ··· 114

Fig. 106 Intake nozzle mounted for Direct test ··· 114

Fig. 107 Supersonic ejector ··· 115

Fig. 108 Heat exchanger model ··· 115

Fig. 109 Intake nozzle ··· 116

Fig. 110 Supersonic Ejector ··· 116

Fig. 111 Pressure and velocity along the ejector ··· 117

Fig. 112 Ejector flow regime ··· 117

Fig. 113 Ejector end face flow ··· 117

Fig. 114 Pressure recovery comparisons of the two ejectors ··· 119

Fig. 115 Pin Tube heat exchanger schematics ··· 121

Fig. 116 Heat Transfer by conduction ··· 124

Fig. 117 Conduction through pipe ··· 124

Fig. 118 Specific heat property of Methylene Chloride ··· 125

Fig. 119 Heat exchanger tube ··· 126

Fig. 120 Boundary Condition of Heat exchanger ··· 127

Fig. 121 Heat Transfer between two fluids ··· 127

Fig. 122 Heat transfer through conduction ··· 128

Fig. 123 Streamline Velocity field over Heat exchange tubes ··· 129

Fig. 124 Velocity Contour through Heat Exchanger ··· 129

Fig. 125 Heat Exchanger Analysis ··· 130

Fig. 126 Heat exchanger simulation results ··· 131

List of Tables

Table. 1 Heating values for typical liquid fuels ··· 26

Table. 2 Coefficients for Quasi-One Dimensional Flow for Variable Molecular Weight · and Isentropic Exponent ··· 36

Table. 3 Coefficients for Quasi-One Dimensional Flow for Constant Molecular Weight and Isentropic Exponent ··· 37

Table. 4 Contraction ratios for internal compression inlets ··· 44

Table. 5 Input parameters ··· 67

Table. 6 Calculation of Total Pressure drop at different flow velocities ··· 75

Table. 7 Selected Engine Characteristics ··· 78

Table. 8 Engine performance data ··· 79

Table. 9 Simulation testing range ··· 86

Table. 10 Ejector CFD Simulation Results ··· 87

Table. 11 Simulation results ··· 103

Table. 12 Prevailing ambient conditions ··· 107

Table. 13 Calculated pressure loss ··· 118

Table. 14 Calculated pressure recovery data ··· 118

Table. 15 Material properties thermal conductivity ··· 125

Table. 16 CFD Temperature heat exchanger simulation ··· 130

Nomenclature

r Density (kg/m³)

ra Air density (kg/m³)

R Universal gas constant (J/kg.K)

T Temperature (K)

Dp Pressure drop (Pa)

Dp Dynamic pressure head (Pa)

P Pressure (Pa)

rw Density of water (kg/m³)

V Flow Velocity (m/s)

g Acceleration due to gravity (m/s²) h Mano metric height (mm of H2O) P_t Total pressure (Pa) (P0)

Q Volume flow rate (m³/s) CP Coefficient of Power C_T Coefficient of Thrust C_Q Coefficient of Torque

hx Efficiency of x

β Open area ratio for screens

δ Boundary-layer height

ν Kinematic viscosity

σ Standard deviation

θ Half diffuser angle

A Area

C Coefficient (lift, drag etc.)

D Drag

F thrust

C function of M and y in adiabatic flow

g gravitational acceleration

h specific enthalpy

ho specific total enthalpy

Hc calorific value

K,k constants

cp specific heat at constant pressure cv specific heat at constant volume

L lift

M Mach number

N function of M and y in adiabatic flow

p static pressure

po total pressure

m mass flow

q, f fuel/air ratio

R gas constant

r pressure ratio

s.c. specific consumption

T static temperature

To total temperature

u,v velocity

X,Y,Z functions of y and N

Abstract

By Owino George Omollo

Advisor : Prof Changduk Kong Ph. D Department of Aerospace Engineering Graduate School of Chosun University

이 논문은 저바이패스 터보팬 엔진 시험장치용 고고도 초음속 이젝터 덕트의 압력 및 열 회복에 관한 연구입니다.

고고도 시험설비는 가상엔진 입구 환경을 위한 설비입니다.

시운전 시험 설비는 엔진 입구를 만든 환경이 실제고도 환경과 비슷해야 합니다.

위의 비슷한 조건을 만들기 위해서 시험 설비 설계와 계산 방법은 이 논문에 표현되어 있습니다.

시험 설비 구성은 첫 번째로 스털링 챔버가 맨앞에 있고 이 역할은 엔진 입구 공기압력 과 온도를 조절하는 것입니다.

두 번째로 입구노즐은 스털링 챔버와 엔진 스탠드 사이에 있으며 엔진 입구에 연결되어

있습니다. 엔진 스탠드는 엔진 시험실에 설치되어 있고, 엔진은 엔진 스탠드 위에 장착

되어 있습니다.

엔진 성능 감시 센서와 필요한 장치들을 엔진 스탠드 주변에 배치해야 합니다.

그리고 시험 챔버 내의 압력은 항상 약 1bar로 유지 되어야 합니다. 왜냐하면 엔진 백프

레셔가 발생하지 않도록 하기 위해서입니다.

배기 이젝터는 엔진 테스트 스탠드 뒤에 설치되어 있습니다.

엔진 배기와 시험실에 있는 냉각 공기는 이젝터를 통해서 밖으로 배출됩니다. 원래 이젝

터 계산 방식은 엔진배기량과 100% 냉각 공기로 계산 되어 집니다.

이 두가지는 이 논문에서 계산 결과가 180Kg/s로 나왔습니다.

이런 큰 공기량은 계산결과 180Kg/s로 배출해야 한다면 이젝터 지름이 1800mm 이상은 되

야 합니다. 이 논문이 제시하는 이젝터의 모양, 크기는 1100mm로 하면 냉각 공기량이

만 이젝터로 통과합니다 이렇게 구성하여 나온 연구 결과는 압력회복이 에서

20% . 0.89

사이로 나타났습니다

0.99 .

이젝터 안에 있는 엔진에서 나온 뜨거운 배기가스 냉각방식은 Pin tube방식으로 합니

다.

냉각수를 Methylene Chloride로 5단계 냉각장치로 구성한다면 안전하게 온도를 줄 일수

있습니다 그리고 이. Pin tube방식을 쓰면 독한 액체가 발생되지 않습니다.

이 논문에 관련되어 있는 학회발표논문들과 출판물들은 밑에 XV 페이지에 수록되어 있습

니

Abstract

Pressure and Heat Recovery in High Altitude Supersonic Ejector of a Low Bypass Turbofan Engine Test Facility

By Owino George Omollo

Advisor : Prof Changduk Kong Ph. D Department of Aerospace Engineering Graduate School of Chosun University

This thesis studies on pressure and heat recovery in environmental supersonic high altitude engine test chamber. High altitude test chambers are building constructions where engines performance are tested on how they would perform in real flight.

The test chamber therefore simulate real time engine inlet parameters similar to those experienced at the test altitude. Simulated environmental conditions for total pressure, total temperature ,air mass flow rate, inlet air and velocity should be equal to those at real time flight

For this conditions to be simulated the testing facility is designed and fabricated with structural feature able to control and deliver several parameters within the required test conditions. Major parts of the test facility includes the stirling Chamber, that delivers air at controlled pressure, temperature and quantity. this makes it to behave somewhat as a compressed vessel with a nozzle that meters out the air flow

Engine test chamber contains an engine stand for mounting the test piece engine and where all engine monitoring sensors and control cable are installed and routed to the control room. The pressure in this chamber is usually maintained at one atmosphere or set to altitude pressure. Advanced technology now is to have a test chamber with similar environmental lapse rate equal to the rate of climb or decent

Exhaust ejector installed behind the test engine to remove exhaust and cooling air from the test chamber this forms the basis of this study.

The ejector is usually sized to remove engine exhaust gasses together with 100% of

cell cooling air, about 180kg/s for the engine test facility being studied here.

This large volume of air limits the frontal area of the ejector. Calculations indicated a frontal ejector diameter of 1800mm. this thesis proposes an ejector with a smaller frontal area of 1100mm big enough just to remove engine exhaust gas with only 20%

of the cell cooling air, the remaining cell cooling air is removed from the chamber through a different bleed port.

Simulation study results indicated improved pressure recovery of 0.89 to 0.99 that does not fluctuate even if cell cooling flow is reduced.

Pin tube exhaust gas cooling method also indicated that heat may be reduced to required limits if the coolant for use is Methylene Chloride with 5 single pass cooling stages this system is simple and does not need to include a water purification systems used in water spray cooling ,employed in most testing facilities.

Several conference presentations, and journal publications related to this study are listed in paper [XV] below according to the chapters they apply.

Chapter 1. Fundamental Classifications

1.0 Introduction

In most basic sense, wind tunnels are ground-based experimental facilities designed to produce flows of air or sometimes other gases, which simulate natural flows occurring outside.

Most aerospace engineering applications, wind tunnels are designed to simulate flows encountered in the flight of airplanes, missiles or space vehicles. Constant endeavored to improve performance and efficiencies of tunnel system to achieve maximum velocity at minimum input power are constantly studied. This work looks at ways on how to improve pressure recovery of exhaust ejector of high altitude wind testing chamber.

1.1 Wind Tunnel Theoretical Summary

When air flows through a channel of varying cross-section it undergoes changes in velocity as per the continuity principle. If there is rise in static pressure then the dynamic pressure will drop down and vice versa. Therefore, The total pressure, defined as the sum of static pressure and dynamic pressure, remains constant. Some energy are lost as heat energy which is not significant when the fluid is incompressible.

The loss along the system include bend, duct length, branches, and screens and other obstructions is dependent on average velocity through it. Here it is assumed that flow is uniform and velocity is constant throughout the cross-section. All these losses are measured in terms of pressure drop ultimately which provides power required. On other hand an experiment is conducted to measure the power supplied to fans at different flow velocities.

Assuming the fact, power is proportional to cube of flow velocities the results obtained are extrapolated to obtain power consumption at higher velocities. Then theoretical and experimental results at measured range and at extrapolated range are co-related to analyze the general trend of power consumption and efficiency of system.

1.2 Wind Tunnel Classifications

They are classified as either open or closed circuit wind tunnel.

Common layout of wind tunnels and testing chambers

Closed Circuit Wind Tunnel Open Circuit Wind Tunnel Fig 1 Wind Tunnel Layout

1.2.1 Closed Circuit Wind Tunnel

In a Closed Circuit wind tunnel, the air that passes through the test section is drawn back into the fan and sent through the test section again and again.

1.2.2 Advantages of closed circuit wind tunnel

1. In a well designed Closed Circuit wind tunnel, some energy is recovered. A smaller motor can be used.

2. Closed Circuit Wind Tunnels are completely enclosed, and so are shielded from rain, snow, and cold weather.

1.2.3 Disadvantages of closed circuit wind tunnel

1. Closed Circuit Wind Tunnels are much more expensive to build due to the construction of the additional air return system.

2. The air in a closed Circuit Wind Tunnel is constantly heated due to friction with the fan. Most designs draw fresh air in to help, some even use air-conditioning, yet enclosed designs are always uncomfortably hot in the summer.

3. The air in a Closed Circuit Vertical Wind Tunnel is full of dust and debris from clothing, cushions, etc. This is constantly recirculated, and is very difficult to remove.

4. Due to the close proximity of the fan, the flight area of Closed Circuit designs is always very noisy.

1.2.4 Open Circuit Wind Tunnel

In an Open Circuit Wind Tunnel, fresh air is drawn into the machine. The air that passes through the test section is discharged from the machine.

1.2.5 Advantages open circuit wind tunnel

1. An Open Circuit Wind Tunnel is much less expensive to build.

2. In a scenic location, an outdoor Open Circuit Vertical Wind Tunnel is very spectacular.

1.2.6 Disadvantages open circuit wind tunnel

Extreme cold or precipitation can make flying in an outdoor Open Circuit Vertical Wind Tunnel somewhat less comfortable

1.3 Main Components of Wind Tunnel

Fig. 2 Main Parts of Wind Tunnel

Major components of a wind tunnel includes the silencer, fan, diffuser, test section and the inlet

Main components of the altitude test chamber consists of settling chamber, test section and the exhauster section

1.3.1 Application Areas of Wind Tunnel and Test Chambers

Wind tunnels and test chambers may practically be used to evaluate and test almost everything whose prior performance or characteristics is of interest to the researcher.

They vary in sizes according to the size of the test piece and so is the development and operating costs from several hundreds to billions of dollars [8]

Aerodynamic model testing Combustion performance Real Scale testing

Nature Studies Design Testing Engine performance Test

Truck Testing Flow Test Laboratory Testing

Fig. 3 Test cell application areas

1.3.2 Applications related to jet engine testing

Engine Altitude Testing Engine performance Testing Overhead Rail Testing Fig. 4 Engine testing chambers

1.4 Summary

Chapter 1 in this thesis explains several classification of wind tunnels and altitude testing facility. most high altitude environmental chambers and certainly the one discussed in this thesis of closed circuit type.

This means that the exhausted gas need to be recirculated back into the system therefore cooling and the use of heat exchanger after the exhaust ejector is a basic configuration

Other fundamental components in this configurations include circulation pumps, compressors, cooling tower, chiller, water purification system for water spray cooling system if contained in the configuration

The following are brief introduction to the contents of every chapter in this thesis

Chapter 2

This explains and refers to previous work from other publisher on the same work and other researches related to wind tunnels and environmental test chambers, I also introduced my innovation in reference to other publishers work I explained the differences in my proposal to the existing designs

Chapter 3

involve introduction to some fundamental theories that govern the operation of wind tunnel and testing chambers together with the operating principles of gas turbine engines, this give an extensive understanding of the conditions required for a flawless test of the engine, test facilities are structures that experience rigorous environment that we would otherwise get from understanding gas turbine and its environment

Chapter 4

Having understood the environment required and created by gas turbine engine.

chapter 4 introduces working principle of a wind tunnels. both gas turbine and test chamber works under the principles of fluid and thermodynamics, and the engine empties its gas inside the test chamber, with knowledge discussed in this chapter we would understand and calculate the impact of having the working together

Chapter 5

Test chambers contains a lot of ducting and flow path contain several nozzle used to

meter the gas to the correct pressure, temperature and mass flow rate. the stirling chamber mentioned in chapter 1 connect to the test chamber and to the engine via the intake nozzle. supersonic flow regimes makes part of this thesis and hence call for a clear understanding of the nozzle sensitive to shock waves

Chapter 6

Similar to nozzles supersonic diffusers are discussed in chapter six. where focus in the throat section is discussed, extensive understanding of the diffuser is vital in order to come up with areas susceptible to possible modification to improve their performance and pressure recovery, shock wave behaviour is also mentioned in this chapter

Chapter 7

Pressure loss in ducting systems is vital as flow quality and pressure losses are sensitive to wind tunnel and test chamber operation both laminar and turbulent flow are explained here and possible way of flow measurements, pressure loss due to changing geometries are also looked at the chapter finishes by introducing a way I developed to calculate losses using blocks and guidelines that indicate the calculation flow

Chapter 8

Selected engine performance is a must obtain data to analyse the ejector, estimated pressure, temperature, mass flow and velocity from the engine is used as governing conditions for the ejector. for these parameters to be obtained, engine simulation was performed using a commercial software Gasturb 9. engine data are corporate

properties and never given to clients hence in this study the only way to receiving required engine information is only through simulation

Chapter 9

This chapter shows how the components that make up the test chamber were designed in 2D using Autocad software. basic sizing and aerodynamics were

determined using several equations introduced in the previous chapters based on the 2D drawings 3D Solid works modelling was done to be used for fluid analysis in the CFD program. my innovative idea is also highlighted here

Chapter 10

Heat exchanger is a fundamental component in a closed circuit for cooling the air returning to the stirling chamber, heat cooling method pin tube cooling is proposed and analysed using temperature results from the engine simulation that form the input

parameters in the CFD program. heat loss level is determined in this chapter Chapter 11

This chapter concludes the whole thesis explained in 10 chapter above based on the discussions in the chapters and the analysis results I propose in this chapter the used of smaller ejector with alternate secondary passages as a way of improving pressure recovery and cost reduction.

List of papers and publications related to this thesis are presented and arranged according to the chapters they apply in the pages that follow

List of Paper Related to this Thesis

Chapter 6

Owino, George,. Omollo, Changduk, Kong,. "CFD Analysis of Pressure Recovery in Supersonic Diffuser of a High Altitude

Environmental Test Facility", Asian Joint Conference for Power and Propulsion March 4-6, AJCPP2010-011, Mayazaki City Japan.

Owino, George,. Omollo, Changduk, Kong,. "Pressure Recovery in a Supersonic Ejector of a High Altitude Testing Chamber". Journal of KSPE Volume14 PP1-7 2010.12.30,.

Chapter 7

Owino, George, Omollo,. Changduk, Kong,. "CFD Analysis of the Pressure Drop due Expansion Flow Along Square and Round Ducts of a Wind Tunnel Testing Facility", KSAS-JSASS 4/16~17/2009

Chapter 8

Owino, George, Omollo,. Changduk, Kong, "Study on Installed Performance Simulation of Aircraft Gas turbine Engine Considering Inlet and Exhaust Losses". Journal of KSPE Volume 10 PP100-108, 2006.12

Chapter 9

Owino, George,. Omollo, Changduk, "Non-numeric Pressure recovery Analysis of Exhaust Ejector Duct in High Altitude Testing Facility".

Asia-Pacific International Symposium on Aerospace Technology,. 2010

List of Publication

Chapter 7

Owino, George,. Omollo, Changduk, "Non-numeric Pressure recovery Analysis of Exhaust Ejector Duct in High Altitude Testing

Facility".Journal Material Science and Technology, JMST 2010.12

Chapter 8

Owino, George, Omollo,. Changduk, Kong, "Study on Installed Performance Simulation of Aircraft Gas turbine Engine Considering Inlet and Exhaust Losses". Journal of KSPE Volume 10 pp100-108, 2006.12

Chapter 9

Owino, George, Omollo,. Changduk, Kong, "Pressure Recovery in a Supersonic Ejector of a High Altitude Turbofan Engine Testing Chamber" Jounal of IEEE 2010.12

Chapter 2. Research and Development of Wind Tunnels

2.0 Literature review

Pressure recovery and related research properties in wind tunnel and supersonic diffusers

2.1 Introduction

The importance of supersonic diffusers to a wide variety of flow processes In research, development, flight and applied science is well known. Efficient pressure recovery is a dominant consideration in establishing the design and power requirements of wind tunnels

Rotating flow machinery may encounter supersonic flow fields with the requirement of providing efficient supersonic diffusers. Flying articles with supersonic inlets require high and well controlled pressure recovery for stable operation and reliable performance.

The duration and strength of the high intensity output from gas dynamic lasers are critically sensitive to predictable and high pressure recovery associated with high mass flow rate.

2.2 Wind tunnel diffuser

Diffusers for supersonic and hypersonic wind tunnels have been studied at a number of wind tunnel installations. These studies were usually made in order to determine the overall pressure ratio required for the operation of a particular wind tunnel configuration. This information is, in turn, used to estimate the power requirements for the wind tunnel. Thus, virtually all the wind tunnel diffuser studies known to us are design oriented and they are optimized for a single facility.

Most of the diffusers were of standard configuration, with a converging entrance, a constant area throat section, and a diverging exhaust section.

The converging and diverging sections were simply frustum of a cone, pyramid, or a wedge. The lengths of each section, the throat area and the entrance angle were varied and an optimum combination of these, giving the most favorable operating condition, were noted.

The studies tend to be very specific usually only the diffuser entrance and exit pressures have been measured. The Reynolds number and Mach number effects in these flows were not systematically investigated.

In 1953, Lukasiewicz made an extensive study of the test results of a number of supersonic wind tunnel diffusers in existence.

They included the 18 cm x 18 cm tunnel Diggins 1951 and the 12 cm x12 cm tunnel Wegener and Lobb 1953 of the Naval Ordnance Laboratory, the 12 cm x12 cm tunnel of CalTech Heppe 1947, the 9 cm hypersonic tunnel at NASA -Langley Bertramn 1950, and the 12 cm x12 cm tunnel of MIT, Neumann & Lustwerk 1951.

These data Lukasiewicz concluded that for test section Mach numbers of 1 < M < 10 the static pressures achievable at the exit of fixed geometry diffusers where M-O were close to those computed from normal shock recovery theory.

With variable-geometry diffusers, a maximum pressure recovery of almost twice the normal shock recovery could be attained. The test section Reynolds numbers based on nozzle exit height ranged from  × ^ to  × ^ in these wind tunnels. all of the test sections had closed jets.

A number of studies have been made on wind tunnel diffusers since the time of Lukasiewicz

The Mach number range has been extended to twenty six, and low Reynolds number data have become avaliable, In addition, some results have been obtained for the monatomic gases argon and helium

The optimum diffuser pressure recoveries, defined as the ratio of nozzle supply pressure to diffuser exit pressure, Pt0/Pt2, realized in these wind tunnels are compared to the theoretical normal shock recovery.

The results were obtained in clean wind tunnels i.e. without models. The results compiled by Lukasiewicz in 1953 concluded that pressure recovery holds for M < 10.

At higher Mach numbers, the recovery is significantly poorer than the normal shock recovery.

However, since the Reynolds numbers in these high Mach number tunnels are lower than those for M < 10, it is not clear that this deterioration in pressure recovery is due exclusively to higher Mach numbers.

The results reported by Hastings in 1954, 1955, by R. Midden and Cooke 1964, and by Austin 1966 all fall in the Mach number range of 1 < M < 10. The test section Reynolds numbers in these wind tunnels ranged from 2 x 105 Austin 1966 to 8 x 10 Hastings 1955, they varied by a factor of forty.

These conditions are roughly the same as those of Wegener and Lobb 1953, Heppe 1947 and S. Neumarnn and Lustwerk 1949, 1951. It is not surprising that the results of these new studies agree with the normal shock recovery theory which was found in the older studies.

The diffusers used by Hastings 1954,55 are of the two dimensional adjustable wall type, similar to that described by Wegener and Lobb Hastings 1954 has moreover studied the effects of suction applied to the wind tunnel test chamber, to remove about 10% of the test gas before entering the diffuser.

The limits of pressure recovery achieved with and without suction indicated that suction improved the diffuser pressure recovery by as much as a factor of two at M=5. It should be remembered that this improvement in recovery is obtained at the expense of additional pumping power. Thus, the usual economic benefits associated with improved pressure recovery, are compromised in this case.

In addition to pressures at the nozzle and diffuser exits, Hastings 1954 also made continuous static pressure surveys along the diffuser sidewall and took some schlieren photographs.

These provide useful information for an understanding of the flow and shock patterns in diffuser flows. He found that the larger amount of static pressure rise was accomplished in the supersonic part of the diffuser. another study by Hastings and Roberts 1957 using the same 18 cm x 18 cm wind tunnel where they found that nearly 100% of normal shock recovery was obtained at M=2.86 and at 4.92 with atmospheric supply conditions.

The wind tunnels used by Austin 1966 and Midden and Cocke 1964 are both axisymmetric open jet systems with fixed geometry diffuser Midden and Cocke found that 18% blockage of the test sectional area 10cm diameter by models may be tolerated in their wind tunnel. Clark 1965, using the Langley 15cm hypersonic ceramic heated tunnel measured the pressure recovered in the fixed geometry axisymmetric diffuser.

The Mach number in the free jet test section is about 13.6, and the Reynolds number based on the nozzle exit diameter ranged from  × ^ to  × ^ depending on the nozzle supply pressure. This nine fold variation in Reynolds number is the widest range covered in a single study. Effects of diffuser blocking were also studied with various models by Clark.

Diffuser performance at much lower Reynolds numbers Re 10 was investigated by Boylan 1964. Here, diffusers of the same basic design, a constant area duct with cones fitted at both ends, were used.

The lengths and cross-sectional areas of the constant area and conical sections were systematically varied. Boylan's 1964 setup permits the free jet length to be varied from zero i.e closed jet configuration to fourteen nozzle exit diameters.

He found that optimum results were obtained with a free jet length of roughly six nozzle exit diameters. Argon was also used by Boylan as the test gas

A model blockage study of a 2cm diameter Mach 10 to 14 free jet wind tunnel was made at Ohio State University by Scaggs and Petrie 1961. Diffuser performance with models 12 cm D 9cm D installed in the test section was investigated. At Mach numbers of 10 and 14.3, pressure recoveries of 44% to 60% of the normal shock value were obtained, depending on the size of the model.

The diffuser efficiencies reported by Thomas, Lee and Von Eschen 1957, 1959 of the Ohio State University 8inch hypersonic tunnel and by Scaggs, Burggraf, and Gregorek 1963 of the ARL-30" tunnels are roughly 100% of the normal shock recovery, as quoted by Clark 1965.

The highest Mach numbers studied were in the range 22<M<26 at Princeton University by Vas and Koppenwallner 1964, Vas and Allegre 1966. The Reynolds numbers in both tunnels are about 3 x 10 the static pressure recovery from 5% of normal shock value at M=17.7 to 46% at M=25.7 was rather poor compared with other wind tunnels.

Hypersonic nitrogen tunnel at the Aerodynamic Research Facility at G. dttingen described by Koppen wallner 1966 is of practically the same design as the Princeton tunnel Vas and Koppen wallner 1964. With a nozzle exit diameter of 25 cm, the Reynolds number in the test section is 3 x 10 < ReD < 4.7 x ^.

The pressure recovery achieved in the diffuser in this tunnel is better than that obtained by Vas and Koppen wallner. Still, only about 50% of the normal shock recovery was attained in the G. dttingen tunnel. It is not clear at this time why the pressure recovery is so much poorer than the normal shock recovery for these hypersonic wind tunnels. Both viscous and nonequilibrium effects may be responsible for this deterioration in diffuser efficiency. Not only is the Reynolds number in these tunnels much lower than the tunnels at moderate Mach numbers, but also the high Mach number flow in the test section is known to be significantly out of equilibrium[14].

2.3 Ramjet diffuser

The ramjet diffuser serves to decelerate air entrained at supersonic speed down to speeds appropriate to the static pressure requirements for internal combustion.

Faro and Keirsey 1967 have reviewed ramjet diffuser performance parameters as a part of a series of reports in ramjet technology.

We shall use and follow their treatment of ramjet diffusers and summarize the principal results contained in their paper.

Faro and Keirsey 1967 restricted their attention to axisymmetric configurations, the principal design considerations regarding external-compression limitations, compression surface design and inlet design are fundamental to all types. For both internal and external diffusion, the three basic characteristics determining the diffusing effectiveness were held to be total pressure recovery the ratio of total pressure in the free stream to total pressure at the diffuser's exit, as previously defined, the capture-area or mass flow ratio, and the total drag of the diffuser.

The idealized ramjet with internal compression with fixed throat, single-shock diffuser has as advantages its low external drag and simplicity of construction. However, the area contraction ratio required during starting imposes low pressure recovery and the overall performance deteriorates rapidly at off-design Mach numbers once the shock is swallowed. Further, the length of the convergent section required for the most satisfactory results typically, a throat length four times the throat diameter gives rise to thick throat boundary layers. Thus, this configuration, which has had a more successful

application to wind tunnels than to ramjet, is usually limited to flight Mach numbers less than about 1.6.

On the other hand, variable geometry devices alleviate many of the adverse effects associated with the fixed area configuration at a cost of increased mechanical complexity. Flexible plates in two dimensional devices. including ones with boundary layer bleed, and translating center bodies in axisymmetric diffusers give consistent improvement in pressure recovery over the fixed inlets by externally compressing the flow through oblique shocks, greater flexibility can be achieved in the ramjet's operation. the recovered stagnation pressure increases, neglecting boundary layer effects, as the number of oblique shocks increases the limit, of course, is achieved when the compression is accomplished through an infinite number of very weak waves, a procedure possible in principle with an isentropic shock free surface.

The primary design variables for oblique shock diffusers are found to be

1. The shape of the external compressing surface

2. The position of the cowl lip with respect to the inner-body tip

3. The position and shape of the shoulder of the inner-body with respect to the cowl lip

4. The geometry of the cowl lip

5. The geometry of the diffuser center body configuration downstream of the inlet.

These parameters are adjusted so as to control boundary layer development and to give stable, un-separated flow in the duct as well as minimum external drag. Although practical considerations such as inlet length, viscous effects, the limit of external compression dictated by a consistent shock solution at the point of coalescence, and reasonable cowl lip drag preclude the occurrence of a completely isentropic compression, several practical inlets have nonetheless been developed based on the principle of isentropic compression.

Maximum theoretical pressure recovery for the basic diffuser assumed that there is only a simple normal shock at the lip external compression and secondly that the maximum internal contraction allowed by the entering Mach number is followed by a simple normal shock wave at the associated throat.

Boundary layer problems, even in the absence of flow separation, can profoundly affect air capture pressure recovery and inlet drag. Beneficial result have been obtained, insofar as boundary layers on the compression surface are concerned, through the use of surface roughness or trip rings to assure transition to turbulence and through suction.

Bleeding off the boundary layer immediately downstream of the sharp turn has been found effective in reducing problems associated with boundary layers at the throat. In addition, pressure recovery losses associated with boundary layer-shock wave interactions in the throat have been alleviated by elongating the throat and by using vortex traps in both cases, improved pressure recovery is achieved at the expense of other previously well controlled parameters.

Diffuser buzz is another profoundly important effect. In this case, a shock wave oscillating at the diffuser's entrance produces fluctuating internal pressures which cause, under extreme cases, a cycle of flame out and reignition and at the very least a heavy penalty in gross thrust in the ramjet's performance.

Since the buzz theories and the one-dimensional flow analysis are not sufficiently developed to predict the performance and stability limits accurately, results from wind tunnel and free jet tests are used in matching the inlet and combustor characteristics in attempts to ensure stable and efficient behavior.

2.4 Ejectors

Ejector-diffuser configurations are important to studies on rocket and jet engine design.

Figure 5 shows flow patterns in a typical supersonic ejector after it has been properly started. Here, as in the other diffusers just reported, optimum stable operating condition is represented by a shock wave in the diverging section of the diffuser.

Many additional complications arise in the case of ejector-diffusers, not the least of which is the extent to which the variations in exit pressure over a relatively short range of values can drastically alter the nature of the flow in the test section as well as the flow in the air settling chamber so critical to effective aerodynamic simulation.

In addition, the ejector performance characteristics are very sensitive to friction influences explicitly and implicitly in their sensitivity to diffuser length and to stagnation

temperatures. Ginoux 1972 has edited a comprehensive summary of the status of research and development on supersonic ejectors. [15]

This summary includes articles by Belhack, Taylor, Addy, and Peters references to both American and European literature on the subjects reported. Topics treated are

(1) a one-dimensional inviscid analysis of supersonic ejectors,

(2) an analysis and design method for ejector systems with second throat diffusers

(3) the analysis of supersonic ejector systems, (4) ejector design for a variety of applications,

(5) an analysis of ducted mixing and burning of coaxial streams.

Taylor's article in Ginoux 1972 paid particular attention to the various empirical ejector design methods developed from experimental results which are used for practical applications; comparisons with one-dimensional theory are made where possible.

Ejector diffuser inlet geometry effects were found to be significant; the use of truncated conical inlets in the cylindrical diffusers produced as much as a 600-percent improvement in diffuser performance.

Although the compression shock system in a long duct is a series of lambda shocks resulting from an interaction between the boundary shock and the boundary layer on the duct wall, the one-dimensional normal shock relationship used with the duct inlet Mach number will predict the pressure rise across the shock system within approximately 6 percent.

Second throat contraction ratio and length of minimum area had the greatest influence on the starting and operating pressure ratios. The significant parameter involving nozzle total pressure level was found to be the unit Reynolds number at the nozzle exit times the nozzle throat diameter; for values of this parameter of less than one million, significant variations in the minimum cell pressure ratio occurred. In addition, Taylor studied the effects of different driving fluids on ejector-diffuser performance Five different gases were used [16]

The known variations in specific heat with temperature were included in a one dimensional isentropic calculation of pressure recovery. However, observed values of pressure recovery were anomalous below the theoretical predictions. These results

have emphasized the importance of real gas phenomena

2.5 Summary

Chapter two discusses on past researches on wind tunnel diffusers. most research focus on exhaust ejectors with a large frontal area designed to evacuate both exhaust gas and cell cooling air, [28] [28]

Supersonic diffuser were investigated for high speed flow the highest with a flow of Mach number 25.7 and pressure recovery focus on normal shock recovery and benefits of gas suction before it enters the ejector [20] [28] [31]

Reynold number changers and pressure recovery was also studied using not only exhaust gasses but also different inert gasses [15] [21] [30]

Most research in the 1970es employed the use of inlet cone in-front of the diffuser to control the formation of intake shocks and location where they come into contact with the nozzle [28]

Innovations

Variable area and moving wall ejectors has also been extensively studied [14] [15]

[16].

Based on these researches this thesis proposes a different smaller configuration where ejector pressure recovery can be improved in supersonic by reducing the ejector area to only eject exhaust gasses with 20% cell cooling air, and introducing an alternative port to exhaust the remaining cell cooling air.

Pressure loss calculation flow chats has been introduced in Chapter 7 from unit 7.4 where blocks and lines has been introduced to show step by step calculation of pressure loss in geometries common to most test cell and wind tunnel.

Both 2D and 3D modeling of each component using Autocad and Solid works has also been discussed and explained in Chapter 9 of this thesis.

Most testing facility use water spray methods of precooling before air reaches tube cooling or water jacket system, although this is an efficient method to bring down heat an expensive onsite water purification system is needed.

Used in this study is the use of pin tube cooling method using multiple stages of

single pass grills that contain methylene chloride as the coolant, with this system since the coolant does not come into direct contact with the exhaust gas, a water cleaning system is not required.

Chapter 3 on page 15 explains the theories how test cell works and several governing equations used in sizing and determining optimal operation

Chapter 3. Fundamental System Theories 3.0 Principles of gas turbine engines

Fig. 5 Gas turbine engine 3.1.1 Conservation Equations

A flow machine is one which ingests a stream of fluid, processes it internally in some fashion, and then ejects the processed fluid back into the ambient surroundings. An idealization of such a generalized flow machine is schematically depicted in Figure 6.

Fig. 6 Schematic diagram of idealized flow machine and associated stream tube control volume

In order to develop the basic features of operation of the idealized flow machine without introducing unnecessary algebraic complexity we make the following assumptions.

1. The flow through the stream tube entering and leaving the machine is steady and quasi-one-dimensional

2. The entrance and exit stations shown are chosen sufficiently far from the flow machine entrance and exit such that the pressures at

those stations are in equilibrium with their surroundings, that is, pe=p0

3. There is no heat transfer across the boundaries of the stream tube or the flow machine into the ambient surroundings.

4. Frictional forces on the entering and leaving stream tube surfaces are negligible Mass injected into the fluid stream within the flow machine, if any, is negligible.

With these restrictions in mind we may assess the consequences of applying the basic conservation principles to the stream tube control volume.

3.1.2 Conservation of mass

The net change in the mass flow passing through the flow machine is zero, which may be written as

0A V0 0 _eA V_{e e} 0

r r

- + = ₍₁₎

This is equivalent to stating that the mass flow m=rAV = constant throughout the system.

3.1.3 Conservation of momentum

The net change in momentum of the fluid passing through the stream tube is equal to the force on the fluid [1]

(

)

(

)

Because the mass flow is constant this equation can be abbreviated to the following [1].

(

)

m V -V =F ₍₃₎

The force acting on the fluid is denoted by F, and, for equilibrium, the force exerted on the control volume by the fluid is F. In general, the forces on the stream tube are– negligible compared to those on the flow machine proper and are neglected. One important case where this is not necessarily true is that of the so-called additive drag of inlets in supersonic flight, where the force on the entering stream tube surface may not be negligible [1].

3.1.4 Conservation of energy

The net change in the total enthalpy of the flowing fluid is equal to the sum of the

rate at which heat and work are added to the fluid, or

(

)

(

)

m héêë -h + V -V ùúû= D +m Q P ⁽⁴⁾

The quantities h, ΔQ, and P denote enthalpy, heat addition per unit mass, and power added, respectively. We may consider some extreme cases to illustrate several basic kinds of flow machines.

Flow Machines with No Heat Addition (The Propeller) Here we assume that ΔQ=0 so that

(

)

(

)

P m h= éêë -h + V -V ùúû ⁽⁵⁾

However, if no heat is added to the flowing fluid it is reasonable to expect that the enthalpy of the fluid is essentially unchanged in passing through the machine so that

0

he »h which results in

(

) ⁽

⁾⁽

⁾

1 1

2 ^e 2 ^{e e avg}

P» m V -V = m V -V V +V =FV

(6)

Thus the power supplied to the fluid is approximately equal to the product of the force on the fluid and the average of the velocities entering and leaving the machine [1].

3.1.5 Zero heat addition with Ve>V0

Here F>0 and therefore P>0, so that work is done on the fluid. This is the case of the propeller, the fan, and the compressor, where the device does work on the fluid and produces a force on the fluid in the same sense as the entering velocity. Note that this means that the force of the fluid on the machine is in the opposite sense, that is, a thrust is developed [1].

3.1.6 Zero heat addition with Ve<V0

Here F<0 and P<0, so that work is done by the fluid. This is the case of the turbine, where work is extracted from the fluid and the fluid experiences a retarding force, that is, the force on the fluid is in the opposite sense to that of the incoming velocity.

The force on the machine is therefore in the same sense as the entering velocity and is therefore a drag force.

3.1.7 Zero heat addition with P =constant >0

In this variation we see that the thrust force drops off with flight speed

0

0

1 1 1 2

avg e

P P

F V V V

V

= =

æ ö

ç + ÷

è ø ⁽⁷⁾

In general, the velocity ratio V_e/V₀ is not much greater than unity. This is the case of a propeller propulsion system where increases in flight speed are limited by the power available [1].

0 0.5 1 1.5 2 2.5 3

0 200 400 600 800 1000 1200

Vavg (fps)

F/P (lbs thrust/horsepower)

Fig. 7 The specific thrust produced by a propeller as a function of the average speed.

3.2 Propulsive efficiency

The total power expended is not necessarily converted completely into thrust power FV₀ the rate at which the force applied to the fluid does work. Instead, it has been shown that the power expended is FVavg- so that the propulsive efficiency may be defined as

( )

0 0

0

1 2

p

avg e

FV V

FV V V

h = =

+ ₍₈₎

This equation 8 shows that at a given flight speed the efficiency drops off with increasing exhaust velocity Ve as shown [1].

Fig. 8 The efficiency of a propeller as a function of the ratio of exit speed to flight speed

Flow Machines with Zero Net Power and Constant Heat Addition (The Jet) Here we assume that no net power is exchanged with the fluid so that [1]

(

)

(

)

But we may write the kinetic energy term as

( )( ) ( )

2 2

0 0 0 0

e e e e

V V V V V V V V F

- = + - = + m

(10)

Substituting this back into the first equation 10 and solving for the thrust yields [1].

(

)

avg

F m Q h h

=V éëD - - ùû

(11)

Some of the consequences of this simple equation are described below as follows

3.2.1 Heat addition, ΔQ>0

If sufficient heat is added to the fluid Equation 11 shows that F>0 and thrust is produced on the flow machine. This is the basis of operation of the simple jet engine.

We shall consider some particular cases of interest.

3.2.2 Constant heat addition, ΔQ=constant>0

in this case the following applies

( )

0

0 0 0

0

2 _e

e

F A V Q h h

V V r

= + éëD - - ùû (12)

Therefore the thrust is essentially constant with flight speed V₀,as shown in This is the basic advantage of the jet engine its thrust is independent of the flight speed and therefore it is not speed limited as is the propeller [1].

Fig. 9 The thrust of a turbojet engine as a function of flight speed

3.3 Overall efficiency.

The overall efficiency in the case of thrust produced by means of heat addition may be defined as the ratio of the thrust power to the rate of heat addition.

0 0 1 ^e 0

o

avg

FV V h h

m Q V Q

h = D = ^éêë - D^{- ù}úû ⁽¹³⁾

the propulsive efficiency is

p 0 avg

V h =V

(14)

We may then define the thermal efficiency as [1].

1 ^e 0 th

h h

h -Q

= - D (15)

Then the overall efficiency is the product of the propulsive and thermal efficiencies

o p th

h =h h ₍₁₆₎

The thermal efficiency accounts for the fact that not all the heat added is converted to useable heat power, since some is rejected as increased internal energy in the exhaust gases. Thus the thermal efficiency illustrates the extent to which the flow machine puts the heat added to good use in increasing the kinetic energy of the exhaust stream, i.e. increasing Ve while the propulsive efficiency illustrates the extent to which that increased kinetic energy provides thrust power to maintain flight at the speed V0. In a jet engine these two efficiencies generally drive in different directions, with the higher exhaust velocities sustainable at high thermal efficiency leading to lower propulsive efficiencies at a given flight speed.

3.3.1 Fuel efficiency

A common measure of fuel efficiency is the specific fuel consumption cj which is defined as the ratio of the fuel weight flow rate to the thrust produced typically this is measured in pounds of fuel per hour per pound of thrust, or simply hr^-1).The fuel weight flow rate may be related to the heat addition by the following equation [1].

( )

b f

m QD =h w HV ₍₁₇₎

This equation is based on the assumption that the rate of heat addition arises from the energy released in the chemical conversion of the fuel added as characterized by HV, the heating value of the fuel. The burner efficiency hb represents the ratio of the heat release actually transferred to the flowing combustion gases to the total heat release possible.

Recall that the set of assumptions made at the outset included the requirement that the amount of fluid added to the general stream entering the flow machine is negligible. It will be shown subsequently, when dealing with combustion chambers, that the fuel weight flow rate is indeed much smaller than the air weight flow rate, so no loss in generality is incurred here. the specific fuel consumption is [1].

( )

f 0 j

p th b

w V

c ⁼ F ⁼h h h HV (18)

This equation 18 shows that the specific fuel consumption of a jet engine increases

with reductions in propulsive efficiency with increases in Vavg and therefore with the exhaust velocity Ve. High heating value fuels will reduce cj while reduced thermal and burner efficiencies will increase it. for the case of typical hydrocarbon fuels and for pure hydrogen fuel. Heating values for some typical fuels in the liquid phase are shown in Table 1. along with HV the heating value per unit volume. Note that hydrogen has about three times the heat release per unit mass of Jet A while only about one-quarter the heat release per unit volume.

Since the volume of an aircraft influences its drag the quantity HV is an important parameter to consider, as well as HV itself, and hydrogen is not generally a good alternative to a hydrocarbon fuel [10].

Table 1 Heating values for typical liquid fuels

Fuel HV (Btu/lb) HV (KJ/kg) HV (Btu/gal) HV (KJ/liter)

Jet A 18,660 43.4 124.5 34.7

Methane 21,500 50.0 76.06 21.20

Ethanol 11,710 27.23 77.57 21.62

Hydrogen 51,690 120.24 30.21 8.42

Fig. 10 Specific fuel consumption as a function of average velocity for turbojet

3.4 The Force Field for Air breathing Engines

Fig. 11 Schematic diagram of the control volume for an air breathing engine

Air is taken onboard at approximately the flight speed V0, fuel is added and burned and the products of combustion are exhausted at the exit velocity V7. Further downstream the pressure pe achieves equilibrium with the ambient pressure at the flight altitude p0, that is pe=p0 Since experimental measurements are generally taken at the engine exit plane station 7,we confine our attention to stations up to and including that point.

We may apply the conservation of momentum principle to a control volume that extends from station 0 to station 7, as shown in Figure 11.

The control volume is the stream tube which enters the airframe structure that houses the engine. For simplicity we will consider a nacelle, or engine pod, bounded by the station 0 and 7. The force F₁ is the force exerted on the fluid by the external flow and the force F2 is the force exerted on the fluid by the walls of the nacelle.

The momentum theorem states that, in the absence of body forces, the resultant force on the boundary of a control volume fixed in inertial space is equal to the momentum flux passing through that boundary. Therefore, assuming there are no body forces and that the flow is quasi-one-dimensional we have,

7 7 0 0

1 2 0 0 7 7

w V w V F F p A p A

g g

+ + - = -

(19)

Fig. 12 Control volume for one-dimensional analysis of an air-breathing engine

F is the force on the nacelle exerted by the aircraft through the pylon, F2 is the force exerted by the fluid on the walls of the nacelle, and F4 is the force exerted on the nacelle by the external stream. Equilibrium of these forces requires that F + F4 - F2 = 0

obtains [1].