 

"5"?

-'

u',t
_ 2 .
u d‘iH'Iﬂ-J

7“—

51:11:“:
- a. . .
{o

<

. .. “.1

9 31?: M QVJ- I-..
. V:

‘
n

wart?

‘ ‘UI

 

:~':‘- ...

1'-

:4

mantras-W:

1.. ‘1
Av» v< »- _ 45‘

.4.-

-. . .-.-u

0.4:

 

x.

1" '5',

vv-rv .—

n ‘-.. -.

1
,ll.”
5 .‘

 

 

“£5, 3
WWIW'
5.} .3'; I :‘twg’
"*ﬁlgﬁgm‘z 95‘" “if

'1

£2“! .
J V

o

 

1“.
.AZ. . .3 1
9:1 . , 1 .
ﬁMM. ’ M .
kmdnm~=4

,W
1:31,:

 

       

 

                         

i. Illlllllll‘llll lllllllllllllll

31293 01682

This is to certify that the

thesis entitled

COMPUTER SIMULATION OF TURBOJET-RAMJET
COMBINATION ENGINE

presented by

Abdul Naeem Khan

has been accepted towards fulﬁllment
”of the .reqioiirements for

M- S . degree in WEI. Engineering

 

Majox professor

Date MaLlls, 1998

0-7639 MS U is an Afﬁrmative Action/Equal Opportunity Institution

 

LIBRARY

Michigan State
Univoroity

 

 

 

PLACE iN RETURN BOX
to remove this checkout from your record.
TO AVOID FINE return on or before date due.

 

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1/” mm.“

 

COMPUTER SIMULATION OF TURBOJET-RAMJET COMBINATION
ENGINE

By

Abdul Naeem Khan

A THESIS
Submitted to
Michigan State University in partial fulﬁllment of the requirements
For the degree of

MASTER OF SCIENCE

Department of Mechanical Engineering

1998

ABSTRACT

COMPUTER SIMULATION OF TURBOJET-RAMJET COMBINATION
ENGINE

By

Abdul Naeem Khan

With the modern developments in the field of science and technology and
growing relations among countries, the need of high-speed air travel has become
increasingly important. Many countries have taken up research work to develop air-
breathing engines for high supersonic ﬂights but its application in the civilian airliners is
scarcely visible.

From the standpoint of an aircraft engine designer the possibility of combining a
turboth engine with a ramjet in a single power plant that could achieve a ﬂight Mach
number close to 5 was explored. As a ﬁrst step, a computer software in FORTRAN 77
has been developed that performs the thermodynamic analysis of the airﬂow as it passes
through each component of the engine. The software consists of two major parts: the ﬁrst
part ﬁxes the engine geometry based upon 14 different inputs provided by the user, and
the second part simulates the off-design operation of the engine for a variety of altitudes
and Mach numbers. The software helps the engine designer to conclude a conceptual
design and optimize the performance parameters as per the mission requirements.

The results produced by the software are in close conformity to the
theoretical results available in the literature. The software can also be used as a teaching

aid in the area of aircraft propulsion.

I dedicate this thesis to my parents,

Abdul Razzaq Khan and Sultan Jahan

iii

ACKNOWLEDGEMENTS

First of all thanks are due to Almighty Allah for His everlasting blessings which
made the completion of this thesis possible.

Next, I wish to express my sincere appreciation to my advisor Dr. Craig W.
Somerton for his commitment; encouragement and guidance that helped me conclude this
study. Appreciation is also extended to Dr. Andre Benard and Dr. Mei Zhuang for their
valuable suggestions and also for serving as members of my guidance committee.

I am grateful to Dr. S. K. N. Zaidi and Dr. Javajd Hayder for their love and
academic guidance that helped me apply many ideas in various stages of software
development for this thesis.

I would like to express my gratitude to all of my valuable friends, especially Mr.
Habeel Ahmad and Dr. Pervaiz Akhtar for their understanding, encouragement and social
support during my stay at East Lansing. I also extend my special thanks to Mr. Craig
Gunn for editing this thesis.

Finally, I wish to acknowledge all kinds of support, sacriﬁce and good wishes of
my parents, the encouragement of my brothers and sisters, and the help their children,
especially Amjad and Adnad, rendered to my wife and children back home during my
stay at MSU that enabled me to fully concentrate on the studies. I am highly grateful to
my beautiful wife, Sajida, who always remained a source of inspiration and
encouragement throughout the course of studies. I also endorse and acknowledge her
patience and courage for successfully running all the affairs in looking after our children,

Haris, Faseeh and Hassaan during my absence from the home country.

TABLE OF CONTENTS

LIST OF TABLES .......................................................................... ix
LIST OF FIGURES ......................................................................... x
LIST OF SYMBOLS AND ABBREVIATIONS ....................................... xii
CHAPTER 1
INTRODUCTION
1.1 The Need of High Speed Aircraft ........................................ 1
1.2 Considerations for a Supersonic Civil Aircraft Engine ................ 2
1.3 The Turbojet-Ramjet Combination Engine ............................. 3
1.4 Adoption of the Concept by Various Countries ........................ 4
1.4.1 France ............................................................... 4
1.4.2 Russia ............................................................... 5
1.4.3 United States of America ......................................... 5
1.4.4 Japan ................................................................ 6
1.4.5 Australia ............................................................ 7
1.5 Objective of the Thesis .................................................... 7
CHAPTER 2
TECHNICAL BACKGROUND
2. 1 Introduction ............................................................... 10
2.2 Engine Performance ........................................................ 10
2.2.1 Engine Efﬁciency .................................................. 11
2.2.1.1 Propulsion Efﬁciency .................................... 11
2.2.1.2 Thermal Efﬁciency ....................................... 12
2.2.1.3 Overall Efﬁciency ........................................ 13
2.2.2 Thrust Speciﬁc Fuel Consumption ............................... 13
2.2.3 Speciﬁc Thrust ..................................................... 14
2.3 The Turbojet ................................................................ 14
2.3.1 Air Intake System ................................................. 14
2.3.1.1 External Compression Supersonic Intake ............. 16
2.3.1.2 The Single Cone Intake .................................. 16
2.3.1.3 The Double Cone Intake ................................. 17
2.3.1.4 Intake Characteristics .................................... 17
2.3.1.5 Shock Location and Engine Air Demand ............. 18
2.3.2 Compressor and Turbine .......................................... 19
2.3.3 Process of Combustion ........................................... 20
2.3.3.1 Flow Conditions During Combustion ............... 21
2.3.3.2 The Raleigh Line .......................................... 21
2.3.3.3 Effect of Heat Transfer on Flow Properties ........... 22
2.3.4 Effect of Flight Mach Number on Turbojet .................... 22
2.3.5 Exhaust Nozzle .................................................... 25

2.4

2.5

CHAPTER 3

The Ramjet .................................................................. 25
2.4.1 Basic Features ..................................................... 25
2.4.2 Effect of Intake and Nozzle Area Variation ................... 26
Turbojet-Ramjet Combination ............................................ 27
2.5.1 Intake ................................................................. 27
2.5.2 Engine Characteristics .......................................... 28
2.5.2.1 Cruise ....................................................... 28
2.5.2.2 Climb ...................................................... 29
2.5.2.3 Turbojet-Ramjet Proportion ............................ 30
2.5.2.4 Speciﬁc Fuel Consumption ............................. 31
2.5.3 Features of Turboramjet .......................................... 31

SOFTWARE CONSIDERATIONS FOR THE TURBORAMJ ET

3.1
3.2

3.3
3.4
3.5

CHAPTER 4

Engine Layout Criterion ................................................... 33
Software Development for the Selected Layout ........................ 34
3.2.1 Capabilities of the Software ....................................... 34
3.2.2 Salient Features of the Software ................................. 34
3.2.3 Assumptions for the Software Development ................... 35
Salient Features of the Selected Engine Layout ........................ 36
The Engine Layout .......................................................... 37
Frequently Used Equations ................................................ 39
3.5.1 General Considerations ............................................ 39
3.5.2 Stagnation State .................................................... 39
3.5.3 Ideal Gas Equation ................................................. 40
3.5.4 Energy Equation .................................................... 40
3.5.5 Conservation of Mass ............................................. 41
3.5.6 Momentum Equation .............................................. 41
3.5.7 Mach Number ...................................................... 41
3.5.8 Isentropic Flow .................................................... 42
3.5.9 Frictionless Constant Area Flow with Stagnation

Temperature Change ............................................... 43
3.5.10 Shock Waves ....................................................... 45

3.5.10.1 Normal Shock ................................. 45

3.5.10.2 Oblique Shock .................................... 46

DESCRIPTION OF SOFTWARE OPERATION

4.1
4.2
4.3
4.4

4.5
4.6

Introduction ............................................................... 48
The Software Structure ..................................................... 48
The Flow Chart .............................................................. 49
The Atmosphere ............................................................. 54
4.4.1 Variation of Temperature and Pressure with Altitude. . . . 54
Free Stream Conditions ..................................................... 55
Intake System ................................................................ 56
4.6.1 Subsonic Flight ..................................................... 56

vi

4.7

4.8

4.9

4.10

4.11

4.12

4.13

4.14

4.15

4.16

4.17

4.18

CHAPTER 5

4.6.2 Sonic Flight ......................................................... 58

4.6.3 Supersonic Flight ................................................ 58
Wedge Design Calculations ............................................. 59
4.7.1 Maximum Pressure Recovery .................................... 60
Intake Area Calculations ................................................... 62
4.8.1 Subsonic Flight Conditions ....................................... 62
4.8.2 Supersonic Flight Conditions .................................... 62
Programming for Diffuser ................................................. 63
4.9.1 On-Design Performance .......................................... 64
4.9.2 Off-Design Performance .......................................... 64
Bypass Doors ................................................................ 64
4.10.1 On-Design Conditions .......................................... 65
4.10.2 Off-Design Conditions ............................................ 67
Compressor ................................................................. 68
4.11.1 On-Design and Off-design Conditions .......................... 69
Diffusers Before Combustion ............................................. 69
4.12.1 On-Design Performance ........................................... 70
4.12.2 Off-Design Performance .......................................... 70
The Combustion Process .................................................. 71
4.13.1 Combustion Calculations at the Design Point ................. 72

4. 13.1 . 1 Turbojet Combustion ........................... 72

4. 13.1.2 Ramjet Combustion ............................. 73
4.13.2 Off-Design Combustion Calculations ........................... 74

4. 13.2.1 Turbojet Combustion ............................ 74

4.13.2.2 Ramjet Combustion ............................. 74
4.13.3 Combustion Parameters ........................................... 76
The Turbine .................................................................. 76
4.14.1 Operation at the Design Point .................................... 77
4.14.2 Off-design Operation ............................................. 78
The Turbojet Nozzle ....................................................... 78
4.15.1 On-Design and Off-Design Operation .......................... 79
The Mixer .................................................................... 79
4.16.1 On-Design Calculations .......................................... 80
4.16.2 Off-Design Calculations ........................................... 82
The Exhaust Nozzle ...................................................... 83
4.17.1 Flow Conditions at the Throat ................................. 84
4.17.2 Flow Conditions at the Exit .................................... 84
4.17.3 On-Design and Off-Design Calculations ....................... 85
Engine Performance Parameters ......................................... 86

BENCHMARKING OF THE SOFTWARE

5.1
5.2
5.3
5.4

Set of Design Conditions .................................................. 89
Fixed Parameters ........................................................... 90
The Target Flow Parameters .............................................. 90
Some Important Formulae for k = 1.4 .................................... 91

vii

5.4.1 Shock Relations .................................................... 91
5.4.2 Isentropic Relations ................................................ 91
5.5 Calculation of Flow Parameters ........................................... 91
5.5.1 Station (1) : Free Stream Conditions ............................. 91
5.5.1.1 Evaluation of Wedge Angle and the Shock Angle. . .. 92
5.5.2 Station (2) : Oblique Shock ...................................... 100
5.5.3 Station (3) : Normal Shock ....................................... 102
5.5.4 Station (4) : Diffuser ............................................... 103
5.5.5 Station (5) and (13) : Bypass Doors ............................. 105
5.5.6 Station (6) and (14) : Turbojet and Ramjet Entry .............. 105
5.5.7 Station (7) : Compressor .......................................... 106
5.5.8 Station (8) : Diffuser for Turbojet Combustor ................. 107
5.5.9 Station (9) : Turbojet Combustion ............................... 108
5.5.10 Station (10) : Turbine .............................................. 111
5.5.11 Station (11) : Turbojet Nozzle ................................. 113
5.5.12 Station (15) : Ramjet Diffuser ................................. 115
5.5.13 Station (16) : Ram Burner ......................................... 116
5.5.14 Station (17) : Ramjet Exhaust ................................. 119
5.5.15 Station (18) : Mixer Exit .......................................... 120
5.5.16 Station (20) : Turboramjet Nozzle ............................... 122
5.5.17 Engine Performance Parameters ................................. 124
CHAPTER 6
DEMONSTRATION OF THE SOFTWARE
6.1 Design Point Performance Characteristics of the Engine .............. 127
6.2 Off-Design Performance Characteristics of the Engine ................ 132
6.2.1 Speciﬁc Thrust and TSFC ......................................... 132
6.2.2 Thrust Ratio Verses Mach Ratio ................................. 138
6.2.3 Thrust Ratio Verses Altitude Ratio .............................. 142
6.2.4 Propulsive Efﬁciency ............................................. 144
6.2.5 Thermal Efﬁciency ................................................ 145
6.2.6 Overall Efﬁciency ................................................. 147
CHAPTER 7
CONCLUSIONS AND FUTURE WORK
7.1 Summary .................................................................... 149
7.2 Conclusions .................................................................. 150
7.3 Future Work ................................................................. 152
APPENDICES
Appendix A Functions Used in the Software .................................. 155
Appendix B Derivation of the Function ‘XMACH’ .......................... 157
Appendix C Calculation of Minimum Mach Number for
Ramjet Operation .................................................. 160
Appendix D Evaluation of Flow Velocity and Pressure at Mixer Exit. 166

viii

Table 2.1

Table 3.1

Table 5.1

Table 5 .2

Table 5.3

Table 5.4

Table 5.5

Table 5.6

Table 5.7

Table 5.8

Table 5.9

Table 5.10

Table 5.11

Table 5.12

Table 5.13

Table 5.14

Table 5.15

Table 5.16

Table 5.17

LIST OF TABLES

Typical values of TSFC for modern engines ........................... 14
Explanation of the stations allocated to the turboramjet engine ...... 38
Comparison of ﬂow properties at Station (1) .......................... 100
Comparison of ﬂow properties at Station (2) .......................... 101
Comparison of ﬂow properties at Station (3) .......................... 103
Comparison of ﬂow properties at Station (4) .......................... 104
Comparison of ﬂow properties at Station (5) and (13) ................ 105
Comparison of ﬂow properties at Station (6) and (14) ................ 105
Comparison of ﬂow properties at Station (7) .......................... 107
Comparison of ﬂow properties at Station (8) .......................... 108
Comparison of ﬂow properties at Station (9) .......................... 11]
Comparison of ﬂow properties at Station (10) ......................... 113
Comparison of ﬂow properties at Station (11) ......................... 114
Comparison of ﬂow properties at Station (15) ......................... 116
Comparison of ﬂow properties at Station (16) ........................ 119
Comparison of ﬂow properties at Station (17) ......................... 119
Comparison of ﬂow properties at Station (18) ........................ 122
Comparison of ﬂow properties at Station (20) ........................ 124
Comparison of engine performance parameters ....................... 126

ix

Figure 2.1
Figure 2.2
Figure 2.3
Figure 2.4

Figure 2.5

Figure 3.1
Figure 3.2
Figure 4.1
Figure 4.2
Figure 4.3

Figure 4.4

Figure 6.1

Figure 6.2

Figure 6.3

Figure 6.4

LIST OF FIGURES

Layout of a typical turbojet engine ....................................... 15
Characteristics of an external compression intake ..................... 17
Raleigh line for different mass ﬂuxes .................................... 21
Typical layout of a ramjet engine ........................................ 26

Layout of a turboramjet engine with separate combustion

chambers ..................................................................... 28
Schematic diagram of the turboramjet engine .......................... 37
A ﬂow stream through oblique shock .................................... 46
Flow chart of the software ................................................ 50
Typical stream pattern for subsonic inlets .............................. 57
Half wedge showing shock formation and geometrical details ...... 59

Section of the turboramjet showing the doors when only the

turbojet is in operation ..................................................... 82
Turboramjet operational range for maximum Mach number and
altitude ...................................................................... 130
Comparison of speciﬁc thrust and TSFC with altitude variation ...134
Comparison of speciﬁc thrust and TSFC with change in ramjet
Starting Mach at 11000 meters .......................................... 136
Comparison of speciﬁc thrust and TSFC for TIT variation at

1 1000 meters ............................................................... 137

Figure 6.5

Figure 6.6

Figure 6.7

Figure 6.8

Figure 7.1

Figure B]

Figure C.l

Comparison of thrust ratio verses Mach ratio with altitude

variation .................................................................... 139
Comparison of total thrust and mass ﬂow rate with altitude

variation ..................................................................... 141
Comparison of thrust ratio verses altitude ratio with increase

in Mach number ............................................................ 143
Plots of engine speciﬁc thrust, efﬁciencies and velocity ratio

at 11000 meters .............................................................. 146
Comparison of known ramjet performance parameters with the
turboramjet in joint operation range ...................................... 151
Mach number calculations for a ﬂow through a divergent passage... 157

Plots of a typical ramjet speciﬁc thrust and fuel consumption ....... 162

xi

'Yc

111:

LIST OF SYMBOLS AND ABBREVIATIONS

cross sectional area [m2]
Speed of sound I [m/s]
speciﬁc heat at constant pressure [kJ/kg K]

fuel-air ratio

enthalpy [kJ/kg]
speciﬁc thrust [N/kg/s]
speciﬁc heat ratio

Mach number

normal component of free stream Mach number w.r.t. oblique shock

mass rate of ﬂow [kg/s]

static pressure at station indicated by the subscript [kPa]

heat of reaction of the fuel [kJ/kmol K]

gas constant [J/kg K]

static temperature at station indicated by the subscript [K]

ﬂow velocity at station indicated by the subscript [m/s]
GREEK

oblique shock wave angle w.r.t. semi-vertex line of the wedge
compressor pressure ratio
efﬁciency

burner efﬁciency

xii

nc

TImt

On

710

“P

n!

nth

Po

isentropic (adiabatic) efﬁciency of compressor
mechanical efﬁciency of turbine

isentropic (adiabatic) efﬁciency of nozzle
overall efﬁciency

propulsive efﬁciency

isentrOpic (adiabatic) efﬁciency of turbine
thermal efﬁciency

semi-vertex angle of the intake wedge

free stream to exit velocity ratio

static density at station indicated by the subscript [kg/m3]
stagnation density at station indicated by the subscript [kg/m3]
SUBSCRIPT

stagnation value

free stream air

burner

compressor

diffuser

nozzle exit

fuel

isentropic or ideal

stagnation value or overall as indicated by the text

propulsive

xiii

t turbine

th thermal
SUPERSCRIPTS

* critical condition where the ﬂow Mach number is unity
ABBRIVIATIONS

ASP Aerospace Plan

ATOS Airplane to Orbit System

CIAM Central Institute of Aviation Motors

HSTC High Speed Civil Transport

MITI Ministry of International Trade and Industry
NASP National Aerospace Plan

TSFC Thrust Speciﬁc Fuel Consumption

UTC United Technology Corporate

xiv

CHAPTER 1

INTRODUCTION

1.1 The Need of High Speed Aircraft

Globalization of the world continues to broaden relations among countries.
Accordingly the role of air travel has become increasingly important. The total number of
airline passengers per year exceeded one billion at the end of the last decade
[Tskhovrebov 1992]. This demonstrates an increasing trend of long range passenger
aircraft in the world airliner ﬂeet. Passenger trafﬁc growth at the beginning of let
century, in conjunction with increasing needs in long range transport, demands more

attention to higher ﬂight speeds.

At present, the ﬂight speed range of air transport is limited mainly to the subsonic
area owing to technical and economic factors. An increase in ﬂight speed leads to ﬂight
time reduction and improved travel comfort, particularly on intercontinental routes. Given
the expected increase in air transportation and the established practice of comfortable
ﬂight-time of no more than 2 to 3 hours for a passenger, one may infer the prospective
development of a supersonic passenger aircraft of a new generation with a ﬂight Mach in
the range of 2 to 4. Furthermore, one needs to consider the distant future where air
transport with hypersonic speeds will be required. This will enable ﬂights on the longest

routes to operate with considerable reduction in ﬂight time.

The development of an effective Aerospace Plane (ASP) for launch of commercial

loads is needed to continue to open up the near-earth space for peaceful goals. The key

factor in low cost launch is the use of reusable launch vehicles from an Aeroplane-To—
Orbit System (ATOS) with horizontal take-off/landing. Furthermore, a fuel—efﬁcient air

breathing engine is needed to affect substantial increase in the relative mass load.

1.2 Considerations for a Supersonic Civil Aircraft Engine

Several designers of transport aircraft have taken on projects for supersonic ﬂight
at Mach numbers of 2 to 4 and in the hypersonic range, even up to Mach 25. In
developing the supersonic or hypersonic power plant, the main factor in defining its
conﬁguration is a wide range of operating conditions. Engine efﬁciency in cruise ﬂight is
ensured by optimizing thermodynamic parameters, which change considerably depending
on ﬂight speed and altitude. On the other hand, a signiﬁcant requirement for the power
plant of a high-speed aircraft is to provide high thrust for acceleration, which at high
ﬂight Mach numbers is determined by the air ﬂow.

Today’s air travel is mostly restricted to the use of the turbojet or turbofan engine.
A typical property of a turbojet is the lowering of the pressure increase and airﬂow in the
turbo compressor part with an increase in ﬂight speed. Speciﬁc thrust parameters of the
augmented turbojet approach ramjet speciﬁc parameters at ﬂight Mach numbers 3 to 3.5.
At higher ﬂight speeds the ramjet gives higher speciﬁc thrust than turbojet at equal air-to-
fuel coefﬁcients. Corrected airﬂow in the ramjet with variable inlet and nozzle can be
maintained constant over a wide ﬂight speed range. As a result the ramjet thrust rises with
Mach number more rapidly than the turbojet thrust. When the Mach number is higher
than 3 to 4, the ramjet thrust exceeds augmented turbojet thrust; and in this ﬂight speed

region, the ramjet can be more effective than the turbojet. The ramjet, however, can not

be used alone because it is incapable of producing static thrust and has a poor efficiency
at low Mach numbers. Thus, in engines designed for a wide operating ﬂight speed range,
it is advantageous to combine high turbojet efﬁciency at Mach numbers up to 3 to 3.5

with the ramjet speciﬁc parameters at Mach numbers higher than 3.5 or 4.

1.3 The Turbojet-Ramjet Combination Engine

When the turbojet and the ramjet engines are combined in a single propulsion
plant, it is possible to obtain air breathing engine class that is operable and effective up to
Mach 5 or higher. A combined turboramjet engine is essentially a bypass engine in which
a high pressure inner part is represented by a turbojet or turbofan and a low pressure

external part by the ramjet.

An idea] combination is achieved when a turbojet having high value of thrust at
low Mach numbers is combined with a ramjet matched to high Mach numbers. The thrust
produced by each of the two engines can thus be added up. There is a common intake to
this combination. Keeping the ramjet exit nozzle variable, the efﬁciency of air intake
increases; and the turbojet takes full advantage of this situation. Usually, in these engines,
afterbumer chambers represent the combustion chamber of the ramjet part too. These
chambers are formed by switching out the turbojet part by means of special devices and
feeding fuel only to the ramjet combustion chambers. The ﬂow requirements of the
turbojet and ramjet vary inversely with variations of Mach number. The solution to this
problem is to have variable geometry both for intake and exit nozzle. This arrangement
displays the air ﬂow coefficient variation much less than that of the turbojet and the

ramjet used separately.

1.4 Adoption of the Concept by Various Countries

1.4.] France

The practical application of the turboramjet engine was first seen in the form of
the Griffon H aircraft. The project was started in 1953 by the French Air Ministry and a
French ﬁrm, Nord Aviation. In April 1957, the Griffon 11 made a successful ﬂight with
the ﬁrst ever operation of the combination engine in air. In May the speed of sound was
exceeded and within a month supersonic ﬂights were made up to Mach 1.3. The Mach
number was progressively increased until December, when the aircraft achieved Mach
1.85 at an altitude of 13000 meters. There was, however, still a large surplus thrust giving
a rate of climb of 8500 m/min. Further advance in Mach number was very slow as the
turbojet limitations were being approached. Finally, the aircraft made one of the best
performances with Mach 2.] at 18500 meters, while still accelerating and climbing

slightly [Daum 1959].

Griffon was acknowledged for excellent performance of the power plant and
smoothness, which was not possible with a turbojet alone with an afterbumer. All the
pilots who ﬂew the aircraft, praised it for maneuverability in supersonic high "g" turns
and acceleration. Griffon achieved the world record of 1640 km/hr for 100 km closed
circuit [Daum 1959]. This record proved not only the aircraft’s speed potential and its
aerodynamic qualities but also laid a milestone for the French research and development

in the area. Presently, France is collaborating with Japan in the development of a zero to

Mach 5 turboramjet engine program.

1.4.2 Russia

The successful experimentation on the turboramjet combination engine attracted
the Russians, and their Central Institute of Aviation Motors (CIAM) started investigations
on advisable engine concepts, operation process parameters, control modes and ground
testing of experimental turboramjets in beginning of 608. In the decades of 705 and 805
the wide testing program of experimental full scale turboramjets of different types were
carried out at CIAM [Sosounov, Palkin 1992]. The experimental turboramjet engines
corresponding to Mach numbers 4 to 4.5 were simulated at the facility. The obtained
results, experimental data, and Russian experience of liquid hydrogen use opened the
possibilities for the development of turboramjet engines for aerospace plane using liquid
hydrogen as fuel. During research, it was found that the ﬂight speed for transition to the
ramjet mode depends on design operating parameters and the size correlation between
typical propulsion system duct areas. The transition Mach number is usually in the range

2.5 to 3.5 [Sosounov, Palkin 1992].

1.4.3 United States of America

In 1986, President Ronald Regan called for congressional support for a National
Aerospace Plane (NASP) — a very high-speed passenger airplane [Korthals-Altes 1987].
Concurrently, another program of NASA was demonstrated as High Speed Civil
Transport (HSCT) aircraft. Studies were conducted by Boeing and McDonnell Douglas
aircraft companies with a view to reduce existing 10 hour Los Angels to Tokyo trip to
four hours or less. The mission required out of HSCT was to produce a non-pollutant

ﬂight and to carry 250 passengers at Mach 2.5 [Korthals-Altes 1987]. US. aeronautical

5

preeminence in hypersonics is currently based on the NASP program to provide the
technological basis for future hypersonic ﬂight vehicles. The program plans to build and
test a manned experimental ﬂight vehicle, the X-30, to validate critical or enabling
technologies demonstrating sustained hypersonic cruise and single-stage—to-orbit space
launch capabilities. The X-30 is being designed to take-off horizontally from a
conventional runway, reach hypersonic speeds of up to Mach 25, attain low earth orbit,
and return to land on a conventional runway. The program is expected to develop and
demonstrate the technology for future ﬂight vehicles that will have technical, cost, and
operational advantages over existing military and commercial aircraft and space launch

systems [US Congress Report October 4, 1991].

1.4.4 Japan

The National Space Development Agency of Japan, Institute of Space and
Aeronautical Science, and the National Aerospace Laboratory are independently
conducting research and development of technologies for separate but complementary
aerospace vehicle concepts or systems [Fujimura 1996]. Japanese advanced propulsion
systems are in various stages of maturation ranging from concept development to being
Operational. In terms of air-breathing engines, the air-turboramjet experimental engine (an
expander-cycle air turboramjet system that uses much of the technology from the high
pressure expander-cycle engine) is also in advanced development stages. Ministry of
International Trade and Industry (MITI) is supporting a Mach 0 to 5 turboramjet engine
development program, announced in 1989, as a basic research and development project

composed mainly of component research. Planned to run through 1998, it is the ﬁrst

large-scale international collaboration program [US Congress Report October 4, 1991].
Besides the local Japanese engine makers, the international participants are GE Aircraft
Engines, United Technology Corp. (UTC), Rolls Royce, and SNECMA. Study results
indicate that four engines with 270 kN take-off thrust are required for the aircraft carrying
300 passengers over a distance of 12000 km [Fujimura 1996]. This would mean a

transpaciﬁc ﬂight of only three hours from Tokyo to New York.

1.4.5 Australia

Australia is developing competence in selected subsystems for future aerospace
vehicles, and its facilities are being used to test various US. and European aerospace
vehicle concepts and components. Australia also conducted feasibility studies for an
international spaceport on its Cape York Peninsula that would accommodate future

aerospace plan [US Congress Report October 4, 1991].

1.5 Objective of this Thesis

In this report an endeavor has been made to bring out the possibilities raised by
turboramjet combination in the formula which one advocates for manned aircraft, a
formula that brings out in a larger range of ﬂight conditions the fundamental virtues of
both types of engines. In order to facilitate the designer to view the combination engine
through the window of software, a computer code has been developed in FORTRAN 77.

This code assumes the layout of the engine as follows:

a) A common intake with variable geometry center body (wedge)

b) Turbojet parts at the inner core with outer annular area as the ramjet

c) Separate combustion chamber each for the turbojet and the ramjet

d) A mixer unit to mix the turbojet and ramjet combustion gases before entering

the exit nozzle

e) A common variable area convergent—divergent exhaust nozzle

f) Doors to change the by-pass ratio and isolate the turbojet or the ramjet as per

the prevailing ﬂight conditions

The software runs in two steps. First, it provides the user with the capability to
input as many as 14 different design parameters of his choice, based upon which it fixes
the geometry of the engine. The main program then initiates the calculation of the
pertinent ﬂow parameters at all the stations of the turboramjet engine both for on-design
and off-design ﬂight conditions. For a known engine geometry, user input of the ﬂight
Mach number and the altitude is required to run the main program. The software has
several built-in features that help the engine simulation to achieve results compatible with
the real engine operation (see Section 3.2.2). It is also capable of suggesting the engine
operation mode (only turbojet, ramjet, or the combination of both), based upon the
selected ﬂight conditions. The ﬂow conditions at different stations are reﬂected on screen
and can be printed through output ﬁle. Depending upon the conditions, various messages

are ﬂashed on screen to enable the user understand the undergoing ﬂow process.

The software also possesses good academic value for the students of aircraft
propulsion and helps them to understand the changes involved in the air ﬂow parameters
while passing through various components of the turbojet and the ramjet engines. It also
serves as a means to give an insight to the subject of compressible ﬂuid dynamics,
especially in the areas of one-dimensional steady ﬂow, isentropic ﬂow conditions, shock
waves, stagnation state, Raleigh line, combustion process, and air ﬂow through varying

area ducts.

CHAPTER 2
TECHNICAL BACKGROUND

2.1 Introduction

For high-speed operation of the aircraft, particularly for civilian use, besides the
reduction in ﬂight time maximum comfort to the passengers is also a subject of concern.
It introduces constraints on the designer that the high speed must not be associated with
excessive acceleration or high aerodynamic loads; and, furthermore, provision must be
made for landing. In such cases the combination of ramjet and turbojet may offer decisive
advantages. It may be useful to begin by recalling the problems that are posed by high
speed ﬂight with air breathing engines; the manner in which these are being tackled; and
the reasons why the composite power plant, which is the object of attention, is the
solution to be preferred.

The material presented in this chapter has been collected from various books and
papers (see page 169) so as to serve as a quick reference to the reader on the subject of
aircraft propulsion. Only some of the standard features that are of vital importance for a

high-speed power plant are brieﬂy addressed.

2.2 Engine Performance

In describing the performance of aircraft engines, it is helpful if several
efﬁciencies and performance parameters are deﬁned ﬁrst. In this section various
deﬁnitions and, for simplicity, representative expressions are presented as they would

apply to an engine with a single propellant stream i.e. a turbojet or ramjet.

10

2.2.1 Engine Efficiency
2.2.1.1 Propulsion Efﬁciency

The product of thrust and ﬂight velocity, is some times called thrust power. One
measure of the performance of a propulsion system is the ratio of this thrust power to the
rate of production of propellant kinetic energy. This ratio is commonly known as the

propulsion efficiency, 77,,. For a single propellant stream

tu

"” ._. m,[<1+f>(u3/2> —u2/2]

 

(2.1)

With the following two reasonable approximations, equation (2.1) may

considerably be simpliﬁed:

a) For air-breathing engines in general, f << 1 and may be ignored without

leading to serious error.
b) In the thrust equation

1' = m, [(1 +f)ue —u]+(ﬁ — Pam, (2.2)

The pressure term, (8 - Pa)Ae, is usually much smaller as compared with the

other terms, so that
t z thaw, — u). (2.3)

thus

11

(u, - u)u _ 2u/uc

17" z[(u3/2)-u2/2]—1+u/u,

 

(2.4)

77,, in no sense is an overall power plant efficiency because the unused enthalpy in
the jet is ignored. Equation (2.3) shows that u, must exceed u so that the right—hand side
of equation (2.4) has a maximum value of unity for u/ue =1. However, for u/ue —-> 1, the
thrust per unit mass ﬂow is practically zero, and for a finite thrust the engine required
would be inﬁnitely large. It is, therefore, concluded that although it, must be greater than
u the difference must not be too great, and it is not realistic to try to maximize the
propulsion efficiency of a jet engine. Hence, other parameters are required to evaluate the

overall performance of the engine.
2.2.1.2 Thermal Efficiency

Another important performance ratio is the thermal efﬁciency, 7),,” of the engine.
For ramjets, turbojets, and turbofans it is deﬁned as the ratio of the rate of addition of

kinetic energy to the propellant to the total energy consumption rate n'zf QR, where QR

is the heat of reaction of the fuel. Thus the thermal efficiency may be written, for a single

propellant stream, as

ma[(1+f)(uf/2)-u2/2]
_ meR

 

HI

= [(1+f)(u3/2)—u2/2]

(2.5)
fQR

 

01" 77:1.

12

2.2.1.3 Overall Efficiency

The product of 1),, 77m. is called the overall efﬁciency, no, and is defined by

1 u
= = -— 2.6
770 "p77"! ml QR ( )

Using equation (2.4), (for f <<1)

770 : 2771;;[—l/'u—e-] (2.7)

1+u/ue

Thus, the overall efﬁciency depends only on the velocity ratio, u/u,, and on the

thermal efﬁciency, rm; which depends somewhat on the velocity ratio. Hence, it is

concluded that the efﬁciency of an aircraft power plant is inextricably linked to the
aircraft speed.
2.2.2 Thrust Speciﬁc Fuel Consumption
The ambiguous concept of efﬁciency is discarded in favor of the Thrust Specific
Fuel Consumption (TSF C) which, for aircraft engines, is usually deﬁned as the ratio of
fuel ﬂow rate to thrust. Hence
mf

TSFC = 7 (2.8)

For a turbojet with Pa = P6, equation (2.2) shows that

 

TSF C (2.9)

_ f
" ma[(1+f)u, -u]

13

Equation (2.9) indicates that the TSF C of a given engine depends strongly upon ﬂight

speed. Typical values of TSF C for modern engines are shown in Table 2.1

Table 2.1 Typical values of TSFC for modern engines [Hills and Peterson 1992]

 

 

 

Engine TSFC
Type [kg/N . hr]
Ramjets 0.17 - 0.26
(Mach 2)

Turbojets 0.075 — 0.11
(Static)

 

2.2.3 Speciﬁc Thrust

Another performance parameter is the specific thrust 1,, namely the thrust per unit
mass of air (e.g. N/kg). This provides an indication of the relative size of the engine
producing the same thrust because the dimensions of the engine are primarily determined
by the air ﬂow requirements. Size is important because of its association not only with
weight but also with frontal area and the consequent drag. The TSF C and speciﬁc thrust

are related by

TSFC = IL (2.10)

where f is the fuel/air ratio.
2.3 Turbojet
2.3.1 Air Intake System
The function of the air intake for a turbine engine is to deliver the required air
mass ﬂow at the compressor face with the highest possible stagnation pressure and with

the smoothest possible velocity distribution. Any loss in stagnation pressure represents a

14

performance loss for the engine while variation in velocity around an intake is liable to
cause compressor surging or blade breakage. These requirements are to be met over a
wide range of ﬂight conditions without introducing too much complexity or weight. It is
important for the intake designed on one set of conditions that the off-design performance
penalties must not become unacceptably high. Modern engine installations are
incorporated with a variable geometry mechanism, which ensures intake area variation

with ﬂight conditions in order to give good off-design performance.

I ' '

 

 

 

 

 

 

 

 

l l l
- ,_ _. _ .- h Burner \ \ \
-_’ 8 0 _.
a/é Compressor :2 After- N I'm-5
-—> " t- burner on e
____._ 0‘ .2 ~--- —*

 

@

(9(2)

 

 

(3)

@@

 

C?)

Figure 2.] Layout of a typical turbojet engine [Courtesy Hills and Peterson 1992]

For supersonic engines there is a penalty of a high momentum drag arising from

the high ﬂight speed but there is a corresponding advantage in the high ram pressure ratio

available. The ram pressure ratio of an isentropic intake is given by

P 2

i=(l+ k_1M2)k/(k-l)

(2.11)

The formula indicates that the ram pressure ratio increases with increase in the Mach

number.

15

In order to have a subsonic velocity at the compressor face, a supersonic intake
must generate at least one shock. Deceleration through a shock is always accompanied
with stagnation pressure loss, and this loss varies with the intensity of the shock. An
efﬁcient intake will use multiple shocks to keep the intensities low so as to keep the loss
in stagnation pressure to a minimum.

Supersonic intakes as currently used can be classified under the headings of
external compression, internal compression, and mixed extemal-internal compression.
However, keeping in mind the requirement of the engine under study, only the external
compression supersonic intake is brieﬂy discussed.
2.3.1.1 External Compression Supersonic Intake

External compression intakes are those in which the shocks pattern is formed
ahead of the outer casing of the intake. Although such intakes involve complex design, an
improved performance is obtainable by their use. For Mach numbers above 1.5 the
compression is achieved through shock waves by setting up a single or a double cone
ahead of intake cowling.
2.3.1.2 The Single-Cone Intake

In this type of intake the cone sets up a conical shock whose intensity will be a
function of the Mach number and the included angle of the cone. The ﬂow Mach number
will still be supersonic but will be lower and deﬂected away from the axial direction. By
suitable selection of the intake geometry the shock can be made to fall on the cowl lip.
For further deceleration to a subsonic Mach number, a normal shock is needed which can

also be made to rest at the lip. Further subsonic diffusion takes place inside the cow].

16

2.3.1.3 The Double-Cone Intake

In a double—cone intake two discontinuities of the ﬂow are set up, first by the tip
of the cone and second by the change in cone angle. With good design the two conical
shocks may meet at the cow] lip, and the ﬁnal normal shock may also settle here. Since
the combined intensity of the two conical shocks is less than that of corresponding single
one, the intake performance is improved.

In principle each intake has a two-dimensional counterpart in which cones are
replaced by wedges. For these the Mach number relationships across the shocks are of the
same general form as are for conical shocks. Thus, the ﬂow characteristics can be
represented in the same way both for a cone or a wedge by taking the upstream Mach
number and cone or wedge angle as the prime variables.
2.3.1.4 Intake Characteristics

The intake characteristics can be well explained by drawing them to the axes of
pressure ratio and non-dimensional engine intake mass ﬂow. By keeping ﬂight Mach
number as another variable constant Mach number lines can be drawn on these

characteristics.

Super-critical Critical
‘ I \
5 I 3'
E W SI percriticel
a
8
t

 

 

c
0
I \ I?
I “a E
. I \ if "T
I it.
I Subcritkct
I.“ ﬂow rate IbH‘hd/pq E

Figure 2.2 Characteristics of the external compression intake
[Courtesy McMahon 1971]

17

Figure 2.2 shows the typical form of intake characteristics. It is observed that the
pressure ratio goes up with increasing Mach number. On the plot of these characteristics a
“critical” line is drawn joining the points of maximum pressure ratio and the regions left
and right to it are labeled as “subcritical” and “supercritical” respectively. By studying
the shock pattern with changes in engine operating conditions it is realized that the
position and intensity of the conical shock depends on the mass ﬂow being swallowed by
the engine. The critical condition represents the shock configuration for design conditions
with shock resting on intake lip.
2.3.1.5 Shock Location and the Engine Air Demand

Depending upon the operating conditions if the engine air demand increases, the
oblique shock will be unaffected, but the normal shock will move down into the intake as
shown in the second sketch of Figure 2.2. The ﬂow, which is still supersonic, will be
accelerated in the divergent portion of the intake and the normal shock will be more
intense causing greater loss in the stagnation pressure. The physical mass ﬂow and the
stagnation temperature will remain unchanged as the two depend on the ﬂight Mach
number and the intake area at the cow] lip.

If the mass ﬂow should decrease from the critical, the normal shock will move
outside the cowl lip (third sketch of Figure 2.2) but will remain about the same intensity.
This concludes that the pressure ratio is virtually constant in the subcritical region. If,
however, the mass ﬂow is reduced too much the intakes are liable to become unstable.

In general the engine operation should be kept close to the critical range in order

to achieve best possible pressure recovery. In the work under study the same concept is

18

utilized by designing a variable geometry wedge, which ensures that the both oblique and
normal shocks always rest on the cowl lip.
2.3.2 Compressor and Turbine

In an aircraft engine the compressor and turbine are often referred as the
turbomachines. For large engines the turbomachines are preferred because they can be
made much smaller in size for a given ﬂow rate. It is because of higher internal velocities
and higher fraction of internal volume allocated to the ﬂow.

The engine performance, and thus aircraft range, is strongly dependent upon
compressor pressure ratio and efﬁciency. Across the compressor the air is made to ﬂow
from a low pressure to a high pressure i.e. against the “natural direction” of the ﬂow in
contrast to the turbine where air ﬂows in its natural direction.

Both compressor and turbine contain rows of stator and rotor blades. One row of
a rotor and stator form a stage. In a compressor, work is done on the air and it gets
accelerated as it passes through the rotor. The function of the stator row of the
compressor is to accept this high velocity air and decelerate it, so as to increase the static
pressure. The axial component of the air velocity almost remains constant while passing
through all the stages of the compressor.

In a turbine the stators as sometimes termed as “nozzle” and the rotor as
“buckets”. Because of generally falling pressure in turbine ﬂow passages, much more
turning in a given blade row is possible without danger of ﬂow separation as compared
with an axial compressor blade row. This implies that more work and considerably higher
pressure ratio is achievable per stage of turbine. This conclusion points at the fact that

with a turbine of two to three stages it is possible to drive a multi—stage large compressor.

19

The airﬂow meets the turbine after the combustion process. Thus, the high
temperature and high pressure gases entering the turbine have a large amount of available
energy with respect to the exhaust conditions and must be extracted as efficiently as
possible. A high percentage of this energy needs to be fed back into the cycle to drive
compressor while the reminder is available for useful output, either by driving a power
turbine or by forming a propelling jet stream.

As in case of an axial compressor the ﬂow axial velocity component across
turbine can also be assumed to remain constant.

2.3.3 Process of Combustion

The combustion process involves the oxidation of constituents in the fuel that are
capable of being oxidized and can therefore be represented by a chemical equation.
During a combustion process the mass of each element remains the same. When a
hydrocarbon fuel is burned, both the carbon and the hydrogen are oxidized. Considering
the combustion of methane as an example

CH4 + 202 —9 C02 + 2H20 (2.12)
In this case the products of combustion include both carbon dioxide and water. The water
may be in the vapor, liquid, or solid phases, depending on the temperature and pressure of
the products of combustion.

In most combustion processes the oxygen is supplied as air rather than as pure
oxygen. The air is considered to be composed of 21 percent oxygen and 79 percent
nitrogen by volume. This leads to the conclusion that for each mole of oxygen, 3.76
moles of nitrogen are involved. Therefore, when the oxygen for the combustion of

methane is supplied as air, the reaction can be written as

20

CH4 + 202 + 2(3.76) N2 —-) CO2 + 2H2 O + 7.52 N2 (2.13)

2.3.3.1 Flow Conditions During Combustion

The combustion chamber is considered to be a constant-area duct in which heat
transfer takes place. The process involves changes in the stagnation enthalpy and in the
stagnation temperature of a gas stream through such a duct without frictional effects.
Such ﬂows are called simple stagnation temperature-change ﬂows.
2.3.3.2 The Raleigh Line

If the conditions upstream of the control volume are ﬁxed (state 1), and conditions
are to be found down stream (state 2), then for a particular value of V2 :

a) p2 can be calculated from the continuity equation

b) P2 may be evaluated from momentum equation

c) T2 may be found from equation of state

Hence, the continuity equation, the momentum equation and the equation of state
deﬁne a locus of states passing through state 1, which is known as the Raleigh line
on the T-S diagram. The states on the Raleigh line are reachable from each other

in the presence of heat transfer effects.

 

 

 

 

 

Figure 2.3 Raleigh line for different mass ﬂuxes [Courtesy Aksel and Eralp 1994]

21

Raleigh lines corresponding to different mass ﬂuxes are shown in Figure 2.2,
which indicates that the entropy and temperature are maximum at points A and B

respectively. At point A, where the slope of the Raleigh line is inﬁnite, the Mach number
is unity whereas, at point B where the slope is zero, M = 1/ J7; . Also it is to be noted that

the lower branch of the Raleigh line corresponds to supersonic ﬂow [Aksel and Eralp
1994].

Since the process of simple heating is thermodynamically reversible, heat addition
must correspond to an entropy increase and the heat rejection must correspond to an
entropy decrease. Therefore, the Mach number increases with heating and decreases with
cooling at subsonic speeds. However, at supersonic speeds, the Mach number decreases
with heating and increases with cooling. Thus, the process of heat addition tends to make
the Mach number unity. The ﬂow can not continue beyond Mach 1 with either heat
addition or heat rejection alone. During the heating of a subsonic ﬂow between points A
and B of the Raleigh line, the static temperature decreases [Aksel and Eralp 1994].
2.3.3.3 Effects of Heat Transfer on Flow Properties

For the combustion process the ﬂow enters of the chamber with a low subsonic
Mach number such that it always remains less than llk. The effects of heat transfer on the
ﬂow properties across the combustion chamber may be summarized as follows:

a) The ﬂow Mach number, static temperature, velocity, stagnation temperature,

and entropy undergo an increase.

b) The static pressure, density, and stagnation pressure decrease.

22

2.3.4 Effect of Flight Mach Number on Turbojet

The turbojet with after—bumer comprises the same elements as the ramjet, plus a
rotating assembly (compressor and turbine) which represents an additional cycle. The
essential function of this additional cycle is to increase the pressure, which must exist at
the entry of the after-bumer chamber. From the stand point of performance, the effect of
increasing Mach number results from the following three considerations:

a) The air temperature at the compressor entry increases rapidly with Mach

number.

b) The gas temperature at the turbine entry is limited to a given value, which is

the function of the state of art at the time.

c) The speed of rotation of the machine can not exceed a certain figure.

These effects mean that as Mach number increases, the turbojet pressure ratio deteriorates
and may even reduce to a value less than unity. The additional cycle thus becomes
superﬂuous at ﬁrst and then harmful. The specific consumption becomes higher than it
would be if the rotating parts were discarded.

At the Mach number where the total delivery head to the after-bumer combustion
chamber is equal to the compressor entry pressure, the turbojet will stop its function of
pressure ampliﬁer. Assuming practical values of compressor and turbine efficiencies and
the turbine limiting temperature as 1000" C, this limiting Mach number is found to be
approximately 3.3 [Daum, 1959]. The problem, however, is not to design an engine
working at a given Mach number only, but to cover a complete ﬂight envelope. For the

turbojet the ﬂight envelope may be defined by the extreme values taken in ﬂight by the

parameter N/JTOC , where N is the engine RPM and 7;), is the air stagnation

23

temperature at the compressor entry. For majority of the high speed aircraft taking 100
percent as the reference value at Mach 0.9, N / JR. reduces to 65 percent for Mach 3 and

to 52 percent for Mach 4, provided the RPM are kept constant [Daum 1959].

It is extremely difﬁcult to achieve correct function of compressor over such a
wide range. An adequate margin against surging (ﬂow separation caused by pulsating
ﬂow due to back pressure at turbine face) must be preserved when the air is cold, i.e. at
low Mach numbers, while maintaining still acceptable values of efficiency when the air is
hot, i.e. at high Mach numbers. Various independent studies relating to ﬁxed geometry
compressor with compressor ratios ranging between 3.5 and 8 at sea level show that at
turbine entry temperature of the order of 1000° C the turbojets ceases to act as pressure
ampliﬁers when the Mach number exceeds 2.7 or thereabouts [Daum 1959]. Beyond this
value, the drop in total pressure is higher the higher the compression ratio at sea level.
Raising the turbine temperature by 100° C only increases the Mach number by about 0.25.
If the variable stator vanes are incorporated, which can adjust as a function of ﬂight
parameters; the limiting Mach number can then reach or even slightly exceed 3 [Daum
1959].

The dimensions and, hence, the weight of the turbojet is determined by the rate of
airﬂow through the engine. It is seen that the ﬂow coefﬁcient decreases as the ﬂight Mach
number increases. This is essentially due to the fact that the Mach number at compressor
entry blades decreases because the blade tip speed remains constant and the air warms up.
The Mach number is highest when cold and can not exceed a certain transonic value. It

concludes that as the Mach number increases, a given turbojet is less and less able to

24

absorb a large rate of air ﬂow. If it is to deliver a high thrust at a high Mach number, it
will have to be larger and larger.
Exhaust Nozzle

For a high performance engine it is highly desirable that a convergent-divergent
propelling nozzle is used, but its use entails a number of design problems. The most
immediate problem is that the ratio of exit to throat area for the divergent portion can
only be at its correct value for only one pressure ratio of the nozzle. If the overall pressure
ratio is less than the design value, a shock system will form inside the divergent portion
of the nozzle and will lead to appreciable losses. There is also a risk that the shocks will
be unstable and may cause vibration of the jet pipe. The next main problem with the
design of the convergent-divergent nozzle is associated with the reheat system. When
reheat is brought into operation there is a large increase in the volume ﬂow through the
nozzle and the area must be increased if the jet pipe pressure and the turbine entry
temperature are to be maintained at a suitable value.

The two problems can be overcome if the nozzle with variable geometry is used.
The study assumes a nozzle with variable geometry both at the nozzle throat and exit.
2.4 The Ramjet
2.4.1 Basic Features

The ramjet is the simplest of the air breathing engines. The engine has no moving
parts in its operating cycle and can not operate until it is moving with fairly high forward
speed. Having no rotating parts (excluding accessory drives), the ramjet can be made
light and compact and can avoid material limitations encountered at high ﬂying speeds by

the turbine engines.

25

L—- Diffuser —‘|-— Combustion chamber —e Nozzlea—‘l

1 Fuel inlet
$:'

\\~ <
W Exhaust jet

, (

<

(s
l .

r ' Combustion IW
0 \@\C5@ @ Ci) é

Supersonic Subso nic
compresswn compression

 

 

 

 

it it v

 

\

 

in
ii ii ii

 

 

b

Figure 2.4 Typical layout of a ramjet engine [Courtesy Hills and Peterson 1992]

2.4.2 Effect of Intake and Nozzle Area Variation

In the case of a ramjet that incorporates an adjustable exit nozzle throat, there is
no relative low temperature limitations imposed by a turbine; neither is there any
compressor whose limiting speed prescribes a law to the intake ﬂow. In this case the
nozzle throat variation directly affects air ﬂow at the entry and allows the intake to work
permanently under matched conditions. Hence, the qualities of a ramjet are determined by
the air intake. If an intake is selected, which has a high pressure recovery at high Mach
numbers; the engine will be incomparable at high Mach numbers but poor at lower ones
when its external drag will be high. On the other hand, if good characteristics are desired
at low Mach numbers, poor performance will be resulted in higher Mach numbers. The

net thrust will differ noticeably in different cases.

26

If the exit nozzle throat is kept constant, i.e. fixed gas temperature at the ramjet
exit is deliberately postulated, then beyond the Mach number chosen for air ﬂow
matching, the ramjet air intake works under supercritical condition. Below that Mach
number,
subcritical conditions are obtained with risk of intake buzz. Surging of the air intake is
essentially linked to the intensity of the normal shock, which decreases together with the
Mach number, resulting in reduced performance.

For an intake with lower efﬁciency the mismatching effect will be more
pronounced, whereas if the intake is of progressive external compression type, matching
remains correct within the range of Mach numbers for which the compression is truly
isentropic.

2.5 The Turbojet-Ramjet Combination
2.5.1 Intake

For the turbojet-ramjet combination, one might be tempted to add the thrust
coefﬁcients of a ramjet and a turbojet with the aim of achieving any desired variation
with Mach number. For instance, one might choose a turbojet having a high compression
ratio and a ramjet matched to high Mach numbers and having a high efﬁciency intake and
add up the thrusts. However, a better solution as advocated by Nord Aviation of France
is to have a common intake. If the ramjet exit nozzle is variable, the compressor no
longer imposes its law on the air intake, and the turbojet can take full advantage of the
high air intake efﬁciency that suits the ramjet.

In the turbojet the air ﬂow requirement is characterized by the Mach number at

compressor entry, whereas in the ramjet it is governed by the Mach number at

27

combustion chamber entry. The variation of ﬂow with change in the Mach number in the
turbojet is opposite to that in the ramjet. Because of this, it is always possible to design an
air intake with a good efﬁciency for which matching to the total airﬂow will remain
correct within alarge range. This matching can further be augmented by using an

exhaust nozzle with variable throat and exit section.

  
 
 
  
 
 

V
8 . -+
combustion chamber ..,
. ‘5 a ‘9 "I
. s )I .
................. —— cantedIne- - — - _
:3” fue' a 5' T .0 A T

  
  

Figure 2.5 Layout of a turboramjet engine with separate combustion chambers
[Courtesy Turboramjet proﬁle (Online Image)]

This combination will provide the sum of the thrust of a turbojet without intake
losses and that of a well-matched ramjet. At the same time it will avoid the complication
of having two variable geometry intake systems.

2.5.2 Engine Characteristics

For an engine intended for a very high speed, the desirable characteristics are
considered one by one.
2.5.2.1 Cruise

The cruising ﬂight at maximum Mach number is assumed to take place in

accordance with the Breguet law for calculating range

28

V W
=-——-l—'log——'- (2.14)
TSFC D W2

Here: R = range i.e. the distance covered

V

Velocity

TSFC = Thrust Speciﬁc Fuel Consumption

L = Lift

D = Drag

W1 = Initial weight of the aircraft

W2 = Final weight
It is observed that speciﬁc fuel consumption is one of the fundamental characteristics of
the engine. It has also been observed that as soon as the Mach number reaches 2.7 to 3.0,
the specific consumption of the ramjet becomes lower than that of turbojet [Daum 1959].
It means that around Mach number 2.7, the speciﬁc consumption is essentially a function
of the intake characteristics. This fact is obvious as regards the ramjet, but the turbojet
also behaves in the same manner because by the time Mach number reaches this value the
turbojet loses its ability to amplify pressure. Thus, at Mach numbers above 2.7, the
speciﬁc consumption of the turbojet would progressively increase while that of the ramjet
would decrease slightly or stay constant. It should be noted here that for the same weight
of fuel using a lighter engine allows a better value of W, / W2 to be achieved resulting in
a longer range for the same speciﬁc fuel consumption.
2.5.2.2 Climb

For that part of the ﬂight that corresponds to acceleration and climb, it is possible

to imagine many different ﬂight patterns. However, due to the structural strength

29

limitations most high speed aircraft projects are based on climb program. This may be
decomposed as follows [Daum 1959]:
a) Acceleration at very low altitude up to Mach 0.9
b) Climb at a constant Mach number of 0.9 up to relatively high altitude, but
always less than 11000 meters
0) Acceleration at constant altitude or in slight climb up to the point when
maximum aerodynamic load allowed by structural strength is reached.
Loading may be expressed in terms of equivalent airspeed
d) Climb at constant aerodynamic loading up to the maximum Mach number
e) Climb at maximum Mach number up to the cruise altitude
If the aircraft is to climb and accelerate, the net thrust of the engine at all points
must be higher than the drag. If the thrust is chosen at too high a value, the engine may
be too large and hence very heavy. If, however, the excess of thrust is too small, the fuel
consumption may suffer owing to long duration of climb. This situation calls for an
optimization study if the size of the engine is determined by this part of ﬂight.
2.5.2.3 Turbojet - Ramjet Proportion
In case of the turbojet alone, the excess of thrust coefﬁcient over drag coefﬁcient
is roughly proportional to the drag coefﬁcient itself within a large range. Thus, the size of
the turbojet may be determined either by conditions at the end of climb at cruising Mach
number or by optimization of the climb and cruise portions taken together. With the
turboramjet, however, an additional variable is identiﬁed which allows to achieve an
almost arbitrary law of variation of thrust coefﬁcient. This variable is the proportion of

the ramjet added to the turbojet. The type of ramjet can be varied, and it is possible to

30

achieve a law such that the excess of thrust should be large in the high supersonic range
and small in the transonic range. This would mean that the turbojet should be small in
size.
2.5.2.4 Specific Fuel Consumption

The high speciﬁc fuel consumption of the ramjet below Mach 2.5 will be largely
compensated by the small duration of acceleration in the supersonic range. The total
weight of the power plant and fuel during the climb will be less than the large turbojet
designed for a high Mach. In any case there will be a large thrust margin under cruise
conditions corresponding to minimum specific consumption. If the ratio of maximum
drag coefﬁcient to cruising drag coefﬁcient is not too high, one may be tempted to
decrease the proportion of the turbojet still further. However, it must then be ensured that
the sea level thrust is sufﬁcient for take-off.
2.5.3 Features of Turboramjet

The lightness of the ramjet fully justiﬁes its use, alone or in combination with the
turbojet, even under conditions in which it is very much inferior thermodynamically to
the turbojet. This lightness is due to the total absence of moving parts and low value of
loads due to internal pressure. Moreover, hot regions are cooled by air at a temperature
equal to the stagnation temperature of ambient air, which is the lowest value obtainable.
If the range is not too important, simpliﬁcation may be made in the turboramjet engine
with a view to reduce its weight.

The turboramjet has other virtues that are not obvious through thermodynamic

analysis:

31

a) It is ﬂexible so that its characteristics can be modified during manufacture or
even after the ﬁrst few ﬂights. The modiﬁcation may be incorporated either in
variation in the drag of the aircraft or with changes in the speciﬁcations.

b) There is no need to have a turbojet capable of working at the maximum Mach
number. It can be switched-off on reaching its design maximum Mach, and
then kept in slow wind-milling in order to maintain ﬂow of liquids in pipes
and at bearings.

This kind of operation is made easy by the coaxial arrangement, which results in
the turbojet remaining in the subsonic environments, the Mach number in the plane of the
inlet being of the order of 0.4 to 0.5 on the average. In the exit plane around the turbojet,
the Mach number is of the same order of magnitude. This arrangement greatly eases the
problem of re-lighting the turbojet when the aircraft comes down to lower Mach number

where operation of turbojet is possible.

Finally, the period required for the development of a ramjet around a turbojet is
quite short as soon as some experience has been acquired through previous tests. Similar

arrangements were investigated in Nord Aviation of France and CIAM of Russia.

32

CHAPTER 3
SOFTWARE COSIDERATIONS FOR THE TURBORAMJET
3.1 Engine Layout Criterion

The performance of the turboramjet engines largely depends on the layout used to
integrate different parts of the two engines involved. The criterion advocating the layout
is the principle of the use or non-use of a part of the gasturbine engine’s free power to
compress air ﬂow in the ramjet part (gasturbine energy transfer to the ramjet part). An
advantage for using the layout that transfers energy to the ramjet parts is that an increase
in the engine thrust at take-off and low ﬂight speeds is achievable. This layout, however,
is advantageous when a turbofan engine is used in place of a turbojet in combination with
the ramjet [Sosounov, Tskhovrebov, Solonin and Palkin 1992].

Turboramjet without energy transfer to the ramjet part is just a typical
combination of a gasturbine and ramjet engine used on ﬂight vehicles for that the
trajectory consists of climb, acceleration, cruise and decent. In this group it is possible to
have two types of engines:

a) One that has a common combustion chamber for both turbojet and the ramjet

b) Another that has separate combustion chambers for each of the two engines
Since this project is conﬁned to the use of a combination of turbojet and the ramjet for a
high—speed commercial aircraft, the study is restricted to the turboramjet engine without
energy transfer to the ramjet part. Moreover, separate combustion chambers are used for

each of the two engines involved, which are restricted to the use of kerosene fuel only.

33

3.2 Software Development for the Selected Layout
3.2.1 Capabilities of the Software

The software for the turboramjet under study is developed with a view to:

a) Allow the user to furnish the selective design parameters of his choice.

b) Fix engine geometry in the light of these parameters.

c) Observe ﬂow conditions at different locations of the engine based upon the
selected design conditions. Both on-design and off-design operations are
covered.

(1) Select automatically the appropriate mode of engine operation, turbojet alone,
combination or only the ramjet.

e) Suggest measures for some “out of ﬂight envelop” operations.

f) Display on screen and store in an output ﬁle the ﬂow properties at different
stations (Section 3.4) of the engine.

3.2.2 Salient Features of the Software

The software has many built in features that enhance the conformity level to the

real aircraft engine design. Some of these are:

a) The calculation of free stream conditions for the selected altitude.

b) Automatic adjustment of the wedge to ensure maximum pressure recovery

through shock waves at supersonic ﬂight speeds.

c) Considerations of maximum thermal limit both for turbojet and the ramjet

that are made user-defined for enhancing the ﬂexibility for the designer.

(1) Inclusion of diffusers before combustion chambers to ensure existence of

ﬂow conditions suitable for a practical combustion process.

34

3.2.3

e) Automatic checking of the choking conditions both at the intake and
combustion chamber under the prevailing ﬂight conditions and adjustment
of wedge to alter the ﬂow conditions to avoid choking problems.

f) The exhaust nozzle adjustment to remain choked at the throat and fully
expanded under all ﬂight conditions.

g) Inclusion of component efﬁciencies to simulate an engine as close to
reality as possible.

h) Use of logic for the mode of operation of the engine, i.e., to decide
whether to run turbojet, combination or the ramjet alone under the
prevailing conditions.

i) Upon reaching the maximum user deﬁned ram burner thermal limit,
providing the user with the following two options:

i. To stop the program

ii. To continue. In this case the program limits the burner temperature
to the deﬁned limit and calculates the ﬂow properties at further
higher Mach numbers. In this case the program stops when the
engine thrust drops to zero.

Assumptions for the Software Development

a) The ﬂow is assumed to be one-dimensional and steady throughout.

b) The diffuser exhibits 4% stagnation pressure loss along its length under all

ﬂight conditions.

c) The diffusers installed prior to turbojet and the ramjet combustion chambers to

reduce the ﬂow velocity to the user-deﬁned valve are isentropic.

35

3.3

d)

e)

Axial velocity component across the compressor and the turbine remains
constant.
The combustion process follows the Raleigh line i.e. the combustion chambers

of both the engines are constant area ducts.

Salient Features of the Selected Engine Layout

a)

b)

C)

d)

g)

h)

i)

j)

k)

The turbojet is incorporated at the inner core whereas; the outer annular area is
used for the ramjet.

A common intake and the nozzle for the two types of the engines.

At design point the inlet area is one square meter.

Maximum pressure recovery at the intake under all ﬂight conditions that is
ensured by a variable geometry moveable wedge.

The diffuser exit area is equally divided for ﬂow to pass through each of the
turbojet and the ramjet.

Bypass doors are kept ﬁxed at 50% under all operating conditions.

The turbojet always operates at 100% RPM.

The volume ﬂow rate (area times velocity) entering the turbojet remains ﬁxed
for all operating conditions.

The turbojet is incorporated with a convergent nozzle, which operates choked
under all ﬂight conditions.

The exhaust area of the ramjet remains equal to that of ram burner at all times.
The engine nozzle is convergent-divergent type, and always operates choked

at the throat and fully expanded at the exit.

36

3.4 The Engine Layout

For the purpose of studying the ﬂow conditions across the turboramjet, different

stations are marked along the longitudinal axis of the engine.

schematic diagram of the engine with marking of these stations.

14

@®

<9 I

ED

 

/'1

l
/ l

 

 

 

 

 

G) ®®®@

Figure 3.1 Schematic diagram of the turboramjet engine

Glossary of the stations as marked on Figure 3.1 is given in Table 3.1

 

Figure 3.1 shows the

 

 

 

 

 

 

 

 

37

 

 

 

Table 3.1 Explanation of the stations allocated to the turboramjet engine

Station Number
Station 1

Between 1 and 2
Between 2 and 3
Between 3 and 4
Station 5

Between 5 and 6
Between 6 and 7
Between 7 and 8
Between 8 and 9
Between 9 and 10
Between 10 and 11
Station 12

Station 13
Between 13 and 14
Between 14 and 15
Between 15 and 16
Between 16 and 17
Station 18

Station 19

Station 20

Flow Condition/Component

Free stream conditions

Oblique shock

Normal shock

Main diffuser

Plane of turbojet entry at bypass doors
Bypass doors

Compressor

Diffuser before turbojet combustion chamber
Turbojet combustion

Turbine

Turbojet convergent nozzle

Not presently assigned for possible future use
Plane of ramjet entry at bypass doors

Bypass doors (ramjet ﬂow)

Diffuser before ramjet combustion

Ramjet combustion

Ramjet exhaust

Exit of the turbojet and the ramjet ﬂow mixer unit
Throat of main convergent-divergent nozzle

Main nozzle exit

38

3.5 Frequently Used Equations
3.5.1 General Considerations

For the purpose of this study, the ﬂow is assumed to be one dimensional, steady
and observing ideal gas law throughout. Furthermore:

a) The gas constant R has a value of 287 [J/kg K] that remains unchanged

b) The ratio of the speciﬁc heats k varies as follows:

i. All conditions without heat or energy transfer, k = 1.4
ii. Turbojet combustion and mixer calculation, k = 1.33
iii. Ramjet combustion, k = 1.30

c) Specific heat with constant pressure c,, is calculated from the relation

_ kR
"(k—I)

C

(3.1)

(1) Within one process under consideration k, R and 0,, remain constant
3.5.2 Stagnation State
The Stagnation State is deﬁned as that state which would be reached by a ﬂuid if
it were brought to rest reversibly, adiabatically, and without work. The energy equation
for such a deceleration reduces to
dh + udu = O

which may be integrated to

2

h, = h 4.“? (3.2)

Here, u is the ﬂow velocity, h is specific enthalpy of the ﬂow and the constant of

integration ho is called the stagnation enthalpy.

39

The stagnation temperature To is the temperature that would be reached upon

adiabatic, zero-work deceleration. For a perfect gas with constant speciﬁc heats

h = cpT
similarly
“2
h0 = c, 1;, = cpT+-2— (3.3)
or
T — T+—“2— (3 4)
O - 2cp '

It follows from the energy equation that if there is no heat or work transferred, To will
remain constant.

The stagnation (or total) pressure P0 is deﬁned in a similar way to To but with the
added restriction that the gas is imagined to be brought to rest not only adiabatically but

also reversibly i.e. isentropically. The stagnation pressure is thus deﬁned by:

k/(k—i)
5 = (Is) (35)
P T

3.5.3 Ideal Gas Equation
P=pRT 66)

3.5.4 Energy Equation

From the steady ﬂow energy equation is represented as
2

km = ho2 = h, +% = Constant (3.7)

Of

40

2

fl—l-_ u
n+2-m+ am

2
_2
2

3.5.5 Conservation of Mass
The conservation of mass for steady one-dimensional ﬂow becomes

~11: Constant = ,olul = ,02u2 (3.9)

m = p 1411 (3.10)
3.5.6 Momentum equation
The momentum equation assuming negligible friction at duct walls and no body

forces, is written as
m
Pr-P2='sz-“i) (3-11)

3.5.7 Mach Number
In compressible ﬂow problems a frequently used variable is the Mach number

which is deﬁned as
M = - (3.12)
c

where c is the local speed of sound in the ﬂuid. The speed of sound is the speed of

propagation of very small pressure disturbances. For a perfect gas it is given by

C=$ﬁf an)

hence

u= MJkRT (3.14)

41

3.5.8 Isentropic Flow

Many actual processes, such as ﬂows in nozzle and diffusers, are ideally
isentropic. The simple results are presented for an isentropic ﬂow of a perfect gas in the
absence of work and the body forces.

In terms of Mach number the ratio of stagnation to static properties are

T k— 1

i=1+ —M2 3.15

T 2 ( )

P0 k— k/(k—l)

$= (1+ +—2—M M2) (3.16)
l/(k—l)

3—=(1+—M ) (3.17)

,0

Using continuity equation the mass ﬂow per unit area in term of k and M can be

expressed as

(k+l)/2(k-l)

' = I’m/2M+ 1 (3.18)

 

 

Ms
>1
:1
‘7‘
3..

For a given ﬂuid (k,R) and inlet state (P010) it may readily be shown that the mass ﬂow
per unit area is maximum at M=I. If those properties of ﬂow at M=I are indicated with

an asterisk, the maximum ﬂow per unit areas becomes

 

. (k+l)/2(k—l)
m __ Pox/k( 2 j (319)
k +1

A‘ _ ,/RT,

The area ratio may thus be obtained by

42

 

(k+l)/2(k-l)
A‘lzi i{1+.k_:lM2} (3.20)
A M k +1 2

It may be noted that for a given isentropic flow (i.e. known k,R,P0,T0,n'1), A’ is a constant
so that it may be used to normalize the actual flow area A.
3.5.9 Frictionless Constant Area Flow with Stagnation Temperature Change

Combustion and evaporation or condensation processes may be analyzed through
frictionless flow in a constant-area duct in which a stagnation enthalpy change occurs.
The stagnation-enthalpy change in this process can be determined from

Aho = q — w

If subscript l signiﬁes an initial condition and 2 as the final state then the

continuity, momentum and energy equations with introduction of M and k, can be

expressed as

 

 

 

5,____1+kM,2 (3.21)
P, 1+kM22
k—l 2 k/(k-l)
1+—M
i=[HkM12] 2 2 (3.22)
P01 “'ka 1.1.5;le
2

Equation (3.22) shows that the change in stagnation pressure is directly related to the
Mach number. The dependence of Mach number on stagnation enthalpy (or stagnation
temperature) can in turn be obtained by using the perfect-gas law, the continuity

condition, and the Mach number relation
2
_T_2_ __ P2 M 2
T1 P1 M1

43

01'

 

 

 

T, 1+ kM,2 M2 2
__ = 2 (3.23)
T, 1+ kM2 M,
It can be shown that the stagnation temperature ratio is governed by
k -1 2

I2;_[l+kM12[M2)]2 1+ 2 M2 (324)
T — 1+ W2 M k -1 '

01 2 1 1+ 7 M,2

Equation (3.24) shows that the Mach number depends uniquely on the ratio of stagnation

temperatures and the initial Mach number.

In order to simplify these relationships the state corresponding to a unit Mach
number is selected as the reference state [Hills and Peterson 1992]. Using an asterisk to

signify properties at M = I , it can be shown from the above equations that

T _( 1+k TM, (325)
T'— l+kM2 '

 

 

k—l
2(k+1)M2(1+—M2)

 

 

 

 

 

 

T0 2
T' = (1+kM2)2 (3'26)
0

P 1+k
P" = 1+kM2 (3'27)
P 2 k/(k-l) 1+ k _1 k/(k-l)

3 =(——) ( k2)(1+—M2) (3.28)
100 k+l 1+kM 2

It may be observed that increasing the stagnation temperature drives the Mach
number towards unity whether the flow is supersonic or subsonic. After the Mach number

has approached unity in a given duct, further increase in stagnation enthalpy is possible

only if the initial conditions change. Under such condition the flow is termed as

“thermally choked”.

When the stream is subjected to energy transfer, it is noted that the stagnation
pressure always drops when energy is added to the stream and raises when energy is
transferred from the stream. Thus, whether the flow is subsonic or supersonic, there may
be signiﬁcant loss of stagnation pressure due to combustion in a moving stream.
Conversely, cooling tends to increase the stagnation pressure.

3.5.10 Shock Waves
3.5.10.1 Normal Shock

The conditions on the upstream side of the normal shock are denoted by subscript
l and that on the downstream side by subscript 2. The equations below assume steady,
one dimensional and adiabatic flow with no change in area across the shock because of its
extremely small thickness.

In terms of k and M these relations are

£_ £1)(Lk-:_) ﬂ 2
1“,"(H 2 M1 k—1Ml 1 2(k-1)Ml (3'29)

 

 

 

P, 1
I =?2+—(1M M, 1+1] (3.30)
2
LL- _[ (“1)M 2] (3.31)
2+(k-1)M
(k—1)M,2+2
= .2
M2 \/2kM,2—(k—l) (33)

45

3.5.10.2 Oblique Shock
The normal shocks are a special case of flow discontinuities. The general
situation observed in practice is for the shock to be inclined to the direction of ﬂow as

shown in the Figure 3.2. These are called oblique shocks.

Deﬂected ﬂow

Oblique shock
M1. 01 \é/ﬁy M2. 112

Flow stream

Figure 3.2 A flow stream through oblique shock
The ﬂow illustrated as a streamline in Figure 3.2, approaches the shock wave with

a velocity u), Mach number M I, and at an angle ,6 with respect to the shock. It is turned
through an angle 6 as it passes through the shock, leaving with a velocity u; and a Mach
number M2 at an angle (,6—6) with respect to the shock. One of the streamlines could be
replaced by a solid boundary, which would represent flow around a wedge or concave
comer with an angle ,3.

Equations for calculating the change in pressure, temperature, and Mach number
across a normal shock may be used to calculate these changes across an oblique shock by
using the normal components. It implies that whenever the term M1 appears in the
equations for the normal shock, it is replaced by the normal inlet component M In, such
that

M1,, = M1 sin 6 (3.33)

For the oblique shock these relationships are

46

:1 It?!

P

N

l

22:, (k+l)M12n
P1

M,2 sinzw‘g )=(

1
k+l ln—k+1)

2+(k-1)M12n)

(k-1)M12n +2

 

2W12n —(k-1)

47

=[1+"—;—1Mf.)(13_£1M'2"'11/[

[2k M2 k—

1

(k+l)2

MT)

2

In

M

(3.34)

(3.35)

(3.36)

(3.37)

CHAPTER 4
DESCRIPTION OF THE SOFTWARE OPERATION
4.1 Introduction

In this chapter the rationale and methodology of the software for the turboramjet
engine are discussed. It explains how the evaluation of ﬂow conditions at various stations
(Table 3.1) was made possible through the use of equations referred in Chapter 3. The
topics discussed in this chapter follow the same order as appeared in the software.

A general rule followed in calculating ﬂow properties is that from the known
conditions at some point an endeavor is made to ﬁrst ﬁnd out the ﬂow Mach number and
then various functions (Appendix A) are used to calculate the respective ﬂow properties.
4.2 The Software Structure

The software developed for the turboramjet operates in two steps:

a) At ﬁrst the design program is run based upon a number of design parameters
the user wishes to select. A list of required parameters along with the
respective practical ranges appears on the screen to facilitate the user. This
part of the program ﬁxes the engine geometry, and the output is stored in a
ﬁle.

b) Considering the known engine geometry obtained from the design program,
the main program is run. The user is required to input only the desired flight
Mach number and the altitude. The program itself calculates the required
parameters and the pertinent ﬂow conditions at all the stations of the

turboramjet engine both for on-design and off-design ﬂight conditions.

48

4.3 The Flow Chart

In the next four pages the ﬂow chart of the software is presented in the form of
block diagram. Each block represents a subroutine for that the respective details will be
discussed in the following sections. Some parameters required for decision making are
also shown in rectangular blocks. The representation is done using the standard symbols

for the flow charts as far as possible.

49

 

C sum 3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

¢ M|>1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MPLOSS
l 4'
SONIC
OBSHOCK
NSHOCK

 

 

 

 

 

 

 

 

 

.3

Figure 4.1 Flow chart of the software

50

AC2A3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

FIND T07

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 4.1 (Continued)

51

 

 

 

 

FUEL

 

 

@ o

 

 

 

 

 

M1

 

 

WEDGE

 

 

 

 

 

 

INLETCH

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

M1<1
RJMACH
COMPRESSOR
V M,j >M, i
M .
<\> COMBUSTOR
MU >M] i
TURBCOM
, 1
ma -m,,j,ril,j —O TURBINE
TJNOZL

 

 

 

 

 

 

 

52

Figure 4.1 (Continued)

GD

 

 

 

 

TJ OUT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

RJDIF
BURNER
r
+
RAMCOM
M 1.5 (M15
M ,‘5 / i
. RJBLEED
M15 )M15

RJEXIT

MIXER

NOZZLE

 

 

 

 

 

 

1
(END)

Figure 4.] (Continued)

53

4.4 The Atmosphere

The domain of the air breathing engines extends up to almost 30,000 meters above
sea level; however, the regularly used altitude for the supersonic transport stays within
18,000 to 21,000 meters. In line with the altitude requirement of the turboramjet the
present study is restricted up to 30,000 meters and US. Standard Atmosphere (1962) is
used as a reference.

The earth’s surface is generally regarded as divided by altitude into regions.
Closest to the earth surface is the troposphere that extends up to a height of about 11,000
meters and has speciﬁc temperature and pressure variation terminating into the
tropopause. Above this is the stratosphere that extends from tropopause to the
stratopause at about 51,000 meters. In this region up to the air breathing range, the
temperature stays constant.

4.4.1 Variation of Temperature and Pressure with Altitude
In the troposphere the atmospheric variation is deﬁned by a constant lapse rate or

decrease of temperature (denoted by k) and has a value equal to -0.0065 K/geopotential

meter. With a deﬁned standard sea-level condition the variation in temperature and

pressure can be established by using hydrostatic and perfect gas equations as follows:

T=(T,—/1Z) (4.1)

and P = P, [1 — (,1 Z/T,)]%1R (4.2)

In the above two equations:
a) T and P are the temperature and pressure respectively required to be calculated

at altitude Z

54

b) T; and P1 are the temperature and pressure respectively at standard sea-level

conditions

c) )1 is the lapse rate and R is the gas constant

Beyond troposphere up to the air breathing range, the temperature stays constant.
The variation of pressure, however, is governed by the relationship that has been

established with the use of hydrostatic and perfect gas equation

’1? = exp[(z, — z)/RT] (4.3)

Owing to the existence of an isothermal or quasi-isothermal region, there is a
good reason for an altitude of about 11000 meters being a common cruising altitude for
long-range transport aircraft. It is because, within the air breathing range, the lowest
temperature is encountered at 11000 meters that benefits the turboengine performance
[Shepherd 1972].

4.5 Free Stream Conditions

Considering the user input of the ﬂight Mach number and the altitude, the
program runs the subroutine ALTITUDE and returns the values of static temperature and
pressure. Assuming constant values of R and k, the other ﬂow parameters can be

calculated as follows:

a) Velocity from equation (3.14), u = M J kRT

b) Density from ideal gas relation (equation [36]), P = p RT
c) Equation (3.1) is used to calculate c,,

d) Enthalpy is evaluated by using equation (3.3), h = cpAT

e) Stagnation conditions:

55

i. Enthalpy from equation (3.2), ha = h + uz/Z
ii. Temperature To by using function 'I'I‘KM
iii. Pressure P0 from function PTKM

iv. Function DTKM is used for calculating density p0

4.6 Intake System

Since the engine under study is designed for higher supersonic speeds, the design
parameter selected for the intake design is the maximum pressure recovery. Another
important consideration was to have a common intake system both for the turbojet and
the ramjet. The efforts were aimed at designing an intake that could provide satisfactory
operation over a wide range of ﬂight Mach numbers with minimum pressure losses
encountered to the airﬂow.

An external compression supersonic intake located at the nose section of the
aircraft is selected for this purpose. The intake embodies a wedge for the shock formation
during supersonic ﬂights. The wedge designed for this intake is of variable geometry and
capable of changing its shape and position in the intake according to the prevailing ﬂight
conditions. For subsonic ﬂight the wedge moves fully inside the intake rendering it able
to behave as a simple pitot intake. Under supersonic conditions the wedge adjusts its
shape and position such that both the oblique and the normal shocks are always located
on the intake lip. In other words the intake always operates in critical mode and hence
maximum pressure recovery is ensured under all operating conditions.

4.6.1 Subsonic Flight
Keeping in mind the role of the engine under study, it is expected that the user

will always opt for a supersonic Mach number for the design program operation. As

56

such, the subsonic ﬂight conditions will be encountered only during off-design ﬂight
conditions of the engine. Moreover, the turbojet alone covers most of the subsonic ﬂight
regime, and the ramjet gets into operation close to transonic Mach range. The ramjet
operating Mach number depends upon the prevailing ﬂight conditions based upon that the
software calculates the minimum Mach number at that the ramjet assumes operation (See
Appendix C).

One of the design considerations for the turboramjet is that the volume ﬂow rate
(area times velocity entering the intake) remains constant for the turbojet unless the intake
is choked. In the subsonic range depending upon the ﬂight speed and the mass ﬂow
demanded by the engine, the inlet might have to operate with a wide range of incident
stream conditions. The streamline patterns for two typical subsonic conditions are shown

in Figure 4.2.

 

Figure 4.2 Typical stream pattern for subsonic inlets [Courtesy Hills and Peterson 1992]

During level cruise the streamline pattern may include some deceleration of the entering
ﬂuid external to the inlet plane. Under these conditions the upstream captured area A; is
less than the inlet area (Figure 4.2[a]). During low-speed high-thrust operation (take-off
and climb), the engine demands more mass ﬂow and the stream pattern resembles Figure

4.2(b). In this case the captured area will be more than the inlet area. It indicates a ﬂight

57

condition where the joint operation of the two engines is not possible. The mass ﬂow rate
barely meets the turbojet demand by being accelerated at the entrance of the intake to
maintain constant volume ﬂow rate.

The software makes use of this fact and does not allow ﬂow to pass through the
rmnjet if the captured area is greater or equal to the intake area. In such a case only the
turbojet operation is possible. Even if at some ﬂight condition, the intake area becomes
greater than the captured area, the ﬂow is not directed to the ramjet until the time
minimum Mach number for the ramjet operation is achieved.

Since there is no shock formed at the intake, the ﬂow conditions at the plane of
entry remain the same as that of free stream. The mass ﬂow rate entering the intake is
calculated with the help of continuity relation (equation [3.3]).

4.6.2 Sonic Flight

At the sonic ﬂight Mach number the wedge remains fully in and the intake has a
simple pitot conﬁguration. A normal shock is formed at the entry of the intake and the
ﬂow properties are obtained using normal shock relationships, equations (3.29) through
(3.32). The software handles these calculations through subroutine SONIC.

4.6.3 Supersonic Flight

At a supersonic Mach number the wedge assumes a shape and transverse location
in the intake such that the intake operates in critical mode. The software calls the
subroutine MPLOSS that determines the wedge geometry and location for critical
operation of the intake. A detailed analysis follows in Section 4.7. The software
calculates the ﬂow properties after the oblique shock by calling subroutine OBSHOCK.

Another subroutine NSHOCK is called for the properties after the normal shock. These

58

subroutines make use of equations (3.29) through (3.37). At this stage, however, in order
to ﬁnd out other properties of the ﬂow, the software follows two different approaches:

a) At the design point it is assumed that with the corresponding position of the
wedge the intake area is one square meter [Section 3.3 (c)]. Hence the
continuity equation and other relevant functions (Appendix A) are used to ﬁnd
out the mass ﬂow rate and the stagnation conditions respectively.

b) For off-design operation the wedge adjusts itself for critical intake condition
and the intake geometry changes. The intake area calculation will be discussed
in Section 4.8. After having known the new intake area the procedure as
discussed in paragraph (a) of this section is adopted for calculation of other
properties of the ﬂow.

4.7 Wedge Design Calculations

Figure 4.2 shows the schematic diagram of a wedge with physical and geometrical

 

 

 

     
  

 

 

 

 

 

 

details.
Intake Cowl

Oblique

ShOCk 7 yz

Y:
> 11!
Air Flow II: Central Axis
x of the Wedge

Figure 4.3 Half wedge showing shock formation and geometrical details

Since the wedge is symmetrical about its longitudinal axis, the Figure reﬂects only

the half wedge with 6 as semi-vertex angle and ,6 as ensuing oblique shock angle under

59

critical condition. Furthermore, for a two-dimensional analysis the half wedge may be
considered a right angle triangle with base as x and height at inlet plane as y), Under this

condition the inlet radius is represented as y;.

The ﬁrst objective is to ﬁnd out the values of 6 and ,6 that correspond to the
critical operation of the intake for a given ﬂight Mach number. After having known these
values a relationship between 6, ,6, x, y) and y; may be established.

4.7.1 Maximum Pressure Recovery

For supersonic ﬂights, pressure recovery is the ratio of stagnation pressure of the
ﬂow after it has passes through the shock system to the free stream stagnation pressure.
For a given ﬂight condition maximum pressure recovery will be established with some

values of 6 and ,B which satisfy the following relation between the two

(k + 1)M 2
C019 = tan/3 [m -1 (4.4)

where M1,, = M 1 sin 6 is the normal component of the free stream Mach number at the

oblique shock.

The correct values of 6 and ,B are obtained through iterative process in that for
some value of ,6 corresponding value of 6 is calculated followed by the pressure recovery.
,6 is varied in small step and new pressure recovery thus obtained is compared with the

previously calculated value. The iteration stops where maximum recovery is obtained and

corresponding values of 6 and ,6 are picked up for subsequent use.

The lowest value of ,6 is determined from the Mach wave relation

60

_ . -1 _1_
6",,“ —51n [M ] (4-5)

1
After obtaining on set of 6 and 6 values, the software calculates the other related

parameters in the following sequence:

a) The Mach number after the oblique shock from equation (3.37)

 

(k—1)M,2,, +2]

M: Sin2(ﬂ_6)=[2kM2 -(k—l)
In

b) The stagnation pressure ratio after the oblique shock is obtained from

P0, (k +1)M,2,, """'" 2k 2 k -1 "“""
—= 2 — M," — — (4.6)
P0, 2+(k—1)M,,, k+1 k+1

c) If the Mach number after the oblique shock is supersonic then:

 

i. Equation (3.31) is used to ﬁnd Mach number after the normal shock

 

ii M_ (k—1)M,’-+2
' 3 2kM,2-(k—1)

iii. Stagnation pressure ratio across the normal shock is calculated with the

help the following equation

2 k/(k-l) l/(l-k)
—= 2 " M2 _ (4'7)
19,,2 2+(k-—1)M2 k+1 k+1

d) If the Mach number after the oblique shock is subsonic:

 

i. M3 is equal to M2

ﬂu. = ﬂ;
P02 P01

ii.

e) The overall stagnation pressure drop across the two shock waves (pressure

recovery) thus can be obtained as

61

ﬂ); = £03. x 592. (4.8)
P01 P02 P01

1) ,6 is increased with a step size of one-tenth of a degree and iteration continues

till the time maximum value of the pressure recovery is achieved.

4.8 Intake Area Calculation
4.8.1 Subsonic Flight Conditions

At the design point the inlet radius yz is calculated that remains unchanged for any
other ﬂight condition for the same design. Since under subsonic ﬂight conditions the
wedge is fully receded inside and conﬁgures the intake to simple pitot type, its area can
simply be obtained as

A, = 7r y§ (4.9)

4.8.2 Supersonic Flight Conditions

At the design point the intake area is assumed to be one square meter. For any
off—design ﬂight condition the wedge adjusts itself for maximum pressure recovery giving
new values of 6 and ,6. Accordingly, the new values of base of the wedge x and wedge

height at inlet plane y, are obtained. The intake area under such condition is calculated

from the right angle triangle rule such that

1‘:er (tanZﬂ—tan26) (4.10)

and 113:7: (yg-yf) (4.11)

 

The calculation of the inlet area in all the cases is done through subroutine INLET.

62

4.9 Programming for Diffuser

By the time the ﬂow enters the intake, its velocity reduces to a subsonic Mach
number. In order to have a suitable Mach or the velocity of the ﬂow at the compressor
face, ﬂow is made to pass through a diffuser. The criteria for the ﬂow condition at the
compressor is:

a) The axial ﬂow approaching a subsonic compressor should not be much higher

than 0.4 [Hills and Peterson 1992]
b) The axial velocity at compressor entry remains within a value 150 meter per
second [Kuchemann 1953] and [Hills and Peterson 1970]

For the engine design under study, option (b) is selected and the software uses the
maximum velocity limit entering the compressor (velocity limit at diffuser exit) as the
user input. This option is selected with a viewpoint of a common user who may have
more familiarity with the velocity parameter over the Mach number

While the ﬂow passes through the diffuser, a rise in static pressure and reduction
of the velocity (to a practical value) is achieved at the diffuser exit. Since the efﬁciency
of the diffuser is a function of the ﬂight Mach number, the ratio of the speciﬁc heats and
stagnation pressure ratio across diffuser, its handling especially in off-design conditions
becomes complicated. However, to include the effect of diffuser efﬁciency a conservative
approach is followed, and it is assumed that the flow encounters 4% stagnation pressure
loss across diffuser under all ﬂight conditions.

Since the ﬂow through the diffuser is essentially adiabatic with no work transfer,
ho, To, k and c,, of the ﬂow remain unchanged across diffuser. Calculation of other ﬂow

conditions at diffuser exit is discussed in the subsequent sections.

63

4.9.1 On-Design Performance
At the design point the diffuser exit velocity, u.,, is user deﬁned, T04 remains the
same as T03 and cp is assumed constant. The static conditions T4 and P4 are obtained using

equations (3.4) and (3.5) respectively. Latter p4 is obtained from ideal gas relation

(equation [36]) followed by diffuser exit area A4 from the continuity relation (equation
[310]). Equation (3.14) is used to calculate the Mach number. Relevant functions are
then used for evaluation of other ﬂow properties.
4.9.2 Off-Design Performance

For off-design operation the known parameters are T04, P04, A4, and the mass ﬂow
rate :12. For known k and gas constant R, the Mach number at the diffuser is ﬁrst
calculated from the function XMACH (Appendix B) followed by T4 and P4 from
respective functions [Appendix A]. W is then found out from Mach number (equation

[314]) and p; from ideal gas relation (equation [36]). For h equation (3.3) is used.

After having calculated the ﬂow properties at diffuser exit, the conditions at the
entry of bypass doors are known.
4.10 By-pass Doors

At the main diffuser exit the bypass doors are installed, which allows the ﬂow to
enter either the turbojet or the ramjet or, in case of joint operation, to both. The doors are
attached with the turbojet compressor casing and can be actuated to increase or decrease
the incoming ﬂow area for either of the engines. However, for the present study the
bypass is kept ﬁxed at 50% such that physically the doors remain parallel to the

longitudinal axis of the engine at their position under all operating conditions.

4.10.1 On-Design Conditions

Based upon the design conditions, the calculated area of the diffuser exit is
divided into two equal halves: one half each assigned to the turbojet and the ramjet. This
corresponds to stations (5) and (13) respectively to the turbojet and the ramjet in Figure
3.1. The local ﬂow conditions at these two stations will be the same as that of station (4),
the diffuser exit, since the ﬂow has not yet passed through the bypass doors. The software
uses the subroutine DOORS for evaluating ﬂow conditions at stations (5) and (13).

At this stage half of the mass ﬂow available at the diffuser exit is assumed to be

entering in each of the two engines isentropically such that
1
Turbojet mass ﬂow = Ramjet mass ﬂow = 5(Total mass ﬂow captured by the combjet)

Across the bypass doors the ﬂow reaches at the plane of entry of the two engines,
station (6) for turbojet and (14) for the ramjet. Since the ﬂow is isentropic, the stagnation
conditions do not change. The other ﬂow properties at the two engines entry are evaluated
as follows:

a) For the turbojet it is assumed that the volume ﬂow rate (area times velocity)

remains constant [Section 3.3(h)]. At design point it is termed as the “engine

demand”. Using continuity equation at stations (4) and (6) reveals that

m, = 124144244 (4.12)

and r516 = p6u6A6 (4.13)
. m4 A4
but m6=7 and [16:3-

Therefore equation (4.10) becomes

65

2.11 : P6115 A4
2 2

or m, = ,06u6A4 (4.14)
Since at low Mach numbers such as at stations (4) and (6) the air behaves as an
incompressible ﬂuid
.06 = .04
and equation (4.13) may be written as
r51, = p4u6A4 (4.15)
Comparing equations (4.12) and (4.15) it can be seen that
u,5 = u4 (4.16)
If the ﬂow velocities are same at two stations, it can be proved from the
isentropic relationships (Section 3.5.8) that for the unchanged stagnation
conditions, static conditions of the ﬂow will also be the same.

b) At the entry to the ramjet the same argument applies, and it is concluded that
the ﬂow properties as calculated at the diffuser exit are valid at the plane of
turbojet and the ramjet entry except for the mass ﬂow rate and the respective
areas which are reduced to half.

The ﬂow velocity entering the turbojet at the design point has an important
signiﬁcance. When the bypass doors are ﬁxed at 50 %, the area of turbojet entry
calculated at the design point will remain unchanged for the same design under all
operations and the engine demand (assumed always ﬁxed) will solely be governed by this

value of the ﬂow velocity. In the software this velocity is described as the “fixed velocity”

66

and denoted by Vf. The ﬂow calculations at the entry of the two engines are done through

subroutine ENGENTRY.

4.10.2 Off-Design Conditions

3)

b)

The ﬂow through the turbojet is governed by the assumption of a fixed
volume ﬂow rate unless the intake is choked. The stagnation conditions at the
turbojet and ramjet entries remain the same as that of the diffuser exit. The
other properties, however, may be calculated keeping in mind the rationale of
the ﬁxed velocity that is also known under off-design conditions. Static
temperature, enthalpy and Mach number are found using the deﬁnition of
stagnation temperature (equation [34]) and the Mach number (equation
[312]) respectively. Static pressure and density are then calculated from the
functions PKM and DKM respectively (Appendix A) followed by mass ﬂow
rate through the turbojet from continuity (equation [310]). Subroutine
TJENT RY is used for these calculations.

From the known stagnation conditions at the ramjet entry (same as the diffuser
exit), the Mach number is ﬁrst obtained from the function XMACH
(Appendix B). Respective functions are then used to calculate static
temperature, pressure, and density and equation (3.3) for enthalpy. After
having known all the relevant parameters, the ﬂow velocity is evaluated from
the continuity equation. These calculations for the ramjet are performed using

the subroutine RJENTRY.

67

4.11 Compressor

The study assumes usage of an axial ﬂow compressor for which the compression
ratio (7,) and the adiabatic efﬁciency (77,.) are user deﬁned. Furthermore, the ﬂow velocity
across compressor is assumed constant (Section 3.2.3). Hence

u7 = u,5

The attention, however, is focused on the calculation of ﬂow properties across the
compressor treating it as one unit. As such inter-stage ﬂow conditions are not addressed.

From the two known parameters (ye and 77C) of the compressor, the stagnation

pressure rise is ﬁrst obtained from

P07 :(7cXPO6) (4.17)
The ideal stagnation temperature (T077), that could have been achieved through an
isentropic process at the compressor exit is calculated from isentropic relation, equation

(3.5), such that

k—I

T071 -_— T06 (7c )T (4-18)

After having known T07), the actual stagnation temperature at compressor exit may be

obtained from the deﬁnition of the adiabatic efficiency of the compressor ( 7],)

(71m - T06)
”C = —— (4.19)
(71) " T06)
such that
To, = T06 + M (4.20)

77.

68

The other stagnation conditions p07 and hay are calculated from the equation of state and
equation (3.3) respectively.

For the static conditions the assumption of constant axial velocity across
compressor is used, and T7 is obtained from deﬁnition of hay (equation [34]) followed by
Mach number from equation (3.12). The functions PKM and DKM (Appendix A) are

called for obtaining P7, and p7, and for In equation (3.2) is used.

Rise in stagnation enthalpy reﬂects the compressor work such that

Compressor Work = ho7 — ho6 (4.21)

4.11.1 On-Design and Off-design Calculations

The procedure followed in the software to calculate design and off-design
conditions is the same except that at the design point the compressor exit area is
evaluated using the continuity equation whereas, in the off-design mode, ﬂow conditions
are obtained assuming the known exit area of the compressor. The software uses the
subroutine COMPRESSOR for all these calculations.
4.12 Diffusers Before Combustion

The performance of the air-breathing jet engine strongly depends upon the mass
ﬂow rate per unit cross-section area of the engine. Keeping in mind the continuity relation
(equation [310]) the requirement of a larger mass ﬂow for a given ﬂight condition may
be met in two ways

a) By having a larger cross-sectional area of the engine, but it induces higher

drags and weight penalties
b) Allowing higher velocity ﬂow entering the engine to compensate for small

frontal area

69

A velocity limitation is, however, imposed by the combustor since it is necessary to
maintain a stationary ﬂame within a moving air stream. A ﬂame remains stationary in a
traveling mixture of reactants if the speed of the ﬂame relative to the reactants is just
equal to the reactant-mixture velocity. For this purpose it is desirable that the average
velocity of the reactants passing through the combustor is of the order of 30-60 m/s
[Cohen, Rogers and Saravanamuttoo 1987].

In the software the velocity limitations in terms of Mach number entering the
combustion chamber are made user deﬁned. While giving inputs for the design of the
engine, the user is expected to feed a velocity within the speciﬁed range entering the
combustion chamber. The software handles the velocity limitation criteria through the
subroutines COMBDIF and RJDIF for the turbojet and the ramjet respectively. In both
the cases the software assumes an isentropic diffuser installed before the two combustion
chambers in order to reduce the ﬂow velocity in accordance with the input conditions.
4.12.1 On-Design Performance

For the isentropic diffuser the stagnation properties of the ﬂow remain unchanged
at the diffuser exit. With the help of known (user deﬁned) ﬂow velocity the static
temperature is calculated ﬁrst using equation (3.4) followed by Mach number from
equation (3.14). The static properties of the ﬂow may then be obtained using the
respective functions (Appendix A) and the diffuser exit area from the continuity relation,
equation (3.10).

4.12.2 Off-Design Performance
Stagnation ﬂow conditions at the diffuser exit are known from its isentropic

behavior. Mach number is obtained from the function XMACH and the respective static

7O

properties from the relevant functions (Appendix A). Velocity at this point is calculated
from the Mach relation, equation (3.14).
4.13 The Combustion Process

The function of the combustion chamber is identical for a gas turbine or a ramjet
engine. The objectives are to introduce and burn fuel in the compressed air ﬂowing
through the combustion chamber with minimum pressure loss and with as complete a
utilization of fuel as possible. In the aircraft jet engines a fresh supply of air is
continuously maintained and the direct method of burning fuel in the working stream is
employed. For a one-dimensional steady ﬂow, this process of combustion is analogous to
a ﬂow process in a constant area duct with stagnation temperature change and is
described by the Raleigh process (Section 2.3.3.2).

For the work under study, the combustion chamber for the turbojet is termed as
“combustor” and that for ramjet as “burner”. In both the engines the combustion process
is tackled by assuming that the ﬂow observes the Raleigh line. The attention is focused to
determine the ﬂow properties and combustion parameters at the end of combustion
process without addressing ﬂow conditions within the combustion zone. An annular type
of combustion chambers layout is considered with a stable combustion process over a
wide range of operating altitude and the forward speed. The losses in the combustion
process are addressed by including: i

a) A user defined combustion efﬁciency (77),)

b) A ﬁxed 2% stagnation pressure loss under all operating conditions to

compensate for the presence of ﬂame holders in the burning area

71

4.13.1 Combustion Calculations at the Design Point
4.13.1.1 Turbojet Combustion

The known conditions at the combustor exit, station (9), are:

a) The stagnation temperature (T09) that is also the turbine inlet temperature
b) The area (A09) from the Raleigh process consideration that assumes a constant
area heat addition process

Considering the known parameters, the software first evaluates the chamber inlet choking
temperature 7;; from the Raleigh line stagnation temperature ratio (equation [326]) and
compares it with T09. The operation continues only if the stagnation temperature at
chamber exit (T09) stays lower than that of corresponding choking temperature 72;. This
condition ensures that the chamber is not choked and the combustion is possible without
changing the inlet conditions. If, however, T09 is greater than T‘; the program terminates
after suggesting that the user either enhance turbine inlet temperature limit or modify the
other design inputs for successful operation of the design program.

In the absence of the choking condition the Mach number at the chamber exit is
calculated from the critical temperature ratio (equation [326]). It forms a quadratic in
terms of Mach number, and the root representing the subsonic Mach number is picked up
as the solution. Stagnation pressure at the chamber exit is obtained from equation (3.22).
The static pressure and temperature at the chamber exit are calculated from equations
(3.21) and (3.23). The exit velocity is evaluated from the Mach relation and static and
stagnation enthalpies from equation (3.3). The software handles these calculations

through the subroutines COMBUSTOR and TURBCOMB.

72

4.13.1.1 Ramjet Combustion

Comparatively higher temperature limits are achievable in the ramjet burner

because it contains no moving parts. The maximum thermal limit (TRC), burner

efﬁciency (17),), and the fuel type are user deﬁned. The software calculates the adiabatic

ﬂame temperature (AFI‘) of the corresponding fuel, compares it with the maximum

thermal limit, and picks the burner temperature (Tom) for any of the two conditions:

a)

b)

If AFT is less than TRC, AFT is assigned as the burner exit temperature (T016).

In this case the theoretical air-fuel ratio (AF ,h) is obtained from the relation

AF”, = —"— (4.22)
mfuel

and the fuel-air ratio (f) from its reciprocal i.e.

1
AF».

 

f = (4.23)

Stagnation enthalpy (hm) is then calculated by using the relationship

combining fuel-air ratio, burner efﬁciency, and heat of combustion of the fuel

(QR)

(h016/ilo15)‘1

4.24
“QR/h015)_(hOl6/h015) ( )

W

The burner temperature (T016) is then obtained from stagnation enthalpy (ho/6)
using equation (3.3).

If AFT turns out to be greater than TRC, the program terminates suggesting
that the user either increase the TRC or change other design parameters to

make engine operation possible.

73

4.13.2 Off-Design Combustion Calculations
4.13.2.1 Turbojet Combustion
The off-design calculations for the turbojet combustion follow exactly the same
procedure as that of the design point calculations. The reason for this similarity is that the
design program is run to ﬁx the engine geometry, but for the combustion process the
Raleigh line approach is used that by default assumes constant area combustion chamber.
As such the ramjet burner area is already known by ﬁxing its diffuser geometry, and it
remains unchanged for the same design. Therefore, for any set of design conditions the
calculation procedure will remain unaltered.
4.13.2.2 Ramjet Combustion
The process adopted for the off-design calculation of the ramjet combustion is
different than the design point operation in two ways:
a) When the deﬁned temperature limit (TRC) is exceeded, i.e., AFT becomes
greater than TRC, the user has two options:
i. To limit the burner temperature equal to TRC and continue
ii. Quit the program for exceeding burner thermal limit
If the user adopts the ﬁrst option, the TRC equals T016, how is calculated from
T016, the actual fuel-air ratio (f) from equation (4.24) and the actual air-fuel
ratio (Afaa) from reciprocal of f. For the other ﬂow conditions, at ﬁrst, the

critical temperature is obtained based on the conditions at burner entry, station
(15), by using equation (3.26). It may be noted that the critical temperature To'
stays the same for both stations (15) and (16) as it describes the burner

choking condition. When His used to represent station (16), the Mach

74

number (M 16) can be obtained using the critical temperature ratio, equation
(3.26) that returns a forth order equation in M16. The subsonic positive root is
picked up representing M16, The stagnation pressure ratio (equation [328]) is
utilized to calculate P016 and to include the ﬂame holder effect; 2% of
calculated P016 is subtracted from its value. The static conditions like T16, P16

and p16 are calculated using the functions TKM, PKM and DKM respectively

and h from the product of cp and T16. Velocity is obtained from the Mach

equation and A16 is assigned equal to A15 because of the Raleigh process.

b) If the combustion temperature (T016) exceeds the critical temperature (7],. ), the
software performs calculations to limit the burner inlet Mach (M15) through an
iterative process such that Tom becomes less or equal to To'. In this case the

new ﬂow conditions at burner entry are established through subroutine
RJBLEED, the new (reduced) mass ﬂow through the ramjet is compared with
that without choking and excess mass ﬂow is bled out. The calculations for
the combustion process are then repeated for the modified input conditions at
the burner entry.
Excluding the above mentioned two conditions, the software makes use of the
same logic and relationships as used for design point calculations for the purpose of
evaluating the ﬂow properties under off—design ﬂight conditions. Subroutines BURNER

and RAMCOMB are used for these calculations.

75

4.13.1 Combustion Parameters
Some parameters associated with the combustion process are calculated in the

program that contributes in establishing engine performance.

a) Fuel mass ﬂow rate (#1,) is obtained from the product of fuel-air ratio and the

air mass ﬂow rate through the engine. Hence
m, = f Xn'ta (4.25)
b) Net mass ﬂow rate at the combustion chamber exit is the sum of air and fuel
mass ﬂow rate
the = the +n'1f (4.26)
c) Actual fuel-air ratio (i) from equation (4.24).

(1) Actual air-fuel ratio (Afaa) by taking inverse of the actual air-fuel ratio (f).

e) Excess air is obtained using the relation

AF... " AF».

AF».

 

% excess air = [ )(100%) (4.27)

f) Theoretical air (TA) is calculated from the relation
% theoretical air = 100% + % excess air (4.28)
4.14 The Turbine
The performance of the turbine is limited principally by two factors:
compressibility and stress. Compressibility limits the mass ﬂow rate that can pass through
a given turbine whereas the stress limits the wheel speed. The performance of the engine

depends very strongly on the maximum operating temperature. For a given pressure ratio

76

and adiabatic efficiency the turbine work per unit mass is proportional to the inlet

stagnation temperature.

In the software the turbine inlet temperature (T09), the adiabatic efﬁciency (77,) and
mechanical efﬁciency (mm) are made user deﬁned. As such a ﬂexibility is offered to the
user to study the changes in engine performance with varying turbine inputs. In doing so,
however, the matter of concern is to calculate the flow properties after the expansion
process through turbine and not within the turbine stages. The software handles the
calculation of ﬂow properties across turbine by calling subroutine TURBINE.

4.14.1 Operation at the Design Point

The turbine inlet conditions at station (9) are known from the turbojet combustion
calculations. The objective is to ﬁnd out ﬂow properties at turbine exit, station (10). At
ﬁrst the turbine work is calculated using the compressor work and the mechanical

efﬁciency of turbine (77,,,,) such that
Turbine Work = 77,", (Compressor Work) (4.29)

also in terms of stagnation enthalpies
Turbine Work = (hog - ha 10) (4.30)
that helps in evaluating ham and subsequently T010 by using equation (3.3).

The adiabatic efﬁciency (77,) is user deﬁned and in terms of stagnation

temperatures can be expressed as

_ (T09 ‘ Tow) (4.31)

77; _
(T09 _ 711101)

where TOIOi is the ideal stagnation temperature that could have been achieved through an

isentropic expansion across the turbine and is calculated from equation (4.31). The value

77

of Tom) is used to find out P010 from the isentropic relation between pressure and

temperature ratios, equation (3.5) such that

k

T . F
P = P 0101]
010 09[ T09

Among the remaining ﬂow properties, ham and paw are calculated using equations (3.3)

and (3.6) respectively and using the assumption of constant axial velocity across the
turbine (Section 3.2.3), T10 is calculated from equation (3.4), M10 form equation (3.12),

hm from the deﬁnition of enthalpy and P10 and p10 using functions PKM and DKM

(Appendix A) respectively. Later A10 may be obtained by using the continuity relation
(equation [310]).
4.14.2 Off-Design Operation

In the off-design calculations the software follows the same procedure that is used
in the design program. It is because of this fact that depending upon the input conditions
and the adopted procedure, the area does not contribute to the evaluation of the ﬂow
properties across turbine.
4.15 The Turbojet Nozzle

The process in the nozzle is very close to adiabatic because the heat transfer per
unit mass ﬂow is much smaller than the difference of enthalpies between inlet and exit.
Therefore, the equation of one-dimensional isentropic ﬂow can describe the nozzle
process quite well.

For the purpose of analysis, the expansion process in the turbojet nozzle is
assumed to be isentropic. A convergent nozzle is selected for the turbojet, and it is

assumed that it operates always choked whenever the turbojet is in operation.

78

From the preceding conditions it is obvious that the stagnation state at nozzle exit
(station 11) will be the same as that at its entry (station 10) and the Mach number (M1,)
will be always unity. Thus making use of equation (3.15) static temperature (T,,) is
obtained, such that

10”
k—l
1+——2 M,,

Thereafter, P“ and p), are calculated using the functions PKM and DKM respectively,

 

TH:

u), from relation, h), from deﬁnition of enthalpy and A“ with the help of continuity
equation. It may, however, be noted that mass ﬂow rate through the turbojet nozzle will
be the sum of turbojet air mass ﬂow rate and the corresponding fuel mass ﬂow rate under
that condition.
4.15.1 On-Design and the Off-Design Operation

Since the turbojet nozzle is considered to be operating always choked, its exit area
(An) can not be ﬁxed. It will keep adjusting for different conditions for the choking ﬂow.
As such, the area at the design point does not contribute to the calculation of flow
properties at any other operating conditions and the procedure adopted for calculating on-
design and the off-design ﬂow conditions remains the same.
4.16 The Mixer

The mixer is the cylindrical channel having a diameter equal to the outer diameter
of the engine. It is installed between the exhaust of the ramjet (station 17) and the entry of
the main convergent-divergent nozzle (station 18) of the turboramjet. Combustion

products from both turbojet and the ramjet enter into the mixer. The two jet streams are

79

mixed such that fully stabilized and steady ﬂow is achieved before entering into the
exhaust nozzle.
4.16.1 On-Design Calculations

The mass ﬂow in the mixer is the sum of the mass ﬂows out of the two engines.

The mass ﬂow from the turbojet is
751,, = (ma 11+(mf)11

similarly, the ramjet contribution of the mass ﬂow is

mm = (ma [7 +(mf ),7
where n'za and m, are the mass ﬂow rates of air and fuel and the subscript 11 and 17
indicate the ﬂow from turbojet and the ramjet respectively.
The total mass ﬂow in the mixer becomes

mm = #1,, +rh,7 (4-32)
The molecular weights (MW) of the ﬂow from the turbojet and the ramjet are obtained
from the analysis of the respective combustion products. The combustion products are
assumed to consist of nitrogen, oxygen, water vapor and carbon dioxide. In each case the
fraction of constituent gases in the combustion product is multiplied with their respective

molecular weights and added up. The subroutine IGPROPL is used to calculate the

molecular weights.

The mole ﬂow rate ( N ) entering the mixer can now be found from
N = __ 4.33
MW ( )

such that

80

N,, = N,, + A7,, (4.34)
The molar composition of the turbojet and the ramjet exhaust gases entering into the
mixer are calculated from the subroutine IGPROPL. At the mixer exit the molar
composition of the turboramjet is obtained by ﬁrst multiplying the composition of the two
exhausts with the respective mole ﬂow rate and the sum of the two compositions is

divided by the total mole ﬂow rate. Thus

N,, (Turbojet composition) + N ,7 (Ramjet Composition)
N13

The stagnation enthalpy at the mixer exit (hora) is calculated from the energy

 

Combjet Molar Composition =

equation
hora : hon +h017 (4-35)

and stagnation temperature is obtained from the enthalpy deﬁnition

T _ 11018
018 _
C

P

(4.36)

The velocity (“18) and pressure (P13) are obtained by simultaneously solving the ﬂow
equations of ﬁrst law of thermodynamics, conservation of mass, momentum integral and
the ideal gas relation. The procedure is elaborated in appendix D.

Once 1418 and P13 are known, .T’8 is obtained from temperature and velocity

relationship (equation [34]), pm from continuity, Mach number from equation (3.12) and

functions PTKM and DTKM are used to calculate P013 and p018.

81

4.16.2 Off-Design Calculations
During off-design conditions as long as both the turbojet and the ramjet are in
operation the procedure adopted for the ﬂow conditions in the mixer is the same as that at
the design point. The procedure, however, is different for the following two conditions:
a) At low Mach number when the ramjet is not yet put into operation, the door
hinged at the mixer exit operates and closes the ramjet exhaust by resting on
the turbojet nozzle (see Figure 4.4). Only the turbojet exhaust ﬂow passes

through the mixer and the main nozzle.

Doors for turbojet
operation only

é,/’\ /

 

 

Ramjet l ’lx/
: r

Turbojet ®

K Ramjet

 

 

(9 ®

Figure 4.4 Section of the turboramjet showing the doors when only the turbojet is in

operation

By doing so a diffuser is formed between stations (11) and (18) and that is
assumed to be isentropic. The stagnation conditions at station (18) remains

equal to that at (11), M18 is obtained from function XMACH, T13, P18 and p18

82

from functions TKM, PKM and DKM respectively. The static enthalpy (h ,8) is
calculated from the product of cp and T18, and u )3 from the Mach relation.
b) When the turbojet is shut down for exceeding the turbine inlet temperature

limit, it allows no ﬂow to pass through. Under this condition 151,, and N1 1 are

set equal to zero and the molar composition of the turboramjet is calculated
based upon the ramjet ﬂow only. There on the software follows the same
procedure that is used at the design point calculation.
The calculations for the mixer are handled by the software through subroutine
MIXER. However, an additional subroutine TJOUT is called for the case
when only the turbojet is in operation.
4.17 The Exhaust Nozzle
The ﬂow from the mixer is exhausted to the atmosphere through the variable area
convergent-divergent nozzle that generates the engine thrust. The nozzle attached with
the turboramjet is designed such that it always operates choked at the throat and fully
expanded to the atmosphere. In Figure 4.4 the entry to the nozzle is represented by station

(18), and throat and exit by stations (19) and (20) respectively. The nozzle efﬁciency (77")
is user deﬁned.
From the given conditions it is evident that
M,9 = 1
and P2. = P.
since the ﬂow in the nozzle is assumed to be adiabatic
hozo = ho19 = h018

and for constant speciﬁc heat

83

71120 = T019 : T018
4.17.1 Flow Conditions at the Throat

Since the nozzle is assumed to be always choked the static temperature (T19) is

calculated from the temperature ratio (equation [315]) using value of M19 as unity
2
719 = T019 k +1 (437)

and u,9 = M,9 kRT,9 (4.38)

Assuming that the nozzle efﬁciency does not change at the throat, the ideal temperature

(T,,-) is calculated from the deﬁnition of the efﬁciency (77")

T018 - T19] (4.39)

Ta = T018 -[ 77,.
Using the value of (Tn) in the relationship between temperature and pressure ratio

(equation [35]), P19 can be obtained

k—l

P -P (EJT (4 40)
19" 019 Tti '

The local density (p19) and the throat area (A 19) are evaluated making use of the equation

of state and the continuity equation respectively.
4.17.2 Flow Conditions at the Exit
For the expansion process through the nozzle the ideal temperature at the exhaust

T020, may be obtained from the known parameters. The ideal temperature is the

temperature that could have been achieved at the nozzle exit through an isentropic
expansion process. Using isentropic relation between temperature and pressure ratio

(equation [35])

84

5;!

P20 "
T0201 = T018 P (4°41)
018

the static temperature T20 can now be found out by introducing the nozzle efﬁciency

77 = (T018 " T20)
n (T018 ’ T201)
or T20 = T018 ‘ 77a (T018 "' T201) (4'42)

By using equation of state (equation [36]) the static density (p20) is calculated. Mach

number (M20) is obtained from the ratio of the temperature (equation [315]), uzo from
Mach relation and A 20 from the continuity equation. The functions PTKM and DTKM are

used to return the values of P020 and p020. The static enthalpy is calculated from the

deﬁnition of stagnation enthalpy in terms of velocity (equation [32]).
4.17.3 On-Design and Off-Design Calculations

The nozzle used in the turboramjet is variable area both at the throat and the exit.
It is so in order to accommodate the design considerations of always-choked throat and
fully expanded exhaust. These considerations call for the requirement of throat and exit
areas adjustment with varying operating conditions and the question of ﬁxing the areas at
design point has no practical applicability. As such the same procedure is followed for the
ﬂow parameters calculation in the nozzle both at the design point and off-design

operations.

85

4.18 Engine Performance Parameters
During the flow expansion process in the nozzle there is no addition or expulsion
of either the air or fuel in the ﬂow stream, and the total mass ﬂow at the nozzle exit is the
same as at the mixer exit. Therefore
mzo = "he
The total mass ﬂow contains the air and fuel fractions that are received at the mixer,
followed by the nozzle, each from the turbojet and the ramjet such that:
the air mass in the nozzle is
maze : mall + man (4-43)
and the fuel fraction in the nozzle ﬂow
m

120 : m111+m117 (4-44)

where subscript (11) and (17) represents fractions from the turbojet and the ramjet
respectively.
It can now be concluded that

mzo : mazo '1' mfZO (4-45)

The fuel- air ratio of the engine becomes

 

The engine thrust (in Newtons) can now be obtained by using the thrust equation

[equation( 2.2)]. Thus
7 = m20[(1+f)“2o " “11'”on " P1)A20

for the fully expanded nozzle P20 = P, , and the thrust equation reduces to the form

86

T : m20[(1+ f)“2o _ “1] (4-46)

The speciﬁc thrust (Is) is the thrust per unit mass ﬂow (in N/kg) such that

I, = ~1— = [(1+ f)u,_O — u,] (4.47)
mzo

The thrust specific fuel consumption (TSFC) is evaluated from the thrust and the fuel

mass ﬂow rate

mfZO

 

TSFC =

Conversion of TSF C in standard units (kg (fuel)/hr/kN) leads to

(1000)(3600)f
1%...)

Thrust Power (TP) is the product of the thrust and ﬂight velocity

 

TSF C = (4.48)

TP=tu,

Propulsion Efﬁciency (77,) is the ratio of this thrust power to the rate of production of

propellant kinetic energy

 

 

77,, _ z "1 (4.49)

_ m... <1+f><u§./2)—u3/2]

Thermal Efﬁciency (17”.) from the definition (Section 2.2.1.2) is obtained as

= [(1+ f)(u220/2) — 1.3/2]
77». fQR

 

(4.50)

87

Overall Efﬁciency (770) is the product of propulsion and the thermal efficiencies

214,

meR

 

”0 = ”pnth = (4'51)

88

CHAPTER 5
BENCHMARKING OF THE COMPUTER CODE

The reliability of the computer code is established through hand calculations for a
typical set of design conditions. These calculations are done using the standard
relationships pertaining to the gas ﬂow through an aircraft engine. An overview of these
relationships has been presented in Chapter 3. The calculations are carried out station-by-
station for the turboramjet (see Figure 3.1). After completing the calculations for each
station, a comparison is made between the values of the ﬂow parameters obtained through
the hand calculations and those from the computer program.
5.1 Set of Design Conditions

The following design parameters are selected for the hand calculations:

a) Flight Mach number, M 1 = 2.5

b) Flight altitude = 11000 m

c) Velocity at diffuser exit, 144 = 120 m/s

d) Compressor pressure ratio, 7C = 6.0

e) Velocity through turbojet combustor, as = 30.0 m/s
f) Turbine inlet temperature,T09 = 1350 0K

g) Ramjet thermal limit, TRC = 3000 OK

h) Velocity across the ramjet burner, u 1 5 = 30.0 m/s

i) Compressor efﬁciency, 7],. = 0.88

j) Turbojet combustor adiabatic efﬁciency, 77m,- = 0.98

k) Adiabatic efﬁciency of turbine, 77, = 0.93

89

1) Mechanical efﬁciency of the turbine, 77,," = 0.97
m) Ramjet burner adiabatic efﬁciency, nbrj = 0.98
n) Adiabatic efﬁciency of the engine nozzle, 77,, = 0.97

5.2 Fixed Parameters
a) The gas constant, R = 287 ”kg 0K

b) Molecular weight of air, MWai, = 28.967 kg/kmol

5.3 The Target Flow Parameters

The ﬂowing properties of the ﬂow are calculated at each station of the
turboramjet:

a) The stagnation temperature, To

b) The stagnation pressure, P0

c) The static temperature, T

d) The static pressure, P

e) The static enthalpy, h

f) The density, p

g) Flow velocity, u

 

h) Flow Mach number, M
1) Mass ﬂow rate, m

j) The area of the engine, A

90

5.4

5.4.1

5.4.2

5.5

5.5.1

Some Important Formulae for k = 1.4

Shock Relations

cot6=tanﬂl: 6M'2 )—l]

 

5(M,2 sin2 ,6— 1

i_ 6M,2 sinzﬂ 3'5 6 25
P0, ‘ M,2sin2,6+5 7M,Zsinzﬂ—1
13%.— 6M: 3.5 6 25

P02_ M22+5 7M22—1

Mzsin(ﬂ_6)=\/M,2sinzﬂ+5

 

 

 

 

 

 

7M,2 sin2 ,8—1

M _ M22+5
3‘ 7M§—1

Isentropic Relations

 

 

Calculation of the Flow parameters

Station (1) : Free Stream Conditions

From the standard altitude tables for 11000 m,

. LzZMJK
. P, = 22.6 kPa

. p, = 0.3648 kg/m3

91

(5.4.1)

(5.4.2)

(5.4.3)

(5.4.4)

(5.4.5)

(5.4.6)

(5.4.7)

0 Velocity of sound, c1 = 295.2 m/s
1. Obtain ﬂow velocity from Mach number relation
u, = Mlc, = 2.5(295.2) = 737.9 m/s

2. From supersonic ﬂow table for M = 2.5 and k = 1.4,

P.

-— = 0.05853
P0

T.

— = 0.4444
721

This leads to
To = 487.6 K
P0 = 386.1 kPa
5.5.1.1 Evaluation of Wedge Angle (0) and the Shock Angle (B)
The evaluation of 6and ﬂ is an iterative process for maximum pressure recovery.
The algorithm to obtain these values is as follows:
a) Initialize the pressure recovery (PR)

b) Assume some value of the shock wave angle (,6) greater than the Mach wave

angle

ﬂmin = Sin-l (1%?)

c) Find the corresponding wedge angle (6) from equation (5.4.1)

P
(1) Obtain pressure ratio across the oblique shock $2 with the help of equation
01

(5.4.2)

e) Find M2 using equation (5.4.4)

92

f) Calculate M 3 from equation (5.4.5)

g) Find pressure ratio across normal shock ~593- using equation (5.4.3)
02

h) Calculate the overall pressure recovery

azaxa

P01 P02 Ell

P
i) Compare 1% with dummy variable PR
01

P
j) If 73> PR, putPR= 03

01

2"?”

P
k) Increase 6 by 10 and perform iteration until maximum value of £ is
01

achieved

Iteration 1

Let PR = 0.0

and ﬂ = 420

this leads to sin2 ,6: 0.4477 and M12 sin2 ,6: 2.7983

 

1. Find0
t6-t 42 375 1]
C0 7 a” 5(2.7983-1)
cot6 = 2.853
6=19.31°
P
2. mai

POI

93

P01-

 

59.2. _ (37.8 x 0.4477 j” 6
2.7983 + 5

P
#2 = (14.6405)(0.05919) = 0.8666

 

 

 

 

POI

3. Find M2
. _ (2.7953+5)

Mm“ 6)7 7(2.7983)—l

M2: 1.678
4. Find M3

2
3: (1.678) 2+5 = .646
70.678) -1

P
5. Find —°i
P 02

fa _ 60.678)2
P02 7

(1.678)2 + 5

02

P

03
— = 0.8647
P02

 

)3.5[ 6
7(1.678)2 —1

P
P_03 = (14.848)(0-0583)

.02 = 0.8647 x 0.8666

POI

7(2.7983) — 1

I.

94

j”

P 03
—— = 0.7493
P

01

7. Compare Pressure recovery

P—m ) PR, another iteration is needed.
01

Iteration 2

Let PR = 0.7493
and ,5 = 430
this leads to sin2 ,6: 0.4651 and M12 sin2 ,6: 2.907

1. Find 6

6(25)2 ]

t =t 43 ——
C0 6 2‘“ (5(2907-1)

cot 6 = 2.7349
6 = 20.080

P
2. Find i
P01

_P,,_2__[6x2.907)35( 6 1”
P0, 7 2.907 +5 7(2.907)—1

P
7;”— : (15.942)(0.05355) = 0.8536

01

 

 

3. Find M2
M “(ﬂ 6)_ (2.907+5)
28’" 7 7(2.907)—1
M2=1.641

95

4. Find M3

 

 

= 0.656

3

\/(1.641)2 +5
70.641)2 -1

 

ﬁl_[ 6(1.641)2 J11 6 J25
P02 7 (l.641)2+5 7(1.641)2-1

P
—"-3— = (13.440)(0.06543)

fa _
_ 0.8794 x 0.8536
P01

P
P = 0.7506
P01

7. Compare Pressure recovery

-P°—3 ) PR , another iteration is needed.
01

Iteration 3
Let PR = 0.75063

and ,6: 44°

96

this leads to sin2 6: 0.4825 and M12 sin2 6: 3.015

1. Find 6

 

_ 6(25)2
cot6— tan44[5(3.0159_1)—1]

cot 6 = 2.6270
6 = 20.840

P
2. Find —92—
P 01

i_(6x3.0159)35( 6 2'5
P0, 7 3.0159 +5 7(3.0159)—1

P
£ = (17.284)(0.0486) = 0.8403

 

 

 

P01
3. Find M2
M2 Sin,ﬂ_ a): (3.0159 +5)
7(3.0159) — 1
M2 = 1.605
4. Find M3

 

_ (1.605)2 +5 _ 0

_ _ .667
3 \/7(1.605)2 -1

 

P
5. F’ d—9-3—
In P

02

IL 60.6092 3'1 6 j”
P02 7 (1.605)2+5 7(l.605)2—1

P
—‘R = (12.135)(0.0736)
P02

 

97

zazaaxfa
P01 P02 P01

ﬁn. _
P _ 0.8932 x 0.8403

OI

P
P = 0.7506
P01

7. Compare Pressure recovery

P
F03— z PR , another iteration is needed to check the trend.
01
Iteration 4
Let PR = 0.7506
and ,6 = 450

this leads to sin2 P= 0.50 and M12 sin2 ,6: 3.125

1. Find 6

2
cot 6 = tan45[ 605) ]

5(3.125 — 1) 7

cot 6 = 25294
6 = 21.570

98

P
2. F’ d —92-
In P

01
5% _(6x3.125)3'5[ 6 J”
P0, 7 3.125+5 7(3.125)—1

P
f = (18.6690)(0.0443) = 0.8269

01

3. Find M2
. (3.125+5)
M —6 = —
2 3mm ) 7(3.125)-1
M2 = 1.569
4. Find M3

 

_ (1569)2+5
3 7(1569)2-1

 

= 0.678

 

5,,_ 6(1569)2 ”ﬂ 6 T5
P02 7 (1569)2 +5 7(1569)2 -1

P
.23. ___ (10.913)(0.0831)

 

99

5.3. _
_ 0.9065 x 0.8268
P01

P03
_’_: .4
P 07 95

01

7. Compare Pressure recovery

P03

P01"

 

( PR , the point of maxima has passed. The previous value is selected

representing the maximum pressure recovery.
Thus for the given conditions the following results are obtained:
a) Maximum pressure recovery = 75.06%

b) Corresponding wedge angle (6) = 20.840

c) The shock wave angle (1] ) = 440

Table 5.1 Comparison of flow Properties at Station (1)

 

 

 

 

 

 

 

 

 

 

Flow To Pa T P p h u M
Properties [K] [kPa] [K] [kPa] [kg/m3] [kJ/kg] [m/s]
By Hand 487.6 386.1 216.7 22.6 0.3648 217.4 737.9 2.5
Computer 487.6 386.9 216.7 22.6 0.3638 217.7 738.0 2.5

 

5.5.2 Station (2) : Oblique Shock
Known parameters:

0 M2 = 1.605 (from pressure recovery calculations)

5;- _
. P _O.8403 => Fog—324.4 kPa

01
0 T02 = To] = 487.6 K

- k=1.4

100

1. From the shock table againsth = 1.605

T
i=1.515
T2

T -4—816--3218K
2 " 1515 ’ '

2. Find P2 using isentropic relation
L
P 02 _ [702 )H
P2 701
324.4

= —— = 75.8 kPa
2 (1515)3.5

3. Equation of state

_ 75.8
”2 “ (O.287)(321.8)

 

= 0.82073 kg / m3

4. Mach relation

u2 = M2 kRT2

 

u2 = 1.605J1.4(287)(321.8) = 577.1 m/ s
5. From enthalpy relation, h = cpT

h2 = 322.8 kJ/kg

Table 5.2 Comparison of ﬂow Properties at Station (2)

 

 

 

 

 

 

 

 

 

 

Flow To Po T P p h u M
Properties [K] [kPa] [K] [kPa] [kg/m3] [kJ/kg] [m/s]
By Hand 487.6 324.4 321.8 75.8 0.8207 322.8 577.1 1.61
Computer 487.6 327.7 319.3 74.5 0.8119 320.7 581.7 1.62

 

101

5.5.3 Station (3) : Normal Shock

Known Parameters:

o M 3 = 0.667 (from pressure recovery calculations)

P
. —°-3-= 0.8932 => P03 = 289.8 kPa
P02

. T03 = T02 = 487.6 K

 

- k = 1.4
1. Equation (5.4.6)
(0.667)2 "
T3 = 733 1+ 5 = 447.8 K

3"

Using enthalpy relation, h = cpT
h3 = 449.8 k] / kg
3. Equation (5.4.7)

(0667)2
5

 

-3.5
P3 = P03(1+ ] =215.0 kPa

4. Ideal gas equation

_ 215.0
p3 ‘ (0.287)(447.8)

 

= 1.6729 kg / m3

5. Mach relation

u3 = MM/kRT3 leads to
u3 = 282.9 m/s

6. Find geometry of the wedge

102

For 19 = 20.840 and ,6: 44°, obtain base X and height Y, of the half wedge (see

Figure 4.3)

 

 

= 0.6357 111

1
X :
\/71'(tanzﬂ—tan2 6)
Y1=Xtan 0 = 0.2499 m

for the critical condition (shock attached to intake lip) the intake radius Y2 becomes

Y2 = Xtan B = 0.6139 m
7. Obtain intake area (A 3) (see Figure 4.2)
A3 = 7r(Y22 — le)
A3 = 0.988 m2
8. Mass flow rate
Continuity equation at station (3), m = p 14A
:52. = (1.6729)(282.9)(0.988) = 467.6 kg/s

Table 5.3 Comparison of ﬂow Properties at Station (3)

 

Flow To P0 T P p h u M A
Properties [K] [kPa] [K] [kPa] [kg/m3] [Id/kg] [m/s]

 

By Hand 487.6 289.8 477.8 215.0 1.6729 449.8 282.9 0.667 0.998
Computer 487.6 290.5 448.3 216.6 1.6815 450.3 280.9 0.662 1.0

 

 

 

 

 

 

 

 

 

 

5.5.4 Station (4) : Diffuser
Known Parameters:
0 m = 120 m/s (user deﬁned)
0 P04 = 0.96 (P03 ) = 278.2 kPa (design consideration)

0 T03 = T02 = 487.6 K (adiabatic flow)

103

2
. Using isentropic relation 7}, = T + §u_ , find T4
0

P

(120)2
2(1.005)(103)

 

T4 = 487.6 + = 480.4 K

. Enthalpy relation h4 = (1.005)(480.4) = 482.8 kJ/kg

. Velocity of sound c = s/kRT leads to c4 = 439.3 m/s
u .
and M = Z g1ves M4 = 0.273

Equation (5.4.7)

(0.273)2

 

—3.5
P4 = 278.2[1+ ) = 264.2 kPa

. Ideal gas equation

_ 264.2
p4 ‘ (0.287)(480.4)

 

= 1.9162 kg/m3

. Continuity

A _ 467.6
4 " (1.9162)(120)

 

= 2.034 m2

Table 5.4 Comparison of ﬂow Properties at Station (4)

 

 

 

 

 

 

 

 

 

 

 

Flow T. P. T P p h u M A
Properties [K1 [kPa] [K1 [kPa] ﬂcg/m3] [Id/kg] [m/s1

By Hand 487 .6 278.2 480.4 264.2 1.9162 482.8 120.0 0.273 2.034
Computer 487 .6 278.9 480.4 264.8 1.9187 482.6 120.0 0.27 3 2.051

 

104

5.5.5 Stations (5) and (13) : Bypass Doors
Design point assumptions are:
0 The bypass doors are ﬁxed at 50% for all ﬂight conditions

0 Isentropic flow over the bypass doors
. ms :15.” =i"-2-‘-=233.2 kg/s

_ _A4_ 2
. 45-43-74.017 m

With in changes in areas and mass ﬂow rates in stations (5) and (13) as compared
with station (4), it is concluded that the ﬂow properties at all these stations will be

identical to that of station (4) (see Section 4. 9).

Table 5.5 Comparison of ﬂow Properties at Stations (5) and (13)

 

Flow To P0 T P p h u M A
Pr0perties [K] [kPa] [K] [kPa] [kg/m3] [kl/kg] [m/S]
By Hand 487.6 278.2 480.4 264.2 1.9162 482.8 120.0 0.273 2.034
Computer 487.6 278.9 480.4 264.8 1.9187 482.6 120 0.273 2.051

 

 

 

 

 

 

 

 

 

 

 

5.5.6 Stations (6) and (14) : Turbojet and Ramjet Entry
The stations (13) and (14) have the same ﬂow properties at the design point as
those of (5) and (13) respectively. It is because the bypass doors are kept ﬁxed at 50%

throughout and ﬂow past the doors is assumed isentropic.

Table 5.6 Comparison of ﬂow Properties at Stations (6) and (14)

 

Flow To Po T P p h u M A
Properties [K] [kPa] [K] [kPa] [kg/m3] [kJ/kg] [m/s]
By Hand 487.6 278.2 480.4 264.2 1.9162 482.8 120.0 0.273 2.034
Computer 487.6 278.9 480.4 264.8 1.9187 482.6 120 0.273 2.051

 

 

 

 

 

 

 

 

 

 

 

105

5.5.7 Station (7) : Compressor

Known parameters:
0 P07 = (ye) P06 = 1669.2 kPa
o x. = 6 (user input)
o m = 12.5 = 120.0 m/s (constant axial velocity across compressor)
0 nc = 0.88
o k = 1.4
1. Find ideal temperature using isentropic temperature - pressure relationship

k—l

T...- =00.) =813.6 K

2. Obtain T07 from the deﬁnition of 77..

(Tow - T06)

"c = (T07 _ T06) => T07 = 858.0 K

3. Isentropic temperature - velocity relation

(120)2
2(1.005x103)

 

T7 = 8580- = 850.8 K

4. h; = cpTy = 855.1 kJ/kg
5. Velocity of sound c = JkRT , leads to C7 = 584.7 m/s

and
“7
M 7 = — = 0.205
c.,

6. Equation (5.4.6)

P7 = 1669.2(0.971) = 1621 kPa

106

 

7. Equation of state leads to p7 = 6.6386 kg/m3

8. Compressor Work = cp(T07 - T06) = 371.5 kJ/kg or 10759 kJ/kmol

Table 5.7 Comparison of flow Properties at Station (7)

 

 

 

 

 

 

 

 

 

 

 

Flow To Po T P p h u M A
Properties [K] [kPa] [K] [kPa] [kg/m3] [kJ/kg] [m/s]

By Hand 858.0 1669.2 850.8 1621.0 6.6386 855.1 120.0 0.205 1.017
Computer 858.0 1673.1 850.5 1624.8 6.6479 854.6 120.0 0.205 1.026

 

5.5.8 Station (8) : Diffuser for Turbojet Combustor

Known Parameters:

=1.4

T03 = T07 = 858.0 K

P08 = P07 = 1669.2 kPa

uog = 30.0 m/s (user input)

m8 = m6 = 233.2 kg/s

3. Isentropic temperature - velocity relation

7;, = 858.0-

5. Velocity of sound 6 = JkRT , leads to c8 = 586.9 m/s

and

(30)2

 

2(1.005 x103)

h. = cpTg = 862.1 kJ/kg

M8 =58—=0.051
C
8

= 8575 K

107

Isentropic flow across diffuser (assumed), therefore:

- . To. —"—'
6. Usmgisentrop1c relation —= ——

k
P08 _

Ps 7?.

8575

1.714
P08 =1669.2(—) = 16675 kPa

858.0

7. Equation of state leads to pg = 6.7756 kg/m3

8. Continuity equation gives

8 = (6.7756)(30)

233.8

 

= 1.15 m2

Table 5.8 Comparison of ﬂow Properties at Station (8)

 

 

 

 

 

 

 

 

 

 

 

Flow To P0 T P p h u M A
Properties [K] [kPa] [K] [kPa] [kg/m3] [kJ/kg] [m/s]
By Hand 858.0 1669.2 857.5 1667.5 6.7756 862.1 30.0 0.051 1.150
Computer 858.0 1673.1 857.5 1670.1 6.7798 861.4 30.0 0.051 1.161

 

5.5.9 Station (9) : Turbojet Combustion

Known Parameters:

Top = 1350 (user defined)
A9 = A8 (Raleigh process approach)

77,, = 0.98 (user deﬁned)

k=1.33

cp=1.157

108

-
P

1. Find T01 (choking temperature) for station (8)

 

 

 

 

_ k —1 .
2 2
n8 _ 2(k+1)M8(1+—2 M8)
708 (1+kM82)2
. (1+ 1.33(0.051)2 )2
T08 = 858 = 69189.0 K

 

2(2.33)(0.051)2 (1 + 0.2(0.051)2 )

Since To; ) 738 , combustion is possible.
2. Also note that 7}); = To; for the same combustor, therefore, for the known T09 and

To; , M9 can be obtained from the temperature ratio.

 

 

 

 

 

P2(133+1)M2 1+1'33"1M2 -
T09 — ' 9 2 9
T09 (1 + 1.33143)2
_ 1
4.66M,2 +0.79 M;
00195:

 

1+ 2.66M,2 + 1.77 M;
this leads to a fourth order equation in M
M: + 6.099M3 — 0.02581 2 0
Assuming M 92 = X , the equation reduces to a quadratic in X. The quadratic formula

returns the roots of X as
X, = 0.00423 and X2 = -6.103

Positive root is selected representing the subsonic Mach in the combustor.
Thus M9 = 1/Xl =0.065

3. Obtain P08 from the Raleigh line pressure ratio

109

k-l k/(k—l)
2
P08 " 1+kM: k—l

1+—2—M82

 

Putting the values and arranging
P09 = P0,,(0.998)(1.000254)‘-03
P09 = P08 (0.999)

P09 = (1669.2)(0999) = 1667.6 kPa

. Find T9 from temperature — Mach relation

T, = T09 (1 + 0.165(0.065)2)”1
T9 = 1350(09999) = 1349.03 K
. Velocity u9 = MngRT9 =717.6 m/s

. Pressure ratio - Mach isentropic relation leads to calculation of P9

)—403

P9 = P09(1+0.165M§
P9 = 1667.6(0.9971) = 1662.4 kPa

. Ideal gas relation

1 662.4

= —— = 4.294 k 3
”9 0.287(1349) 3""

. Enthalpy h9 = 1.157(1349) = 1560.8 kJ/kg

. Fuel-air ratio

(T09/708)—1
(QR/CpTos)" (709/708)

 

for C12 H26 the value of QR = 44108.3 kJ/kg K

110

 

putting the values and solving results in,

0.573
f - m — 0.01338

10. Fuel flow rate

I71] = fm8 = 0.01338(233.8) = 3.1282 kg/s

11. Net mass flow rate

at, = m, + m, = 236.93 kg/s

12. Air-fuel ratio (Afaa) = l/f = 15.006

 

Table 5.9 Comparison of flow Properties at Station (9)

 

Flow To P0 T P p h u M A
Properties [K] [kPa] [K] [kPa] [kg/m3] [kJ/kg] [m/s] [m2]
By Hand 1350.0 1667.6 1349.0 1662.4 4.2940 1560.8 46.6 0.065 1.150
Computer 1350.0 1671.5 1349.0 1666.7 4.3013 1355.1 46.1 0.064 1.161

 

 

 

 

 

 

 

 

 

 

 

5.5.10 Station (10) : Turbine

Known Parameters:
o u ,0 = up = 46.6 m/s (design assumption)

0 77, = 0.93 (user deﬁned adiabatic efﬁciency)

 

' 771m = 0.97 (user deﬁned mechanical efﬁciency)
0 k = 1.33
0 cp=1.157kJ/kgK

1. Turbine Work

111

2. Turbine work in terms of temperatures

 

“limb = Cp (T09 _ 7010)
383.0 = 115703500 — Tom)

or T010 =1018.9 K

3. Temperature - velocity isentropic relation

 

2
u
710 = 7010 ——2;—:- 11H
91.
(46.6)2 1
Tlo =1018.9— 3 = 1017.9 K
2(1.157x10 ) ~ .

4. hm = (1.157)(1017.9) = 1177.7 kJ/kg

46.6

Mlo = = 0.075
71.33x 287 x 1017.9

 

From the deﬁnition of adiabatic efﬁciency ﬁnd ideal temperature (T0101)

 

77, : T09 " 7010
T09 " 70107
1350.0- 1018.9
Tm, =1350.0— 0 9 3 = 994.0 K

7. Temperature - velocity relation

 

2
“10

K

P

Tior' = 70101 "

Tm, = 994.0— 0.938 = 993.0 K

8. Isentropic relation

I:
T. U 993.0 “’3
P = —‘°'— =1662.4 —) =483.6kP
'0 {7,1 (13490 a

112

9. Isentropic relation

1:
T 5 1018.9 “’3
P = P ﬂ] =483.6(————) =4855 kPa
0‘0 ‘01 T10 1017.9

10. Equation of state

_ 483.6
pm ' 0.287 x 1017.9

 

= 1.6554 kg/m3

Table 5.10 Comparison of flow Properties at Station (10)

 

Flow To Po T P p h u M A
Properties [K] [kPa] [K] [kPa] Lkg/m3] [kl/kg] [m/s] [m2]

 

By Hand 1018.9 485.5 1017.9 483.6 1.6554 1023.0 46.6 0.075 1.150
Computer 1018.4 485.6 1017.5 483.8 1.6554 1022.1 46.1 0.074 1.161

 

 

 

 

 

 

 

 

 

 

5.5.11 Station (11) : Turbojet Nozzle
Assumptions:

- Isentropic

0 Always choked
Known parameters:

0 T0,, = T010 2 1018.9 K

0 P0“ = P010 = 485.5 kPa

0 M11 = 1.0

o k = 1.33

o cp=l.157kJ/kgK

. 82,, = 71110 = 236.9 kg/s

113

. Isentropic temperature - Mach relation

k—l 2 "
T11=70111+ 2 M11

1.33 — l

 

-1
T,,=1018.9(1+ x1) =874.6 K

 

. Velocity u” = Mm/kR ,, = 71.33x287 x8746 = 577.8 m/s

. Isentropic relation

. Equation of state

_ 262.4
‘0” ‘ 0.287 x 874.6

 

=1.0452 kg/m3

. Continuity

236.9

“ 1.0452 x 577.8 m

 

. h“ = CpT11= 1011.9 kJ/kg

Table 5.11 Comparison of ﬂow Properties at Station (11)

 

 

 

 

 

 

 

 

 

 

 

FIOW To Po T P p h u M A
Properties [K] [kPa] [K] [kPa] [kg/m3] [kJ/kg] [m/s] [m2]
By Hand 1018.9 485.5 874.6 262.4 1.0452 1012.0 577.8 1.0 0.392
Computer 1018.4 485.6 874.2 262.4 1.0450 101 1.5 577.9 1.0 0.398

 

114

5.5.12 Station (15) : Ramjet Diffuser

Known Parameters:
- Isentropic flow across diffuser (assumed), therefore:
T015 = T014 = 487.6 K
P015 = P014 = 278.2 kPa
0 1415 = 30.0 m/s (user input)
0 k = 1.4
0 cp = 1.005 kJ/kg
o n’t15 = at”: 233.2 kg/s
1. Isentropic temperature - velocity relation

(30)2
= 7. - =487.15 K
T” 48 6 2(1.005><103)

 

2. 1115 = CpT15 = 489.6 kJ/kg

3. Velocity of sound c = w/kRT , leads to c15 = 442.4 m/s

and Ml5 = -"—'-5- = 0.068

C15

. . Po To a
4. Using isentrop1c relation -P-= -T-

487.6 ‘35
= . — = . kP
P,5 2872(4872) 2773 a

5. Equation of state leads to p15 = 1.9834 kg/m3

6. Continuity equation gives

233.8

: = 3.93 2
A” (1.9834)(30) m

 

115

7. I105 = CpT015 = 489.8 kJ/kg

Table 5.12 Comparison of ﬂow Properties at Station (15)

 

Flow To P0 T P p h u M A
Properties [K] [kPa] [K] [kPa] [kg/m3] [kJ/kg] [m/s] [m2]

 

By Hand 487.6 278.2 487.2 277.3 1.9834 489.6 30.0 0.068 3.93
Computer 487.6 278.9 487.1 278.0 1.9864 489.3 30.0 0.068 3.96

 

 

 

 

 

 

 

 

 

 

5.5.13 Station (16) : Ram Burner

Known Parameters:
0 Burner thermal limit (TRC) = 3000 K (user defined)

0 A16 = A5 = 3.93 m2 (Raleigh process approach)

77,, = 0.98 (user deﬁned)

0 k=1.3

cp = 1.244 kJ/kg K
1. Establish adiabatic flame temperature and compare with known thermal limit
For the given fuel (C12 H26)

_ 4.76 x 185 x 28.97 _
"' ‘ 170 "

 

1 5.006

_1 :
f—AFM 0.06664

From the deﬁnition of fuel-air ratio

(h016/h015)_1
anR/h015)-(h016/h015)

(for Cu H25 the value of QR = 44108.3 kJ/kg K)

 

’7

putting values and arranging for how

116

_ [489.8 + (0.06664 x 0.98 x 441083)]

,6 1.06664 =3159.8kJ/kg

this implies that T016 = 2540.0 K

T016 is obtained using AF 0,, so it represents the adiabatic ﬂame temperature (AFT). Also
since AFT < TRC, the operation at this temperature is safe.

2. Mass ﬂow through ramjet

m, = f x m,” = 0.06664 x 233.8 = 1558 kg/s
mm = mm +m, = 249.4 kg/s

3. Find To. (choking temperature) for station (15)

 

 

 

 

 

 

- T -
2(k +01142 [95—]
7015 _ 15 T15
7015 (1+ka!)2
T 4.8 0.068 2 1.000924
0.” = ( H 2 ) =0.0218
7015 (1+(1.4)(0.068) )
. 487.6
=—= K
0‘5 0.0218 22363

S1nce T015 ) 75,5, combustion 1s poss1ble.

4. Finding M16

It may be noted that 7315 = T016 for the same burner, therefore, for the known

Tom and 7016’Ml6 can be obtained from the temperature ratio.

—

 

1.30- 1 l
20.30 +1)M,26(1+ M36)

(1+ 1.30M,26 )2

2"}
as

 

2H

 

 

117

4.6M,26 + 0.69 M,“6

0.1136 =
1+ 2.611436 +1.69M,“6

 

this leads to a fourth order equation in M16
M 146 + 8.645M126 — 0.229 = 0
Assuming M ,26 = Y , the equation reduces to a quadratic in Y. The quadratic formula

returns the roots of Y as
Y; = 0.0264 and Y 2 = -8.67

Positive root is selected representing the subsonic Mach in the ramjet burner.

Thus Ml6 = 77, = 0.163

. Temperature - Mach isentropic relation

k—l , "
716:70161'1' 2 M16

1.3—1
2

 

—1
716 = 2540.0(1+ (0.1632) = 2529.8 K

. Enthalpy

h", = 1.244(25298) = 3147.1 kJ/kg

. Obtain P03 from the Raleigh line pressure ratio

Pr. _ l+kM125
P. ' ”ka.
Putting the values

 

i _(1+1.4(0.068)2
P15

= 0.973
1+ 1.3(0.163)2 1

P16 = (0.973)P15 = 269.8 kPa

118

8. Pressure - Temperature isentropic relation

k
P016 = (2013)“.
P16 T16

P0,6 = P,6(1.0176)

 

P016 = (269.8)(10176) = 2745 kPa
9. Ideal gas relation

_ 269.8
p“ ’ 0.287(25298)

 

= 0.3716 kg/m3

10. Velocity ul6 = Mm/kR ,6 = 0.163(9715) = 157.9 m/s

Table 5.13 Comparison of ﬂow Properties at Station (16)

 

 

 

 

 

 

 

 

 

Flow To Po T P p h u M A
Properties [K] [kPa] [K] [kPa] [kg/m3] [kJ/kg] [m/s] [m2]
By Hand 2540.0 274.5 2529.8 269.8 0.3716 3147.1 157.9 0.163 3.93
Computer 2538.6 269.8 2529.0 265.4 0.3653 3146.1 154.1 0.159 3.96

 

 

 

5.5.14 Station (17) : Ramjet Exhaust

The passage between ramjet burner and its exhaust is assumed to be constant area

duct in that the ﬂow behaves isentropically. Therefore, the ﬂow properties does not

change between stations ( 16) and (17).

Table 5.14 Comparison of flow Properties at Station (17)

 

Flow To P0 T P p h u M A
Properties [K] [kPa] [K] [kPa] [kg/m3] [kJ/kg] [m/s] [m2]
By Hand 2540.0 274.5 2529.8 269.8 0.3716 3147.1 157.9 0.163 3.93
Computer 2538.6 269.8 2529.0 265.4 0.3653 3146.1 154.1 0.159 3.96

 

 

 

 

 

 

 

 

 

 

 

119

 

5.5.15 Station (18) : Mixer Exit
Known parameters:
0 n'rl8 = m“ + "'217 = 486.3 kg/s
0 A13 = A3 + A17 = 5.08 m2 (maximum area of the engine)
0 k = 1.33
0 cp = 1.157 kJ/kg K
1. Energy equation
n'zmcplﬂz,18 = mncpnﬂ,” +ﬁzl7cpl772m
miscplsﬂm = (236.9 x1.157 x1018.9)+(249.4 x1244 x 2540) = 10673178 kJ/s

T _ 10673178
0'8 ‘ (486.3 x 1.157)

 

= 1896.9 K
2. Simultaneously solving ﬁrst law, continuity, momentum equation and equation of
state and rearranging for “18 (see appendix C)
(2a,,18 + R)ir,,u3, — 2X,u,,,cpl8 — RX, = 0
where

X1:(ml7ul7 +mllull _ A17P17 _ AMP”)

X2 : m11(2h11+ “121)+’ill7(2h17 + “127)
For compatibility of the units use P in [N/mz] and c,, in [J/kg K]
The equation is a quadratic in variable u. Putting known values to obtain coefficients

and the constant term

(2cp18 + Rh, = [2(1.157 x 103)+ 287](486.3) = 12648663

120

2X,cp,3 = 2(— 991651.7)(1.157 x 103) = -2.2947 x 109

RX2 = 287(2.1345 x 109): 6.126 x 10“

Applying quadratic formula

 

—bi~/b2 —4ac
“1802) = 2a
where
a = 12648663

b = -2.2947x109 l
c = 6.126><10ll
the two roots are:
ngm = 236.2 m/s
“18(2) = -2050.3 m/s
Disregarding the negative root, 1413 = 236.2 m/s

3. The pressure P13 is obtained from 1113 (see appendix C)

P _ m,,,u,,, —X, _ (486.3x236.2)—(- 9.9165x105)
'8 " 4,, ‘ 5.08

 

 

= 2178236 N/m2

or P18 = 217.8 kPa

 

4. Temperature

2

7,8 = To,8 — 2:” = (1896.9-24.1) = 1872.8 K
p18

 

5. Mach number

M _ 14,8 _ 236.2 _0279
'8 ' 1.111,, ‘ 8455 "'

121

6. Enthalpy [1,, = (1.157 x 1872.8) = 2166.8 kJ/kg

7. Ideal gas equation

p” = 0.287(18728)

217.8

 

8. Pressure - Mach isentropic relation

= 0.4052 kg/m3

2 4.03
P0,8 = 217.8[1+0.165(0.279) ] = 229.3 kPa

Table 5.15 Comparison of ﬂow Properties at Station (18)

 

 

 

 

 

 

 

 

 

 

 

Flow To Po T P p h u M A
Properties [K] [kPa] [K] [kPa] [kg/m3] [kJ/kg] [m/s] [m2]
By Hand 1896.9 229.3 1872.8 217.8 0.4052 2166.8 236.2 0.279 5.08
Conﬂuer 1894.4 225.9 1869.4 214.1 0.3987 2163.0 240.8 0.285 5.12

 

5.5.16 Station (20) : Turboramjet Nozzle

Assumptions:

Fully expanded under all conditions

Always choked at the throat

Adiabatic

Known parameters:

T020 = T018 = 1896.9 K

P20 = P1 = 22.6 kPa

M19=1.0

k=1.33

c,,=1.157kJ/kgK

mm = m,,, = 486.3 kg/s

122

 

”-
.1

L.
In
I

l

o 77,. = 0.97

. Find ideal temperature T20,-

k-l
h — i T —( 22.6 )02481 — 057
T,,, ’ P,8 ’ 217.8 ’
T20, = 057(18728) = 10675 K
. Find T20 using 77,,

77,. = 718 "720
Tls‘Tzot'

T20 = 1872.8 — 0.97(1872.8 -10675)= 1091.6 K

. Equation of state

_ 22.6
p20 ’ 0.287(1091.6)

 

= 0.0721 kg/m3

. Find M20 from the temperature ratio

Tm" =(1+——k—l M22)

 

 

 

T20 2
1.7378- 1.0
,0 = ( ) = 2.11
0.165

. Use pressure - temperature relation for P020

1896.9 “’3
P020 = 1920(1—0—9—1—6') = 22.6(9.2725) = 209.6 kPa

. Find uzo

 

1.2,, = M20 kRT20 = 2.1 1\/(l.33x287 x 1091.6) = 1362.0 m/s

. Enthalpy h20 = (1.157 x1091.6) = 1263.0 kJ/kg

123

 

8. Continuity equation

 

 

 

6220 486.3 2
A = = = 4.
2" p2,,u22 0.0721x1362 95 m
Table 5.16 Comparison of ﬂow Properties at Station (20)
Flow To P. T P p h U M A
Properties [K] [kPa] [K] [kPa] [kg/m3] [kJ/kg [m/s] [m2]

]
By Hand 1896.9 209.6 1091.6 22.6 0.0721 1263.0 1362.0 2.11 4.95

Computer 1894.4 206.0 1094.8 22.6 0.0720 1266.7 1360.0 2.10 5.02 (2"

 

 

 

 

 

 

 

 

 

 

 

 

5.5.17 Engine Performance Parameters it.

1. Fuel flow rate
n'zf =rizm. +7712”. = 3.13+15.58= 18.71 kg/s

2. Air mass ﬂow rate

in = m, = 467.6 kg/s

a

3. Fuel - air ratio

n‘z, 18.71
= —-- = -—— = 0.040013
f m, 467.6

4. Thrust for fully expanded nozzle

 

T: mu[(l+f)“2o ““l]
T = 467.6[(l + 0.040013X1362)— 737.7] = 317410 N

or z = 317.4 RN

5 S '1' th t _z 6788 ——.S
. rus = = .
peel 1c , kg

0

124

. Propulsive efﬁciency

"P = ma[(1+qu§0/2)-(u12/2)1

 

_ 317410x737.7
467.6[(1.040013)(927522)- (272101)]

 

77,, = 0.723

. Thermal efﬁciency

n _ [(1+quio/2)-(u3/2)]
(h - fQR

 

for C,2 H26 fuel, QR = 44.1 111106
therefore

an = 1.765x106

and
6925343
= — = 0.392
'7‘” 1.765 x 106
. Overall efﬁciency

77., = 77,, 77,,l = 0.723 x 0.392 = 0.284
. Thrust speciﬁc fuel consumption

ml
TSFC = —1- kg(fuel) / s/ N

In conventional units of [kg(fuel)/hr/kN]

m, (1000)(3600)
I

 

TSF C = = 212.2 kg(fuel)/hr/kN

125

‘1
.‘i

1
1
l
l
'1

 

Table 5.17 Comparison of engine performance parameters

 

 

 

Parameter m2 rhf 1: TSFC 77p ”at no f
[kg/s] [kg/S] [kN] [kg/hr/N]
By Hand 467.6 18.71 317.41 212.2 0.723 0.392 0.284 0.040013
Computer 472.3 19.75 320.77 221.6 0.725 0.376 0.272 0.041808

 

126

 

i

_ ‘AA- .‘

ii:
‘
I

CHAPTER 6
DEMONSTRATION OF THE SOFTWARE
6.1 Design Point Performance Characteristics of the Engine

The computer software of the turboramjet is capable of handling any design
considerations within the bounds discussed in Section 3.2.3. However, for the purpose of
demonstration the set of design conditions as appeared in Section 5.1 are taken as
reference. The goal set forth was a combination engine for a commercial aircraft use that
could achieve a maximum Mach number in the range of 6 to 7. As such the design
parameters, including the altitude and the Mach number, were selected to represent nearly
the average values. The user deﬁned design parameters indicate that the design point
performance of the engine depends largely on a number of variables such as ﬂight Mach
number, diffuser efﬁciency, compressor pressure ratio, cycle temperature ratio,

compressor, turbine, burner and the nozzle efﬁciencies.

Generally the suitability of an aircraft engine to a speciﬁc propulsion system is

adjudged based upon the following parameters:

a) The thrust developed per unit of the frontal area (T/ A F)
b) The thrust developed per unit of engine weight (”r/W2)

c) The speciﬁc thrust, i.e. thrust developed per unit of mass ﬂow rate (T/rita)

127

"I
.1

“it. - .
»

 

d) The thrust speciﬁc fuel consumption (TSF C)

The parameter (z/AF) is a measure of the thrust available for overcoming the
combined drag of the airframe and the engine. To achieve high ﬂight speeds it is essential
that (z/AF) has a large value. This factor becomes more important as higher speeds are

approached because of the rapid increase in the aerodynamic resistance of an aircraft with

increase in the ﬂight speed.

The parameter (T/W2) is a measure of the sum of structural weight, fuel weight
and the payload that an aircraft can carry at a given ﬂight speed. Engines having larger

values of (“t/W2) make it possible to load the aircraft with either a large quantity of fuel

or more payload. Hence it is desirable that (T/W2) be as large as possible.

The parameters TSF C and (T/W2) are useful for predicting the range of an
aircraft. It is obvious that the engine giving the lowest value for TSFC will also give the
longest range for a given fuel load. Since the parameter (T/W2) also exercises an
inﬂuence on the range, judgments regarding the range of an aircraft must be based on the

considerations of both the TSF C and (T/W2 ).

The design parameters (T/AF) and (T/W.) are more related to the engine

integration with the aircraft, as such these issues are not addressed in the software under
review and the study is restricted to the performance parameters like specific thrust,

TSF C and the engine efﬁciencies.

128

11
11
1.

 

For the purpose of study, the engine operation was simulated to cover the entire
operational envelope for the design point by varying Mach number and the altitude. For
the selected design, the operational limits of the engine are depicted in Figure 6.1. It
reveals that the turbojet operated alone between Mach 0.65 at sea level and 0.6 at 19000
meters. The joint operation of the turbojet and the ramjet was commenced upto Mach
2.89 at sea level and 3.56 at 19000 meters. Beyond this Mach number the ramjet took
over alone and kept producing positive thrust upto Mach number 6.73 at sea level and

upto the Mach 7.9 at 19000 meters.

At higher altitudes beyond 13000 meters, it is observed that the limiting Mach for
the turbojet alone, joint operation and the combination stayed almost constant. This trend
agrees with the fact that at higher Mach numbers when operational thermal limits are
approached, the thrust goes down and approaches zero when free stream velocity

approaches the exhaust jet velocity.

The design turbine inlet temperature (TIT) is kept as 1350 K against a value of
1700 K now achievable [Hills and Peterson 1992]. If enhanced, this limit may

considerably increase the turbojet thrust and the maximum operable Mach number.

The ramjet exhaust is kept fixed equal to the burner area and exhausted in the
mixer. As such, the nozzle effect for better ramjet thrust is absent. This arrangement does
not take full advantage of ramjet thrust at low Mach numbers. The compressor pressure
ratio required to minimize the speciﬁc fuel consumption is much less for the supersonic

ﬂight than for subsonic ﬂight.

129

 

 

 

262:.“ can BEES. non—2 EsEcaE 8.. owcﬁ Ecocﬁoao “6.563023% _.o oSmE

52:52 £022

o.® mK 0.x. no o.© Wm 0.0 0+ 044 0.0 oh. mam ON 0.—

O.—

md 0.0

 

 

 

 

c c o I. u a o I o a a o o o o a a Q o u o no. - o n no. 0 o a an. a o o n o I a o .oo o n 0 too o c I 0.: n o 0 one u n V 0 c o s .1

L

o. 1 a - cl

u....1

 

 

 

mOZ<m U<ZOP<WEQO Hm22<m0mm31r

o
N

OF
NF
2:
or
mp
ON

(W1) epnmlv

130

The lower value of compressor pressure ratio at designed point improves the
turbojet thrust at supersonic Mach numbers and correspondingly lowers the speciﬁc fuel
consumption. In other words the lower the compressor ratio the higher the limiting Mach

number the turbojet can attain in supersonic ﬂights.

At present the design point considerations are limited to the use of total air mass
ﬂow rate for the useful thrust and no air tapping is provided either for cooling purpose or
for wind milling of the turbojet when it is shut down. Practically the air tapping is
required for both of these purposes. Inclusion of these considerations may change the

thrust and TSFC picture a little.

The velocities of the air entering the combustion system are of the same order of
magnitude for both turbojet and the ramjet. Consequently, both engines require
approximately the same combustor cross sectional area to pass the same volumetric
airﬂow rates. For the ramjet engine, the frontal area is equal to the burner cross-sectional
area, but for the turbojet the frontal area is dictated by the diameter of either the
compressor or the turbine, whichever is larger. In general, the cross-sectional area of
either the compressor or the turbine greatly exceeds that of the combustion chambers.
Therefore, the frontal area of a turbojet is inherently larger than that of a ramjet having
the same air induction capacity. The difference may become relatively small when axial
ﬂow compressor with increased air induction capacity per square meter of the frontal

area, and turbine with cooled blades and disc is made available.

131

“V.

 

m.
.-

 

6.2 Off-Design Performance Characteristics of the Engine

 

Off-designed engine performance was checked by plotting various performance
parameters by varying ﬂight altitude and the Mach number. The results obtained from the

software in respect of these parameters are discussed in the following paragraphs.

6.2.1 Specific Thrust and TSFC

“-h‘ﬂ
- l

The speciﬁc thrust (thrust per unit mass ﬂow rate) is a criterion of the size of the
engine required for producing speciﬁed total thrust. For a fully expanded nozzle the

speciﬁc thrust is given by

mi=[(1+f)u.-u.l

a

since f << 1, it may be ignored, then

 

Jib—5‘4) (6.1)
ma u

It is apparent from equation (6.1) that to achieve a large value of speciﬁc thrust the

velocity ratio must be kept small.

132

From equation (4.48) the TSF C in standard units [kg (fuel)/hr/kN] is defined as

(1 000)(3600) f

(a)

Clearly, for a given fuel-air ratio TSF C is inversely proportional to the speciﬁc thrust.

TSFC:

 

Figure 6.2 shows the comparison of plots for speciﬁc thrust and the TSF C verses
Mach number at sea level and 11000 meter altitude. At low Mach numbers where only
the turbojet operates, the engine produces a higher speciﬁc thrust value because of low
velocity ratio. The plot shows a slightly decreasing trend as the Mach number increases
with gradual decrease in the slope of the curve as the Mach approaches a value closer to
0.6. This refers ﬁrst to an increase in the velocity ratio with increasing Mach and then
stability in the velocity ratio as the Mach number increases up to 0.6. Correspondingly,
the TSF C reﬂects ﬁrst a gradual followed by a sharp increasing trend owing to decrease in

the specific thrust in that Mach range.

Above the minimum Mach of the ramjet operation (0.604 at 11000 meters), the
joint operation of the two engines is realized. At that Mach number, a sudden fall in
speciﬁc thrust and sharp rise in the TSF C is observed. It is because the code calculates the
minimum Mach number of the ramjet operation taking reference of the Mach where
ramjet just starts to produce positive thrust. At that point, the ramjet gets comparatively
less airﬂow that is surplus after meeting the turbojet engine demand and the velocity ratio
is close to unity that results in a marginally positive speciﬁc thrust produced by the
ramjet. Although at this point a higher proportion of speciﬁc thrust is realized by the

turbojet, an overall decrease in the speciﬁc thrust is observed due to poor contribution of

133

 

Stat? 2632a 53» Dump. 95 385 2.38% Co :omEQEoU Nd oSmE

59:32 5022

m m to m N r o

 

...........

 

 

................................................

b h -

 

 

F _ _ u
Acomtoquov

Emsiz :93 m> 8mg 4.6 emamzbam

00 —
OON
00m.
00¢
com
000
com
00m
00m
000 P
00 r _
CON F

3331 78150114198

134

by the ramjet. Consequently, a sudden rise in the TSF C takes place at this Mach number.

Figure 6.3 shows a comparison between the speciﬁc thrust and TSF C for the
minimum Mach for ramjet operation of 0.6 and 1.0. It can be seen that when the ramjet
operation was suppressed up to Mach 1.0 a substantial increase in the engine speciﬁc

thrust was observed between Mach 0.6 and 1.0. The effect on the TSF C can also be noted.

In the range of the Mach numbers where the two engines operated jointly it is
observed that the engine produces the maximum speciﬁc thrust at Mach 2.0. The thrust
curve starts to fall beyond this Mach and reaches to its minimum at Mach 3.57 where the
turbojet is shut down for temperature reaching to the deﬁned turbine inlet temperature.
The reason for this behavior is that between Mach 0.6 and 2.0 both the engines contribute
positively towards thrust. After Mach 2.0 the temperature difference across the turbojet
combustor starts decreasing for the ﬁxed turbine inlet temperature and less and less fuel is
needed to be burned in the combustor. This reduces the turbojet thrust more rapidly than
the increase in the thrust proportion by the ramjet with increasing Mach numbers. The
overall effect is reﬂected as a marked decrease in the speciﬁc thrust. On the contrary, in
this Mach range due to less fuel burning in the combustor an increase in the ﬂight Mach

has only a small effect on TSF C and its slope stays almost zero.

The rise in engine speciﬁc thrust with increase in the turbine inlet temperature is
depicted in Figure 6.4. It can also be noted that for a given compressor pressure ratio,

raising the turbine inlet temperature may or may not rise the speciﬁc fuel consumption.

135

 

 

 

 

£268 000: 3
£632 mecca; 6:5: 5 owcazu £3, Ummk new $25 658% 00 588225 m6 oSwE

08:32 £022
0% 0+ 0.0 0.0 ON ON 0; 0; 0.0

 

 

 

 

 

 

AE coo a F 26 an: Bag 88883 6.56%
1032 m> 010m? 6% HmDmImim Hmw§<mOmmDm

00 F
000
00m.
004
000
000
00x1
000
000
000 F

3381 7813910198

136

 

 

320E 000: a count? PE. ..8 Dump. 93 385 2.060% 00 8030800 v.0 Emmi

$9532 5002

0R OK 0.0 0.0 0.0 0.0 0.4 0.4 0.0 0.0 0N. ON 0; 04 0.0 0.0

 

 

 

 

 

 

A....._......._m....__. 3
88 6% emamzbom do 20942638

0

00 F
00m
000
00."4
000
000
00\.
000
000

000 F

3381 818084198

137

For pressure ratios associated with minimum fuel consumption, increasing the turbine

inlet temperature can reduce specific fuel consumption somewhat.

At the ﬂight Mach numbers above 3.57, the turbojet is shut down since the
temperature reaches its maximum thermal limit and the ramjet alone produces the engine
thrust. Because of higher thermal limits associated with the ramjet, comparatively higher
thrust values are obtainable than the turbojet for the same Mach number. A sudden rise in
the engine speciﬁc thrust at Mach 3.57 is the result of sole thrust contribution of the
ramjet in the absence of rather inefﬁcient turbojet at such a high Mach number. The
engine achieves the highest value of speciﬁc thrust close to Mach 3.52 because of lowest

speed ratio in the sole ramjet operational Mach range.

At ﬂight Mach of 4.52, the ramjet designed thermal limit (3000 K) was reached
and the stoichiometric burning of the fuel was no longer possible. The speciﬁc thrust
starts decreasing sharply and the TSFC shows an increasing trend beyond that Mach and
continues to increase further as the ramjet approaches the limiting Mach number of

engine operation.

6.2.2 Thrust Ratio Verses Mach Ratio

The engine performance was also studied by plotting different ratio curves. These
ratios were obtained from dividing the actual parameter under the prevailing ﬂight
conditions by its respective value at design point. Figure 6.5 shows the plot of thrust ratio

verses Mach ratio for different altitudes. It is observed that:

138

 

 

 

1......—

 

'1 .hﬂa

cocci; 2632a 53, 0:8 £622 833 0:8 SEE 00 538880 We 2sz

Ac0_m60\_030<v 030m 3002
00.N ONN omé 044 00. F

 

110 .

anom\..\ ..... H
. .11.. H .....

/l

............ n... c u u a s r o a

©7541 1912 m> 95E HmDKIF

 

 

(ubyseg/mnpv) 01103 180.111]

139

a)

b)

The trust ratio is minimum both at extreme Mach ratios and attains its
maximum value close to the median Mach ratio. The trend is in line with the
natural behavior of the thrust generation of an aircraft engine that initially
increases with the Mach number, and then starts falling beyond a certain Mach
when the thermal limits are approached and the mass ﬂow through the engine

decreases (also see Figure 6.6).

For a given Mach number, the thrust ratio decreases with increase in the
altitude. It is because of decrease in density with increase in altitude that in
turn reduces the mass ﬂow rate for a given velocity and intake area. Since the
thrust is directly proportional to the mass ﬂow rate (Continuity equation), it

falls as the altitude is increased.

At Mach ratio of 1 (ﬂight Mach 2.5), the thrust ratio curves at lower altitudes
are discontinuous and tend to shift at higher Mach ratios as the altitudes is
increased. For altitudes beyond 11000 meters, the discontinuity stays at Mach
ratio 1.4. This behavior refers to the thrust jump (Section 6.2.1) when turbojet
is shut down and the ramjet takes over the operation alone (Figure 6.6). At
lower altitudes the turbojet turbine thermal limit is reached at comparatively
lower Mach numbers than that at higher altitudes (density effect). Moreover,
at higher altitudes beyond 11000 meters the maximum operable Mach for the
turbojet almost stays constant at 3.57 (Figure 6.1). This fact is depicted in
Figure 6.5 by a noticeable reduction in the thrust ratio between altitude curves

for 9000 and 11000 meters at Mach ratio 1.4.

140

 

 

 

 

COSEHA; OUSumu—m r235 OHM.— BOG mmmE 6:0 “mar: :30“ “HO COmCdQEOU 0.0 ohswmnm
59:32 5002
Om 0.5 0.0 0.0 0.0 0.0 044 0.0 0.0 0.0 0N ON 0; 04 0.0 0.
_ _ _ _ t

.___._.zl____.

 

~ M ‘ ( (

   
  

T .

1

0
0

00m
00¢

 

 

 

 

ACOmCOQEOQV

£00232 IQ<§ m> “1:50 >>Ot_l._ mm<§ bco HmDmIH 0<FOF

(s/bx) 9103 MOH ssow

(N4) 18001110101

141

d) The smooth negative slope of the thrust ratio curves beyond Mach ratio 1.8
represent the gradual decrease in the engine thrust at higher Mach numbers
when only the ramjet is in operation. In this region the slope of the curves
become less and less negative with increasing altitude. It refers to the

maximum achievable Mach by the engine as the altitude is increased.

e) The engine maximum achievable Mach above 11000 meters stays almost
constant at 7.9 (Figure 6.1) and the engine produces no positive thrust. It
explains the reason for most of the thrust ratio curves representing higher

altitudes to converge around Mach ratio 3.

6.2.3 Thrust Ratio Verses Altitude Ratio

Figure 6.7 shows the plots of thrust ratio verses altitude ratio for different Mach

numbers. It represents the following:

a) At lower altitude ratios, the thrust ratio is higher particularly in supersonic
ﬂight below Mach 6.5. It corresponds to the fact that for the same ﬂight Mach
the mass ﬂow rate increases more rapidly at lower altitudes than that at higher
altitudes (Figure 6.6). This results in higher thrust ratios for the engine
operation at low altitudes. At higher Mach numbers (4.5 at sea level and 5.5 at
11000 meters), the mass ﬂow rate starts decreasing and the thermal limits of
the engine are approached that cause a decrease in the thrust of the engine.
Hence, the thrust ratio exhibits lesser and lesser change with change in altitude

ratio for a given Mach number and the slope of the curve becomes almost zero

142

 

 

 

528:: :82 E 6882: £3, 38 83:3 8.3? 2:3 3.25 00 cemtaanU 5.0 0.23.»

0:00 @0352.

 

 

 

 

 

 

 

w._. 0% #4 NF Oé m0 0.0 .vd N0 0.0
I“ 0
P
N
ll—
Ur
mm
m...
/. a
l ...................................................... / . ................ L .Vm.
. n/ - m.
on.
I ......................................................... . ixus/ . . ...... J m
B H
l / L
F ................................................................ ... ...... 1 Q
U /
I D i
.. ................................................................. . ..... J a
_ L _ _ . V L P H _ a _ _ 0 _ L r

 

OE<m 003:5,4 m> 95$ 003mm:

143

over a substantial range of altitude ratios. The curve for Mach 6.5 in Figure
6.7 represents this situation. Figure 6.6 also qualiﬁes the conclusion where it
may be noted that the thrust at Mach 6.5 has almost the same value for both

sea level and that at 11000 meters.

b) For a given altitude ratio, the thrust ratio is directly proportional to the Mach
number up to Mach 3. At Mach 3.5 between altitude ratios of 0.82 to 1.0, a
sudden rise in the thrust ratio corresponds to the altitude range where the
turbojet shuts down and ramjet alone takes over the engine operation (also see

Figure 6.6).

c) The engine achieves the highest thrust ratio of 7.2 while operating at Mach 3.5
at sea level. At this Mach, higher thrust ratios are obtained up to the thrust
ratio of 0.8. For altitudes ratios above 0.8 the engine produces maximum

thrust ratios over the entire range of its operation while operating at Mach 4.5.

d) The convergence of all the curves close to altitude ratio 1.8 represents the

engine operation at Mach ratio 3 as explained in Section 6.2.2.
6.2.4 Propulsive Efficiency

It can be seen from equation (4.49) that neglecting the fuel-air ratio for a fully
expanded nozzle the propulsive efﬁciency may be deﬁned as

214.7“.

z 6.3
1+ua/u2 ( )

77,,

144

 

Equation (6.3) indicates that large values of 17,, are obtained as the ratio

ua /u2 approaches unity: i.e. when speciﬁc thrust is small.

Figure 6.8 shows the plots of speciﬁc thrust in [kN/kg/s], the velocity ratio v and

propulsive, thermal and overall efﬁciencies verses Mach number. The propulsive
efﬁciency follows the trend as described by equation (6.3). In the low Mach region when

only the turbojet operates 77,, is lowest at Mach 0.1 where the velocity ratio is minimum.
As the velocity ratio improves with the increasing Mach, 7],, also rises until Mach 3.52 is

reached where turbojet is shut down and sudden rise in speciﬁc thrust is observed for

ramjet operation alone. Correspondingly 77,, encounters a sudden drop and then gradual

increase as the engine speciﬁc thrust deteriorates on higher Mach numbers.
6.3.5 Thermal Efficiency

The thermal efﬁciency was deﬁned in equation (4.50) as follows

n .. [<1+f)<u3/2)-uZ/2]
rh fQR

 

with the assumption (1+ f) «- 1 it becomes

 

“2 — “2
nth _ ZfQR

By introducing the velocity ratio v = u, /u2 the equation can be written as

145

 

 

$268 002 _ 3 2:: .9623 new 38:3qu .3422 6:6on 059.... ..o 203 wd 2:30

59:52 £622

 

 

 

 

A8865 000 _ 4 20
59:32 £022 m> 63%: .Q0 Uco 86:66:00 oc_0cm_

 

0.0

_.0

N0

'9.
0

‘1.
0

'\. ‘0. L“.
O O O
193 78 891998101113

«“41

00.
O
lsn

97.
0

O.

146

,2 2M (24,
rh ZfQR '

It can be seen from equation (6.4) that thermal efﬁciency 77,, reduces to zero when v = l:
i.e. when ua = u, . That conclusion is logical because when v = 1, the engine develops no
thrust and no energy is added to the ﬂuid ﬂowing through the engine. On the other hand
when v = 0, the thermal efﬁciency of the engine depends entirely on the exhaust jet

velocity and increases with at.

In Figure 6.8, the effect of v is obvious on the thermal efﬁciency, and the curve
follows an increasing and decreasing pattern of the speciﬁc curve as the velocity ratio

affects the latter. The effect of v on speciﬁc thrust has been discussed in Section 6.2.1.

6.2.6 Overall efficiency

From equation (4.51) it is seen that the overall Efﬁciency (770) is the product of the

propulsive and the thermal efﬁciencies

zu,

 

’70 = "pnth =

from equation (6.3) and for f << 1, it is reduced to
_ 2 “a /ue
7?. — 77'” 1+u2/u2

V
= __ 65
no 2n!h(l+ V) ( )

147

 

Equation (6.5) shows that the overall efﬁciency depends only on velocity ratio v and on
the thermal efﬁciency which depends somewhat on the velocity ratio.

From the Figure 6.8, the dependence of propulsive and overall efﬁciencies on the
velocity ratio is evident. The propulsive efﬁciency follows almost the same trend with
increase in Mach number as that of velocity ratio. Moreover, the propulsive and overall

efﬁciencies fall to zero for v = 0 whereas, under this condition the thermal efﬁciency

 

entirely depends on u... For v = 1, however, all the three efﬁciencies go down to zero.

F
13.
l
1
1
(1..

 

148

 

CHAPTER 7
CONCLUSIONS AND FUTURE WORK
7.1 Summary

The concept of combining a turbojet engine with a ramjet engine in a single power
plant for a high-speed aircraft is a subject of research and development in many countries
today. Although in some cases the application of a turboramjet engine has been
materialized in the form of prototype small aircraft, its large-scale commercial usage has
not yet been witnessed.

The software for the turboramjet engine under study is developed to join the
fundamental virtues of the turbojet and the ramjet in a single power plant for a supersonic
aircraft that could achieve a ﬂight Mach number over 5 and comfortably be used in civil
aviation. This software is useful for an aircraft engine designer in the conceptual design
phase for enabling the designer to simulate the ﬂow conditions through the engine for the
selected design parameters. As such, it may be regarded as a tool to reduce the decision
time in reaching the ﬁnal design of the engine. The built-in features of the software such
as variable area inlet and nozzle, logic for mode of operation as per prevailing ﬂight
conditions, inclusion of maximum thermal limits criteria and minimum Mach number
calculation at which to put ramjet in operation adds afﬁnity to the actual aircraft engines.
The design program of the software has a ﬂexibility to select, as per designer’s
requirement, any combination of 14 different parameters important to the engine design.
Through the main program, it is possible to simulate the engine operation for any Mach

number and altitude of the designer’s desire within air breathing range.

149

 

 

Simulation of the engine is possible over a large range of on—design and off-design
ﬂight conditions. However, for the purpose of demonstration a typical set of ﬂight
conditions at an altitude of 11000 meters and Mach number 2.5 was simulated. In the
absence of any real turboramjet operational data, the results are compared with the
turbojet and the ramjet individually and conclusions are drawn accordingly.

7.2 Conclusions

Some of the conclusions are as follows:

0 For the selected design, the engine could achieve the maximum Mach number

of 7.9; the limits may vary according to the design parameters selection.
0 The engine could generate maximum total thrust of 800 kN at Mach 4.25,
maximum speciﬁc thrust of 1.04 kN/kg at Mach 3.57, and the lowest TSFC at
Mach 2.5.

o The joint operation of the turbojet and the ramjet was realized between Mach
0.64 and 3.57. The speciﬁc thrust, TSFC and the engine efﬁciencies in this
range are comparable with a known example of an aircraft engine (Figure 7.1).

0 As expected, a sudden rise in the engine thrust is observed when the turbojet
shuts down and the ramjet alone assumes the operation at Mach 3.57. It is
because of better operational characteristics of the ramjet at higher Mach
numbers.

0 The overall engine performance parameters follow the trends of a real aircraft

engine.

0 The changes in ﬂow properties across the engine follow the standard one-

dimensional ﬂow rules and show trends in line with the actual aircraft engine.

150

Turboramjet Joint Operational Range

 

 

 

 

 

 

 

  

 

  
    

 

 

(1 1000 meters)
T T I
O m
t?) 3
°3 m
"’ m
‘3 3
L o
f— ,3-
8 o
5.
m
1 2. 3
M o c h N u m b e r
. Tau ‘ 301) K
'0 :sou Spccil'lc mm _ 0.:0
i 1
0,3 _
2. I _
”I; | -—1 a
. U 6 _‘ k;
k.\'~
T; '7‘ d 0.10 ‘5'"
‘ S ‘ 11' 1' l
0 ‘1 £54.51?“ —
I 300“ .1
0.: 20m \— ..
2500
l 1 1 l 1 l
00' ‘ ‘ 7

 

 

 

 

n l l l 1
0"l .‘ 5

 

Mach numbcr. M

‘

Figure 7.1 Comparison of a known ramjet performance parameters with the turboramjet
in joint operation range [Ramjet polts taken from Hills and Peterson 1992]

151

The results show that the software returns the logical results, is useful in
understanding ﬂow conditions across the engine, and helps in the conceptual
design process of a turboramjet engine.

The ﬂexibility in both on-design and off-design Operation in the software
makes it possible to optimize the engine performance for any criteria of

optimality; speciﬁc thrust, TSFC or the engine efﬁciencies.

7.3 Future Work

During the present development of the software, few simpliﬁcations were made

following a rather conservative approach. Improvements in these areas can further

enhance the versatility of the software. Some of these are identiﬁed as the areas of the

future work.

Instead of calculating the diffuser efﬁciency, a 4% stagnation pressure loss
was introduced across the diffuser under all operating conditions. Since the
diffuser efﬁciency depends strongly on the mass ﬂow rate and the ﬂight Mach
number, it can not have a ﬁxed value for all operating conditions. The
criterion for obtaining diffuser efﬁciency may be evolved using its relationship
between the stagnation pressure ratio and the Mach number.

At present, the area allocation of the turbojet and the ramjet has been done by
ﬁxing 50% area at the diffuser exit to each of the two engines. Optimization
for area allocation is required because the overall performance of the
turboramjet engine is improved if a smaller but efﬁcient turbojet at lower

Mach numbers is coupled with the ramjet suitable for higher Mach numbers.

152

 

hi1...“

1“. *T.
I.

 

More area available to the ramjet can improve the thrust and limiting Mach of
the engine.

The bypass doors are kept ﬁxed at 50% bypass ratio. This precludes the
possibility of changing the mass ﬂow to obtain the optimum advantage from
the engine for a given ﬂight condition. Presently the ﬂow through the two
engines entirely depends on the turbojet demand and the ﬂight Mach number.
If the bypass doors are capable of changing the bypass ratio mass ﬂow may be
changed through any of the two engines and performance can be improved for
a given ﬂight condition.

The ﬂow conditions within the compressor and the turbine are not presently
addressed. Future work may include the effects on ﬂow within the
turbomachines that may affect the overall performance.

Some study is required to include taping of the airﬂow for cooling and wind
milling of the turbojet once it is shut down. The wind milling is required to
keep positive pressure in the oil and fuel system, and restart the engine at low
ﬂight speeds or for coming in for landing.

Study may be conducted to use some alternate fuel like liquid hydrogen
instead of kerosene type. It can improves the thrust to weight ratio and in turn,

the range of the aircraft.

153

APPENDICES

154

APPENDIX A

FUNCTIONS USED IN THE SOFTWARE

The following functions were use in the software developed for the turboramjet

engine. Various relationships as discussed in Chapter 3 were used to build these

functions.

A.l

A.2

A.3

A.4

A.5

FUNCTION TTKM (T, k, XMACH)

For the given value of T, k, and M this function returns the value of T0 of the ﬂow
at a given station. Equation (3.12.1) is used as the basis.

FUNCTION PTKM (P, k, XMACH)

This function calculates the value of P0 at a station for known P, k and M
respectively. Equation (3.12.2) is used for this purpose.

FUNCTION DTKM (D, k, XMACH)

With the help of equation (3.12.3) this function returns the value of pa using p, k,
and M as the input for a given station.

FUNCTION TKM (T0, k, XMACH)

By using equation (3.12.1) this function calculates for a given station the value of
T. Inputs are To, k, and M.

FUNCTION PKM (P0, k, XMACH)

If the values of P0, k, and M are given at some point, P is calculated by this

function with the help of equation (3.12.2).

155

 

 

 

A.6

A.7

A.8

A.9

A.10

FUNCTION DKM (D0, k, XMACH)

For the known values of pa, k, and M at some point, this function returns the
corresponding value of p. Equation (3. 12.3) is used for the calculation.
FUNCTION XMACH (TM, TT, PT, k, R, A)

For the ﬂow condition where mass ﬂow rate, T0,Po, k, R and duct area are known,
the ﬂow Mach number is found with the help of this function. The continuity
equation is used for its calculation. Derivation of the function appears in
appendix A.

FUNCTION CPK (k, R)

Equation (3.5.1) is used in this function in order to calculate value of cp for known
value of k and R. The unit returned for c,, is [kJ/kg 0K].

FUNCTION AR (XMACH, k)

This function returns the value of Critical Area Ratio for the ﬂow for given values
of Mach number and k. Equation (3.12.6) is used for the calculation.

The IGPROPL software

A function-based software named IGPROPL was provided by the advisor. The
software has the capability to calculate any of the thermodynamic properties for a
variety of ideal gases provided any two properties at the state in question are
known. However, in the code for the combination engine its use is restricted to the
minimum and direct use of basic equations (section 3.5 through 3.15) is preferred
solely for the purpose of the understanding of the process involved. The use of
software IGPROPL in the code for calculation of the ﬂow properties may reduce

the length of the program and it can easily be incorporated at any time.

156

APPENDIX B

DERIVATION OF THE FUNCTION ‘XMACH’

This Appendix explains the procedure adopted in formulating the function
XMACH (Appendix A). The function evaluates the exit Mach number of a subsonic

incompressible ﬂow as it passes through a varying area duct under given conditions.

 

 

 

m

I T
T’ ’ ’ P:
P, A
A, 2
M1

(1)
(2)

Figure B.1 Mach number calculations for a ﬂow through a divergent passage

The known parameters are m, 7] , Pl, A1 , M,, 732 , $2,142, and k, parameter M2 is

required to be calculated.
Procedure
From continuity equation

ﬁt: .01 “1A1 = :02 “2A2 03‘”

157

 

 

Using Ideal gas equation it becomes

liar/1| =

_ B-
RT, R u2A2 ( 2)

as 3°

it may be represented as

kP. u, Ar “’2 u: A2
,/kR7;,/kRT, _,/kRT,,/kRT,

From the deﬁnition of the Mach number, it can be written as:

 

kl"1 kP
——M = 2 M (B-3)
m .A. ,7sz 2A.
“”1 kPoz P2
M1A|= _M2A2
W. T. Po.
kR— 02
T02

&

kn kPa. 2

 

 

 

 

k-l 1/2
1+-—-M2)
[CRT 1 l JkRT k 1 k/k-l 2A2
‘ (’2 (1 M22)
2
k
“”1 MA = kPonzAz [1+k-1M2](277‘)
kRT, ‘ ‘ Hero, 2 2

158

 

Rearranging and simplifying

 

 

 

 

 

kRT —
kP1 “MiAix 02 =M2(l+k l 22TH: 1)
kRT, kpo,
-(k+l)
_P,_ MIA] 732 —M2(l+k—1 2212mm
T. 1m 2
-2(k—])
[13. IQAAIMI M =(1+__k— M22)
02 731/421”: 2
-2(k-l)
M22=(_2_) {i am _1
k_1 P02 To] AzMz
-2(k—l)
k+1
M: (i) {5 LM. _, (1,4,
k—l Rn 731142542

The parameter M2 appears on both sides of the equation (B-4) so the solution is

obtained through an iterative process.

Let the Mach (M2) on the Right Hand side be M2, and that on the Left Hand Side be Ma.
At ﬁrst Mb is put equal to zero and value of Ma is calculated. Till the time the absolute
difference of (Ma-Mb) appears greater than a value (say 8), Mb is replace by Ma. When
the difference converges within 8, the exit Mach (M2) is obtained by taking the average of

Ma and Mb.

159

APPENDIX C

CALCULATION OF MINIMUM MACH NUMBER FOR RAMJET OPERATION

The schematic diagram of a typical ramjet is shown in Figure 2.4. The flow in a
ramjet engine suffers stagnation pressure losses as it ﬂows through the engine. The Mach
number at which minimum TSFC occurs and that at which TSFC becomes inﬁnite

('c—>O), are dependent upon the severity of the component stagnation pressure losses. The

compression process (a) to (02) is not isentropic hence the stagnation pressure at the end
of the process is lower than it would be if the compression were isentropic.

The performance of diffusers may be characterized by a stagnation pressure ratio
rd deﬁned by

r 1 02
C- 1
d POa ( )

Similarly, stagnation pressure ratios can be deﬁned for combustors (re) and nozzles (r,,) as

follows:

P02
C. = 5‘6- (C-3)
P04
The overall stagnation pressure ratio is
i = rd rc rn (C'4)
Po.

160

The actual exhaust pressure PC and P6 may not equal the ambient pressure P,. However,

for constant k, the exhaust Mach number may be written as

2 k 1 P P “4”"
M3 — (1+——M2) —99-—“ —1
k—l 2 P0,}:

In terms of component pressure ratios

2 k-l P (k-l)/k
M3=—— (Hm—M2) rdrcrn—a —1 ((3-5)
k—l 2 P

C

If heat transfer from the engine per unit mass of ﬂuid is assumed negligible, then the

exhaust velocity in terms of exhaust stagnation temperature is given by

u, = M, \lkRTm/(l+%Mf) (C-6)

Since the irreversibilities have no effect on stagnation temperature throughout the engine,

 

the fuel-air ratio necessary to produce the desired T04 is given by:

(Tm/711a)_1
77b QR /Cp 711a)-(T04/7ba)

 

“1

where 772, is the combustion efﬁciency and m, QR is the actual heat release per unit mass

of fuel. The thrust per unit airﬂow rate then becomes

-_1— = [(1+f)u, —u]+—.1—(P¢ —Pa)A,
ma ma

by using equations (C-5) and (C-6) the above equation can be reduced into the form

P
- " C-7
[1 a] < >

 

i- _ 2kRTo,(m—l)_ r—
m ’0'“ (k-l)m M km”

a

 

 

 

1’. A.
ma
in that

161

k -1 P "‘"”"
m=(l+—2—M2)[rd ’2: ’3. )5] (C-8)

For a typical ramjet engine Figure B-l shows the plots of the speciﬁc thrust and
the speciﬁc fuel consumption as a function of ﬂight Mach number and peak temperatures.
The Figure B-l indicates that the slope of the speciﬁc thrust curve is positive below Mach
2.6 and if extended, will have a point of intersection on the Mach number axis some
where in the subsonic range. The study in this appendix aims at determining the point
where thrust curve intersects the Mach number axis in the subsonic range. It corresponds

to the minimum Mach below which the ramjet will not produce any positive thrust and

should not be put in to operation below that Mach.

rd 3 0,7. rb x 0.95, r" = 0.98, QR: 45.” kllkg, Ta 8 220 K

 

  

 

 
 
  

 

 

 

 

|.2
TMIX = m K
1.0 2500 Swim "W“ a 0.20
l _.
g 0.8 E
“a — 9
06 ‘ ks
kN-s ‘ —
kg ' - 0.10 “’3
/ Speciﬁc fuel _
0-4 / ‘ consumption
', -
0.2 2000 “
2500
1 1 l 1 l L
Mach number. M

Figure C.1 Plots of a typical ramjet speciﬁc thrust and fuel consumption
[Curtsey Hills and Peterson 1992]

162

After having obtained equation (C-7) it is now possible to ﬁnd out the limiting

Mach number below which the ramjet must not be operated in the combination engine.

For this analysis the following assumptions are made:

a) The ramjet nozzle is fully expanded i.e. P2 = P,

b) The mass of fuel consumed is negligible as compared with the mass of air

Considering the Left Hand Side of equation (C-7), it can be observed that in order to have

positive thrust the following condition must be satisﬁed

 

 

 

_ 2kRT0,(m—1) 12A, _Pa
(1_f)\[ (k—1)m )MVW” m. [I P]

C

if the above assumptions are incorporated in equation (C-9), it becomes

 

 

 

 

2kRT0, (m—l) > M kRT
(k -1)m “
or
ZkRT (m—l)
(1.“. W > wow.)
Let 2kRT04 = XI
(k - 1)
kR]; = X2
(rd rc rn )(HW = X3

then equation (C-11) can be written in the form

X.(-’—"—’—‘) > MZX.
m
X,(m—1) ) mMzX2

and m becomes

163

(C-9)

(C-lO)

(C-ll)

(C— 12)

 

A‘a- Ii
‘1

IF

 

m=X3[l+£2_—1M2) (C-13)

putting equation (C-12) in (013) it is evident that

X[X(1 5:1sz I] M2[X (I k—iszX]
1 3 + 2 _ ) 3 + 2 2

01'

k—l k-l
[xx3 + X1X3[—2-)M2 - X1] ) [X2X3M2 + X2X3(T)M‘]

for limiting case (zero thrust) the two sides should be equal

thus X,X, — X, + X,X3(-k2;l)M2 — X2X3M2 — X,X,(5—2——1)M4 = 0

or X,X,(52‘—1)M4—[X,X,(k—2‘l)—X,X,]M2 —X](X3—l)=0

taking X3 common

X2(k—2_1-)M4 —[X,(k—2——1)—X2]M2—X1[1—3(1—]=0 (GM)
3

Equation (014) is a quadratic of the form

aY2+bY+c=0
where

Y=M2

_X (k—l)

a— 2 —2

k—l

b=— X1—2_ —X2

and

164

 

 

1
c=-Xl[1—-—]
X3

The roots of Y can be obtained from quadratic formula

Y= —b:t\/b2 —4ac

2a

 

and M is found out from
M = H? (0.15)
The value of Y and M used should be:
(a) A positive number
(b) Smaller in magnitude out of the two values
The Mach number so obtained represents the minimum Mach at which the ramjet

operation is possible under the prevailing ﬂight conditions.

165

 

APPENDIX D

EVALUATION OF FLOW VELOCITY AND PRESSURE AT MIXER EXIT

The procedure of calculating ﬂow velocity and the static pressure at the exit of the
combination engine mixer unit is elaborated in this Appendix. The mixer has a diameter
equal to the outer diameter of the engine and receives ﬂow from the both turbojet and the
ramjet. Its mixes the two ﬂows before passing through the exhaust nozzle. For the
purpose of calculating the ﬂow conditions at mixer exit the ﬂow properties from the
turbojet are represented by subscript “a”, that from the ramjet by subscript “b” and at the
mixer exits by subscript “c”.

For the given conditions various laws pertinent to steady ﬂow may be represented
as follows:

First Law of Thermodynamics

2 2 2
ma ha+u“ +n'rb hb+£‘—’- =n’zc hc+-u—C— (D-I)
2 2 2

Unknowns are he and uc

 

Conservation of Mass

mc =ma +mb

pm). =puA>.+puA>. a”)
Unknowns are ac and p2
Momentum Integral

mau, +mbu, —mcuc = 14,1”, + Abe — ACPC (D3)

166

Unknowns are uc and P2.

Ideal Gas Relation
,, = 1:
RT
and
h = 6,, T

By converting p and h in terms of P and T only three unknowns (PC, Tc, and 14,) are left
against three equations (1 thru 3), which can be solved simultaneously.

Substituting for p and h the ﬁrst two equations take the form:

:52, (2h, + u: )+ :51, (2h, + 14,3): 1110(2ch + uf) (D-4)
and

RTcpaua Aa + RTchubAb — PcpcucAc : O (D-S)
from equations (D-2) and (D-S)

I’cucAc _ PcucAc

 

 

“W Rm.) (”6)
putting equation (D-6) in (D—4) gives

R[ma (2h, + u: ) + m, (2h, + 143)] = (2C, PcuCAc + Rn'rcuf) (1)-7)
arranging equation (D-3) for P2.

PC ___ mcuc ' (maua +mbub ' Abe - Aa Pa) (D-8)

Ac

By putting equation (D-8) in (D-7) and rearranging a quadratic in ac is obtained
(ZCP + Ryhcuf — 2Cp (maua + thbub - Abe — A, P, )uc (D-9)

- R[ma(2ha + u§)+ma (2h, + 143)]: O

167

 

Solution of equation (D-9) returns two roots, the smaller positive root represents the
mixer exit velocity (uc) in [m/sec].
The mixer exit static pressure (PC) is obtained by putting the value of uc in equation (D-8).
The static pressure P, is calculated in [Pascal].

It may be noted that subscripts a,b and c correspond to stations (11), (17), and

(18) respectively as appeared in Figure 3.1.

168

 

REFERENCES

Aksel and Eralp, Gas Dynamics. Hertfordshire: Prentice Hall International (UK) Ltd.,
1994.

AMES Research Staff, National Advisory Committee for Aeronautics Report 1135,
Equations, Tables and Charts for Compressible Flow. Washington DC: US
Government Printing Office, 1953.

Bathie William W., Fundamentals of Gas Turbines. John Wiley & Sons, Inc. 1984.

Benedict, Robert P., Fundamentals of Gas Dynamics. John Wiley & Sons Inc. 1983.

Bertin and Smith, Aerodynamics for Engineers. Englewood Cliff, New Jersey: Prentice
Hall, 1989.

Cohen, Rogers and Saravanamuttoo, Gas Turbine Theory - 3rd edition. Longman
Scientific & Technical co-published with John Wiley & Sons, Inc. 1987.

Daum, Noel. “The Graffon aircraft and the Future of the Turbo-Ram-jet Combination in
the propulsion of Supersonic Aeroplanes”. The Journal of the Royal Aeronautical
Society 63 (June, 1959) 327-340.

Foa J. V., Elements of F light Propulsion. John Wiley & Sons, Inc., 1960.

Fujimura, Tetsuji. “Hypersonic Transport Propulsion”. Aerospace Engineering (June,
1996): 7-11

Hill and Peterson, Mechanics and Thermodynamics of propulsion - 2nd edition.
California: Addison-Wesley Publishing Company Inc., 1992.

Jones and Hawkins, Engineering Thermodynamics - 2nd edition. John Wiley & Sons, Inc.
1986.

Korthals-Altes, Stephen W. “Will the Aerospace Plan Work?” Technology Review 1
(January, 1987): 43-51

McMahon P. J ., Aircraft Propulsion. Harper and Row Publishers, Inc., USA, 1971.
Portter and Somerton, Engineering Thermodynamics. McGraw-Hill, Inc. 1993.

Shepherd Dennis G., Aerospace Propulsion. American Elsevier Publishing Company,
Inc., 1972.

169

Sosounov, V. A., Tshovrebov, M. M., Solonin, V. I., Palkin, V. A., ”The Study of
Experimental Turboramjets”. CIAM, Russia, 1992.

Space Transatmospheric Propulsion Technology. [Online] Available
http://itri.loyola.edu/ar93_94/stpt.htm

Tskhovrebov, M. M., “Turboramjet Engines - Types and Performances”. CIAM, Russia,
1992.

Tskhovrebov, M. M., Solonin, V. I., Adjardouzov, P. A. K., “CIAM Experimental
Turboramjets”. CIAM, Russia, 1992.

Turboramjet proﬁle. [Online Image] Available
http://www.metaspace.com/ff/eto/SPBI102.HTM

US. Congress. House. Committee on Science, Space, and Technology. Aerospace Plane
Technology: Research and Development Eﬁ‘orts in Japan and Australia. [Online]
Available
httpzl/www.gwjapan.com/ftp/pub/policy/gao/1993/92-5.txt, October 4, 1991

Zucrow, M. J ., Aircraft and Missile Propulsion. John Wiley & Sons, Inc. 1958.

170

 

"‘11111111111111