Aerothermal Flow Path Analysis and Design of a

Hypersonic Propulsion Unit

A dissertation submitted for Master of Technology

(under the dual-degree program)

by

Amit Batra

97D01002

under guidance of

Prof. Bhaskar Roy

Department of Aerospace Engineering Indian Institute of Technology, Bombay

June-2002

CONTENTS

Abstract .................................................................................................................................. 4

Nomenclature......................................................................................................................... 5

1. Preamble ............................................................................................................................ 7

1.1 Objectives and scope of the project .......................................................................... 7

1.2 Approach ..................................................................................................................... 8

2. Introduction: hypersonic airbreathing propulsion ........................................................ 11

2.1 Ramjet ....................................................................................................................... 12

2.2 Scramjet..................................................................................................................... 13

2.3 Fixed geometry dual mode ramjet-scramjet .......................................................... 13

2.4 State of the art........................................................................................................... 14

3. Issues in hypersonic airbreathing propulsion ................................................................ 17

3.1 Combustor design..................................................................................................... 17

3.2 Fuel/Cooling .............................................................................................................. 18

3.3 Injection/Mixing ....................................................................................................... 18

3.4 Shockwave - boundary layer Interaction ............................................................... 19

3.5 Optimum inlet diffusion........................................................................................... 20

3.6 Struts.......................................................................................................................... 21

3.7 Variable geometry vs. fixed geometry .................................................................... 21

3.8 Ground testing .......................................................................................................... 21

3.9 Performance enhancement ...................................................................................... 23

3.10 Flight speed ............................................................................................................. 23

4. Theoretical background .................................................................................................. 24

4.1 Generalized one-dimensional flow .......................................................................... 24

4.2 Combustion pressure loss ........................................................................................ 27

4.3 Shock reflection and intersection phenomena ....................................................... 28

5. One-dimensional design methodology............................................................................ 30

5.1 Preliminary design methodology............................................................................. 30

5.2 One-dimensional analysis of combustor gas flow path ......................................... 31

5.3 Numerical implementation ...................................................................................... 33

2

6. Analysis ............................................................................................................................ 35

6.1 Available information .............................................................................................. 35

6.2 Data verification ....................................................................................................... 37

6.3 Cycle analysis ............................................................................................................ 38

6.4 Component analysis: inlet........................................................................................ 40

6.5 Component analysis: isolator .................................................................................. 43

6.6 Component analysis: combustor ............................................................................. 44

6.7 Component analysis: Nozzle.................................................................................... 49

6.8 Preliminary layout.................................................................................................... 49

7. Parametric performance analysis ................................................................................... 51

Closure ................................................................................................................................. 59

References............................................................................................................................ 61

Acknowledgements .............................................................................................................. 64

3

Abstract

Application of airbreathing hypersonic powerplants for propulsion poses a challenge to the

world scientific community, even though the gasdynamics and aerodynamics of hypersonic

flow have been investigated for several years now. In the present work, preliminary level

work has been done to cover the ground for the design of a dual-mode ramjet scramjet

powerplant for hypersonic vehicles. Various issues in the design of such powerplants have

been presented. Brayton cycle suited to the mission requirements have been constructed and

analyzed. An analytical approach to aid the initial design of the dual-mode ramjet-scramjet

powerplant for a hypersonic vehicle has been laid down. ‘Method of influence coefficients’

have been suggested and numerically implemented for developing one-dimensional

analysis capability. A detailed user manual for this software is separately made available.

‘Method of characteristics’ has been suggested for detailed flow mapping in the nozzle.

Simplistic estimate of the boundary layer and the forebody shock reflections in the inlet is

made. The empirical laws available from earlier literature have been implemented to obtain

the required length of the isolator, without going to the details of the shockwave-boundary

layer interaction. A preliminary geometry of the propulsion unit has been proposed, which

makes use of the detail combustor design studies done separately by others. The parametric

performance studies for the engine has been done using an available in-house developed

code.

4

Nomenclature

a = sonic velocity (m/s)

A = cross-sectional area of gas flow path (m2)

b = width of strut (m)

CA = concentration of species A (mol/m3)

Cd = coefficient of drag

Cp = specific heat (kJ/kg K)

d = exit diameter of fuel injection nozzle (m)

DAB = molecular diffusivity of A in B (m2/s)

Ea = energy of activation for a reaction (kcal/mol)

f/a = fuel air ratio of mixture

f = friction factor

h = height of strut (m)

j = molar diffusivity flux (kmol/m2·s)

k = rate of reaction constant

k0 = frequency factor

Lm = mixing length (m)

M = Mach number

m = mass flow rate (kg/s)

P = pressure (kN/m2)

PRF = pressure recovery factor

r = air fuel velocity ratio

Re = Reynolds number

s = air fuel density ratio

T = temperature (K)

u = velocity of stream (m/s)

w = rate of reaction (kmol/s·m3)

x = axis parallel to motion of vehicle (origin is kept at center of first injector)

y = an axis parallel to pitch axis of the aircraft

γ = ratio of specific heats of a gas

5

δm = mixing layer thickness (m)

φ = equivalence ratio

η = efficiency

ρ = density (kg/m3)

ψ = static temperature ratio between combustor inlet air and free-stream air.

Subscripts :

A = air

F = fuel

L = lean

R = rich

b = burner (combustor)

c = compression

e = expansion

st = stoichiometric condition

0, t = stagnation property (stagnation temperature, stagnation pressure)

6

1. Preamble

1.1 Objectives and scope of the project This project aims toward the design of a dual-mode (ramjet & scramjet based) air-breathing

powerplant for an air-launched hypersonic research vehicle (HRV). To achieve preliminary

analysis and design capability, one-dimensional aerothermodynamic analysis methodology

of the hypersonic propulsion unit is to be developed and numerically implemented. A 1-D

gas flow path analysis code is to be developed based on the selected methodology. The

code will take into account the average flow path parameters across forebody, intake,

isolator, combustor and nozzle ducts. The output will predict the performance of the

propulsive unit in terms of thrust, SFC etc. at design point as well as off-design points. The

software will be capable of analyzing various geometries so that different designs can be

compared and parametric study is made possible, leading to a good preliminary design.

The above task requires integration of diverse fields, e.g. subsonic and supersonic

gasdynamics and combustion phenomena, shock-boundary layer interaction, forebody

compression, aftbody expansion and intake shock structures etc. under varying operating

conditions.

The output from the project would contain:

- Geometric details of engine intake, isolator, combustor and nozzle.

- 1-D analytical modeling of the entire flow including a simple combustion

modeling.

- Flow parameters (Mach number, pressure, temperature) along the length of the

engine.

- Performance map of the engine (in terms of the thrust, SFC, pressure recovery).

- Effects of the following parameters on the performance of the engine

Altitude and Mach number

Inlet flow angle

Flow path geometry.

7

1.2 Approach One-dimensional aerothermodynamic solution of the flow inside the propulsion unit is

utilized to arrive at a baseline configuration. This analysis would produce the aerodynamic

and thermal map and decide the geometry of the flow path of the propulsion unit. The 1-D

solver facilitates a preliminary optimization of the design of various components. For the

development of understanding for modeling and design, the various aspects of the problems

are identified.

Gas dynamics aspects: The flow inside the propulsion unit is essentially a generalized

flow with area variation, heat addition, mass injection and friction. The vehicle makes use

of the shocks arising from the vehicle for compression. It is, therefore, important to

understand the shock phenomena, predicting the onset of shocks and the reflection and

absorption phenomena.

Hypersonic flows normally have thin shock layers, which interact with the boundary layers

and make the flow phenomena complex [1]. Shock - boundary layer interaction phenomena

in the forebody affects the capture area and therefore affects the inlet design [13]. It

interferes with the diffusion in the inlet-isolator region and is of prime concern in the

isolator design. At high temperature, substantial amount of flow energy goes to dissociation

and excitation of vibration degree of freedom of the molecules [1]. This results in what is

known as high temperature gas dynamics and involves certain special effects, which are

essential to the design. Numerical methods such as method of influence coefficients (MIC)

and method of characteristics (MoC) have been extensively used in literature and detailed

3-D codes based upon it are found [1]. They find utility in the present study.

Air chemistry and real gas effects: The predictions would be better if the Cp and γ values

are taken based upon the local temperature and composition. Equilibrium air chemistry

software based on minimization of free energy is available in open literature. It can be

modified to suit present requirements. Turbulence levels of air largely dictate the losses in

flows. The transition Reynold’s number, up to Mach 10 is of the order Re ~ 107. At Mach

20, transition Reynold’s number is of the order Re ~ 108. The effect of low-density rarified

flow is studied using Knudsen number. At Knudsen number, Kn ~ 0.03, the temperature and

velocity slip starts occurring at the surface. After Kn ~ 0.2, the continuum assumption

8

becomes invalid. For the present mission, the maximum Kn would be around 10-5. So,

rarified gas dynamics may not be considered for the present problem [13].

Combustion model: Single or multiple fuel options are available. The thermo-chemistry for

one-dimensional equilibrium can be obtained by NASA-ODE codes. For 1-D analysis,

combustion phenomena can be considered as a simultaneous mass and heat addition

phenomena. Scalability limitation in the combustion test results is a serious problem.

Vehicle aspects: The engine-airframe integrity here is much more important than in the

conventional aircrafts. This is because the forebody contour is used to generate oblique

shocks that compress and direct the flow into the inlet. Also, at the nozzle end, it’s the

vehicle body that acts as the nozzle wall.

Forebody compression: This is needed to increase the capture area for the intake and hence

the mass flow rate. The oblique shocks also help in directing the flow to the engine inlet. A

choice between finite and infinite number of such oblique shock appears. Normally, for

design simplicity, a finite number of forebody shocks are preferred [13]. Basic cycle

estimates show that in order to achieve adequate compression efficiency, at least two, and

preferably three or four oblique shock configuration should be used. The design chosen for

HRV is a two-shock configuration.

Typically, the underside of the vehicle to which the engine is mounted, consists of a wedge

(~ 15o). If necessary, for approximate aerodynamic analysis, local surface inclination

methods can be applied [1].

Isolator may not be required if proper shaping of the combustor area is achieved.

The number of injectors, their configuration and strut geometry is a critical factor. Struts

may be used to divide the combustor into smaller parts as well as housing of the injectors.

For the present engine size, two struts (resulting in three flow regions) appear to be

appropriate.

Combustor: There are two different concepts based on whether to separate spatially the

ramjet and the scramjet combustion zone. In designs with separate combustion zones, it is

proposed to use as much of the scramjet portion as isolator for the ramjet. The injector

design for the two combustion modes is a highly specialized task. Prediction of engine hot

points is important for designing re-generative cooling.

9

Performance estimation: The engine works on the Brayton cycle. Thermodynamic cycle

analysis is carried out to estimate the performance of the engine. This estimation requires

various efficiencies as lumped input quantities. In absence of detailed design and analysis

tools, some realistic values should be taken from literature to estimate the cycle

coordinates. Better estimates of efficiency will be through performance maps for engine

components, i.e. inlet, nozzle etc. that can separately be generated. This would require the

modeling of separate parts.

Modeling aspects: A simple one-dimensional software tool for the analysis of a particular

geometry can readily be made based on method of influence coefficient (MIC) [36].

Preliminary analysis of some representative geometry can thus be done.

The flow domains to be analyzed are:

Forebody: The forebody oblique shock structure can be obtained for a given geometry and

operating condition. Thus, average flow quantities at any station between the forebody and

the inlet cowl can be obtained. An estimate of ‘spillage’ flow can also be obtained form

this.

Inlet and isolator: The shock reflections expected for a given geometry can be analyzed

using inviscid shock reflection theory. For the region of isolator free from shocks MIC can

be employed.

Combustor: For one-dimensional analysis, it would be appropriate to assume combustion as

a heat and mass addition process and so an existing model can be used with the MIC [36].

Boundary layer losses: For performance estimation purpose, the influence of boundary

layer friction can be accounted by including a hypothetical, constant pressure duct with

friction [13]. For simplicity, the presence of forebody boundary layer can be accounted for

by estimating its displacement thickness at the inlet face.

Nozzle: The wave structure resulting in the nozzle part needs to be studied in detail. This

may need more detailed methods like method of characteristics, left beyond the scope of the

present work.

10

2. Introduction: hypersonic airbreathing propulsion

Air-breathing ramjet and scramjet engines are attractive because of the high-speed,

sustained atmospheric flight that they promise. Until now, hypersonic velocities have been

achievable only using rocket engine. Due to the large weight of the oxidizer that needs to be

carried in a rocket, its payload fraction is very poor as compared to air-breathing engines

(e.g. gas turbine engines), where the atmospheric air is used to assist fuel combustion. But

the maximum Mach number range that the gas turbine engines can reach is far lower than

what the rockets offer. Hypersonic air-breathing propulsion proposes to offer best of both

the worlds. The benefit of ramjets over rockets is that they utilize the oxygen in the

atmosphere to burn the fuel rather than having to carry the oxygen in the vehicle. The

elimination of the need to carry the oxidizer along translates into increased payload. This

will result in cheaper access to space as well as fast inter-continental travel. The proposed

ramjet and scramjet engines will extend the atmospheric flight envelop to Mach number

range as high as 25.

Ramjets and scramjets are jet engine with no rotating machinery as present in current jet

engines. Rather than using rotating compressor blades it utilizes the speed of the vehicle

and the contour of the vehicle undersurface to compress the incoming flow. Therefore term

Fig. 2.1 Extension in flight envelope offered by ramjets and scramjets

11

‘ramjet’ is coined because the compression takes place due to the ramming action of the

high-speed flow. Scramjet is a special type of ramjet suited for higher Mach number

operations. Scramjet engine is termed so because the flow through the engine stays

supersonic throughout. The fuel is added and burned at supersonic speeds.

Just as a gas turbine engine, the ramjet and scramjet are based on Brayton cycle. The

difference in the operating regimes of different engines results in the difference in the

mechanism and the extent of compression and expansion in the thermodynamic cycle.

2.1 Ramjet A ramjet achieves compression of intake air by the forebody shocks and forward speed of

the air vehicle. Before entering the diffuser passage, the free-stream air meets the oblique

shocks emanating from the vehicle forebody. This partially diffused air, upon entering the

intake of the aircraft is further diffused in the diffuser passage, by the convergent-divergent

contour and shock structure (consisting of a normal shock train), to subsonic velocities

comparable to those in a turbojet. The expansion of hot gas (through a Convergent-

Divergent nozzle) after fuel injection and combustion accelerates the exhaust air to a

supersonic velocity higher than that at the inlet and creates positive thrust. Hydrocarbon

fuel is normally used [31].

Fig. 2.2 Schematic of a ramjet propulsion unit [13]

12

2.2 Scramjet Scramjet stands for ‘supersonic combustion ramjets’. Beyond a certain Mach number range

( ) it becomes inefficient to diffuse the high inlet velocities to subsonic range for

combustion. The scramjet differs from the ramjet in that the diffusion of flow is only partial

and uses oblique shock train to obtain it. Thus fuel injection, mixing and combustion takes

place at supersonic speeds through the engine. It has a simpler gas-flow path, but is vastly

more complex, aerodynamically, than a jet engine. Hydrogen is normally the fuel used [31].

7≈

Fig. 2.3 Schematic of a scramjet propulsion unit [13]

2.3 Fixed geometry dual mode ramjet-scramjet Any air-breathing flight vehicle operating at hypersonic speeds will require a combined

cycle engine that operates efficiently through out the mission, from low subsonic speeds to

the high supersonic or hypersonic speeds. Curran and Stull proposed the dual-mode ramjet-

scramjet engine concept in 1964 [17]. This concept integrates the ramjet and scramjet into

one with an aim to operate in either mode depending on the speed range requirement. Here,

the gas-flow path geometry is more or less similar to the pure scramjet, so that the

Convergent-Divergent (C-D) geometry present in a ramjet is not present here. The ability to

shift from one mode to the other requires two things. Firstly, the control of shock-train

structure in the inlet so that a choice can be made between the normal shock train and

oblique shock train during ramjet (full diffusion) and scramjet (partial diffusion) modes

13

respectively. This is done by controlling the combustion backpressure and fuel flow rate by

the injectors. The second requirement, which occurs only during the ramjet operation mode,

is to choke the subsonic flow in the combustor “thermally” to make it supersonic again.

This requires high rates of combustion and energy release. It is further discussed in chapter

3. The mode transition is a complicate system level problem and requires special attention.

Fig. 2.4 Schematic of a fixed geometry dual-mode ramjet-scramjet [17]

2.4 State of the art The concept of supersonic combustion ramjet attracted attention after the conventional

ramjet technology matured, about forty years ago. Early work was started by Ferri in

Brooklyn Polytechnic Institute, Billig with Avery and Dugger [8] in John Hopkins

University, and Weber and MacKay [35] for NACA. Based on this foundation work, a

number of projects like Incremental Flight Test Vehicle (IFTV), Hypersonic Research

Engine, Aerothermodynamic Integration Model, Supersonic Combustion Ramjet Missile

(SCRAM), National AeroSpace Plane (NASP), started in the USA. Scramjet program in

Russia or former USSR, has been in progress since late 1950s. Flight tests were conducted

on Kholad, the Hypersonic Flying Laboratory. Curran [5] gives further review over last 40

years of efforts in the USA, Russia, France, Germany, Japan, Australia and other countries.

Most of the work was terminated in 1980s in favour of rocket propulsion, but interest in

14

scramjet has revived in last decade. Hypersonic airbreathing propulsion offers mission

effectiveness by reducing on-board propellant load in favor of payload and therefore

making it cost-effective. According to an estimate, the space launch cost can be reduced

form the present $25000 per kg to $2500 per kg [30]. Till date, extensive study and

experimentation at the laboratory level has been carried out through out the world. But

only a little progress could be made at flight test level. The fastest airbreathing engine-

powered airplane, the SR-71, can cruise just above Mach 3. History’s only hypersonic

plane, the Mach 6.7 X-15 of U.S. used rockets only [25]. Recently, NASA’s hypersonic

experimental vehicle X-43A had an accidental failure during the first attempted flight test.

Till date, very few full scale ground testing could be carried out, owing to various problems

(discussed in chapter 3). Under the Hyper-X program of NASA, wind tunnel tests of a high

fidelity models in Mach 6 and 10 tunnels have been carried out to obtain detailed

aerodynamic characteristics [14]. Actual flight engine has been tested in the high

temperature tunnel at full flight conditions to evaluate fueling techniques and to determine

engine performance for comparison with the flight data [14]. In order to keep pace with the

world, India has entered the field with getting initiated on projects on hypersonic reusable

launch vehicle (Avatar, DRDL), hypersonic transport vehicle (ABPP, ISRO) and small dual

mode ram-scram engine for missile propulsion. The preliminary design, database

development and development of test facilities is under progress. The rate of progress and

the amount of manpower involved certainly promises a bright future. Table 2.1 summarizes

the various programs going around in different countries.

15

Table 2.1 Hypersonic program - world scenario [24].

country Program Application Status Remarks X-30 (NASP) SSTO mission Postponed indefinitely Speed –Mach 25

Scramjet propulsion – Hydrogen fuelled

X-34 Demonstrator for re-usable launch vehicle

First flight test completed

LOX-Kerosene Rocket Development of TPS materials

Hypersoar Global reach and strike mission

Design under progress RBCC engine with skip trajectory

USA

Hyper-X (X-43)

Hypersonic experimental research vehicle

Wind tunnel testing Test flight in 2001

Demonstration of Ramjet/Scramjet engine with hydrogen

Japan HYPR project Re-usable launch vehicle

Under progress Variable cycle engine HYPR-90-T Air turbo ram expander

-

Trans-atmospheric vehicle and military application

Demonstrated Hydrogen burning scramjet model on top of rocket in 1991

Further work not known

Russia MARK (Multi-purpose aerospace system)

TSTO transport Design under progress Hybrid powerplant with airbreathing engine in Mach range 0-20

Hypersonic Technology Program (HPT)

Technology development

Hydrogen Combustion Intake tests up to Mach 7

Program initiated in 1998

Germany Hypersonic

Technology Experimental demonstrator (HYTEX)

Flight testing to validate hypersonic technology

Inlet models tested at hypersonic speeds

Flying laboratory or test beds

FESTIP (Future European Space Transportation Investigation Program

Space Transportation

-

To develop hypersonic technologies

France

PREPHA Military application - -do-

UK Skylon Low cost space access

Design under progress Airbreathing and rocket propulsion

16

3. Issues in hypersonic airbreathing propulsion

Issues such as mission requirements, integration of inlet/isolator, combustor, nozzle,

airframe, fuel system specifications and cooling concepts are essential considerations in

design. Also, factors such as size, weight, and design complexity are as important

considerations as the performance characteristics. Some of these important design issues

are briefly investigated here. The various classes and general characteristics of

hypersonic airbreathing vehicle concepts are summarized in table 3.1 below. Table 3.1: General Characteristics of hypersonic airbreathing vehicle concepts [32].

Mission Flight Mach Propulsion System Flow-path

geometry Fuel Flight duration Vehicle length (ft)

Tactical Missile 6 – 8 Dual combustor ramjet

and/or rocket

Fixed, passively cooled

Liq. HC, slurry, solid HC 10-12 min.

Overall: 5-15 Combustor: 2-5

Nozzle: 2-5

Trans-atmos. Missile

0 – 25 Dual mode

ramjet/scramjet +many low speed options

Variable geometry

Liq. H2, Liq. O2 20-30 min.

Overall: 100-200 Combustor: 2-5 Nozzle: 50-80

Hyper-cruise

0 – 8 0 – 15

M 6-8: Turboramjets M 15: scramjet

Variable, actively cooled

Mach 6-8: HC Mach 15: Liq. H2

M 6-8: 1-3 hr.

M 15: 1hr.

Overall: 100-200 Combustor: 2-6 Nozzle: 50-80

3.1 Combustor design It can be noted in table 3.1 that the combustor length remains the same for all the classes

of vehicles. The wall-shear losses can drastically reduce scramjet engine performance.

Simply adding combustor length for better mixing/combustion efficiency is usually not

possible. This suggests that the supersonic combustion processes are inherently mixing-

limited [32]. In fact, the progress in realizing a scramjet powered hypersonic vehicle is

hindered mainly by the design of a combustor. Technical hurdles like fuel injection and

mixing without severe shocks, combustor cooling, wall friction losses, thermal choking,

and combustor gas dynamics poses a challenge. Appropriate matching of gas dynamics

and combustion is essential for production of useful thrust. Injection of suitable fuel in an

appropriate amount, in an appropriate fashion and into a conducive environment is to be

ensured for sustaining flame. Also a check is to be put on heavy losses in total pressure.

An assessment of mixing, chemical kinetics, heat liberation and pressure losses is to be

incorporated in the gas dynamic analysis of the combustor.

17

3.2 Fuel/Cooling Hydrocarbon is preferred for ramjet and hydrogen is preferred for scramjet operation.

However, possibility of JP based fuel for Mach 6-8 operation is being extensively looked

into [32]. The idea of ‘thermal choking’ being inherent to a fixed geometry ramjet-

scramjet design demands high rate of combustion and endothermicity of the fuel, which

the kerosene based fuel is yet to demonstrate at supersonic combustion speeds.

A strong coupling between the fuel endothermicity, combustor characteristics and

cooling requirements has been identified. The vehicle structure can be used as a heat

exchanger to crack the hydrocarbon fuel, thereby shedding its heat content. The

composition of cracked fuel products depends strongly on the time-temperature history of

the vehicle. The hydrocarbon fuel remains near its thermodynamic critical point within

the heat exchanger. So small changes in temperature and pressure may lead to large

variations in density, viscosity, ratio of specific heats etc. and may result in instability

and catastrophic failure. The precise control of thermal cracking process is thus essential

to the process is essential to the production of desired fuel constituents at the burner entry

through out the flight trajectory [32].

3.3 Injection/Mixing The shear/mixing layer theory is widely employed to understand the physics of fuel-air

mixing and combustion. The total pressure loss created by the injector and the injection

and mixing processes is of great concern because of its effect on the engine thrust. The

injector must produce rapid mixing and combustion of fuel with air. The injector

distribution in the engine should also result in a uniform combustor profile. Up to Mach

10, the fuel may have a normal injection into the flow but at higher Mach numbers, the

injection must be nearly axial since the fuel injection provides a significant portion of the

engine thrust [32]. Several phenomena result in the reduction of mixing with increasing

flow velocity, including velocity differential between fuel and air, compressibility and

occurrence of exothermic chemical reaction. On the other hand, mixing is augmented by

the shocks emanating from the struts and walls. Several options available for injector

18

design include transverse injection from combustor walls (intrusive or otherwise) and in-

stream injection from struts [13, 32]. Intrusive injection devices can provide good fuel

dispersal but they require active cooling of the injector structure. Transverse injectors

offer relatively rapid near-field mixing and good fuel penetration. In-stream injection

results in slower mixing but has advantage of adding to the thrust component of the

engine. Injection from ramps has also proven to be effective means of injection-cum-

flame holding in scramjets. Novel configurations like pulsed injection and cavity injector-

flame holders are also under study [32].

Energetic fuel injection [7]

At high altitude, for expansion ratios of order 1000, greater level of frozen atomic species

can be expected. The thrust being very sensitive to the exit velocity is highly dependent

on factors such as friction, mixing, profile and wave drag which reduce the exit velocity.

Builder and Czysz [4, 7] have given the concept of “energetic fuel injection” where the

idea is to use the fuel as an active fluid through controlled injection and mixing, thereby

using the momentum contributed by the injected fuel to add to the nozzle thrust and

absorb the frozen energy of the dissociated gas through molecular collision.

3.4 Shockwave - boundary layer Interaction The inlet and isolator part of the vehicle consists of shock structure used to compress the

captured air stream. For the requirement of minimum total pressure loss, it is required to

obtain this compression through sufficiently weak oblique shock reflections. An inviscid

shock reflection and intersection phenomenon is relatively simple and is described in

section 4.9. However, when the shock wave interacts with the boundary layer along the

wall, the flow becomes highly complicated. In such a case, the shock no longer remains

to be a sharp discontinuity; instead the pressure recovery takes place rather continuously

over a length as large as 8-10 times the tube diameter [17]. Also, this region of shock

compression may involve several curved or oblique shocks with bifurcated ends [17].

The interaction of boundary layer with normal shock, for different Mach numbers is

shown in the figure 3.1.

19

Fig. 3.1: Schematic sketch of normal shock wave/turbulent boundary layer interaction in a

constant area duct [17].

This phenomenon becomes important for the inlet design as the total pressure recovery

and the recovery length become increasingly dependent on the Mach number, Reynold’s

number and boundary-layer parameter [21]. There is no clear-cut theory available that

captures the above phenomenon analytically, however, many experimental and numerical

results are available in the open literature.

3.5 Optimum inlet diffusion In a Ramjet engine, the inlet air is fully diffused to subsonic velocities while in Scramjet

engine it is only partially compressed and remains supersonic. This is primarily because

the static pressure after compression is constrained on the higher end by structural

limitations (10 atmosphere approx.) and on the lower end by the combustion stability

requirements [13]. In that sense, partial diffusion and thus supersonic combustion is an

effect of the diffusion limits and not the cause of it.

As a conventional practice, represented by all known aircrafts, is to design for maximum

inlet diffusion. At hypersonic speeds, maximum diffusion produces a greater entropy rise

than a lesser compression. So a question pertinent to selection of engine from this family

is the optimum amount of compression for the Brayton cycle [4, 7]. The cycle that

maximizes jet thrust for a given heat-energy input is the one that minimizes the overall

entropy rise. Higher compression ratio in Brayton cycle results in minimized entropy rise

during the heat addition but also results in increased entropy rise in the compression and

20

expansion. Thus the optimum compression ratio occurs when the above two exactly

offset each other and the overall cycle efficiency is maximized.

3.6 Struts Struts are flow dividers used in inlets and combustor region of the ramjet-scramjet

engine designs. Most significant need of struts in the design arises from the fact that the

results of ground-based combustion experiments carried out on small test beds are not

scalable to large engine sizes. The two adjacent strut walls form a self-contained

combustor unit with possible housing of injector in the struts itself [27]. Also, the inlet

design is enhanced by the use of struts that channel the flow into separate smaller flow

paths thereby diffusing the flow in shortest possible inlet length. Struts also provide an

efficient mixing and combustion environment. In inlet and isolator, the struts also serve

as supporting structure. This results in elimination of panels and other supporting

structure leading to significant weight reduction [27]. Other uses of struts appear in

ducted rocket operation where small ‘strut rockets’ embedded in each strut provide the

motive force when required.

The number of struts to be used is an optimization issue as it increases the overall engine

drag and heat-load on the cooling system.

3.7 Variable geometry vs. fixed geometry Even though the variable geometry intake offers advantages in terms of performance at

off-design conditions, it is avoided due to practical constraints of weight and

containment. Especially for reusable vehicles, it is difficult to ensure integrity of the

variable geometry mechanisms during repeated cycles. For nozzle, however, variable

geometry seems to become inevitable owing to small margin of thrust available over drag

under off-design conditions.

3.8 Ground testing Hypersonic airbreathing propulsion has been studied throughout the world for nearly 60

years. Numerous ground tests have been performed and tremendous improvement in

21

understanding has taken place. Simulation for Mach number, altitude (T∞, P∞, ρ∞),

Reynold’s number and full running time has been made possible. Existing aerothermal

testing and aeropropulsion system testing facilities are capable of studying aerodynamic

stability and control, flow path performance including inlet, isolator and simulated

combustor performance, heat transfer, net thrust, net lift and moments and mass capture.

However, scramjet ground testing has its challenges and limitations. For example, facility

size generally limits the experimental scale, resulting in subscale or partial simulation of

the flow path. Also, scaled testing does not properly captures the combustion related

phenomena, the boundary layer formation and fuel mixing characteristics. Studies

performed at NASA indicate that at least a 3-4 meter vehicle could be a ‘smart-scale’ for

a 65-meter vehicle concept while demonstrating scramjet propulsion [25]. Typically, a

test section of 1m diameter for engine testing and 3m diameter for vehicle testing is

required. This amounts to setting up mass-flow rates of up to 150 kg/s for 180 seconds

and a storage capacity of 50 tons. [24].

Fig. 3.2: Scramjet test facilities in the United States [ 24]

22

3.9 Performance enhancement During certain critical parts of its mission, a hypersonic vehicle needs to meet stringent

requirements of aerodynamic efficiency or L/D ratio. This calls for an instantaneous

performance boost through lift enhancement and drag reduction. This can potentially be

accomplished by incorporating external burning [33]. It is known that external heat

addition to one side of the airfoil would offer both drag reduction as well as lift

enhancement. It is also known to offer some additional benefit in the form of external

pressure thrust. This concept tends to increase the specific impulse and therefore fuel

efficiency [33]. The vehicles incorporating this concept are popularly known as “flame

riders”.

Scramjet performance (especially specific thrust at supersonic and low hypersonic Mach

numbers) can also be improved by injection of evaporative coolants into the intake or the

airflow upstream [33]. This concept has, for long, been used successfully in aircraft

intakes.

3.10 Flight speed Some initial studies claimed speeds of the order of Mach 25 and beyond for the

hydrogen-fueled systems and Mach 14-16 for hydrocarbon-fueled systems. Subsequent

studies in 1960s and 1970s revised these estimates to Mach 15-20 and Mach 12-14

respectively. Most of these early estimates were crude did not incorporated the detailed

operation and performance models of the scramjets. Also, these studies were not

configuration specific. Waltrup, in his recent studies, incorporated the performance

model and the variation in chemistry inside the combustion chamber [34]. The reasonable

upper bounds on the flight Mach number would appear to be between Mach 9 and 10 for

hydrocarbon fueled, axi-symmetric missile shaped vehicle. The precise values are highly

dependent on the configuration. The upper bound is highly sensitive to the ratio of area of

nozzle and diffuser exit as well as combustor area. For hydrocarbon fueled vehicles, it is

found to be highly insensitive to the type of hydrocarbon used [34].

23

4. Theoretical background

4.1 Generalized one-dimensional flow The various driving potentials for an internal flow through a duct are area variation, wall

friction, heat transfer, mechanical work, mass addition, body forces, drag of entrained

particles and chemical reaction. Analytical and numerical methods are available for

solution of simple flows with perfect gas assumption and otherwise. In addition to simple

flows, there are complex flows (generalized flows), in which two or more driving

potential act simultaneously. Because of the complexity arising due to the simultaneous

action of potentials, the governing differential equations for complex flows are, in most

cases, solved by applying numerical scheme. In absence of rotating/moving parts, ramjets

and scramjet engines use an aerothermodynamic duct to impart compression or expansion

to the flow. The flow in the propulsive unit can thus be seen as a generalized flow with

varying area duct with mass addition, heat addition and wall friction. Therefore schemes

such as ‘method of influence coefficients’ can be used for numerical implementation.

Fig. 4.1 presents a physical model for generalized steady one-dimensional flow. The

various independents driving potentials for the flow are:

1. Area change, dA

2. Wall friction, δFf

3. Heat transfer, δQ

4. Work, δW

5. Drag and other body forces, δD

.

.md addition, Mass 6.

24

Fig. 4.1: Physical model for generalized steady one-dimensional flow [36].

Applying basic conservation laws:

Continuity equation:

VdV

+A

dA+

ρdρ

=m

md.

.

Momentum Equation:

where DH = hydraulic diameter, Cf = Coeff. of friction, y=(Vix/V).

0=m

mdy)(1ρV+AδD+

Ddx4C

2ρV+ρVdV+dp .

.

2

H

f2

-⎟⎟⎠

⎞⎜⎜⎝

⎛

Energy Equation:

0m

md2

Vh2

Vh2

VddhδQ Wδ .

.2i

i

22

=⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+−⎟⎟

⎠

⎞⎜⎜⎝

⎛++⎟⎟

⎠

⎞⎜⎜⎝

⎛++−

25

Making assumption of perfect gas (h = Cp; Cp = constant) and assuming equation of state

p=ρRT, the equations take the final form as:

( )

( )

( )⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

+

−

=

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

−−

+−−

−

−

−

−−

0

AdA

0

TdT

0

0

LK

AdAm md

CdsFdFPdPMdMVdVtdtρdρpdp

1000010γ1γ

010 M γ1

M 2γ0001

001ψM γ0001

000ψ

M 1γ0100

000112100

00000111

000γM02M γ01

00001010..

p

2

2

2

2

2 2

Where P, T, A and V denote total pressure, total temperature, area and velocity. Also,

2M

21γ1ψ −

+= ⎥⎦

⎤⎢⎣

⎡+⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

pAγMD) 2(δ

Ddx4C

2γMK 2

H

f2

( ) .

.

2

m

mdy1γML −−=

The incremental change in flow properties at a particular state can thus be obtained by

inverting the above matrix and giving the values of all flow potentials. It should be noted

that the above matrix is non-invertible at sonic point [36].

Formulation for transition through the sonic point

At M=1, and the analytical expression for dM2/M2 takes 0/0 form and the determinant of

the matrix above becomes zero. To deal with this, L’Hospital’s rule may be applied at

limit of M tending to unity. In general, starting with [36],

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

⎥⎦⎤

⎢⎣⎡ −++⎥

⎦

⎤⎢⎣

⎡++++−

−=

.m

.md2M 2yγ)2γM2(1ddC

HDdxf4C2γM

TdT)2γM(1

AdA2

)2M(1

ψ2M

2dM

26

where,

pA2γM

D 2δddC =

Writing the derivative in terms of x yields:

2

2

M1G(x)

dxdM

−=

where,

[ ]⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

−++⎥⎦

⎤⎢⎣

⎡++++−=

dx)m d(lnM 2yγ)γM2(1

dxdC

D4CγM

dxd(lnT))γM(1

dxd(lnA)2ψMG(x)

.

22d

H

f222

Applying L’Hospital’s rule as M approaches unity yields:

*σ2

2

*φ2

*φ*

dx

2dM−⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛±−=⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛

where,

( )

( ) [ ]⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

−++⎥⎦

⎤⎢⎣

⎡++++−

+⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−+⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛++⎥⎦

⎤⎢⎣⎡+

=

dx)

.md(ln2yγ1)2(γ

dxddC

HDf4C

γdx

d(lnT)1)(γdxlnAd2γ

2γγ2γdx

).md(ln

dxddC

HDf4Cγ

dxd(lnT)γ

21)(γ*φ

and,

( ) ( )⎪⎪

⎭

⎪⎪

⎬

⎫

⎪⎪

⎩

⎪⎪

⎨

⎧

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

−−++⎟⎟⎠

⎞⎜⎜⎝

⎛

++++−+

=dx

).md(ln

dxdy2γ

2dx

).m(ln2d2yγ2γ2

dxHDfC

d4γ

2dxdC2d

γ2dx

T ln2d1)(γ2dx

(lnA)2d22

1γ*σ

The increment dM may thus be obtained near the sonic point. 4.2 Combustion pressure loss Total pressure in combustor of a scramjet is lost due to turbulence and shocks due to

injector geometry, angle of injection, friction, change in Mach number, which is in turn

caused by mass addition, heat addition and area variation. Other than the adiabatic and

Rayleigh loss, part of the total pressure loss is also due to friction and turbulence in

27

boundary layer. It is taken into account by introducing viscous head term in energy

equation. Pressure loss, is given by,

2

2VDxfdPt ⋅−= ρ

where f is the friction factor, given by

⎟⎟⎠

⎞⎜⎜⎝

⎛+⋅−=

fReDe

f51.2

7.3/log21 , when 3000 < Re < 108

e is the absolute roughness of duct surface,

D is characteristic dimension and

Re is Reynolds number.

For practical assessment of pressure loss due to injection at a particular angle by a given

geometry, data given in literature [9] was used. Estimation of total pressure drop in

ramjet combustor zone is possible by the method given by Pinkel [23]. The chart given

by Pinkel is useful to calculate the pressure loss due to friction and combustion, upto

combustion chamber Mach number of about 0.35.

4.3 Shock reflection and intersection phenomena The reflections of waves occur because the flow has to conform to the boundary

conditions. An oblique shock (or expansion fan) occurs when the supersonic flow is

turned into itself (or away from itself). An oblique shock (or expansion fan) turns the

flow towards (or away from) the wave. At a given Mach number, there is a maximum

wedge angle through which the flow can be turned by means of an attached oblique

shock wave. Beyond this maximum turning angle, the flow experiences Mach reflections.

The above rules give a unique shock structure for a given geometry and boundary

conditions as can be seen in the figures.

28

Fig. 4.2: Reflections at wall

Fig. 4.3: Reflection form free pressure boundary

Fig. 4.4: Mach reflections

Fig. 4.5: Neutralization of incident shock

Intersection of two incident shocks result in formation of two transmitted oblique shocks

and a slip line separating two flow domains downstream (fig. 4.6). The transmitted

shocks adjust themselves so that the static pressure and flow direction on both sides of

slip line is same (so that the mechanical equilibrium is maintained). In some cases, there

is no solution for transmitted oblique shocks that satisfy all the flow conditions. In such

case, a normal shock develops at the intersection. This is known as mach intersection

(fig. 4.7)

Fig. 4.7: Regular intersection Fig. 4.6: Mach intersection

29

5. One-dimensional design methodology

In the currant work, design based on properties predicted by one-dimensional models is

attempted. One-dimensional methods are capable of suggesting the properties on a

section as a whole. This means that the variation in properties over a particular section is

suppressed in these models, and in most cases, the predicted properties are to be treated

as the average over the section. One-dimensional models are known to have limited

accuracy. They are popular and extensively used because they give useful insight into the

phenomena while being easily to implement. Thus they are useful for the purpose of

preliminary design.

5.1 Preliminary design methodology The preliminary design steps have been devised. The first step is to lay down the

thermodynamic cycle of the propulsion unit. This can be summarized as follows:

i. Pressure Ratio Factor has been applied to arrive at P03.

ii. T03/T01 has been assumed as per expected thermodynamic cycle configuration.

iii. Compression efficiency, ηc has been assumed.

iv. Between station 1 (inlet face) and station 3 (combustor entry), above assumptions

have been applied without any further gasdynamic analysis.

v. Combustor length is decided by cold-mixing criteria.

vi. Combustor exit conditions are decided by energy requirements for thrust

production.

vii. Combustor geometry and combustion products (including heat release model) are

studied using equilibrium chemistry model.

viii. Combustor area ratio and air/fuel ratio (equivalence ratio) are being optimized

meeting T04 and M4, which would meet the thrust requirements.

ix. Nozzle gasdynamic analysis is being carried out on the basis of full expansion

assumption to meet the exit velocity requirement (for the required thrust). This is

then used to obtain an estimate of the required nozzle area ratio.

30

5.2 One-dimensional analysis of combustor gas flow path In designing the combustor of a dual mode, air-breathing power plant following factors

are to be decided.

1. Area variation along x

2. Heat release rate along x

These parameters govern the flow in a complex manner which is captured by first order

governing equation given by Heiser and Pratt [13].

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛++⎟

⎠⎞

⎜⎝⎛−

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

−

−+

=⋅

dxdT

TM

dxdA

AM

Mm

dxdM t

t

12

111

21

1 2

2

2γ

γ

222

1

2

2

22

2

222

2

22

22

)()()(

)()(

)()(

)()()(

)(

)(2

11

211

)()()(

TxT

MxMuxu

TxT

xTT

pxpPxP

TxT

xMM

xAApxp

xM

M

xTxTTxT

t

ttt

c

t

t

=

⎥⎦

⎤⎢⎣

⎡=

=

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛ −+

⎟⎠⎞

⎜⎝⎛ −

+=

−γγ

γ

γ

here, the subscript `t’ signifies total quantities, ‘2’ signifies station number at the entry to

the combustor and ‘x’ is the axial direction.

Since the rate of change of Mach number is decided by rate of change of area and rate of

change of heat content, we can achieve an appropriate geometry by varying these two

parameters. The geometry should be capable of operating in both ramjet and scramjet

modes. There cannot be a physical throat in the combustor, as that geometry will not

operate in scramjet mode. So the combustor is entirely a diverging duct. The divergence

31

should be such that flow chokes thermally towards the end of combustion in ramjet

mode.

So by choosing different A(x) and Tt(x) we can obtain a number of geometry that suit to

all operating conditions. These geometries can later be compared for best performance.

The equations above can be used to obtained the static temperature, pressure and velocity

profiles in the combustor.

This differential equation can be solved using the Runge-Kutta method. A computer

program is written in FORTRAN. It requires conditions at inlet of combustor (x=0) as

boundary conditions. Geometry (A(x)) and heat released (Tt(x)) also need to be supplied.

The value of Cp and γ also changes with progress of combustion and this should also be

considered. Pressure lost due to friction, heat addition and momentum change is

calculated in the code, however a correction factor (discussed in section 4.8), which fills

the gap between theoretical and actual pressure loss, needs to be applied. The procedure

is outlined in figure 5.1.

32Figure 5.1: Gas flow path analysis of scramjet combustor

5.3 Numerical implementation The program developed, achieves the solution of complex flow by marching along the

flow direction. The conditions at the entry of the duct are given as input. The

distributions of the abovementioned driving potentials are also given as input. Flow

variables such as pressure, temperature, Mach number and entropy are obtainable as

output. The composition of fluid, here, is assumed to be constant throughout. The

formulation of equation assumes the specific heat, Cp to be constant at any point. Its

value, however, changes from point to point with the change in static temperature.

The program MAIN handles the inputs and outputs to the various subroutines. The

subroutine POTENTIAL calculates the values of flow potentials from the inputs and the

flow properties at a particular point. The value of Cp for different static temperature

values have to be supplied in a separate file. Subroutine POTENTIAL also calls

subroutine INTERPOL that is a general-purpose subroutine to give linearly interpolated

value between two known values. Subroutine SOLVER then calculates the influence

coefficients and gives the values of increments in the flow properties. The program, in its

present state fails near the singularity (i.e. Mach No. approaching unity). Modifications

are underway so that the program shifts to subroutine SING for the solution near the

singularity.

Fig. 5.2: Structure of the program

33

Extensive validation of the program has been carried out using simple flow situations like

isentropic flow, Rayleigh flow, Fanno flow etc. In general, the results obtained have an

excellent matching with the ideal values. A detailed user manual for the program is

prepared separately.

Limitations

a. MIC is limited to shock-less domains, so that the program, in its present form, is

useful for the analysis of the sections free of shock structure. Thus the solution

obtained from the program corresponds to those of an adapted, shock free duct.

b. MIC has an inherent singularity at Mach number of unity. A general derivation

based on L’Hospital’s rule is done for dealing with the singularity at the sonic

point. However, the program stops at the point of choking and has to be manually

started again.

c. The program helps to arrive at a design only by recursive manual runs.

34

6. Analysis

6.1 Available information Flight envelope and mission requirements

The flight envelope of the proposed vehicle is given briefly in table 6.1.

Total range Launching Mach number Launching altitude Total mass at launch Empty mass Cruise Mach number Cruise altitude

Fig. 6.1: Range vs. alti

The mission requirements i

table 6.2.

Table 6.1: Flight envelope details

1500 km (approx.) 3.5 13 km 2500 kg (approx) 1500 kg 7 35 km

tude Fig. 6.2: Mach number vs. altitude

n terms of thrust profile and estimated drag profile is given in

35

Altitude Press13045 1808215573 1185319670 5855 21815 4098 23193 3280 24996 2475 27903 1556 35000 583

Fig. 6.3: Angle of attack

Reference geometry

The reference external geo

tentative, it helps to visuali

idea of the overall size. The

reference geometry.

Table 6.2: Mission input data for HRV

ure Mach Air kg Drag Thrust 3.511 108.59 52186.71 93991.83 4.002 89.01 41420.35 76635.48

4.501 56.67 24358.48 46284.52 5.003 48.69 19270.91 37583.26 5.5 48.75 17566.5 35132.4 6.001 42.77 14951.81 28555.49 6.501 33.39 11235.51 20446.26 7.0 18.37 9908.159 10045

Fig. 6.4: Vehicle drag profile profile

metry has been supplied as an input. Even though it is

ze the airframe-propulsion system integration and gives an

vehicle lift and drag estimates have been made using this

36

Fig. 6.5: HRV configuration

6.2 Data verification It is required to understand the input data provided (table 6.2) in terms of engineering

parameters like SFC, Isp and efficiencies. This is necessary for understanding the

performance requirements to meet the mission.

The two forebody wedge angles are fixed at 4o and 14o. Therefore, for the above

configuration, there will be two oblique shock waves emanating from the forebody,

separating the free-stream conditions from the inlet face conditions. Using the above

information and the following,

Vexit = Vintake face + Specific thrust Specific thrust = (thrust)/(mass flow rate), taking constant fuel-air ratio of 1/15,

37

SFC = (fuel-air ratio)/(Specific thrust) Isp = 1/(g*SFC) Overall efficiency = Vfreestream/(spec. thrust * SFC)

we obtain, the mission data in terms of engineering parameters as given in table 6.3.

Altitude Mach 13045 3.511 15573 4.002 19670 4.501 21815 5.003 23193 5.5 24996 6.001 27903 6.501 35000 7

For the above m

number is foun

which showed

analysis, theref

35 km and Mac

design point.

6.3 Cycle an The thermodyn

the Brayton c

expansion legs

points on the t

map. It becom

These are given

Table 6.3: Mission data in terms of engineering parameters (computed)

Inlet Mach V exit Spec. thrust SFC Isp

Overall eff.

2.79 1906.5 865.6 7.702E-05 1324.907 0.306 3.15 2002.4 861.0 7.743E-05 1317.821 0.334 3.5 2118.5 816.7 8.163E-05 1250.109 0.361 3.7 2235.9 771.9 8.637E-05 1181.462 0.384 3.99 2355.1 720.7 9.251E-05 1103.058 0.400 4.26 2456.5 667.7 9.984E-05 1022.036 0.405 4.46 2577.2 612.3 1.089E-04 937.2655 0.408 4.24 2782.6 546.7 1.220E-04 836.7347 0.415

ission data, the variation of parameters with respect to altitude and Mach

d to be gradual. This is in contrast to an earlier mission data (not reported),

fluctuations in terms of the specific thrust and SFC requirements. Such an

ore, helps to fine-tune the mission data. For further analysis, the altitude of

h number 7 (which is the cruise point of the vehicle) has been taken as the

alysis

amic cycle analysis is carried out as an attempt to fix the coordinates of

ycle of the engine at the ends of the compression, combustion and

. This is, however, not a complete cycle construction as the intermediate

hermodynamic path are unknown in absence of a complete aero-thermal

es necessary to rely on representative numbers in order to move further.

in table 6.4.

38

Table 6.4: Representative values of parameters for cycle analysis

Specific heat of air in free-stream, Cpo 1004.5 Specific heat of air in compression, Cpc 1090.0 Specific heat of air in burner, Cpb 1510.0 Specific heat of air in expansion, Cpe 1510.0 Temperature ratio across compression, T3/To, ψ 7.0 Compression efficiency, ηc 0.9 Burner efficieny, ηb 0.92 Expansion efficiency, ηe 0.95

Note that the value of temperature ratio across the compression leg, ψ, is a strong

parameter and is changed again and again to arrive at optimal quantities over the cycle.

From the basic gasdynamic equation, we have:

1oT

xT

e −ψ

−ψ=η

where,

c)c1(oTxT

η+η−ψ=

and Tx is the temperature resulting from isentropic compression.

Therefore,

RpcCψ

xToT

=oP3p

For the combustion part, from conservation of energy, ( )3T4TpbC3h4h −=−

where h is the enthalpy.

Now, similar to Tx, we define Ty which is the temperature attained after isentropic

expansion (of expansion efficiency =1.0). So that,

)4TyT

1(e14T

10T−η−=

T4 and T10 being the combustor exit and exhaust temperatures respectively.

This leads to a cycle efficiency expression:

( ) ( )⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

−−

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛+

−ψ−=η

3h4hoTpoC

4ToT

pbCpoC

3h4hoTpoC

.poCprC

1tc

Implementing the above, for the data given, we obtain, the cycle analysis result given in

figure 6.6 and table 6.5.

39

0

1000

2000

3000

4000

5000

6000

7000

0 1000 2000

Entropy (J/K)

Tem

pera

ture

(K)

M=3.5M=5.5M=7

Fig. 6.6: Brayton cycle constructed from preliminary analysis

Table 6.5: Cycle analysis results

Altitude Mach Pfree-stream Tx/To p3/po T4/T3 Ty/T4 T10/T4 cycle eff. 13050 3.51 17973.95 1.38 110.95 2.735 0.456 0.4833 0.4898 15570 4 11923.26 1.41 128.63 2.783 0.445 0.4728 0.5008 19670 4.5 5965.67 1.39 116.72 2.766 0.452 0.4797 0.4946 21820 5 4210.34 1.39 116.72 2.751 0.452 0.4797 0.4936 23190 5.5 3380.15 1.36 99.83 2.660 0.464 0.4910 0.4787 25000 6 2548.2 1.38 110.95 2.688 0.456 0.4833 0.4863 27900 6.5 1633.78 1.42 134.77 2.823 0.441 0.4695 0.5059 35000 7 581.95 1.4 122.61 2.774 0.448 0.4762 0.4977

6.4 Component analysis: inlet The inlet has a dual purpose of catering to the required mass flow and provide some

initial compression through the shock structure. The nature of the shock structure

depends highly on the installation of the inlet with respect to the airframe, because the

free-stream flow passes through two oblique shocks (emanating from the forebody) to

reach the inlet face. Interestingly, as shown in figure 6.7, irrespective of the angle of

attack of the vehicle, the flow at the inlet face is aligned to the vehicle under-surface

40

when it enters the inlet. The sizing of the inlet is done so that it is capable of catering to

the mass-flow requirements.

Fig. 6.7: Flow from free-stream to the inlet face.

Inlet shock structure

To estimate properties across the inlet, it is necessary to estimate the shock reflections

inside the inlet. The shock structures in the inlet for various operating conditions are

given in figure 6.8. The results are summarized in table 6.6.

freestream mach inlet entry mach hot_x hot_y pressure ratio density ratio vel. ratio Downstr. Mach3.5 2.73 284.99 193 2.567 1.915 0.878 2.071

383.62 100.125 2.184 1.723 0.83 1.5264 3.1 319.32 193 2.833 2.038 0.893 2.347

423.032 110.411 2.327 1.797 0.856 1.765487.377 193 2.094 1.676 0.774 1.222

4.5 3.43 345.709 193 3.095 2.152 0.902 2.58450.825 117.665 2.468 1.867 0.871 1.953523.593 193 2.136 1.698 0.814 1.417

5 3.63 360.1 193 3.264 2.222 0.907 2.715465.241 121.428 2.557 1.91 0.878 2.059540.623 193 2.179 1.721 0.828 1.516

5.5 3.92 379.117 193 3.523 2.325 0.912 2.905483.591 126.217 2.689 1.972 0.886 2.203561.043 193 2.249 1.757 0.844 1.643585.369 152.781 2.139 1.7 0.722 1.057

6 4.17 393.958 193 3.76 2.414 0.916 3.062497.404 129.823 2.804 2.025 0.891 2.319575.607 193 2.311 1.789 0.854 1.741602.473 157.246 2.094 1.676 0.767 1.195

6.5 4.36 404.379 193 3.948 2.482 0.919 3.177506.859 132.29 2.892 2.064 0.895 2.402

7 4.15 393.958 193 3.76 2.414 0.916 3.062497.404 129.823 2.804 2.025 0.891 2.319575.607 193 2.311 1.789 0.854 1.741602.473 157.246 2.094 1.676 0.767 1.195

Table 6.6: Summary of the inlet shock structure estimate

41

Oblique Shock Reflection Structure in the InletFreestream Mach=3.5 & Inlet entry Mach=2.73

0

50

100

150

200

250

0 100 200 300 400 500 600

x (mm)

y (m

m)

Mach no. at downstream of the shock structure=1.52

Oblique Shock Reflection Structure in the InletFreestream Mach=4.5 & Inlet entry Mach=3.43

0

50

100

150

200

250

0 100 200 300 400 500 600

x (mm)

y (m

m)

Mach no. at downstream of the shock structure=1.41

Oblique Shock Reflection Structure in the InletFreestream Mach=7.0 & Inlet entry Mach=4.15

0

50

100

150

200

250

0 100 200 300 400 500 600 700

x (mm)

y (m

m)

Mach no. at downstream of the shock structure=1.74

Oblique Shock Reflection Structure in the InletFreestream M ach=5.5 & Inlet entry M ach=3.92

0

50

100

150

200

250

0 100 200 300 400 500 600

x (mm)

M ach no. at downstream of the shock structure=1.64

Fig. 6.8: Inlet shock structure for various operating conditions

Inlet boundary layer estimate

Making use of the seventh root profile [20], the inlet boundary layer displacement

thickness is estimated. Therefore, a correction to the required inlet area is obtained as

given in fig 6.9.

42

Fig. 6.9: Result of the inlet boundary layer estimate at the inlet face

6.5 Component analysis: isolator The isolator contains the shock structure that gets “smeared” due to its interaction with

the boundary layer. Thus the isolator can be seen as an “elongated throat” to

accommodate the terminal normal shock train, across which the flow turns subsonic from

supersonic in the ramjet mode. Thus, the design of isolator is essentially based on ramjet

mode requirements. In scramjet mode, where the diffusion is partial as compared to

ramjet mode, the isolator space is utilized for fuel injection and mixing.

43Fig. 6.10: Duct L/H vs. entry Mach no. for different boundary layer thickness cases

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

[x/H] / [L/H]

[p/p

i] / [

p(st

)/pi]

Realativised Pressure Distribution through Normal Shock Train in Rectangular Section Constant Area

Duct

Isolator Enrty Mach = 1.25 to 4.0 at steps of 0.25 (curve 1 and 12 correspond to Mach 1.25 and 4.0 respectively)

Curve is independent of (theta/H) and Reynold's no. value

1

12

Fig. 6.11: Pressure distribution in duct containing shock train

From the extensive experimental work by Billig et. al. reported in [17], it is known that

the pressure distribution characteristics in a rectangular constant area duct, with

accommodated shock train, follows the characteristics given by fig. 6.11. Therefore using

fig. 6.10 and 6.11, depending upon the required static pressure rise and the isolator entry

Mach number, L/H for the isolator can be selected.

6.6 Component analysis: combustor The dual mode power plant of a hypersonic airbreathing vehicle can operate in either

ramjet or scramjet mode. The first step towards designing the power plant would be to

estimate cycle parameters i.e. the temperature ratio and the pressure ratio of the power

plant. For the present exercise, data from flight conditions of the mission (table 6.2) is

taken. After cycle analysis, the data can be used for further analyses of combustor. These

are discussed in subsequent articles here.

44

Calculating cycle parameters

For the thermodynamic cycle to give useful work, incoming air from free-stream should

be compressed to raise the static temperature above fuel auto-ignition temperature. This

compression also increases the cycle pressure ratio, and higher cycle pressure ratio

implies high work output. But this compression is accompanied with pressure loss which

is proportional to the pressure ratio. So there exists an optimum pressure ratio that gives

maximum work from cycle. Heiser and Pratt [13] have given relations between static

temperature ratio ψ and pressure recovery factor for typical dual mode combustor. A

reasonable set of values was obtained by choosing different Mach numbers in the

combustor. The process is outlined in figure 6.12. Initially, using Tatm from table 6.2, and

using appropriate values of compression efficiency (ηc = 0.85) and static temperature

ratio (ψ), the pressure recovery factor (PRF) is calculated. Then the co-ordinates at

combustor inlet were calculated. The procedure was repeated if any of the parameters

was inappropriate.

Figure 6.12: Fixing conditions at combustor inlet

During the exercise, it was observed that above Mach 5 it is possible to achieve sufficient

compression without going through a normal shock. The parameters obtained at

combustor inlet (station 3) are given in table 6.7. Here it should be noted that the station 3

is physically different for ramjet and scramjet modes. The ramjet mode combustor is

downstream compared to the scramjet mode combustor.

45

M3 PRF

0.40 0.39

0.44 0.32

0.49 0.27

1.35 0.30

1.50 0.27

1.68 0.24

1.84 0.22

2.00 0.21

One dimensional flow path

Prior to the analysis, it is n

geometry is defined by area

amount of fuel added throu

[16, 6] the first cut geom

combustor and low diverge

shown in figure 6.13.The fu

and first divergence and th

analysis of the geometry wa

us the output parameters Ma

pressure recovery at the exi

of choking. The fuel inject

number (M=1 for ramjet m

combustor. Despite using a

could not satisfy the requ

modifications were made

combustor, however the con

combustor design, paramete

row locations are to be va

thrust.

Table 6.7: Conditions at combustor inlet

ψ P03 (kPa)

T03 (K)

T3 (K)

P3 (kPa)

2.90 546.3 578 560.3 489.3

3.50 577.4 613 590.5 505.5

4.17 449.6 718 685.4 381.5

3.80 641.9 901 660.6 216.3

4.20 808.7 1058 729.8 220.3

4.53 946.6 1207 771.5 197.6

4.87 906.8 1397 833.1 148.4

5.18 506.8 1753 973.6 64.8

analysis

ecessary to select a suitable geometry for the analysis. The

variation, A(x), location of fuel injectors laid out in rows and

gh each row. Based on engineering judgment and references

etry was taken as constant area isolator, high divergence

nce nozzle-cum-combustor. This geometry is schematically

el injectors were distributed in four rows, one each in isolator

e remaining two in second divergence zone. Gas dynamic

s carried out at various operating points. This analysis gives

ch number, static temperature, static pressure and theoretical

t station of combustor. This analysis also gives an indication

ion scheme is to be selected so as to get the desired Mach

ode and M>1 for scramjet mode) towards the end of the

ll possible schemes of fuel injection, the first scheme of A(x)

irements at all operating conditions. So, a few rounds of

to A(x). This geometry is satisfactory for working of the

figuration is not the optimum configuration. To optimize the

rs like combustor area A(x), fuel injection rate and injector

ried for objective of minimum pressure loss and maximum

46

Combustor analysis: One dimensional flow path analysis

A dual-mode combustor must: (a) be capable of thermal choking in the ramjet mode and

(b) sustain supersonic flow, throughout, in the scramjet mode. With constant area

geometry, it is difficult to meet this simultaneously. Prospective geometry is one with

increasing (divergent) area. Addition of fuel (and therefore mass & heat) to a stream

tends to choke the flow. Area variation is a much stronger flow potential and an

appropriate variation of these potentials (area, mass and heat) is thus required for meeting

the requirements of a dual-mode combustor.

Analysis is done using the MIC code and the mission data provided.

Air/fuel ratio 15 (near stoichiometric)

Air mass flow 18.37 kg/s

Fuel rate 1.22 kg/s

Total heat added 54 MJ (Hydrocarbon fuel; 44MJ/kg)

For a representative combustor in scramjet mode at Mach 7, the conditions at combustor

inlet are:

Static Pressure 64776 Pa

Density 0.222 Kg/m3

Temperature 1012.0 K

Mach number 2.00

Velocity 1276.5 m/s

Total Pressure 506840.0 Pa

Length of combustor 0.7 m

Area at combustor entry 0.069 m2 (from continuity)

It is obtained that the flow chokes even at an area ratio of as high as 2.5. Therefore, it

appears that the air fuel ratio should be significantly reduced at this point for this

configuration. But that comes with a penalty of reduced total temperature at the

combustor exit, which has direct influence on thrust. (Note that the temperature at

combustor exit is analogous to ‘turbine entry temperature’ of the gas-turbine cycle.)

47

The MIC code has been used repeatedly to come up to better combustor geometry as

follows.

Inlet area 0.069m2

Exit area 0.190m2 (divergent geometry)

Combustor length 0.7m

Total heat addition 40 MJ (equivalence ratio, φ = 0.74)

The corresponding predictions at the combustor exit are:

Static pressure 69540 Pa

Static temperature 2722.5 K

Mach no. 1.184

Total temperature 3272 K

This configuration appears to fulfill the total temperature and Mach number requirements

at combustor exit (station 5).

Figure 6.13: Combustor area variation and injector layout

48

6.7 Component analysis: Nozzle The required thrust is obtained by letting the combustor exhaust to expand through the

nozzle. The thrust requirement at various operating points is provided with the mission

data. Considering full expansion taking place, the exhaust gas velocity can be obtained

since the inlet face velocities are known, i.e. using,

Thrust = mass-flow rate*(V exit - V inlet).

The preliminary Brayton cycle analysis gives the nozzle exhaust temperature which thus

leads to a value of nozzle exhaust Mach number. The MIC code can thus be used to

arrive at a value of the area ratio required to obtain these exit conditions.

At design point, in this case,

Thrust 10045 N

Vinlet face 1947 m/s

Mass flow 19.5 kg/s

Using the procedure described above, we obtain,

Vnozzle exit 2475 m/s

Tnozzle exit 1336 K

Mnozzle exit 3.5

Area ratio, A4/A3 13.2 (using isentropic assumption).

Similar analysis is possible at the off-design points also. Note that the detailed nozzle

flow map is possible using method of characteristics, which is presently out of scope of

this report.

6.8 Preliminary layout The preliminary layout of the combustor and the complete propulsion unit based on this

analysis is given below in figures 6.14 and 6.15.

49

Fig. 6.14: Layout of the combustor

Fig. 6.15: Layout of the propulsion unit

50

7. Parametric performance analysis

In this chapter, a parametric analysis of the vehicle performance is attempted. The

sensitivities of some parameters are examined by monitoring other performance relevant

quantities. For this purpose, an available code is made use of. This is a simplistic code

that starts with the generation of 1000 random trajectories around a baseline trajectory,

serving a particular mission. It then does the basic performance calculations along these

random trajectories and chooses a trajectory requiring minimum fuel and other trajectory

requiring minimum inlet area.

The approach taken is as follows. Table 7.1 gives the list of sensitivity parameters and the

monitored quantities.

Table 7.1: List of sensitivity parameters and monitored quantities

Sensitivity parameters Monitored quantities

Cd engine Fuel consumed in ram-mode

Scram starting Mach no. Fuel consumed in scram-mode

Nozzle inlet temperature Fuel consumed in climb & accelerate mode

Initial (max.) vehicle weight Fuel consumed in cruise mode

Maximum Mach number Minimum total fuel

Maximum height Minimum required inlet area

Pressure loss in combustor --

It should be noted that only a single parameter is varied at a time. The results obtained are

all presented as quantities normalized by their reference values. The reference values for

the sensitivity parameters are given in table 7.2.

51

Table 7.2: Reference values of the sensitivity parameters

Sensitivity parameters Reference values

Cd engine 0.2

Scram starting Mach no. 5.5

Nozzle inlet temperature 3600 K (ram mode); 4000 K (scram mode)

Initial (max.) vehicle weight 25000 N

Maximum Mach number 7

Maximum height 35000 m

Pressure loss in combustor 15% (ram mode); 20%(scram mode)

The results for this analysis are presented in figures 7.1 to 7.7.

It should be noted that for all the results presented, on any particular graph, each point is

chosen corresponding to the best trajectory among 1000 random trajectories. So, different

points on the same curve would correspond to a different trajectory (which is best suited

for that set of parameters among the 1000 trajectories).

In figure 7.1, it can be seen that the fuel consumption in all the individual phases as well

as the total fuel consumption over the mission increases with increase in Cd engine. The

steepest rise is obtained for the climb and accelerate mode.

The benefits of increasing nozzle entry temperature can be seen in figure 7.3, causing the

total fuel consumption as well as the inlet area requirement to go down. The fuel

consumption as well as the inlet area can be seen to increase with the increase in the

vehicle weight in figure 7.4. It is evident from fig. 7.5 that going beyond a certain

maximum Mach number would result in drastic increase in required fuel and inlet areas,

however, small variation around the reference values are possible. Figure 7.6 shows the

benefit in fuel consumption, but with increased inlet area (assuming constant Cd engine),

made available with the increase in the cruise altitude of the vehicle. Figure 7.7 predicts

the effect of the combustor pressure loss on the fuel and inlet area. These results can be

summarized in terms of the numerical values of the partial derivatives of the monitored

quantities with respect to the sensitivity parameters at the reference value points.

Graphically, this would correspond to the slopes of the curves given in fig. 7.1 to 7.7 at

the reference point (1.0,1.0). These values are presented in table 7.3.

52

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 0.5 1 1.5 2 2.5 3 3.5 4

Cd_engine/Cd_engine(ref)

min

. inl

et a

rea/

min

. inl

et a

rea(

ref)

Fig. 7.1(b): Variation in min. inlet area with Cd engine.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 1 2 3 4

Cd_engine/Cd_engine(ref)

fuel

/fuel

(ref

) fuel in ram modefuel in scram modefuel in climb and accelerationfuel in cruisetotal fuel

Fig. 7.1(a): Variation in fuel cons. with Cd engine.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0.65 0.75 0.85 0.95 1.05 1.15

switchin mach/switching mach(ref)

fuel

/fu

el(r

ef)

fuel in ram mode

fuel in scram mode

fuel in climb and acceleration

fuel in cruise

total fuel

Fig. 7.2(a): Variation in fuel with scram starting Mach no.

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

0.7 0.8 0.9 1 1.1 1.2

switching mach/switching mach (ref)

min

. inl

et a

rea/

min

. inl

et a

rea(

ref)

Fig. 7.2(b): Variation in min. inlet area with

scram starting Mach no.

0.6

0.8

1

1.2

1.4

1.6

1.8

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3

scram nit/nit(ref)

ram

fu

el/r

am f

uel

(re

f)

ram nit/nit(ref) = 0.88

ram nit/nit(ref)=1.0

ram nit/nit(ref)=1.11

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3

scram nit/nit(ref)

scra

m fu

el/s

cram

fuel

(ref

)

ram nit/nit(ref) = 0.88

ram nit/nit(ref)=1.0

ram nit/nit(ref)=1.11

Fig. 7.3(b): Variation in scram-mode fuel consumption with

nozzle entry total temperatures.

Fig. 7.3(a): Variation in ram-mode fuel consumption with

nozzle entry total temperatures.

53

0.8

1

1.2

1.4

1.6

1.8

2

2.2

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3

scram nit/nit(ref)

clim

b& a

cclr.

fuel

/clim

b &

acc

lr. fu

el (r

ef)

ram nit/nit(ref) = 0.88

ram nit/nit(ref)=1.0

ram nit/nit(ref)=1.11

Fig. 7.3(c): Variation in climb & accelerate fuel consumption

with nozzle entry total temperatures.

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3

scram nit/nit(ref)

crui

se fu

el/c

ruis

e fu

el (r

ef)

ram nit/nit(ref) = 0.88

ram nit/nit(ref)=1.0

ram nit/nit(ref)=1.11

Fig. 7.3(d): Variation in cruise fuel consumption with

nozzle entry total temperatures.

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3

scram nit/nit(ref)

tota

l fue

l/tot

al fu

el (r

ef)

ram nit/nit(ref) = 0.88

ram nit/nit(ref)=1.0ram nit/nit(ref)=1.11

Fig. 7.3(e): Variation in total fuel consumption with

nozzle entry total temperatures.

0.65

1.15

1.65

2.15

2.65

3.15

3.65

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3

scram nit/nit(ref)

min

. inl

et a

rea/

min

. inl

et a

rea

(ref

)

ram nit/nit(ref) = 0.88

ram nit/nit(ref)=1.0

ram nit/nit(ref)=1.11

Fig. 7.3(f): Variation in min. inlet area with

nozzle entry total temperatures.

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

0.7 0.8 0.9 1 1.1 1.2 1.3

max wt./max wt. (ref)

fuel

/fuel

(ref)

fuel in ram modefuel in scram modefuel in climb and accelerationfuel in cruisetotal fuel

Fig. 7.4(b): Variation in min. inlet area with initial (max)

vehicle weight.

Fig. 7.4(a): Variation in fuel consumption with initial (max)

vehicle weight.

0.95

0.97

0.99

1.01

1.03

1.05

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3

max wt./max wt. (ref)

min

. inl

et a

rea/

min

. inl

et a

rea(

ref)

54

0

0.5

1

1.5

2

2.5

3

3.5

4

0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

max mach/max mach (ref)

fuel

/fuel

(ref

) fuel in ram modefuel in scram modefuel in climb and accelerationfuel in cruisetotal fuel

Fig. 7.5(a): Variation in fuel consumption with max. Mach no. Fig. 7.5(b): Variation in min. inlet area with max. Mach no.

0

2

4

6

8

10

12

14

16

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

max mach/max mach (ref)

min

. inl

et a

rea/

min

. inl

et a

rea(

ref)

0

0.5

1

1.5

2

2.5

3

3.5

4

0.5 0.7 0.9 1.1 1.3 1.5

h max/h max (ref)

fuel

/fuel

(ref

) fuel in ram modefuel in scram modefuel in climb and accelerationfuel in cruisetotal fuel

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

h max/h max (ref)

min

. inl

et a

rea/

min

. inl

et a

rea(

ref)

Fig. 7.6(b): Variation in min. inlet area with max. height Fig. 7.6(a): Variation in fuel cons. with max. height

0.9

0.95

1

1.05

1.1

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

scram ploss/ploss(ref)

ram

fu

el/r

am f

uel

(re

f)

ram ploss/ploss(ref) = 0.66

ram ploss/ploss(ref)=1.0

ram ploss/ploss(ref)=1.33

0.9

0.95

1

1.05

1.1

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

scram ploss/ploss(ref)

scra

m f

uel/scra

m f

uel (r

ef)

ram ploss/ploss(ref) = 0.66ram ploss/ploss(ref)=1.0ram ploss/ploss(ref)=1.33

Fig. 7.7(b): Variation in scram-mode fuel with

combustor pressure loss

Fig. 7.7(a): Variation in ram-mode fuel with

combustor pressure loss

55

Fig. 7.7(d): Variation in cruise fuel with

combustor pressure loss

0.9

0.95

1

1.05

1.1

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

scram ploss/ploss(ref)

cru

ise

fu

el/c

ruis

e f

ue

l (re

f)

ram ploss/ploss(ref) = 0.66

ram ploss/ploss(ref)=1.0

ram ploss/ploss(ref)=1.33

Fig. 7.7(c): Variation in climb & accelerate with

combustor pressure loss

0.9

0.95

1

1.05

1.1

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

scram ploss/ploss(ref)

clim

b&

acc

lr. f

uel

/clim

b &

acc

lr. f

uel

(re

f)

ram ploss/ploss(ref) = 0.66

ram ploss/ploss(ref)=1.0

ram ploss/ploss(ref)=1.33

Fig. 7.7(e): Variation in total fuel with

combustor pressure loss

0.9

0.95

1

1.05

1.1

0.2 0.7 1.2

scram ploss/ploss(ref)

tota

l fue

l/tot

al fu

el (r

ef)

ram ploss/ploss(ref) = 0.66ram ploss/ploss(ref)=1.0

ram ploss/ploss(ref)=1.33

0.9

0.95

1

1.05

1.1

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

scram ploss/ploss(ref)

min

. inl

et a

rea/

min

. inl

et a

rea

(ref

)ram ploss/ploss(ref) = 0.66ram ploss/ploss(ref)=1.0

ram ploss/ploss(ref)=1.33

Fig. 7.7(f): Variation in min. inlet area with

combustor pressure loss

Partial derivatives at the reference point

Table 7.3 presents the numerical values of the partial derivatives of the various monitored

quantities in terms of the sensitivity parameters. The notations are as follows:

P1 = Cd engine/Cd engine (ref.)

P2 = scram starting mach/scram starting mach (ref.)

P3 = scram-mode nozzle inlet temp./ scram-mode nozzle inlet temp (ref.)

P4 = max. wt./max. wt. (ref.)

P5 = Max. Mach/max. Mach (ref.)

P6 = Max. height/ Max. height (ref.)

P7 = scram-mode combustor pressure loss/ scram-mode combustor pressure loss (ref.)

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Q1 = ram-mode fuel/ram-mode fuel (ref.)

Q2 = scram-mode fuel/scram-mode fuel (ref.)

Q3 = climb & accl. fuel/climb & accl. mode fuel (ref.)

Q4 = cruise fuel/cruise fuel (ref.)

Q5 = min. total fuel/min. total fuel (ref.)

Q6 = min. inlet area required/min. inlet area required fuel (ref.)

Table 7.3: Numerical value of the partial derivatives of the monitored quantities w.r.t. the

parameters at the reference point.

PQ∂∂ Q1 Q2 Q3 Q4 Q5 Q6

P1 0.569 0.618 1.184 0.263 0.607 0.32

P2 2.270 -0.404 -0.443 0.584 0.200 0.000

P3 -0.341 -0.580 1.455 -1.650 -0.526 -2.380

P4 0.784 0.473 0.789 0.396 0.543 0.000

P5 1.490 -1.150 2.960 -2.650 -0.550 -0.760

P6 1.750 -2.840 1.960 -4.050 1.800 2.160

P7 0.101 -0.021 0.135 -0.070 0.006 0.021

The fidelity of the numerical values obtained here are questionable in view of the fact

that a very basic performance model has been used. But comparison of these values

among themselves would essentially give a qualitative insight into the relative sensitivity

of the parameters and therefore help finding out the most relevant parameters. Using the

detailed and appropriate knowledge of the variation of the parameters with the operating

conditions, it is possible to achieve an optimized trajectory, to serve the mission, taking

its course intermediate among all the 1000 random trajectories. The above exercise can

be made more useful and realistic if the effect of variation of one parameter on the other

is taken into account (presently only one parameter is varied at a tie, assuming all others

to remain constant). However, this has not been attempted in the present work.

57

Limitations

1. The code uses a fixed profile of the vehicle ballistic coefficient (Cd*S) versus

Mach number. Actually, as the weight and trajectory varies, the vehicle angle of

attack varies resulting in the variation of the Cd of vehicle. This has not been

taken into account.

2. The structure of the code does not allow using ‘pressure recovery factor’ as a

parameter, which would have provided very relevant information.

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Closure

In this project, it is tried to cover the ground for the preliminary design of a dual-mode

ram-scram based powerplant for hypersonic vehicle. The work is limited to preliminary

level analysis and design.

A detailed literature survey is carried out, understanding various issues and

considerations involved in the field of hypersonic gasdynamics. From the basic mission

requirements, the required Brayton cycle coordinates are computed.

Complex flow is modeled using popular one-dimensional scheme called the ‘method of

influence coefficients’, where the complex flow is seen as one with simultaneous action

of potentials. The numerical code developed based on this scheme is capable of giving

aerothermal map of flow inside a adapted shock free duct with simultaneous area

variation, heat addition, mass injection, wall friction and particle drag. To use this code, a

good starting estimate of these flow potentials would be required. Parametric analysis

around a baseline configuration can then be done.

In inlet where the shock-boundary layer interaction phenomenon starts taking control of

the flow, simple inviscid oblique shock reflection phenomena is applied, to estimate the

flow. Similarly, boundary layer development over the forebody is estimated using the

‘seventh root profile’, based on suggestion found in literature. Thus shock-boundary layer

interaction phenomenon is not taken into account in the inlet.

The need of isolator arises from the shock-boundary layer interaction phenomenon,

which causes the sharp shock (discontinuity) to get smeared over a length. A detailed

flow mapping in this region would require a CFD analysis, instead of which, we have

used a highly acclaimed one-dimensional empirical formulation suggested though

extensive experimentation by Billig et. al. Charts are prepared based on this formulation,

using which, isolator length is calculated. In scramjet mode, the isolator length is not

required and is used for pre-injection and pre-combustion. Thus, housing of some scram-

injectors in isolator region is also suggested and incorporated by other student involved

with detail combustor design.

59

For the nozzle design, present model is found to be insufficient and would require

schemes like ‘method of characteristics’ to arrive at better estimates. This is especially

true in the region of the nozzle that is partially open to the atmosphere and makes use of

the jet boundary. The divergence requirements in the nozzles of hypersonic vehicles

make the use of the concept of these free-jet nozzles inevitable. However, for present

purpose, it is taken as completely ducted to estimate exit pressure, exit velocity and

therefore thrust.

Towards the end of this project, parametric performance studies were carried out for the

vehicle. Here, parametric sensitivities of various parameters (such as Cd engine, nozzle

entry temperature, maximum Mach number, maximum height and weight etc.) were

found by monitoring other quantities (like fuel consumed, minimum required inlet area

etc.). For this purpose, an available in-house developed code was made use of. In its

present state, this exercise is a partial success. This code can be extended to incorporate

the effect of variation of one parameter on the others, rather than taking them as

independent.

60

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63

Acknowledgements

My heart felt acknowledgements are due to Prof. Bhaskar Roy, for providing his able

guidance, never-ending encouragement, freedom, infrastructure and personal support. I

consider myself to be fortunate to have his guidance, company and friendship.

Let me take this opportunity to also thank Shri Prahlada, Director, DRDL for making it

possible for people at IIT-Bombay to take up this interesting activity. Sincere thanks are

due to Dr. Pannerselvam, project director, HRV for his active guidance and direction

through out the project. His enthusiasm towards the project has always been very

inspiring. Sincere thanks to Dr. Panyam, Shri T. K. Anavardham and Dushyant Mahadik

for the fruitful technical discussions and guidance.

Thanks are due to Swapnil Pawar, for making the code available for the parametric

analysis. Heartfelt thanks to Gaurav Jain, for making the VC++ version of the code up

and running.

Special thanks to Praveen ‘jim’ Gill, Devendra Ghate, Gaurav Jain, Tuhin Sahai, Jai

Mirpuri, Jannu Bharath Kumar, Dushyant Mahadik, Vishal Borikar, Samir Tambe and P.

M. Sivadas for making my stay comfortable with wonderful discussion sessions.

Thanks are also due to Rajath Kedilaya, Tarun Gupta, S. Ajanavit, Naresh Mulchandani,

Vardan Kabra, Manan Chauhan, Ryan Gazder and Sanghamitra Korukonda for being

great companions.

Amit Batra

16-06-2002

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