[american institute of aeronautics and astronautics 18th aiaa computational fluid dynamics...

American Institute of Aeronautics and Astronautics

1

Quasi-One-Dimensional Modeling of Hydrogen Fuelled

Scramjet Combustors

Cristian Birzer1 and Con J. Doolan

2

University of Adelaide, Adelaide, South Australia, 5005

A computationally efficient, quasi-one-dimensional supersonic combustion ramjet

propulsion model has been produced for use in hypersonic system design studies. The model

uses a series of ordinary differential equations, solved using a 4th order Runge-Kutta

method, to describe the gas dynamics within the scramjet duct. Additional models for skin

friction and wall heat transfer are also included. The equations were derived assuming an

open thermodynamic system with equilibrium or simplified chemistry combustion models.

The combustion was also assumed to be mixing rather than kinetically limited. This

assumption allows simplification of the modeling and was found to be justified when the

model was compared against experimental results. Three test cases are used to validate the

performance of the scramjet propulsion model: (1) modeling a reflected shock tunnel

hydrogen fuelled scramjet experiment, (2) a continuous flow hydrogen fuelled scramjet

ground test and (3) a segment of the HyShot II flight test.

Nomenclature

A Geometric area of the duct

c Speed of sound

fc Skin friction coefficient

pc Specific heat

D Chemical species

d Number of moles of species D

d Constant

D Hydraulic diameter

FAS Stoichiometric fuel / air ratio

h Enthalpy

SPI Specific impulse

pK Equilibrium constant

*K Proportionality constant

L Length

M Mach number

m& Mass flow rate

MW Molecular weight

N Number of moles

p Pressure

Pr Prandtl number

R Gas constant

Re Reynolds number

1 Research Associate, School of Mechanical Engineering.

2 Lecturer, School of Mechanical Engineering, Senior Member, AIAA.

18th AIAA Computational Fluid Dynamics Conference25 - 28 June 2007, Miami, FL

AIAA 2007-4314

Copyright © 2007 by Con Doolan. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


2

wP Perimeter of duct cross section

T Temperature

Th Thrust

U Velocity

x Location along duct length

Y Mass fraction

Greek symbols

γ Ratio of specific heats

mη Mixing efficiency

ρ Density

φ Equivalence Ratio

ω ODE solution

Subscripts

a Air

aw Adiabatic wall

i Species

inj Injection conditions

f Fuel

fo Fuel at the injectors

mix Mixing conditions

imix, Incompressible mixing conditions

w Wall

I. Introduction

HE development of supersonic combustion ramjet (scramjet) propulsion systems is accelerating, with recent

flight test successes demonstrating their viability1,2. This activity has renewed interest in predicting the

performance of complete hypersonic vehicles utilizing scramjet combustors, such as single-stage-to-orbit launch

systems, long range cruise vehicles and missiles. The accurate prediction of vehicle performance early in the design

process is vital if conceptual vehicles are to be successfully developed into complete systems in a timely manner. In

addition, hypersonic vehicle performance calculators are useful for system analysis studies.

To facilitate these activities, accurate and computationally efficient models of all aspects of the vehicle are

required. In the present work, a quasi-one-dimensional solver is developed that is specifically designed to simulate

the performance of scramjet combustors. The model uses a unique formulation of the gas dynamic equations

incorporating an equation of state with equilibrium chemistry. Wall skin friction and heat transfer are also

considered.

Quasi-one-dimensional modeling has been used in previous design and performance studies3,4. These models

use a series of ordinary differential equations to model the flow field and incorporate chemical kinetics as part of

their thermodynamic description of the flow. Results from these studies show that scramjet performance is

extremely sensitive to small changes in design, thermodynamic and mixing parameters. It has been concluded from

these studies that it is better to design a scramjet to operate using mixing-controlled combustion that is ignited via

external or well controlled means, rather than relying upon kinetically controlled ignition.

For the current model, supersonic combustion is assumed to be mixing-controlled. In practice, this can be

achieved by either a hot combustor inlet temperature (hence negligible ignition delay), or by incorporating of an

igniter system into the scramjet that effectively eliminates the ignition delay. As will be shown, this assumption

appears valid, along with the assumption of equilibrium or simplified chemistry. Attention has been placed upon

modeling the major processes associated with mixing and heat release, rather than the computationally expensive

kinetics process.

This paper has four parts. Section I is the Introduction. Section II is a summary of the theory that controls the

quasi-one-dimensional solver. Section III compares simulation results with hydrogen fuelled ground tests and part

of the HyShot II flight test. Section IV concludes the paper.

T


3

II. Quasi-One-Dimensional Flow Solver

The governing equations for the engine are formulated using a strategy similar to Ref. 3. However, the current

model assumes equilibrium chemistry or a “mixed-is-burnt” combustion model that is mixing rather than kinetically

limited. This requires the problem to be treated as an open thermodynamic system. In the following discussion, the

scramjet combustor is sometimes referred to as “the duct” and will be used interchangeably with term “the

combustor”.

The governing equations are based on the following assumptions:

• Quasi-one-dimensional flow, which assumes that all flow variables and the geometric area of the duct

are functions of the axial distance (x) along the duct.

• The flow is steady-state.

• The flow behaves as an ideal gas.

A. Conservation of Mass

Following Ref. 3, the conservation of mass in a steady-state flow is governed by the continuity equation,

UAm ρ=& (1)

This can be expressed in a differential form,

x

A

Ax

U

Uxx

m

m d

d1

d

d1

d

d1

d

d1++=

ρρ

&

& (2)

What is important to appreciate from Eq. (2) is that fuel injection and duct area changes can be incorporated

using a mass injection rate ( xm dd & ) and an area profile ( xA dd ).

B. Conservation of Momentum

The conservation of momentum is based on the quasi-one-dimensional formulation of Ref. 4,

0d

d2

d

d

2d

d1 222

2

2

=+++x

m

m

McM

x

U

U

M

x

p

p

f &

&

γγγD

(3)

The friction coefficient (cf) is calculated using an analytical technique (Anderson, 2000) based on the reference

enthalpy method.

The hydraulic diameter is calculated from,

wP

A4=D (4)

C. Equation of State

The equation of state for an ideal gas is,

MW

Tp

Rρ= (5)

The differential form will be used to derive the quasi-one-dimensional model,


4

x

M

MWx

T

Txx

p

p d

Wd1

d

d1

d

d1

d

d1−+=

ρρ

(6)

The mean molecular weight (MW ) allows for changes in species due to combustion and high temperature

effects. The mean molecular weight is defined using3,

∑=

i i

i

MW

YMW

1 (7)

The differential form allows the calculation of the variation of mean molecular weight along the duct,

−= ∑

i

i

ix

Y

MWMW

x

MW

d

d1

d

d 2

(8)

The model assumes i chemical species are present in the flow field. The rate of change of each species mass

fraction is determined by the rate of change of local equivalence ratio which, in turn, is set by the fuel injection rate

along the duct. The change in local equivalence ratio and species mass fraction are controlled by,

( )

=

FASmx

m

xa&

& 1

d

d

d

df

φ (9)

x

Y

x

Y

d

d

d

d

d

dii

φφ

= (10)

The rate of change of mass fraction with equivalence ratio is determined from the combustion model presented

in Section F.

D. Conservation of Energy

The differential form of the conservation of energy is derived using the formulation given by Ref. 7 and the

control volume analysis of Ref. 3. A modified version has been derived here to describe the energy flow in the

scramjet combustor. This includes energy transported into the combustor by the fuel, energy liberated by

combustion and energy lost through heat transfer through the walls.

This formulation is given below,

( )

x

UU

x

m

m

h

A

TTcc

x

m

m

h

x

h fowawpfff

d

d

d

d

Pr

2

d

d

d

d

32

−−−

−=&

&

&

& D (11)

Equation (11) has been derived using the Reynolds analogy that relates the skin friction coefficient to the Stanton

number,

3

2

Pr2

f

h

cc = (12)

The adiabatic wall temperature (Taw) is given by Ref. 6,


5

( ) ( )

−+= 1

2

1Pr1 2

3

1* γMTT

aw (13)

In all cases it has been assumed that,

71.0PrPr * == (14)

E. Flow field Enthalpy

It is assumed that the composition of the flow field is set to be the product side of the single step combustion

reaction mechanism,

( ) ProductsAirFuel →+φ (15)

The fuel can be either hydrogen or a hydrocarbon fuel (ethylene, Jet A, etc) and the equivalence ratio (φ) determines the composition of the products. The products are either set to the major species (O2, N2, H2O, CO2) or

are in thermodynamic chemical equilibrium. In this paper, we assume hydrogen fuel only.

In either case, the flow field thermodynamic chemical equilibrium will be a function of the pressure (p),

equivalence ratio (φ) and the temperature (T),

( )Tphh ,,φ= (16)

The differential form of the flow field enthalpy can then be written as,

x

T

T

h

x

h

x

p

p

h

x

h

d

d

d

d

d

d

d

d

∂∂

+

∂∂

+

∂∂

=φ

φ (17)

Equating Eqs. (17) and (11) results in an expression for the temperature gradient along the combustor,

( )

∂∂

−

∂∂

−

−−

−−

∂∂

=−

x

h

x

p

p

h

x

UU

x

m

m

h

A

TTcc

x

m

m

h

T

h

dx

dT fowawpfff

d

d

d

d

d

d

d

d

Pr

2

d

d

32

1

φφ

&

&

&

& D (18)

The partial derivatives of enthalpy (Eq. 16) are determined numerically using a combustion model.

F. Combustion Model

The flow field enthalpy is determined by a summation of individual chemical species specific heats, multiplied

by the temperature and weighted by the species mass fraction,

∑=i

iip TYch , (19)

The individual species specific heats are calculated from the NASA polynomials8,

( )4,5

3

,4

2

,3,2,1, TaTaTaTaaMW

c iiiii

i

ip ++++

=R

(20)

Determination of the species mass fraction can be achieved using either a simplified combustion model or a

model that assumes thermodynamic chemical equilibrium.


6

In the simplified model, the products are limited to the major species (O2, N2, H2O) and the mass fractions are set

according to a global chemical reaction mechanism (Eq. 15) that accounts for the atom balance between reactants

and products.

When thermodynamic equilibrium is assumed, the following product species dissociation reactions are

considered,

2OO

2HH

O HOH

2

2

221

2

→

→

+→2

(21)

It is assumed that the dissociation of molecular nitrogen and the formation of the oxides of nitrogen are not

significant contributors to the chemical heat release for the scramjet flow fields of interest in this study.

The approach to solve for chemical equilibrium is the approach as presented by Borman and Ragland9. It has

been found that this iterative technique can be computationally expensive, making the time required to achieve a

converged scramjet solution large (the order of a minute or more for a 2005 IBM PC). While this solution time may

not be a concern for some studies, it would make a complete mission simulation study tedious. However, solution

times using the simplified combustion model described above are very low and are suitable for mission or trajectory

studies.

In order to investigate the difference in results obtained between the equilibrium combustion model and the

simplified combustion model, a series of constant volume methane-air combustion simulations were performed. As

a benchmark solution, a 10 species equilibrium chemistry calculation was performed using the GasEq solver10. It

was found that reasonable agreement was observed between all simulations, suggesting that if a small loss in

accuracy is permitted, than significant increases in computational efficiency can be gained.

G. Complete Equation Set

Combining Eqs. (2), (3), (6) and (17) gives the differential equation for velocity in the duct,

( )

( )

∂∂

∂∂

−

∂∂−

−+−

−

∂∂

+++−

=

−

−

−

1

1

32

2

1

2

d

d1

1

Pr

2

d

Wd1

11

d

d1

d

d1

1

d

d

T

h

x

h

T

T

h

T

TTcAM

c

x

M

MW

hhT

h

TAM

x

m

mx

A

A

x

U wawp

o

f

ofo

φφ

γ

γ

α D

&

&

(28)

∂∂

∂∂

+=−

p

h

T

h

T

pAo

1

1 (29)

∂∂

+−=−12

211

T

h

T

UAM

Uo

γα (30)

The equations derived above now represent a set of stiff ordinary differential equations (ODEs) that can be

solved using an ODE solver in a space marching technique. Using the equation of state with conservation of mass

and energy allows closure of the equation set.


7

−−=x

A

Ax

U

Ux

m

mx d

d1

d

d1

d

d1

d

d &

&ρ

ρ (31)

+

+−=

x

m

m

c

x

U

UpM

x

p f

d

d14

2

1

d

d1

d

d 2 &

&Dγ (32)

+−=

x

MW

MWxx

P

pT

dx

dT

d

d1

d

d1

d

d1 ρρ

(33)

H. Ordinary Differential Equation Solver

The ODEs are solved using a 4th order Runge-Kutta method. The computational time is near instantaneous for

the simplified combustion model and results produce a reasonable level of accuracy. Nonetheless, higher orders for

the classical Runge-Kutta method may be employed if desired for higher accuracy, at the expense of computational

time.

I. Supersonic Mixing Model

The key to accurate combustor performance measurements is determining the correct release of energy along the

duct. In the current model, this is performed by deriving a supersonic mixing model.

Typically, mixing of fuel and air is calculated by solving the Navier-Stokes equations in conjunction with a

turbulence model. In order to keep the computational overheads low, the problem is simplified using the concept of

mixing efficiency that is defined as the ratio of fuel that is available for combustion to the amount that was injected.

A relation specifically for mixing efficiency in scramjet combustors is derived using results from the literature.

It is assumed that the fuel available for reaction can be determined using a mixing efficiency,

fomf mm && η= (46)

where fm& is the mass flow rate of fuel available for reaction, ηm is the mixing efficiency and fom& is the mass

flow rate of fuel through the injectors. The mixing efficiency changes in value from zero at the injector exit until it

reaches unity at a defined mixing length Lmix where all the available fuel is mixed with the combustor air and is

ready for combustion. Driscoll et al. (Ref. 11), in their work on scaling supersonic flames, derived fuel mixture

fraction profiles along the centrelines of incompressible jets,

n

F

n

FAA

FFC

d

x

dU

Ucf

222 −−

=

θρρ

(47)

where n = 1 for jet-like flows. Assuming x = Lmix,i (the incompressible mixing length) and n = 1, re-arranging Eq.

(47) shows that the incompressible mixing length is,

2

1

,

∝

AA

FF

F

imix

U

U

d

L

ρρ

(48)

Papamachou and Roshko12 show that the rate of growth of a compressible turbulent mixing layer (dδ/dx) is

related to the convective Mach number (Mc) and incompressible growth rate (dδi/dx). It is therefore reasonable to

assume that mixing length is inversely proportional to the mixing layer growth rate,


8

1−

∝dx

dLmix

δ (49)

Hence compressible and incompressible mixing lengths are related by,

)(

1,

c

imixmixMf

LL ×= (50)

Given,

AF

AF

c

M

c

aa

UUM

eMf c

+

−=

+= − 23

75.025.0)(

(51)

By using the proportionality constant *K , the compressible mixing length can be written,

( )

21

*

=

AA

FF

cF

mix

U

U

Mf

K

d

L

ρρ

(52)

The constant K* is found by using the multi-dimensional CFD results of Gerlinger and Brüggermann13. In their

work, mixing efficiency was calculated along a hydrogen-fuelled strut injected scramjet duct and compared with

experimental measurements. These results show that mixing efficiency is reasonably independent of injector nozzle

exit dimensions. Using the results from this study, the value of the constant was found to be K* = 390 and mixing

efficiency was found to have the form,

( )( )

80586.0

69639.3

06492.1

1 )(

=

=

=

−= −

d

k

a

ead

xk

mη

(53)

Where,

mix

inj

L

Lxx

−= (54)

Hence a simple method is available to calculate the mixing efficiency and amount of fuel available for reaction.

In all test cases presented in this paper, Eq. (53) is used to calculate mixing efficiency by differentiating it and

using it in a differential form of Eq. (46). The mixing length is either calculated using Eq. (52) for strut injected

engines or is specified by the user for other types of fuel injection.

III. Comparison with Experimental Data

A. Test Case 1: T4 Refected Shock Tunnel Experiment

Boyce et al14 conducted experiments in the T4 free-piston reflected shock tunnel at the University of

Queensland. As this type of facility has a steady test period of approximately 1 millisecond, reflected shock tunnels


9

are described as ‘pulse’ facilities to describe the transient nature of the test flow. The scramjet test simulated here

used a diverging duct where both the top and bottom plates of the scramjet were set to 1.72 degrees. Supersonic air

at Mach 2.47, a temperature of 1025 K and a static pressure of 59 kPa was generated at the entrance to combustion

chamber, which represents a flight Mach number of approximately 7. Hydrogen fuel was injected at sonic

conditions using a central strut to achieve an overall equivalence ratio of 0.38. Figure 1 illustrates the experimental

setup used by Ref. 14.

Figure 1. Experimental arrangement used by Ref 14.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.850

60

70

80

90

100

110

120

130

140

150

Distance [m]

Pressure [kPa]

Experimental Data Φ = 0.38

Model Φ = 0.38

Figure 2. Comparison of ground test data from Ref. 14 with quasi-one-dimensional flow solver results.

Figure 2 compares the experimental scramjet combustor measurements of Ref. 14 with numerical data generated

using the quasi-one-dimensional model. While the model does not resolve the pressure fluctuations associated with

the shock waves generated by the central strut injector, it does successfully reproduce the mean pressure rise along

the duct. By simulating the mean pressure distribution along the combustor correctly along with wall skin friction

losses, the quasi-one-dimensional model is capable of calculating the thrust and specific impulse of a scramjet

combustor. As the model is also very computationally efficient, it can be directly incorporated into design

optimization, performance and trajectory simulations and called repeatedly during the solution time.


10

B. Test Case 2: The University of Virginia Supersonic Combustion Experiments

Goyne et al.15 conducted experiments in The University of Virginia Supersonic Combustion Facility. The

geometry of their facility consists of a constant area rectangular duct, followed by a divergence of the duct ceiling

by an angle of 2.9 degrees (Figure 3). A ramp injector was used for hydrogen fuel injection into the hot supersonic

test gas. Supersonic air was provided with a Mach number of 2.1, static temperature of 670 K and a static pressure

of 39 kPa, which represents a flight Mach number of approximately 5. Ignition was performed using a hydrogen-

oxygen detonation driven ignition system and combustion was self-sustaining after ignition. Two cases are

investigated in this study. The first is a case where no fuel was injected, and the second is a case where hydrogen

fuel was injected sonically from the ramp injector so that the overall equivalence ratio was 0.32.

Figure 3. Schematic of The University of Virginia Supersonic Combustion Facility (Ref. 15).

-0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40.5

1

1.5

2

2.5

3

Distance [m]

Normalised Pressure [P/P

ref ]

Experimental Data Φ = 0.32

Model Φ = 0.32Experimental Data Φ = 0.0

Model Φ = 0.0

Figure 4. Comparison of ground test data from Ref. 15 with quasi-one-dimensional flow solver results (Pref =

40 kPa).

Figure 4 compares both the fuel-off and the fuel-on experimental results of Ref. 15 with simulation results

obtained from the quasi-one-dimensional model. The fuel-off experimental data shows pressure fluctuations along

the duct due to weak shocks generated by the ramp injector. While the quasi-one-dimensional model does not

capture these, it does reproduce the mean pressure distribution along the duct. The large pressure rise at the


11

downstream end of the combustor is due to an exhaust shock that compresses the test flow to atmospheric

conditions. This was not modelled using the quasi-one-dimensional solver.

Figure 4 also compares supersonic combustion data with simulation results for an equivalence ratio of 0.32.

Again, the model adequately resolves the mean pressure rise, however, the mixing-length was found to be longer

than the engine, resulting in a combustion efficiency of 90.3%. It is interesting to observe that the experimental

results show a plateau in pressure between 0.1 m and 0.18 m, while the model pressure peaks at 0.1 m before

monotonically decreasing. This may be explained by the fact that the mixing model used in the numerical model

was derived from non-reacting, cold supersonic mixing data for a central strut and the Mach number in the duct

approaches unity. The ramp injector achieves rapid mixing utilizing a pair of counter rotating vortices that are not

present during central strut injection. The mixing length model used here is modified to incorporate this effect, but

this modification is not adequate to resolve this pressure plateau. Nevertheless, the model still achieves a

remarkable reproduction of the scramjet flow field, suitable for use in performance studies. It should be noted that

Ref. 15 also presents a prediction using the multi-dimensional GASPex v 3.2 code. Their predictions (not shown in

the current report) show a similar peak instead of a plateau.

C. Test Case 3: Hyshot II Flight Tests

Flight tests of the HyShot II program1 are also used for validation study. The HyShot II combustor is a 300 mm

long, 9.8 mm x 75 mm duct followed by a 147 mm long, 12 degree divergence of the duct ceiling (Figure 5). Fuel

injection into the HyShot combustor was achieved via 4 x 2 mm diameter circular fuel injection ports in the floor of

the combustor, 58 mm from the entrance. Two flight conditions are simulated in this study; both are at an altitude of

33 km and at a Mach number of approximately 7.7.

Figure 5. Hyshot II Flight Experiment Details (Ref. 1)

The first flight test experiment was obtained with no fuel injection and while the vehicle was travelling at an

angle of attack of 5.26 degrees at Mach 7.75. The hypersonic inlet supplied the combustor with supersonic air at a

Mach number of 2.0, a temperature of 1571 K and a pressure of 65.9 kPa. The second flight test experimental result

was obtained with fuel injection and with the vehicle at an angle of attack of 4.26 degrees and a Mach number of

7.74. The combustor inlet was supplied with supersonic air at a Mach number of 2.0, a temperature of 1528 K and a

pressure of 73.76 kPa. The nominal equivalence ratio was 0.3 for this experiment.

Figure 6 compares both fuel-off and fuel-on experimental results with numerical data obtained from the quasi-

one-dimensional solver. The fuel-off experimental results are matched well by the solver, indicating that the model

is correctly modelling gas dynamics and viscous losses acting internally within the engine.


12

0.1 0.15 0.2 0.25 0.3 0.35 0.40

0.5

1

1.5

2

2.5

Distance [m]

Normalised Pressure [P/P

ref]

Experimental Data Φ = 0.3Model Φ = 0.3

Experimental Data Φ = 0.0Model Φ = 0.0

Figure 6. Comparison of flight data (Ref. 1) with quasi-ne-dimensional flow solver results (Pref = flight test

Pitot pressure).

The fuel-on experimental results show that the pressure rise is delayed beyond what would be considered normal

in a hot, turbulent supersonic combustor. It is postulated here that the hydrogen fuel is initially injected into a

laminar boundary layer. This therefore limits mixing to what is achievable my molecular diffusion, which is very

low. It is not until the mixing rate is suddenly increased at a position of approximately 100 mm from the combustor

leading edge, that significant pressure rise due to supersonic combustion can be measured. It is unclear what exactly

causes this, but it is reasonable expect that turbulent transition of the boundary layer or shock induced mixing

enhancement, from the reflected injection shock from the duct cowl, will rapidly increase the mixing rate. It is

likely that both these phenomena are coupled within the combustor but further analysis is required to achieve a

complete understanding of the ignition process in this engine. However, this phenomenological framework is useful

for applying the quasi-one-dimensional model to the analysis of these particular flight test results.

For the Hyshot test case, it was assumed that the initial molecular diffusion phase of supersonic mixing was

negligible. Fuel injection was therefore initiated at 100 mm from the combustor entrance. Figure 6 compares the

simulation results against the fuel-on experimental data and shows a reasonable comparison. In order to achieve this

result, a mixing length of 0.9 m was required, which resulted in incomplete combustion at the combustor exit, with a

combustion efficiency of 78.3% predicted.

IV. Conclusion

In conclusion, a quasi-one-dimensional model has been developed and used to describe hydrogen fuelled

scramjet combustor reacting flows in a high enthalpy pulse facility experiment, a continuous flow supersonic

combustion facility ground test and in the HyShot II flight test. In each test case, the model is capable of simulating

the mean pressure distribution along the combustor, therefore making it suitable to predict the performance of

conceptual, or more developed, scramjet vehicles. The model is also useful for the analysis of ground test and flight

data, increasing understanding concerning mixing and combustion within the scramjet combustor.

Further comparisons with flight and ground test data are required for further validation of the model.

Specifically, the fuel injection and supersonic mixing model can be improved to include various injection methods

as well as modeling other fuels, such as hydrocarbons. Techniques to extend the theoretical method of predicting

the mixing length are also required. Finally, it is planned to include a subsonic combustion capability in the quasi-

one-dimensional model so that dual mode scramjet performance can be predicted.

Acknowledgements

This work was supported by the Australian Defence Science and Technology Organisation, Weapons Systems

Division, South Australia.


13

References 1Smart, M.K., Hass, N.E. and Paull, A. “Flight Data Analysis of the HyShot 2 Scramjet Flight Experiment”, AIAA Journal,

Vol. 4, No. 10, 2006, pp 2375-2366. 2Moses, P.L., Rausch, V.L., Nguyen, L.T. and Hill, J.R. “NASA Hypersonic Flight Demonstrators – Overview, Status and

Future Plans”, Acta Astronautica, Vol. 55, 2004, pp. 619-630. 3O’Brien, T., Starkey, R. and Lewis, M. “Quasi-One-Dimensional High-Speed Engine Model with Finite Rate Chemistry”,

Journal of Propulsion and Power, Vol. 17, No. 6, 2001, pp. 1366-1374. 4Starkey, R. P. and Lewis, M. J. “Sensitivity of Hydrocarbon Combustion Modeling for Hypersonic Missile Design,”

Journal of Propulsion and Power , Vol. 19, No. 1, 2003, pp. 89–97. 5Shapiro, A. The Dynamics and Thermodynamics of Compressible Fluid Flow, Vol. 1, Ronald, New York, 1953. 6Anderson, J.D. Hypersonic and High Temperature Gas Dynamics, AIAA, Reston, VA, USA, 2000. 7Turns, S.R. An Introduction to Combustion, McGraw Hill, New York, 1996. 8Gordon, S. and McBride, B.J. “Computer program for calculation of complex chemical equilibrium compositions, rocket

performance, incident and reflected shocks, and Chapman-Jouguet detonations”, NASA Special Publication, NASA SP-273,

1976. 9Borman, G.L. and Ragland, K.W. Combustion Engineering, McGraw Hill, Boston, 1998. 10Morley, C. GasEq, Version 0.79 http://www.gaseq.co.uk, 2005. 11Driscoll, J.F., Huh, H., Yoon, Y. and Donbar, J. “Measured Lengths of Supersonic Hydrogen-Air Jet Flames – Compared to

Subsonic Flame Lengths – and Analysis”, Combustion and Flame, Vol. 107, pp. 76-186, 1996. 12Papamoschou, D. and Roshko, A. “The Compressible Turbulent Shear Layer: An Experimental Study”, Journal of Fluid

Mechanics, Vol. 197, pp. 453-477, 1988. 13Gerlinger, P. and Bruggemann, D. “Numerical Investigation of Hydrogen Strut Injections into Supersonic Airflows”,

Journal of Propulsion and Power, Vol. 16, No. 1, pp. 22-28, 2000. 14Boyce, R.R., Paull, A., Stalker, R.J., Wendt, M., Chinzei, N. and Miyajima, H. “Comparison of Supersonic Combustion

Between Impulse and Vitiation-Heated Facilities”, Journal of Propulsion and Power, Vol. 16, No. 4, pp. 709-717, 2000. 15Goyne, C.P., McDaniel, J. C., Quagliaroli, T.C., Krauss, R.H. and Day, S. W. “Dual -Mode Combustion of Hydrogen in a

Mach 5, Continuous-Flow Facility”, Journal of Propulsion and Power, Vol . 17, No. 6, pp 1313-1318, 2001.

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