American Institute of Aeronautics and Astronautics

1

Preliminary Design of a Hypersonic Air-breathing Vehicle

F. Bonelli*, Università degli Studi della Basilicata, Potenza, 85100, Italy

L. Cutrone†, R. Votta‡ Centro Italiano Ricerche Aerospaziali (CIRA), Capua, 81043, Italy

A. Viggiano§ and V. Magi¶ Università degli Studi della Basilicata, Potenza, 85100, Italy

This paper describes the capabilities of a new in-house code, named SPREAD 2.0, to provide real time guidance to select the optimal parameters for preliminary design of hypersonic propulsion systems. Such a new solver drastically reduces the time and costs associated with excessive use of Computational Fluid Dynamics (CFD) and/or experimental tests. The accuracy of the model has been assessed by comparing the results with a 2-D CFD simulation performed with the C3NS-CIRA code. Finally, SPREAD 2.0 has been used to address the influence of air/fuel equivalence ratios and of craft angles of attack on the thermodynamic variables, which in turn affect the design, and on the pollutant emissions.

Nomenclature A = duct cross sectional area AoA = angle of attack

= Chapman-Rubesin constant ER = equivalence ratio

= molar specific enthalpy of species i

= specific enthalpy of the mixture = mean molar mass of the mixture

= Mach number = total mass flow rate

n = constant for the computation of the Chapman-Rubesin parameter = number of reacting species

= number of reactions = number of species

= pressure = Prandtl number

= heat transfer rate per unit area = universal gas constant = gas constant of the mixture , = forward and reverse molar reaction rates per unit volume of reaction j

* Graduate Research Assistant, Department of Environmental Engineering and Physics, via dell'Ateneo Lucano 10. † Researcher, PhD, Aerospace Propulsion and Reacting Flows Unit, AIAA Member, l.cutrone@cira.it . ‡ Researcher, PhD, Aerospace Propulsion and Reacting Flows Unit, AIAA Member. § Assistant Professor, PhD, Department of Environmental Engineering and Physics, via dell'Ateneo Lucano 10. ¶ Full Professor, Department of Environmental Engineering and Physics, via dell'Ateneo Lucano 10.

17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference 11 - 14 April 2011, San Francisco, California

AIAA 2011-2319

Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

American Institute of Aeronautics and Astronautics

2

= Reynolds number = recovery factor = temperature = normal velocity across oblique shock = tangential velocity across oblique shock = axial velocity

X = x-coordinate Y = y-coordinate y = mass fraction

= shock wave angle

= displacement thickness = specific heat ratio = dynamic viscosity = deflection angle = density

= number of moles of species i per unit mass of mixture

= stoichiometric coefficients of reactant and product species i in reaction j

= constant of the viscosity power law Superscript * = reference enthalpy condition Subscript 1 = input variable 2 = output variable ∞ = freestream air = air-related aw = adiabatic wall c = combustor e = edge of boundary layer fuel = fuel-related peak = peak value w = wall

I. Introduction ODAY, there is a growing interest in hypersonic air breathing propulsion systems both as the most promising technology to reduce the travelling time of long-distance civil flights (e.g. Brussels to Sydney) and as Single

Stage To Orbit vehicle (SSTO) for reducing the cost of sending payloads to orbit. The absence of moving parts, such as compressors and turbines, makes these vehicles able to fly at hypersonic velocities. Such an absence allows these engines to reach higher temperatures at the end of the combustor and, as a consequence, higher thermal efficiencies and larger thrust to weight ratios. However, these engines are not able to generate any static thrust, so the acceleration of the vehicle must be obtained by using either a turbine based (TBCC) or rocket based combined cycle (RBCC). At hypersonic speeds, i.e. Mach number in the range 5÷12, the flow remains supersonic also throughout the combustor, in order to reduce thermodynamic and chemical losses.

Such losses will be much larger when the flow is decelerated at subsonic speeds. Based on this particular flow configuration, this engine is named supersonic combustion ramjet, or scramjet for short. Unlike other propulsion

T

Fig. 1. Schematic view of a hypersonic air-breathing

vehicle (taken from NASA – LaRC).

American Institute of Aeronautics and Astronautics

3

systems, hypersonic engines must be highly integrated with the airframe in order to avoid excessive external drag due to pylons or struts which connect the engine to the vehicle, thus the separation between the engine and the aircraft becomes less evident, as shown schematically in Fig. 1. In order to assess the proper operating range of the engine and its performances, an extensive use of CFD simulations and experimental tests, which simulate the whole integrated configuration, is needed. Among the most significant flight tests of hypersonic vehicles there are the Australian HyShot1 and NASA’s Hyper-X vehicles1. Other scramjet projects currently underway are the Joint Australia-USA HIFiRE, the X-51 Flight Program, the FALCON Program of DARPA and the LAPCAT Program of ESA. From a computational point of view, efforts have been addressed especially in the field of supersonic combustion models (Battista et al.2; Cecere et al.3). Nevertheless, simplified mathematical models, that are able to quickly provide information on the set of optimal parameters to be used and on the geometrical configuration of the engine, can be useful for more complex investigations.

In this scenario, the present work, starting from an idea of Bonifacio et al.4, describes the development of the SPREAD 2.0 (Supersonic PREliminary Aerothermodynamic Design version 2.0) code which allows a fast and reliable preliminary design of hypersonic propulsion systems.

This work has been carried out in the framework of LAPCAT II task 4.3 “Engine-Airframe Integration Methodology”. Such a program is devoted to the development, verification and validation of engineering tools for nose-to-tail numerical modeling of hypersonic vehicles.

The solver has a flexible structure based on a “black box” logic as shown in Fig. 2. A generic propulsive system is divided into its main components, each of them modeled as a box with inputs, outputs and ad-hoc mathematical models to obtain the outputs from the given inputs. It will be shown that this approach can be used for the design methodology of a generic propulsive configuration. Moreover, this solver can address other tasks, such as free-stream parameter sensitivity analysis, off-design analysis and reverse design analysis.

In this paper, the capability of the proposed methodology will be demonstrated by assessing its accuracy and robustness through the comparison of one-dimensional predictions with CFD simulations performed by using an in-house two-dimensional CFD code (Battista et al.2).This code solves the Navier-Stokes equations in integral form, and discretized with a finite volume, cell centered technique. Eulerian fluxes are computed with a second order Flux Difference Splitting (FDS) method5 with a ENO reconstruction of the interface values. Viscous fluxes are computed with a classical centered scheme. Time integration is performed by employing an explicit Euler forward algorithm coupled with an explicit evaluation of the source terms in a time-marching approach. For further details about the 2-D solver, the reader can refer to the work of Battista et al.2.

The analysis of the influence of the air/fuel equivalence ratio and of the hypersonic vehicle’s angle of attack on specific thermodynamic variables and, consequently, on the scramjet design will be also presented. Finally, the assessment of pollutant emissions will be addressed.

This work is organized as follows: the governing equations and the computational method are firstly given, then the validation of SPREAD 2.0 versus CFD results is presented and the parametric analysis is shown and, finally, the conclusions are summarized.

II. Governing Equations and Computational Model The propulsion system under investigation is numerically studied by considering and assembling individual

modules. Each of them involves a mathematical model that describes the performance and capabilities of the corresponding engine’s component. The mathematical model can be implemented with different levels of accuracy, from a just theoretical one, to one tied to empirical correlations, to a merely numerical model.

The engine’s component modules, that are considered in this work to simulate the operating conditions of a scramjet engine, are:

• INLET RAMP; • MIXER;

Fig. 2. SPREAD 2.0 black box approach.

American Institute of Aeronautics and Astronautics

4

• COMBUSTOR; • NOZZLE.

For example, Figure 3 shows the modules and the “black box” layout of a scramjet engine with a double-ramp deflection of the intake.

In what follows, the subscripts 1 and 2 will be used to identify the inlet and the outlet conditions of each

component, whereas the subscripts air and fuel will be used to identify the variables which refer to air and fuel, respectively.

A. INLET RAMP This module simulates the flow passage through an oblique shock with different levels of accuracy. The flow

field is simulated by solving the mass, momentum and energy conservation equations, given by: , (1)

, (2) , (3)

, (4)

where , , , and are the density, the pressure, the normal and the tangential velocities across the oblique shock and the specific enthalpy of the mixture, respectively. The mixture enthalpy is evaluated by applying Gibbs theorem6, i.e. by summing the contribution of each species

(5)

where NS is the number of species, is the molar specific enthalpy of species i and is the number of moles of

species i per unit mass of mixture. For each species, is computed by using the empirical equations given by Gordon and McBride7. The pressure is computed by means of the equation of state , (6)

where is the ratio between the universal gas constant and the mean molar mass of the mixture, ,

and is the temperature. The shock wave angle, , is computed by using the geometrical relation

, (7)

where is the deflection angle.

Fig. 3. Black box layout of a scramjet engine with a double deflection of the intake.

INLET RAMP COMB NOZZLE INLET RAMP

TWO RAMPS SCRAMJETTWO RAMPS SCRAMJET

MIX 1 2

INLET RAMP 3 4 5 6

American Institute of Aeronautics and Astronautics

5

For the inlet ramp, different degrees of simplifications are implemented. In the simplest assumption, the gas flow is considered steady, adiabatic, non-viscous and calorically perfect. However, more sophisticated models have also been implemented in the code to simulate conditions that are closer to real ones. For example, the influence of the viscous effects can be included by predicting the displacement thickness, , which enables to consider the new slope of the wall ramp, as shown in Fig. 4. As described in the Chapman-Rubesin theory8, can be computed as

, (8)

where x is the coordinate tangential to the wall, is the Chapman-Rubesin constant, Re is the Reynolds number, γ

is the specific heat ratio, M is the Mach number and the subscripts ∞, w and aw stand for freestream, wall and

adiabatic wall conditions, respectively. The Chapman-Rubesin constant, by considering the viscosity power law

( where ω varies in the range 0.75-1), is given by:

, (9)

where n is equal to 0.5 and 0.2 under laminar and turbulent flow conditions, respectively, is the reference temperature corresponding to reference enthalpy conditions, that for perfect gas yields

, (10)

with

, (11)

where the subscript e stands for properties at the edge of the boundary layer and with the recovery (adiabatic wall) temperature defined as

, (12)

where r is the recovery factor. This factor is conventionally equal to under laminar conditions and under turbulent conditions, where Pr is the Prandtl number.

Moreover, the fluid can be also treated as a mixture of thermally perfect gases in chemical equilibrium to include the effects of air dissociation on thermodynamic variables behind oblique shocks. The evaluation of the chemical equilibrium state is made by LSENS code9, developed at the NASA Lewis Research Centre.

Hence, the most accurate model implemented in SPREAD 2.0 to simulate an oblique shock wave considers a steady, adiabatic, viscous flow of a thermally perfect gases mixture in chemical equilibrium.

B. MIXER The mixing process is simulated by means of a one dimensional analysis, by considering the gas perfectly mixed

at the mixer out. The governing equations are:

Fig. 4. Definition of the displacement thickness to account for the viscous effects.

θ θ new

β δ∗

American Institute of Aeronautics and Astronautics

6

, (13)

, (14)

, (15)

where is the axial velocity, and are the air and the fuel mass fractions, respectively. The pressure is

evaluated from the equation of state (Eq.(6)).

C. COMBUSTOR and NOZZLE The combustion and expansion nozzle modules are implemented starting from LSENS code. They are

implemented by assuming a steady, non-viscous, adiabatic, one-dimensional flow of a chemically reacting ideal gas mixture in a duct. The duct area A is specified, either as a constant or as a function of distance. The transport equations for mass, momentum and energy are, respectively:

, (16)

, (17)

, (18)

where NRS is the number of chemical reacting species, is the heat transfer rate per unit area and is the total mass flow rate.

Equation (6) is used to evaluate the pressure, while the transport equation for each reacting species is given by

, , (19)

where and are the stoichiometric coefficients of the ith reactant species and product species, respectively, in

the jth reaction and the terms and are expressed according to the classical Arrhenius formulation. In order to simulate the chemical kinetics, the corresponding set of Ordinary Differential Equations (ODEs) is solved by the packaged code LSODEErrore. L'origine riferimento non è stata trovata. (Livermore Solver for Ordinary Differential Equations).

Finally, the complete set of governing equations consists of a number of non linear algebraic equations

depending on the number of assembled modules. Such a system of non linear equations is solved by employing a globally convergent method for non linear system of equations, which is based on the Newton-Raphson method11.

III. Model Validation The accuracy of the model has been assessed by a detailed comparison between the results obtained by this

model and an accurate 2-D CFD solver, named C3NS2, available at CIRA. The test case is related to a scramjet engine, with a double-ramp air intake configuration, flying at an altitude of 30 Km (T=226.5 K, p=1197 Pa) with Mach number equal to 7.5. The first and the second deflection angles of the air intake are equal to 5.62 deg and 18.86 deg, respectively; the axial lengths of the air intake, of the combustor and of the nozzle are 4.055 m, 1.595 m, 2.35 m, respectively, and the expansion ratio of the nozzle is equal to 13.84. The comparison with the 2-D CFD solver has been performed considering three cases:

1. simulation of the complete engine without combustion, by including the dissociation of air and neglecting its viscosity (case 1);

2. simulation of the complete engine without combustion, by including the viscosity of air and assuming frozen conditions with the air modeled as a calorically perfect gas (case 2);

American Institute of Aeronautics and Astronautics

7

3. simulation of the combustor and the nozzle with combustion, by assuming a non equilibrium chemically reacting gas mixture of fuel and air and neglecting the gas viscosity (case 3).

For the non-viscous cases, the dissociation of the chemically reacting flow of air is modeled by using Park’s kinetic scheme12. For all these simulations, it is assumed that the hypersonic vehicle flies with an angle of attack (AoA) equal to zero.

A. Test-Cases without Combustion In the case of non-viscous, chemically reacting air flow (case 1), the SPREAD 2.0 code provides the geometry of the engine, as sketched in Fig. 5. For the sake of completeness, the engine geometry is summarized in Table 1,

where the X-Y coordinates of the six points, i.e. G1 thru G6, are given.

POINT X [m] Y [m] 1 0.00000 0.00000 2 2.68165 0.26383 3 4.05500 0.73307 4 3.75976 0.78700 5 5.65000 0.73307 6 8.00000 0.00000

Table 1. Coordinates of the points (case 1).

For the 2-D CFD simulation, a structured grid has been used, as shown in Fig. 6, with 21534 grid points and 10184 numerical cells. The figure shows a relatively high grid resolution in correspondence of the region where it is expected the presence of the oblique shock. The Mach number contour plot obtained by using the 2-D code is reported in Fig. 7. In particular, the strong shock-shock interaction and the impingement of the resultant shock on the cowl of the combustor are shown. Moreover, Fig. 8 shows the presence of a normal shock located at the entrance of the combustor. However, the one dimensional model is not able to predict its presence. The normal shock occurrence results in a low spillage of air, that is limited to 0.25% (0.082 Kg/s out of 32.80 Kg/s), and in an increase of pressure after the combustor cowl, as shown in Fig. 9, where the pressure distribution along the upper wall of the engine is given for both simulations. The figure shows that the two simulations are able to give a very good agreement through the air intake, whereas the agreement is fair in the combustor. Nevertheless, the nozzle exit pressure is correctly captured.

Fig. 5. Engine geometry configuration.

American Institute of Aeronautics and Astronautics

8

Fig. 6. Computational grid of the engine (case 1).

Fig. 8. Blow-up of the normal shock. Fig. 9. Pressure distribution at wall (case 1).

Fig. 7. Mach number contour plot (case 1).

American Institute of Aeronautics and Astronautics

9

For the test-case no. 2, the SPREAD 2.0 code provides the geometry of the engine which is summarized in Table 2, while Table 3 give the X-Y coordinates of the points located along the boundary layer when the displacement thickness is taken into account.

In this case, a structured grid with 51550 grid points and 24832 numerical cells is used for the 2-D simulation. Such a grid is much finer than the previous one near the walls, as shown in Fig. 10, to accurately capture the wall boundary layer.

A comparison of the pressure distribution between the 2-D solver and SPREAD 2.0 is reported in Fig. 11 which shows, this time, a very good agreement.

POINT X [m] Y [m] 1 0.00000 0.00000 2 2.67692 0.26337 3 4.05500 0.73422 4 3.73776 0.80023 5 5.65000 0.73422 6 8.00000 0.00000

Table 2. Coordinates of the points (case 2).

POINT X [m] Y [m] 1’ 0.00000 0.00000 2’ 2.67555 0.27730 3’ 4.05364 0.73819

Table 3. Coordinates of the points at the boundary layer (case 2).

Fig. 10 Blow-up of the computational grid at wall in the case 1 (left) and in the case 2 (right)

Fig. 11. Pressure distribution at wall (case 2).

American Institute of Aeronautics and Astronautics

10

B. Test-case with Combustion Hydrogen is used as fuel and its oxidation is modeled by using a 7-steps scheme13 obtained from Jachimowski’s

detailed kinetic scheme14, which is made up of 33 reactions involving 13 chemical species. In order to predict NOx production, the three steps Zel’dovich sub-mechanism14 is employed. Hydrogen at 150 K is injected at sonic conditions with an equivalence ratio (ER) equal to 0.5. In order to perform a comparison between the 2-D code and SPREAD 2.0 with combustion, the reactants must be perfectly mixed at the inlet of the combustor. Hence, only the combustor and the nozzle have been simulated with the combustor inlet conditions taken from the simulation previously done with SPREAD 2.0. Figures 12 and 13 show the pressure and the temperature distributions, respectively, obtained by employing both solvers, as a function of axial distance. For the two-dimensional simulation, the values at each axial location are computed as the mean value along the corresponding cross sections. The figures show a very good agreement.

The mean mass fraction of hydrogen along the axial direction, given in Fig. 14, also shows a good agreement in terms of ignition delay.

Fig. 12. Mean pressure distribution (case 3). Fig. 13. Mean temperature distribution (case 3).

Fig. 14. Mean hydrogen mass fraction distribution (case 3).

American Institute of Aeronautics and Astronautics

11

IV. Parametric study A parametric analysis of the engine performance and emissions along an assigned flight path is performed, in order to evaluate the influence of several design parameters. It has been considered an engine with a three-ramp air intake configuration that flies at an altitude of 30 Km (T=226.5 K, p=1197 Pa) and with a Mach number equal to 8. The deflection angles of the air intake are equal to 3.0 deg, 6.3 deg and 13.0 deg, respectively; the axial lengths of the air intake, of the combustor and of the nozzle are 4.0 m, 15.0 m, 5.0 m, respectively; finally, the expansion ratio of the nozzle is equal to 9.28. Given these geometrical constraints, it has been considered that other parameters, i.e. the angle of attack and the equivalence ratio, may be consistently varied. Therefore, several simulations have been carried out by varying AoA in the range 0÷6 deg and ER in the range 0.2÷1.4. Hydrogen has been used as fuel and it has been injected at 250 K in sonic conditions. Figure 15 shows the ignition length as a function of the equivalence ratio for different values of the angle of attack.

The ignition length is computed as the axial distance at which the percentage increase of temperature is greater than 5%. The figure shows that the ignition length increases with equivalence ratio, since the increase of the hydrogen mass flow rate, injected at 250 K, with respect to the hotter air mass flow rate, leads to a lower temperature of the mixture, as shown in Fig. 16, where the combustor inlet temperature is shown as a function of ER for different values of AoA. In addition, the ignition length decreases as the angle of attack increases, because there are stronger shock waves which lead to higher temperatures, as again shown in Fig. 16.

Figure 17 shows NOx concentration at the outlet of the nozzle as a function of ER for different values of AoA. The emissions increase with AoA due to the increase of the maximum temperature at the outlet of the combustor (Tc peak), as shown in Fig. 18. As regards the ER effect, for lean mixtures with ER up to 0.8, the emissions increase with ER

Fig. 15. Ignition length as a function of ER and AoA.

Fig. 16. Mixture temperature at combustor inlet as a function of ER and AoA.

American Institute of Aeronautics and Astronautics

12

due to the increase of Tc peak , as also shown in Figure 18. On the other hand, by using mixtures with ER higher than 0.8, the opposite trend is encountered, since NOx emissions decrease with ER, whereas the maximum temperature at the outlet of the combustor still increases with ER. These findings can be explained by considering the incompleteness of combustion when relatively high values of ER are considered, as shown in Fig. 19, where the ratio between the hydrogen mass at the end of the combustor and the mass of hydrogen injected is plotted versus ER. Such a ratio provides information about combustion efficiency for different values of AoA. Figure 19 also shows that combustion completeness is practically independent of AoA. As the combustion is more and more incomplete, nitrogen is less oxidized and NOx concentration is lower.

One of the main contributions of this work is that this simplified model is able to provide the best strategy to

reduce NOx emissions. Specifically, in order to reduce NOx emission an RQL (Rich-burn, Quick-mix, Lean-burn) strategy is suggested, i.e. a kind of staged-liked combustion where an initial fuel rich combustion is followed by a fast injection of air providing a secondary zone of lean combustion. In this way the peak of NOx formation, as a function of fuel/air equivalence ratio, is prevented.

Fig. 17. NOx concentration (PPM) as a function of ER and AoA.

American Institute of Aeronautics and Astronautics

13

V. Conclusions In this work, the capability of an in-house code, named SPREAD 2.0, as an aerothermodynamic/propulsive tool

for the preliminary design of scramjet engines has been assessed. The accuracy of the code has been demonstrated by comparing the results with those obtained with an accurate and reliable 2-D CFD code, named C3NS, developed at CIRA. The comparisons with the 2-D CFD computations have been performed by considering three different cases:

1. simulation of the complete engine without combustion, by including the dissociation of air and neglecting its viscosity;

2. simulation of the complete engine without combustion, by including the viscosity of air and assuming frozen conditions with the air modeled as a calorically perfect gas;

3. simulation of the combustor and the nozzle with combustion, by assuming a non equilibrium chemically reacting gas mixture of fuel and air and neglecting the gas viscosity.

The results show that, by including the viscous effects, a good agreement between the two solvers for the prediction of pressure and temperature distributions and of the oblique shock position is obtained. These results show that the SPREAD 2.0 code is a powerful tool for a preliminary design of hypersonic propulsion systems, thus reducing the costs and time associated with a massive use of either Computational Fluid Dynamics (CFD) or experimental tests. In addition, SPREAD 2.0 is able to give real time guidance on the set of optimal parameters to be employed in an aircraft with variable geometry. Moreover, the code has been used to assess the influence of fuel/air equivalence ratio and of angle of attack on some thermodynamic variables and on the pollutant emissions. The results show that the ignition length increases with ER and decreases with AoA, since with the increase of ER the temperature at the combustor inlet decreases,

Fig. 18. Maximum temperature in the combustor chamber as a function of ER and AoA.

Fig. 19. Hydrogen outlet mass per unit of hydrogen mass injected.

American Institute of Aeronautics and Astronautics

14

whereas the opposite trend is encountered with the increase of AoA . The emission of NOx reaches its maximum for ER=0.8, whereas lower values are obtained for leaner and richer mixtures. This is the result of two opposite trends: the increase of the maximum temperature, reached at the end of combustor, with ER, that prevails when ER is lower than 0.8, and the level of incompleteness of combustion, that is more effective for rich mixtures. Hence, in order to reduce NOx emission an RQL (Rich-burn, Quick-mix, Lean-burn) strategy is finally suggested.

Acknowledgments This work was performed within the ‘Long-Term Advanced Propulsion Concepts and Technologies II’ project to

investigate high-speed transport. LAPCAT II, coordinated by ESA-ESTEC, is supported by the EU within the 7th Framework Programme Theme7 Transport, Contract no.: ACP7-GA-2008-211485. Further info on LAPCAT II can be found on http://www.esa.int/techresources/lapcat_II.

References 1 Fry R.S., A century of Ramjet Propulsion Technology Evolution, Journal of Propulsion and Power, Vol. 20, No 1,

January-February 2004. 2 Battista F., Cutrone L., Amabile S. and Ranuzzi G., Supersonic Combustion Models Application for Scramjet Engines,

16th AIAA/DLR/DGLR International Space Planes and Hypersonic Systems and Technologies Conference, Bremen, Germany, AIAA-2009-7207.

3 Cecere D., Ingenito A., Romagnosi L., Bruno C., Giacomazzi E., Shock/Boundary Layer/Heat Release Interaction in the HyShot II Scramjet Combustor, 46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Nashville, TN, AIAA-2010-7066.

4 Bonifacio S., Borreca S., Ranuzzi G. and Salvatore V., SPREAD: a Scramjet PREliminary Aerothermodynamic Design Code, 14th AIAA/AHI Space Planes and Hypersonic Systems and Technologies Conference, Canberra, Australia, AIAA-2006-7910.

5 Borrelli S., Pandolfi M., An Upwind Formulation for the numerical Prediction of Non Equilibrium Hypersonic Flows, 12th International Conference on Numerical Methods in Fluid Dynamics, Oxford, United Kingdom, 1990.

6 Hwang, J-T, Dougherty E. P., Rabitz S., and Rabitz H.: The Green’s Function Method of Sensitivity Analysis in Chemical Kinetics. J. Chem. Phys., vol.69,1978,pp.5180-5191.

7 Gordon 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 SP-273, 1971, Interim Revision, 1976.

8 Chapman D.R., Kuehn D.M. and Larson H.K., Investigation of Separated Flows in Supersonic and Subsonic Streams with Emphasis on the Effect of Transition, NACA report No. 1356, 1958.

9 Radhakrishnan K. and Bittker D.A., LSENS, A General Chemical Kinetics and Sensitivity Analysis Code for Gas-Phase Reactions: User’s Guide, Nasa Technical Memorandum 105851, January 1993.

10 Hindmarsh A. C., LSODE and LSODI, Two new initial value ordinary differential equation solvers, Acm-signum newsletter, vol. 15, no. 4 (1980), pp. 10-11.

11 Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.T., Numerical Recipes in Fortran 77 Second Edition: The Art of Scientific Computing, Cambridge University Press 1992.

12 Park C., Assessment of a two-temperature kinetic model for dissociating and weakly ionizing nitrogen Journal of Thermophysics and Heat Transfer (ISSN 0887-8722), vol. 2, Jan. 1988, p. 8-16.

13 Baurle R.A., Girimaji S.S., Assumed PDF turbulence-chemistry closure with temperature-composition correlations, Elsevier, Combustion and Flame 134 (2003) 131-148.

14 Jachimowski C.J., An Analytical Study of Hydrogen-Air Reaction Mechanism with Application to Scramjet Combustion, NASA-TP-2791, 1988.