Manan A. Vyas

Glenn Research Center, Cleveland, Ohio

William A. Engblom

Embry-Riddle Aeronautical University, Daytona Beach, Florida

Nicholas J. Georgiadis and Charles J. Trefny

Glenn Research Center, Cleveland, Ohio

Vishal A. Bhagwandin

U.S. Army Research Laboratory, Aberdeen Proving Ground, Maryland

Numerical Simulation of Vitiation Effects on

a Hydrogen-Fueled Dual-Mode Scramjet

NASA/TM—2010-216756

July 2010

AIAA–2010–1127

U.S. ARMY

RESEARCH LABORATORY
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Manan A. Vyas

Glenn Research Center, Cleveland, Ohio

William A. Engblom

Embry-Riddle Aeronautical University, Daytona Beach, Florida

Nicholas J. Georgiadis and Charles J. Trefny

Glenn Research Center, Cleveland, Ohio

Vishal A. Bhagwandin

U.S. Army Research Laboratory, Aberdeen Proving Ground, Maryland

Numerical Simulation of Vitiation Effects on

a Hydrogen-Fueled Dual-Mode Scramjet

NASA/TM—2010-216756

July 2010

AIAA–2010–1127

U.S. ARMY

RESEARCH LABORATORY

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

48th Aerospace Sciences Meeting

sponsored by the American Institute of Aeronautics and Astronautics

Orlando, Florida, January 4–7, 2010
Acknowledgments

The authors would like to thank the Test Resource Management Center (TRMC) Test and Evaluation/Science and Technology 

(T&E/S&T) Program for their support. This work is funded by the T&E/S&T Program through the Advanced Propulsion Test 

Technology focus area. The authors would also like to thank NASA Fundamental Aeronautics Program’s Hypersonics Project 

for its generous support. The authors wish to thank Dr. Christopher Goyne and Dr. Robert Rockwell at the University of 

Virginia for providing experimental data, Embry-Riddle Aeronautical University for providing supercomputer resources,

and the NPARC Alliance for providing Wind-US technical support.

Available from

NASA Center for Aerospace Information

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Hanover, MD 21076–1320

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5301 Shawnee Road

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Available electronically at http://gltrs.grc.nasa.gov

Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2010-216756 1 

Numerical Simulation of Vitiation Effects on a 

Hydrogen-Fueled Dual-Mode Scramjet 

Manan A. Vyas 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

William A. Engblom 

Embry-Riddle Aeronautical University 

Daytona Beach, Florida 32114 

Nicholas J. Georgiadis and Charles J. Trefny 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Vishal A. Bhagwandin 

U.S. Army Research Laboratory 

Aberdeen Proving Ground, Maryland 21005 

Abstract 

The Wind-US computational fluid dynamics (CFD) flow solver was used to simulate dual-mode 

direct-connect ramjet/scramjet engine flowpath tests conducted in the University of Virginia (UVa) 

Supersonic Combustion Facility (SCF). The objective was to develop a computational capability within 

Wind-US to aid current hypersonic research and provide insight to flow as well as chemistry details that 

are not resolved by instruments available. Computational results are compared with experimental data to 

validate the accuracy of the numerical modeling. These results include two fuel-off non-reacting and eight 

fuel-on reacting cases with different equivalence ratios, split between one set with a clean (non-vitiated) 

air supply and the other set with a vitiated air supply (12 percent H2O vapor). The Peters and Rogg 

hydrogen-air chemical kinetics model was selected for the scramjet simulations. A limited sensitivity 

study was done to investigate the choice of turbulence model and inviscid flux scheme and led to the 

selection of the k-ε model and Harten, Lax and van Leer (for contact waves) (HLLC) scheme for general 

use. Simulation results show reasonably good agreement with experimental data and the overall vitiation 

effects were captured. 

Nomenclature 

Cf, Cb forward and backward reaction rate coefficients 

C turbulent viscosity coefficient 

Df, Db forward and backward reaction rate energies 

D mass diffusivity 

H compression ramp height at the fuel injection location 

Kb Boltzmann constant 

k turbulent kinetic energy 

M Mach number 

ma mf  ,  Air and fuel mass flow rates 

Po, P stagnation and static pressure 
NASA/TM—2010-216756 2 

Pref reference pressure at isolator entrance 

Prl, Prt laminar and turbulent Prandtl number 

Scl, Sct laminar and turbulent Schmidt number 

Sf, Sb forward and backward reaction rate exponent 

To, T stagnation and static temperature 

 thermal diffusivity 

 dynamic viscosity 

 kinematic viscosity 

EXP, CFD experimental and numerical fuel-equivalence ratio 

I. Introduction 

Significant progress has been made in hypersonic research and scramjet technology in recent years, 

mostly in the areas of vehicle design and propulsion. Now that hypersonic research and development 

programs are testing and refining their designs, there is a general need for efficient, safe and cost-effective 

tools to aid the development of these vehicles. Numerical simulation is one approach to aid experimental 

tests, perform parametric studies and check if design changes are worth testing experimentally. It also 

provides important insight into complex flow phenomena like separations, shockwave boundary layer 

interactions, mode transition, and turbulence-chemistry interactions, thus significantly improving the 

flowpath design process for relatively lower costs compared to costly experimental tests alone. One such 

tool is Wind-US, a computational fluid dynamics (CFD) platform developed by the NPARC Alliance, a 

partnership between NASA Glenn Research Center (GRC), USAF Arnold Engineering & Development 

Center (AEDC), and Boeing Phantom Works. Wind-US is a general-purpose Reynolds-averaged NavierStokes (RANS) flow solver that supports equation sets governing turbulent and chemically reacting, 

compressible flows (Refs. 1 and 2). It has a set of pre- and post-processing utilities that helps in analyzing 

a case from start to finish. 

The validation of Wind-US for scramjet applications was a primary objective of this research work. 

The scope of current research included simulating a dual-mode direct-connect ramjet/scramjet engine 

flowpath using Wind-US. Results obtained from the simulations are compared with the experimental data 

from the UVa Supersonic Combustion Facility (SCF). Comparisons are made in terms of static pressures 

along the centerline of the experimental facility. Numerical simulations are performed for a set of 

experimental run conditions (referred to as scans in reference to specific experimental measurements), 

which include a range of fuel-equivalence ratios within the mode transition regime, i.e., transition from 

supersonic to subsonic combustion. In addition, the effects of H2O flow vitiation on the combustion 

process and thus the mode transition was also investigated. This is largely motivated by the fact that large 

experimental tunnel facilities burn fuel to heat supply air for matching the flight conditions, i.e., 

enthalpies and stagnation temperature. Burning of the fuel can add H2O and CO2 vitiates to the flow 

entering the combustion chamber. However, the smaller UVa SCF uses an electric heater to heat the 

supply air for matching the flight conditions. As a result, for the vitiated air experimental runs, H2O and 

CO2 vitiates could be added to the air stream from a separate supply rather than a combustion process in 

order to replicate the situation of larger facilities. This research work only focused on H2O vitiate cases. 

The results and experience of the current work should contribute to the validation of Wind-US for 

hypersonic propulsion applications. To accomplish this, the study attempted to provide results as well as 

the procedure required to obtain the results in order to help other hypersonics researchers make the best 

choice of chemical kinetics, numerical scheme, turbulence model and various other choices associated 

with the CFD simulation of combusting flow. 
NASA/TM—2010-216756 3 

II. Background 

Some previous work on simulating a ramjet/scramjet flowpath was done by Baurle and Eklund 

(Ref. 3) on the US AFRL/Aerospace Propulsion Laboratory scramjet combustor. The entire flowpath was 

modeled using the VULCAN RANS flow solver to perform a Schmidt number and grid sensitivity study. 

The focus of the study was to understand the precombustion shock train, flameholding, and turbulent 

mass and heat transfer characteristics. Another such study was performed by Goyne et al. (Ref. 4) where 

individual components of the UVa dual-mode direct-connect ramjet/scramjet flowpath were also 

simulated using VULCAN. The results concluded that the turbulent mixing as well as the levels of heat 

release of combustion are under-predicted. Engblom et al. (Ref. 5) successfully simulated a direct-connect 

ramjet/scramjet flowpath derived from X-43B using Wind-US. A study preceding the current work was 

done by Bhagwandin et al. (Ref. 6) where the UVa dual-mode direct-connect ramjet/scramjet flowpath 

was simulated in its entirety. The study focused on limited fuel-equivalence ratios as the primary goal was 

investigating various finite-rate chemistry models and overall successful simulation of UVa flowpath. 

Present work expands on the knowledge of previous work and examines fuel equivalence ratios 

corresponding to mode transition and the effects of flow vitiation. 

Mode transition is a process that starts with a ramjet mode and evolves into a scramjet mode. In a 

ramjet the combustor operates at subsonic speeds, i.e., a subsonic combustion process (Ref. 7). This 

means that the isolator, which precedes the combustor, slows the flow down via a series of shocks ending 

with a normal shock to deliver a subsonic flow to the combustor. The hybrid shock structure is comprised 

of lambda and normal shocks, which also produce large boundary layer separations. As the vehicle flight 

speed increases from the ramjet envelope (Mach 2-5) to the scramjet envelope (Mach 5-20), the loss in 

total pressure associated with diffusing inlet airflow to subsonic speeds for combustion becomes very 

large, lowering the performance of the dual-mode engine. Thus, it becomes necessary to carry out the 

fuel-air mixing and combustion process at supersonic speeds, transitioning the engine to scramjet 

operation. The transition from ramjet to scramjet mode occurs as the flight speed increases which brings 

the total temperature ratio across the combustor down, effectively reducing the pressure rise in the 

combustor (Ref. 8). The reduced combustor pressures decrease the shock train strength, eliminating the 

terminal normal shock to the combustor entrance giving way to the supersonic combustion. The boundary 

layer separation decreases as a result of a weaker shock train. Additionally, adjustments made to the fuelequivalence ratio results in the shock train being entirely swallowed by the combustor, resulting in 

scramjet mode. However, in the UVa facility, the mode transition is achieved by throttling the fuel supply 

to the combustor. 

Finite-rate chemistry modeling is one of the most important aspects of the ramjet/scramjet flowpath 

simulation. A variety of multi-reaction chemistry models exist for use in simulations of reacting flow in a 

ramjet/scramjet combustor. Generally speaking, the more detailed the reaction set the better the accuracy 

expected of a model to simulate the highly complex and unsteady nature of the combustion process. In the 

study performed by Engblom et al. (Ref. 5), a 7-species, 3-reaction as well as a 5-species, 1-reaction 

ethylene-air kinetics model were used. The former gave a better prediction of heat release and thus the 

flow characteristics. Particular to the present research were various hydrogen-air chemistry models. One 

such model investigated by Goyne et al. (Ref. 4) was a 7-species, 7-reaction mechanism, however it was 

unable to simulate flame holding and thus was replaced by a simpler 4-species, 1-reaction mechanism. 

In the previous efforts to simulate UVa’s dual-mode direct-connect flowpath, Georgiadis et al. 

(Ref. 9) used a 1-reaction mechanism and Bhagwandin et al. (Ref. 6) used a 7-species, 8-reaction Evans 

and Schexnayder (Ref. 10) mechanism, modified to include third-body efficiencies. However, for the 

current work a 9-species, 18-reaction, Peters and Rogg (Ref. 11) chemistry model is used. The primary 

motivation behind using Peters and Rogg is the fact that it is a nearly complete H-O reaction set. It 

includes 18 out of 20 possible H-O reactions (Ref. 12) reactions making it a comprehensive hydrogen-air 

chemistry model, which is essential to investigate vitiated air effects on the mode transition behavior. The 

model also includes species-dependent third-body efficiencies of 3 species. 
NASA/TM—2010-216756 4 

Turbulence-chemistry interactions have a considerable effect on the species production rates in the 

chemically reacting flows (Refs. 13 to 16). Even though several CFD solvers have the capability of 

simulating chemically reacting flows, most turbulence models are only capable of representing turbulent 

effects of the momentum transport in the flow field, thus ignoring the fluctuations in the species 

production rates and disregarding the turbulence-chemistry interactions. Essentially speaking the 

turbulence is decoupled from the chemical kinetics. The usual practice is to then employ a constant Sct

and Prt number or the ratio of the previous to latter called the Lewis number. Sct is the ratio of momentum 

diffusivity to mass diffusivity, Equation (1). Thus, Sct dictates the turbulent mixing behavior of the 

various species. 

momentum diffusivity

mass diffusivity t Sc

D D

    

(1) 

A high value of Sct results in reduced mixing, and possible flameout while a low value of Sct results 

in mixing that is too fast, elevating the pressures in the combustor and producing a shock train which 

reaches the inlet causing an unstart. Prt is defined as the ratio of momentum eddy diffusivity to thermal 

eddy diffusivity, and is used to quantify the heat flux or temperature fluctuations in the flow field caused 

by turbulent transport. 

momentum diffusivity

thermal diffusivity t Pr    

 

(2) 

A study of Prt sensitivity was done by Engblom et al. (Ref. 5) and Keistler et al. (Ref. 13). Both 

similarly demonstrated that the effect of decreasing Prt was reduced reaction rates and delayed ignition. 

However, this sensitivity to Prt was limited. It is expected that Sct has a greater effect on ignition and 

subsequent combustion behavior because it has a higher influence on increasing the concentration of 

reactants needed to move a chemical reaction forward. 

For the purpose of the current work a constant Sct and Prt number are assumed. Variable Sct and Prt

models are currently in development and may result in improved prediction of scramjets in the future, but 

are not considered ready for realistic scramjet simulations at the time of this work. Efforts have been 

undertaken by Xiao et al. (Ref. 16) and Keistler et al. (Ref. 13) to model scramjet flows with variable Sct

and Prt models. The results obtained by Xiao et al. (Ref. 16) showed a promising capability in predicting 

chemically reacting flows. The results also showed that the use of a multi-variate -Probability Density 

Function (PDF) is highly dissipative which results in reduced mixing and ineffective capturing of the 

turbulence-chemistry interactions. 

III. Experimental Configuration 

Experimental data acquired at the UVa SCF was used for comparison with the numerical flow 

simulations performed in the current work. The direct-connect facility is vertically mounted and has dualmode direct-connect capabilities. Figure 1 shows the supply nozzle, isolator, combustor, extender, fuel 

lines, coolant lines and numerous pressure transducers as well as thermocouples. 

As discussed earlier, the facility has a unique ability to provide clean as well as vitiated airflow. The 

supply nozzle is connected to a 300 kW, 14-stage electrical resistance heater, fed by the oil-free 

compressor, which accomplishes air heating (Ref. 4) to match flight conditions and is capable of 

delivering a clean vitiate-free airflow of about 1200 K for the clean air experiments. However, in order to 

provide the vitiated airflow, H2O was added to the airflow from an external source. In an effort to 

precisely match the conditions in the large tunnels, make-up oxygen was also added to the airflow to 

obtain 21 percent O2. 
NASA/TM—2010-216756 5 

The convergent-divergent supply nozzle delivers a Mach 2 flow to the constant-area isolator. This 

direct-connect nozzle is used to replicate the flow that an inlet would provide to the isolator in an actual 

flight. The isolator ends where the fuel-injector ramp begins. The isolator and combustor have a crosssectional area of 1.51.0 in.2

. The compression ramp has an angle of 10° and a base height (H) of 0.25 in. 

The dimensions in Figure 2 are normalized using this base height. Immediately after the combustor 

follows the 2.9 diverging extender-nozzle. At the exit of the extender-nozzle the airflow is exhausted to 

the ambient atmosphere. The exhaust plume is captured by a catch-cone, which directs the exhaust gases 

vertically out of the building. 

Hydrogen fuel is injected in the core flow at the base of the compression ramp using a Mach 1.7 

conical nozzle. Once the fuel injection reaches a steady-state, it is ignited using a detonation-driven 

igniter system. Combustion is self-sustaining once ignited. 

One of the challenging aspects of simulating the UVa SCF flowpath is properly modeling the thermal 

boundary conditions. The facility is fabricated with various metals and a sophisticated cooling channel 

topology. These metals and cooling channel patterns differ within the three major sections (isolator, 

combustor, and extender-nozzle), making it an extremely difficult problem from the numerical simulation 

point of view. 

Figure 3 shows the metals used in the fabrication, cooling channels, and window locations on each 

wall of the facility. The supply nozzle, isolator and extender-nozzle are all made with Nickel 200. 

However, the inner isolator walls are coated with 0.4 mm zirconia coating. The north and south walls 

have side windows that do not span the entire width of the wall in the combustor. The west wall is the 

fuel injector wall. The fuel injector wall of the combustor section is made with Nickel 200, unlike the 

other three walls, and coated with zirconia to protect the inner wall from high temperatures. It also has 

internal parallel cooling channels. The east wall is opposite to the fuel injector wall. Here, an observation 

window spans the entire width of the wall. All windows have a ceramic blank insert. The black bold line 

shows the flowpath perimeter for each face while the solid black lines are external cooling channels and 

dotted lines are embedded in the wall. The arrows show the direction of flow through the cooling 

channels. The orange channels in the combustor section represent the cooling channels located in the 

corners but they are not directly part of the wall. To summarize, the effects of internal versus external 
NASA/TM—2010-216756 6 
NASA/TM—2010-216756 7 

cooling channels, heat transfer through nickel versus stainless steel versus zirconia coated surfaces, wallcooling channels versus the corner cooling channels and the presence of the ceramic blanks adds a 

considerable uncertainty in the experimental thermal data, especially in the combustor and extendernozzle, and make for a challenging comparison with the results of the current numerical simulation. 

IV. Methodology 

A. Computational Mesh 

Several computational grids were examined during the course of simulations with Wind-US. 

Significant efforts were undertaken to apply sufficient grid resolution in the areas of interest, namely the 

isolator, isolator-ramp, combustor, and fuel injector in order to resolve the key flow features. 

For the purpose of this work, a three-dimensional, structured grid was created for the UVa dual-mode 

direct-connect flowpath, shown in Figure 4. Symmetry was used to model one half of the flowpath with 

the symmetry plane being the central (z = 0) plane. The colored planes in Figure 4 denote the plane of 

symmetry. The final mesh contains 5.82 million structured grid points split into 39 zones for parallel 

processing. In order to better resolve the turbulence and the fuel-air shear layer mixing, the combustor 

zones adjacent to the fuel injection were mismatched with the adjacent zones. A mismatch or a non pointto-point match between two zonal boundaries allowed for a denser grid in the area of interest and coarser 

grid away from it. 

Lastly, care was taken to ensure proper wall packing was maintained throughout the entire flowpath 

to better capture shock boundary layer interactions and boundary layer separations. The resulting grid had 

a nominal y

+

 of below 5, which was deemed sufficient to model wall boundary layer effects in these 

numerical simulations. 

B. Flow Conditions 

For the purpose of this research work, a total of ten cases were identified for numerical simulation 

(see Table 1) with the objective of investigating the fuel equivalence ratios corresponding to the mode 

transition regime for clean as well as vitiated air. The fuel-off cases were also simulated with clean and 

vitiated air to verify the data in absence of the combustion. The vitiated air cases were examined to better 

understand the flow vitiate effects on combustion process. 
NASA/TM—2010-216756 8 

TABLE 1.—UVa TEST CASES 

Cases Equivalence 

ratio 

Stagnation conditions H2 Fuel plenum 

conditions 

Ambient conditions 

Clean air 

Scan 1 0.000 Po = 327.72 kPa 

To = 1201 K 

ma  = 0.202 kg/s 

--------------------- Patm = 99.1 kPa 

Tatm = 294.4 K 

Scan 4 0.172 Po = 326.97 kPa 

To = 1202 K 

ma  = 0.201 kg/s 

Po = 527.14 kPa 

To = 298.86 K 

mf  = 1.01E-3 kg/s 

Patm = 99.1 kPa 

Tatm = 294.4 K 

Scan 14 0.260 Po = 327.20 kPa 

To = 1202 K 

ma  = 0.201 kg/s 

Po = 709.94 kPa 

To = 298.96 K 

mf  = 1.54E-3 kg/s 

Patm = 99.1 kPa 

Tatm = 294.4 K 

Scan 5 0.341 Po = 327.12 kPa 

To = 1202 K 

ma  = 0.201 kg/s 

Po = 1042.70 kPa 

To = 299.32 K 

mf  = 2.01E-3 kg/s 

Patm = 99.1 kPa 

Tatm = 294.4 K 

Scan 9 0.454 Po = 327.07 kPa 

To = 1202 K 

ma  = 0.201 kg/s 

Po = 1394.04 kPa 

To = 299.74 K 

mf  = 2.66E-3 kg/s 

Patm = 99.1 kPa 

Tatm = 294.4 K 

12% H2O vitiate air 

Scan 35 

(11% H2O) 

0.000 Po = 329.56 kPa 

To = 1203 K 

ma  = 0.198 kg/s 

--------------------- Patm = 98.9 kPa 

Tatm = 294.4 K 

Scan 28 0.175 Po = 326.80 kPa 

To = 1204 K 

ma  = 0.196 kg/s 

Po = 548.55 kPa 

To = 297.80 K 

mf  = 1.04E-3 kg/s 

Patm = 99.1 kPa 

Tatm = 294.4 K 

Scan 18 0.267 Po = 326.87 kPa 

To = 1203 K 

ma  = 0.196 kg/s 

Po = 829.67 kPa 

To = 298.64 K 

mf  = 1.59E-3 kg/s 

Patm = 99.1 kPa 

Tatm = 294.4 K 

Scan 23 0.349 Po = 326.95 kPa 

To = 1204 K 

ma  = 0.196 kg/s 

Po = 1092.27 kPa 

To = 297.75 K 

mf  = 2.08E-3 kg/s 

Patm = 99.1 kPa 

Tatm = 294.4 K 

Scan 22 0.460 Po = 326.88 kPa 

To = 1203 K 

ma  = 0.196 kg/s 

Po = 1447.78 kPa 

To = 298.55 K 

mf  = 2.75E-3 kg/s 

Patm = 99.1 kPa 

Tatm = 294.4 K 

C. Boundary Conditions 

As discussed in Section III, the facility components were made of different materials and some 

surfaces were coated while others were simply ceramic blanks. This, in addition to the various cooling 

channels made the choice of appropriate thermal boundary conditions a challenge. 

A lack of thermocouple data in key components like the combustor and extender-nozzle made the 

choice of accurate wall temperatures difficult to determine. The combustor is certainly one of the key 

components considered in this numerical simulation. The combustion process provided a large 

temperature gradient axially along the flowpath and along the height of the flowpath. This means that the 

heat transfer profile on the fuel injector wall, the location where thermocouple wells are drilled and 

cooling channels exist is significantly different than the wall opposite to the fuel injector. The remaining 

walls in the combustor are ceramic blanks and 304 stainless steel with no cooling channels. Thus, based 

on the available information any choice of a single wall temperature will be far from an accurate 

representation of the entire combustor component. To investigate effect of the wall temperature a variety 

of simulations were performed and the results showed a significant effect on the peak combustion 

pressure and length and location of the shock train. However, due to Wind-US limitations and to facilitate 

the research work a representative average wall temperature of 1000 K in the combustor section was used. 
NASA/TM—2010-216756 9 

This was an average of thermocouple data obtained from the fuel injector wall and typical temperature 

observed in numerical simulations when the combustor walls were set to adiabatic condition. A choice of 

constant temperature was also made for the supply nozzle, isolator and extender-nozzle based on the 

available thermocouple data. 

D. Numerics 

The Roe second-order upwind-biased flux-difference splitting scheme (Ref. 18), modified for 

stretched grids was the initial choice for the present simulations, however early results using the Roe 

scheme were not found to be consistent in predicting the flow separation in the isolator. The predicted 

numerical separation would switch walls depending on how the solution was initialized. This predicted 

flow separation behavior was very sensitive to the choice of overall parameters and a small change would 

cause the switch to occur. Thus, an alternate numerical scheme was examined. 

The HLLC scheme due to Harten, Lax and van Leer (for contact waves) (Ref. 19), which is also 

available within Wind-US, was the next choice based on past experience and other successful simulations. 

HLLC was found to be much more consistent in predicting the flow separation behavior, and thus it was 

chosen for all subsequent numerical simulations. The minmod Total Variation Diminishing (TVD) limiter 

was also used in conjunction with the HLLC numerical scheme. As the name suggests it prevents 

overshoots in the flow properties in the areas having steep gradients like the combustor and shocks. 

Local time stepping with a constant Courant Friedrichs Lewy (CFL) number was used to advance the 

solution to a steady-state. Thus the solution advances at different rates in various parts of the 

computational domain. Care was taken to identify a converged steady-state solution by comparing 

solutions at various times in the non-dimensional time advancement. Various key parameters were 

monitored to determine the convergence; namely 1) the residuals of Navier-Stokes equations, 2) water 

mass flux at the exit plane, which is a key indicator of combustion characteristics, 3) the net mass flux, 

and 4) pressure along the symmetry plane of the fuel injector wall. 

E. Turbulence and Chemistry Modeling 

The Chien k- (Ref. 20) and the Shear Stress Transport (SST) (Ref. 21) turbulence models were 

initially picked for evaluation. Based on the results obtained for the fuel-off and preliminary calculations 

for fuel-on (i.e., EXP = 0.341) case, the Chien k- model was picked for the scramjet simulations. It is 

well known that the k- model is prone to over-prediction of skin friction drag in flow with adverse 

pressure gradients and diffusers. To help overcome this issue, the variable C option of the k- model 

(Ref. 22) was used to reduce turbulent viscosity in the flow field where production of turbulent kinetic 

energy is much higher than the rate of dissipation. Based on some preliminary investigation a choice of 

baseline constant Sct of 0.6 and Prt of 0.9 were made for all simulations. 

The 13-species, 27-reaction Peters & Rogg (Ref. 11) chemical kinetics model was selected and first 

validated using the Burrows-Kurkov (Ref. 23) supersonic combustion benchmark case. The benchmark 

case was validated using two versions of the chemistry model, 1) full 13-species, 27-reaction set and 

2) 9-species, 18-reaction set. Since CO2 was not a vitiate used for cases examined in this work, carbon 

species were removed from the model (1) to obtain a subset model (2). The validation showed identical 

results for both versions of the model as expected. However, the subset model provided a significant 

speed-up in the computations because the additional species equations were not being solved. Thus, the 

subset model was used for the remaining UVa flowpath simulations. Table 2 shows the subset chemistry 

model. It should be noted that the UVa experiments (Ref. 17) did make measurements of vitiated air runs 

including CO2 vitiates. 
NASA/TM—2010-216756 10 

TABLE 2.—9-SPECIES, 18-REACTIONS PETERS AND ROGG CHEMISTRY MODEL (REF. 34) 

Reaction Sf

Sb

Df/KB

Db/KB,

K 

Cf

Cb,

cm3/mole-sec 

H2 + O2  2OH 0.0 

0.0 

2.4230E+04 

0.0 

1.70E+13 

0.0 

H + O2  OH + O 0.0 

0.0 

0.8455E+04 

0.0 

2.00+14 

0.0 

H2 + OH  H2O + H 1.6 

0.0 

1.6608E+03 

0.0 

1.00E+08 

0.0 

H2 + O  OH + H 2.67 

0.0 

3.1631E+03 

0.0 

5.06E+04 

0.0 

OH + OH  O + H2O 1.14 

0.0 

0.5033E+02 

0.0 

1.50E+09 

0.0 

H + OH + Ma  H2O + Ma –2.0 

0.0 

0.0 

0.0 

2.22E+22 

0.0 

H + H + Ma  H2 + Ma –1.0 

0.0 

0.0 

0.0 

1.80E+18 

0.0 

H + O2 + Ma  HO2 + Ma –0.8 

0.0 

0.0 

0.0 

2.30E+18 

0.0 

HO2 + OH  H2O + O2

0.0 

0.0 

0.0 

0.0 

6.00E+13 

0.0 

HO2 + H  H2 + O2

0.0 

0.0 

352.3 

0.0 

2.53E+13 

0.0 

HO2 + H  OH + OH 0.0 

0.0 

505.28 

0.0 

1.50E+14 

0.0 

HO2 + O  OH + O2

0.0 

0.0 

–203.8 

0.0 

1.80E+13 

0.0 

O + O + Ma  O2 + Ma –1.0 

0.0 

0.0 

0.0 

2.90E+17 

0.0 

HO2 + H  H2O + O 0.0 

0.0 

865.63 

0.0 

3.00E+13 

0.0 

HO2 + HO2  H2O2 + O2

0.0 

0.0 

–626.57 

0.0 

2.50E+11 

0.0 

OH + OH + Ma  H2O2 + Ma –2.0 

0.0 

0.0 

0.0 

3.25E+22 

0.0 

H2O2 + H  H2O + OH 0.0 

0.0 

1804.2 

0.0 

1.00E+13 

0.0 

H2O2 + OH  H2O + HO2

0.0 

0.0 

505.28 

0.0 

5.40E+12 

0.0 a

The third-body efficiencies are H2O: 6.5, O2: 0.4, N2: 0.4. 

V. Results 

A. EXP = 0.000 (Fuel-Off) 

The boundary conditions for the fuel-off case were modified in order to account for lack of fuel flow in the 

injector. The entrance to the fuel injector is sealed off and replaced with a viscous wall. No calculations were 

performed in the fuel injector zones. 

A turbulence model sensitivity study is performed in order to find a suitable model for the flowpath 

simulations. The results are compared with that of the experiment in Figure 5 and show a good match between 

numerical and experimental pressure distributions when the k- turbulence model is used. The simulation was 

not capable of picking up small pressure fluctuations in the isolator from x/H = –45 to –10, however the 

pressure estimates stayed within the range. The pressure peak caused by the fuel injector ramp at x/H = –5 

matches very well with the experiment. The peak pressure in the combustor is over-predicted but overall k-

results in the combustor and extender-nozzle matched well with that of the experiment. The SST model was 

unable to predict the flow behavior from x/H = 25 to 40. This was somewhat surprising because the SST 

model usually provides better predictions of separated flows than k- in benchmark validation exercises. 
NASA/TM—2010-216756 11 

The shock produced by the compression ramp propagates downstream to the combustor and the 

extender-nozzle. These shock structures cause the peaks and valleys in the pressure profile. Figure 7 

shows the core flow through the combustor, and the extender-nozzle remains supersonic in the absence of 

the combustion. There is also the presence of a recirculation region in the combustor immediately aft of 

the compression ramp. As the flow enters the extender-nozzle and turns the 2.9 expansion corner it 

further accelerates and reaches nearly Mach 2. At x/H = 40 the flow shows signs of separation but does 

not separate until x/H = 50. This phenomenon is also evident from Figure 5. This eventually leads to a 

modest discrepancy between numerical and experimental pressures at the exit of the extender-nozzle. This 

could be attributed to the k- turbulence model as it is well known for over-predicting skin friction in wall 

boundary layers that have adverse pressure gradients and experimentally tend to separate (Ref. 22). 

However, the agreement with experimental data is still surprisingly much better than that provided by the 

SST model. Based on the turbulence model sensitivity study, the k- model was chosen for remainder of 

the mode transition and vitiation effects investigation. 

Figure 6 shows a comparison between the clean and H2O vitiated air with that of the experimental 

data. The numerical simulation provides a good match to the experimental data. However, at the 

beginning of the isolator, it may be observed that the normalized clean air numerical result is 

approximately 8 percent higher than the vitiated air. This modest discrepancy is observed for other fuelequivalence ratios as well. The experimental reference pressure, Pref (measured at the beginning of the 

isolator) for each scan is used to normalize all numerical result, and is the source of this discrepancy. For 

the same inflow conditions (i.e., upstream stagnation pressure and temperature) the experiments indicated 

that the clean air reference pressure was nearly 8 percent lower than 12 percent H2O vitiated air, while the 

computations indicated approximately 1.5 percent lower pressure for the clean air cases. A subsequent 

one-dimensional analysis of the nozzle indicated an expected difference close to the Wind-US prediction. 

Also, the experimental reference pressure is within 2 percent of one-dimensional analysis and the WindUS prediction for vitiated air, however, it is within 8 percent of one-dimensional analysis and the WindUS prediction for the clean air. Further investigation is needed to determine the source of this discrepancy 

between experimental, one-dimensional analysis and Wind-US predictions for clean air cases. 
NASA/TM—2010-216756 12 
NASA/TM—2010-216756 13 

B. EXP ≈ 0.170 

Figure 8 shows a comparison of numerical results for EXP = 0.172 (clean air) and 0.175 (vitiated air) 

with that of experimental data. Both the experimental data and the numerical results show a subtle 

reduction in the peak pressures in the combustor and overall reduced pressures in the isolator and 

extender-nozzle when 12 percent H2O is added to the supply nozzle airflow. While the numerical results 

show good qualitative agreement in the isolator, a choice of Sct = 0.6 did not provide a good prediction of 

the combustor pressure distribution for either case. The pressures are under-predicted in the combustor as 

well as in the extender-nozzle. The numerical simulation also failed to predict a rapid drop in pressure at 

x/H = 25, which becomes less evident for high fuel-equivalence ratios. The constant Sct model likely 

causes a quick mixing of fuel-air resulting in abrupt combustion. A variable Sct model would better 

represent the turbulent effects of the species fluctuation, and could in turn potentially better represent the 

fuel-air mixing over the length of the combustor and the increased pressures due to the combustion 

process. 

Since the qualitative behavior of the flow is similar for both cases, Figure 9 shows the Mach number 

contours for the EXP = 0.172 (clean air). It is evident that the first shock is caused by the compression 

ramp at x/H = –5. The shock reflections propagate downstream to the combustor, however the majority of 

the flow entering the combustor is supersonic, thus the combustor is operational in scramjet mode. 

The flow separation in the extender-nozzle occurs at x/H = 30 in the numerical results while the 

experiment shows a flow separation at x/H = 40. This could be due to a combined effect of limitation in 

the turbulence model, the constant Sct model, which does not account for turbulence-chemistry 

interactions, and/or the temperature boundary conditions used. Further analysis is needed to identify the 

cause of this behavior. 
NASA/TM—2010-216756 14 

C. EXP ≈ 0.260 

Figure 10 shows an important result illustrating the effects of the flow vitiates on the combustion 

process and overall qualitative behavior of a dual-mode combustor. The numerical result and the 

experimental data presented for the clean air case demonstrate the high peak pressure in the combustor 

which results in the upstream movement of the shock train with an established leading edge at x/H = –22. 

The flow decelerates moving through a series of lambda shocks that terminate in a normal shock. As a 

result a significant portion of the flow entering the combustor in Figure 11 is near sonic or subsonic. 

Experimental data and numerical results presented for the 12 percent H2O vitiate show that the presence 

of flow vitiates results in a lowered peak combustor pressure. In fact, as seen in Figure 12 the decrease in 

combustor pressure results in the shock train being swallowed, thus the flow entering the combustor is 

supersonic. This was expected because the experiment showed a considerable hysteresis in the fuel 

equivalence ratio range of 0.220 to 0.260 (Ref. 24). It seems that the mode transition can happen in this 

range depending on the flow conditions that would trigger it. For the UVa experiments it was the change 

in the fuel-equivalence ratio. However, in practice it would be the changing flight conditions combined 

with fuel-equivalence ratios. 
NASA/TM—2010-216756 15 
NASA/TM—2010-216756 16 

The use of a constant Sct model gives an interesting result for both cases. The peak pressure in the 

combustor is over-predicted for the clean air case, thus the numerical result shows the leading edge of the 

shock train to be more forward than the experimental result. However, it provides a good match with 

experimental data in the extender-nozzle. In contrast, the peak pressure for the vitiated air case is underpredicted in the combustor and this discrepancy continues in the extender-nozzle as well. 

From an evaluation of Figures 11 and 12, it is clear that the addition of H2O vitiate to the supply 

nozzle airflow changed the operation of the combustor from subsonic to supersonic. A previous study was 

unable to capture this transition using a 1-reaction kinetics mechanism (Ref. 8). Figure 11 shows an 

upstream moving shock train due to relatively high combustor pressure. For clean air, the flow separation 

starts at x/H = –20 and gets thicker as the flow approaches the combustor entrance. The majority of the 

flow entering the combustor is subsonic, thus the combustor is operational in ramjet mode. However, with 

the addition of H2O vitiate to the airflow, Figure 12 confirms an absence of the shock train. The 

compression ramp generates an initial shock that propagates downstream to the combustor. The majority 

of the flow entering the combustor is supersonic, thus the combustor is operational in scramjet mode. 

D. EXP ≈ 0.340 

Figure 13 shows a comparison of numerical results and the experimental data for clean and vitiated 

air cases at EXP = 0.341 and 0.349, respectively. The experimental data show a logical trend that is the 

addition of H2O to the supply nozzle airflow reduces the overall pressures. The numerical results show a 

similar trend, however there is a subtle difference between the numerical results. They both show a good 

match to the peak pressure in the combustor and extender-nozzle. The leading edge of the shock train is 

accurately predicted for the clean air case at x/H = –26. But, the location of the leading edge of the shock 
NASA/TM—2010-216756 17 

train for the vitiated air case is more upstream than the experimental data. Moreover, the vitiated air case 

predicts combustor pressures relatively identical to that of the clean air case. This is likely due to the fact 

that the fuel-equivalence ratio for vitiated air is higher than for the clean air case. The pressures in the 

extender-nozzle look more reasonable for the vitiated air case when compared to the clean air result, i.e., 

lower pressures due to addition of flow vitiate. 

It is important to mention that Sct was calibrated with the clean air case. This is likely the reason that 

the numerical simulation provides an excellent match to that of the experimental data for clean air. 

Figure 14 shows the Mach number contours for the clean air case. It is obvious that the high pressure in 

the combustor causes the shock train to move upstream. The shock wave boundary layer interactions 

cause a flow separation, which continues to grow through the isolator. As a result, the majority of the 

flow entering the combustor is subsonic, thus the combustor is operational in ramjet mode for both cases. 

E. EXP ≈ 0.460 

Figure 15 shows the comparison between numerical results and experimental data for clean and 

vitiated air cases at EXP = 0.454 and 0.460, respectively. As expected, the experimental values of the 

overall pressure for clean air case are higher than the vitiated air case. A similar qualitative trend is 

observed in the numerical results as well. The clean air result shows a good overall match with the data in 

the combustor and extender-nozzle, but predicts the leading edge of the shock train upstream from where 

the data suggest. This could be due to the fact that the peak pressure is over-predicted, which forces the 

shock train upstream. 

The vitiated air results show an excellent agreement with data in the isolator, combustor, and extender 

nozzle. The leading edge of the shock train is accurately predicted along with the peak pressure in the 

combustor. With the majority of flow entering the combustor being subsonic, the combustor operation is 

in ramjet mode for both cases. 
NASA/TM—2010-216756 18 
NASA/TM—2010-216756 19 

F. Results Summary 

Figures 16 and 17 show a summary of all clean and vitiated air simulations compared with the 

experimental data. The investigation shows a good qualitative match to the data. For the choice of 

baseline Sct = 0.6, the high fuel-equivalence ratios (EXP = 0.260 to 0.460) provided a good quantitative 

match with experimental data in the isolator, combustor and extender-nozzle. However, for the low fuelequivalence ratio (EXP = 0.172, 0.175) a discrepancy was observed in the combustor and extender 

nozzle. Especially in the flowpath from x/H = 10 to 27, where the pressures are under-predicted and the 

simulation was unable to capture the steep decrease in pressure at x/H = 25. This was likely due to the 

fact that the Sct was calibrated for the higher fuel-equivalence ratios. The fuel-air mixing behavior that a 

constant Sct provides for a high fuel-equivalence ratio is significantly different than a low fuelequivalence ratio. A variable Sct model is highly desirable and may also account for turbulence-chemistry 

interactions, which play a key role in fuel-air mixing and thus the combustion process. The results also 

showed that the mode transition happened in the fuel-equivalence range of 0.172 to 0.260. 

The flow vitiation effects on the operation of a dual-mode combustor are also demonstrated in 

Figure 17. Especially for EXP = 0.267 (compare to EXP = 0.260), where the addition of flow vitiates 

effectively changed the operation of combustor from ramjet to scramjet mode. This is a key finding of this 

work. As discussed earlier, this result should also help researchers conducting experiments in large 

experimental facilities where fuel is burned to match the flight enthalpies, which inadvertently adds flow 

vitiates to the airflow. Similar to the clean air results, the fuel-equivalence ratios which demonstrated the 

scramjet mode showed a poor agreement with pressure in flowpath from x/H = 10 to 27. Overall, the 

pressures in the vitiated air cases were comparatively lower than the clean air counterparts. 
NASA/TM—2010-216756 20 

VI. Conclusions 

Wind-US was successfully utilized to perform numerical simulations of mode transition and 

investigate the effect of flow vitiation on the mode transition process. A range of fuel-equivalence ratios 

is examined for clean as well as vitiated air. A choice of HLLC numerical scheme, k- turbulence model, 

and 9-species, 18-reaction Peters and Rogg chemical kinetics model provided a good agreement with 

experimental data. A baseline constant Sct of 0.6 and Prt of 0.9 were utilized for all simulations. 

The low fuel-equivalence ratio cases under-predicted the pressures in the combustor and extendernozzle. This is attributed to the choice of a constant Sct and possibly the wall temperature boundary 

conditions. The discrepancy in the pressures at x/H = 25 was still unresolved at the time of this 

publication. The EXP = 0.267 case showed a clear effect of flow vitiation on the combustion process, 

namely that the addition of flow vitiates changed the combustor operation from ramjet to scramjet mode. 

The high fuel-equivalence ratio cases provided a good match with experimental data in the combustor and 

extender-nozzle, however the pressures in the isolator were slightly over-predicted for the vitiated air 

cases. 

Lastly, the temperature boundary condition plays a key role in such scramjet simulations. As 

discussed earlier, the complex nature of the UVa facility presents a challenge from the numerical 

simulation point-of-view. Even though care was taken to pick temperature boundary conditions that were 

representative of the actual facility, they could be improved, especially in the combustor and extendernozzle. More temperature thermocouple data would be required to facilitate a more realistic 

representation of the thermal boundary conditions using the multiple boundary temperature specification 

capability of Wind-US. 
NASA/TM—2010-216756 21 

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14. ABSTRACT

The Wind-US computational fluid dynamics (CFD) flow solver was used to simulate dual-mode direct-connect ramjet/scramjet engine

flowpath tests conducted in the University of Virginia (UVa) Supersonic Combustion Facility (SCF). The objective was to develop a 

computational capability within Wind-US to aid current hypersonic research and provide insight to flow as well as chemistry details that are 

not resolved by instruments available. Computational results are compared with experimental data to validate the accuracy of the numerical 

modeling. These results include two fuel-off non-reacting and eight fuel-on reacting cases with different equivalence ratios, split between 

one set with a clean (non-vitiated) air supply and the other set with a vitiated air supply (12 percent H2O vapor). The Peters and Rogg 

hydrogen-air chemical kinetics model was selected for the scramjet simulations. A limited sensitivity study was done to investigate the 

choice of turbulence model and inviscid flux scheme and led to the selection of the k-ε model and Harten, Lax and van Leer (for contact 

waves) (HLLC) scheme for general use. Simulation results show reasonably good agreement with experimental data and the overall vitiation 

effects were captured. 

15. SUBJECT TERMS

Scramjet; Mode transition; Vitiated air; Equivalence ratio; Schmidt number 

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