Jack R. Edwards, D. Scott McRae, and Ryan B. Bond

North Carolina State University, Raleigh, North Carolina

Three Dimensional Numerical Simulation

of Rocket-Based Combined-Cycle Engine

Response During Mode Transition Events

NASA/CR—2003-212193

March 2003

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Jack R. Edwards, D. Scott McRae, and Ryan B. Bond

North Carolina State University, Raleigh, North Carolina

Three Dimensional Numerical Simulation

of Rocket-Based Combined-Cycle Engine

Response During Mode Transition Events

NASA/CR—2003-212193

March 2003

National Aeronautics and

Space Administration

Glenn Research Center

Prepared under Grant NAG3–2658
Acknowledgments

The subsonic combustion analysis has been funded under an NRA grant from NASA Glenn Research Center, under

the Base Research and Technology Programs Office; grant number TP–01–45. The authors would like to express

their appreciation to Dr. Hani Kamawi for help with interpreting the direct-connect test results.

Available from

NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22100

This report contains preliminary

findings, subject to revision as

analysis proceeds.

The Propulsion and Power Program at

NASA Glenn Research Center sponsored this work.

Available electronically at http://gltrs.grc.nasa.gov
NASA/CR—2003-212193 1 

Three Dimensional Numerical Simulation of Rocket-Based Combined-Cycle Engine 

Response During Mode Transition Events 

Jack R. Edwards, D. Scott McRae, and Ryan B. Bond 

North Carolina State University 

Raleigh, North Carolina 27695 

Overview 

The GTX program at NASA Glenn Research Center is designed to develop a launch vehicle 

concept based on rocket-based combined-cycle (RBCC) propulsion [1]. Experimental testing, 

cycle analysis, and computational fluid dynamics modeling have all demonstrated the viability of 

the GTX concept, yet significant technical issues and challenges still remain. Our research effort 

develops a unique capability for dynamic CFD simulation of complete high-speed propulsion 

devices and focuses this technology toward analysis of the GTX response during critical mode 

transition events. Our principal attention is focused on Mode 1/Mode 2 operation, in which 

initial rocket propulsion is transitioned into thermal-throat ramjet propulsion. A critical element 

of the GTX concept is the use of an Independent Ramjet Stream (IRS) cycle to provide 

propulsion at Mach numbers less than 3. In the IRS cycle, rocket thrust is initially used for 

primary power, and the hot rocket plume is used as a flame-holding mechanism for hydrogen fuel 

injected into the secondary air stream. A critical aspect is the establishment of a thermal throat in 

the secondary stream through the combination of area reduction effects and combustion-induced 

heat release. This is a necessity to enable the power-down of the rocket and the eventual shift to 

ramjet mode. 

Our focus in this first year of the grant has been in three areas, each progressing directly toward 

the key initial goal of simulating thermal throat formation during the IRS cycle: 

• CFD algorithm development 

• Simulation of Mode 1 experiments conducted at Glenn’s Rig 1 facility 

• IRS cycle simulations 

The remainder of this report discusses each of these efforts in detail and presents a plan of work 

for the next year. 

CFD Algorithm Development 

The key tool used in this research is a validated Navier-Stokes solver for unsteady reactive-flow 

calculations on massively parallel machines [2–4]. Several enhancements have been added to 

this solver during the past year to make it more suitable for simulations of the complete GTX 

engine flowpath. These include: 
NASA/CR—2003-212193 2 

Fig. 1: Typical grid for GTX 

calculations 

1.) Addition of modified Menter and Wilcox ’98 turbulence models. The original code used 

the Menter hybrid k-ω model with the shear-stress transport (SST) modification as its baseline 

turbulence model. In comparing with cold-flow Rig 1 data (discussed later), it was found that 

this model tended to produce larger regions of flow separation than indicated in the experimental 

data. This is a known weakness of the SST modification, but the obvious fix of simply removing 

the SST modification lead to excessive growth of turbulence kinetic energy in corner regions, 

where the grid spacing was not (apparently) small enough to allow for the proper near-wall 

behavior for the turbulence frequency ω. A solution was found by restricting the SST 

modification to the laminar sublayer of the boundary layer. This prevented excessive growth of 

turbulence kinetic energy while alleviating the tendency of the original SST model to reduce eddy 

viscosity within separated-flow regions. Before this simple fix was identified, we also coded the 

Wilcox ’98 k-ω model, which is supposedly less-sensitive to free-stream values than the original 

k-ω model. Our results with this model were decidedly inferior to those of the Menter variants 

and as such, this addition was not pursued further. 

2.) Addition of a patched grid procedure. The requirement to resolve details of the fuel 

injection ports located around the perimeter of the cowl required the addition of a grid patching 

procedure to allow better circumferential resolution of these features. This implementation 

follows from general procedures developed in [5], and it allows for conservative interpolation of 

data among patched grid regions. A procedure for integrating these regions within the MPI 

message-passing framework was also developed. 

3.) Addition of better implicit coupling among blocks: One of the issues in applying implicit 

methods to solve large multi-block problems is a loss in effectiveness as the block numbers 

increase. This is due to the fact that there is typically no mechanism to couple solution 

corrections generated on one block with those generated on a neighboring block. We have 

devised a sub-iterative strategy that provides better information transfer among blocks and thus 

more rapid information transfer throughout the domain. The sub-iteration procedure attempts to 

solve the linear system formulated at each block more accurately while also accounting for 

coupling with neighboring blocks. Though more work per iteration is required, the additional 

robustness provided by this procedure makes it a useful addition. 

4.) Addition of time-derivative preconditioning. Some of the GTX conditions result in large 

pockets of low Mach number flow in the 

engine. One way of alleviating time-step 

restrictions and enhancing the overall 

convergence rate is through the use of timederivative preconditioning [6,7]. We have 

implemented a preconditioning algorithm 

described fully in Ref. [8] and are currently 

examining its effectiveness in accelerating the 

GTX calculations. 

Other aspects of the simulations are as follows. 

GridGen Version 14 is used to generate grids 

for the GTX engine. These are somewhat 

complex due to the need to blend the circular 
NASA/CR—2003-212193 3 

rocket exit plane with the semicircular combustor section. Half-plane symmetry is invoked for all 

calculations. The grid sizes used in this investigation range from about 0.4 million grid cells to 

about 3.3 million grid cells, depending on the case. A sample grid is shown in Figure 1. As of 

now, we are using Tecplot Version 9 for visualization. Later this year, we will receive $10,000 

from the NCSU College of Engineering as part of the cost-sharing agreement for this grant. We 

will use this to purchase a high-end Dell graphics workstation and will load the Ensight Gold 

visualization package on it. We expect that this will facilitate the production of quality 

animations of time-dependent flowfield responses during later stages of this investigation. 

Simulation of Mode I Experiments in the Rig 1 Test Facility 

Simulations of two cases were carried out with no 

rocket or secondary fuel injection. These two cases 

corresponded to ESP #41 and ESP #39 from the 

Rig 1 test matrix. Both cases correspond to 9.94 

lbm/s of air flow and an inlet total temperature of 

547 R. The difference between the two cases is the 

back pressure, which is 3.1 psi for the ESP #39 case 

and 8.2 for the ESP #41 case. These cases were 

performed on an incorrect version of the geometry 

prior to the 2002 JANNAF conference, so they 

were repeated with geometry corrections and the 

changes to the turbulence model outlined above. 

The total number of grid cells is about 2.2 million. 

Figure 2 and Figure 3 present pressure distributions 

along the centerbody/flat plate surface and along 

the cowl surface at the y = 0 plane. The scale of 

the x-axis is referenced to station #3. Both cases 

resulted in a transition to supersonic flow at the 

minimum area location (station #2), followed by a 

compression and expansion region resulting from 

the changing flowpath area profile. Downstream 

of about x = -15, the two solutions differ. Both 

cases contained large regions shock-induced 

separated flow. In order to correctly model the exit 

plane, the grid was extended to x = 100 inches by 

extruding the exit plane as a straight semicircular 

duct. The ESP #39 simulations matched the 

experimental pressure along the cowl surface, but 

along the centerline, there were deviations from the 

experimental data caused by a difference in shock 

and expansion wave locations. The ESP #41 case matched the experiment almost exactly along 

both surfaces for the entire length of the rig. 

Several ejector-ramjet (ER) runs have also been completed to date. ER operation corresponds to 

an operating rocket but no secondary fuel injection. Of the ER cases completed, only case ER 

8687 had experimental data with which solutions could be compared. This case corresponded to 

an inlet mass flow rate of 10.016 lbm/s, inlet total temperature of 413 °F, and inlet total pressure 

of 13.4 psi. The rig back pressure is 2.6 psi, and the chamber pressure of the rocket is 750 psi. 

The oxidizer-to-fuel ratio of the rocket is 4 (4 parts oxygen by mass to 1 part hydrogen by mass), 

and the total number of mesh cells is about 3.3 million. 

x (inches)

pressure (psia)

-40 -20 0 20 40 0

2

4

6

8

10

12

14

16

18

20 Centerline Pressure (CFD)

Centerline Pressure (Experiment)

Cowl 0° Pressure (CFD)

Cowl 0° Pressure (Experiment)

Fig. 2: Pressure distributions for 

ESP #39 case 

x (inches)

pressure (psia)

-40 -20 0 20 40 0

2

4

6

8

10

12

14

16

18

20

Centerline Pressure (CFD)

Centerline Pressure (Experiment)

Cowl 0° Pressure (CFD)

Cowl 0° Pressure (Experiment)

Fig. 3: Pressure distributions for 

ESP# 39 case 
NASA/CR—2003-212193 4 

Fig. 4: Temperature contours for ER 8687 

Figure 4 shows temperature contours for this case. Temperatures of around 2500 K are found in 

the flame front, while temperatures of around 3200 K are found where the rocket plume impinges 

on the flat plate. The heat release is not enough to form a thermal throat, which is what would be 

expected for ER operation. The rocket exhaust enters the combustion chamber at approximately 

1460 K, and the additional fuel in the exhaust ignites almost immediately. The flame front can be 

seen in the OH contours, shown in Figure 5. The mixing is incomplete, so the mixing layer does 

not extend through the entire air stream at the combustor exit. 

Figure 6 compares the centerline and cowl pressures with the experimental data. The results are 

in good agreement with the experiment except for minor discrepancies along the cowl in the latter 

half of the combustor section. The higher pressures are attributed to an over prediction in the 

amount of heat release. 

IRS Cycle Simulations 

Due to time limitations and other difficulties, no 

experiments corresponding to IRS cycle conditions 

were conducted in the Glenn Rig 1 facility this year. 

Over the last several months, we have attempted to 

simulate portions of the Rig 1 test matrix 

corresponding to IRS cycle conditions in an effort to 

determine strategies that lead to the proper response 

– the formation of a thermal throat in the secondary 

air stream followed by an expansion of hot reaction 

products to supersonic speeds. We have considered 

the Rig 1 geometry as the starting point and have 

used a smaller mesh of 0.8 million cells to allow for 

more rapid turn-around time. Our initial efforts in 

simulating the IRS cycle were hindered by our specification of a constant mass flow rate at the 

inlet of the geometry. While this is consistent with the manner in which the Rig 1 tunnel is 

operated, it does not appear to allow the formation of a stable thermal throat. Rather, choke 

points are alternately established at the physical throat of the engine, at a location midway along 

the combustor, and at the combustor exit. The solutions never converge as a result. Our most 

current efforts follow Steffen and Yungster [9] by enforcing a constant total pressure, rather than 

a constant mass flow rate, at the inlet. This allows the mass flow to adjust in response to heat 

Fig. 5: OH mass fraction contours for 

ER 8687 

axial location (inches)

pressure (psi)

-25 0 25 50 0

5

10

15

20

25

30

35

CFD Centerline Pressure

Experimental Centerline Pressure

CFD Cowl Pressure

Experimental Cowl Pressure

Fig. 6: Pressure distributions for 

ER 8687 
NASA/CR—2003-212193 5 

release, and as a consequence, we have made some progress in simulating IRS operation. The 

current procedure for establishing a ramjet-type mode of operation in the secondary stream is as 

follows: 

1.) Obtain a partial solution of the 

engine flowfield under purely 

subsonic conditions by enforcing 

a back pressure only slightly less 

than the enforced total pressure. 

As shown in the temperature 

contours of Fig. 7a and the 

hydrogen mass fraction contours 

of Fig. 8a, this leads to a very 

fuel rich combustion process, 

with a flame extending across to 

the cowl. 

2.) Drop the back pressure to levels 

low enough to force an 

acceleration to sonic flow 

somewhere in the device. 

3.) Restart the solution and run until 

the mass flow rate stabilizes. 

 Due to our current choices for the secondary fuel injection conditions, the last process actually 

results in flashback upstream of the physical throat. As the calculation converges, the flame 

position moves forward. Figures 7, 8, 

and 9 present temperature, hydrogen 

mass fraction, and Mach number at 

different stages of the calculation. After 

the flashback event, the flame front 

moves forward toward the nozzle exit. 

(Figs. 7b, 8b, and 9b). The combination 

of an effective area decrease due to 

volumetric expansion of the rocket 

plume, combustion induced heat release, 

and combustor wall divergence results in 

a gradual transition to sonic and then 

supersonic flow in the secondary air 

stream. This is nearly a ramjet mode 

response, with most of the combustion 

taking place upstream of the rocket exit 

plane and the combustor section serving 

as a nozzle for the expansion of hot 

products. As the calculation continues, 

the mass flow rate increases, and the 

thermal choke point shifts downstream toward the combustor exit. (Figs. 7c, 8c, and 9c) A 

secondary choke point is established downstream of the fuel injector locations. As of this 

writing, this calculation has not yet converged and it is unclear what the final state will be. 

Fig. 8: Hydrogen mass fraction 

contours during IRS cycle calculation 

Fig. 7: Temperature contours during IRS 

cycle calculation 
NASA/CR—2003-212193 6 

Plan of Work for Year 2 

As we have not yet been able to firmly 

establish proper IRS cycle operation, 

our attention for the remainder of this 

year will be focused toward this goal. 

If simulations based on the Rig 1 

conditions continue to be problematic, 

we will focus toward other points in 

the trajectory nearer to the point in 

which cycle analysis indicates thermal 

choking should first occur. We will 

also investigate the effects of other 

reaction mechanisms for hydrogen 

combustion. Steffen and Yungster 

were able to achieve a stable thermal 

choke point in their axisymmetric 

simulations using Jachimowski’s 

hydrogen oxidation mechanism. [10] Once we have been able to converge to a thermally-choked 

solution, we will 

1.) Investigate modulation of the thermal throat position by varying the fuel injection 

conditions. Cycle analysis indicates that this is a key for high propulsive efficiency. The 

types of modulation may include shutting off portions of the injector banks or simply 

changing the injection pressure. We will start from a converged solution for a particular 

positioning of the thermal throat and will vary the fuel injection conditions to shift the 

position upstream or downstream as necessary. We will conduct quasi-steady simulations 

of this type and if necessary, time dependent simulations. We also hope to develop a 

better means of initializing the IRS simulations so that flashback effects are avoided and 

will repeat successful simulations on finer grids to gain an understanding of the gridindependence of the predictions. 

2.) Investigate power-down of the rocket and flame stabilization during the shift to ramjet 

mode. This will entail starting from a steady condition with an upstream positioning of 

the thermal throat, then powering down the rocket in a time-dependent manner. Detailed 

animations of the response of the flowfield under power-down conditions will be 

extracted, and the results made available for use in designing future Rig 1 mode transition 

experiments. 

Publications 

Two publications have resulted from this work this year: 

1.) Steffen, C.J., Bond, R.B., and Edwards, J.R. “Three-Dimensional CFD Analysis of the GTX 

Combustor,” Proceedings of the 26th JANNAF Interagency Propulsion Committee Meeting, 

JANNAF/CPIA, Destin, Fl. 2002. 

2.) Bond, R.B. and Edwards, J.R. “CFD Analysis of an Independently Fueled Ramjet Stream 

Operation in a Rocket Based Combined Cycle Engine,” Abstract accepted for presentation as 

AIAA Paper 2003-0017 at the 41st Aerospace Sciences Meeting, Reno, NV, Jan. 2003 

Fig. 9: Mach number contours during IRS cycle 

calculations 
NASA/CR—2003-212193 7 

Honors, Awards, and Other Miscellaneous Information 

Ryan Bond was awarded the Ziglar Graduate Fellowship in Aerospace Engineering for the first 

and second years of his Ph. D. study. Ryan also tied for first place in the Ph.D category in the 

third annual MAE Department Graduate Student Research Posters Competition. His poster 

emphasized his work on the GTX project. Ryan also managed to pass his written Ph.D. 

preliminary exams and spent three weeks during the summer at NASA Glenn, working closely 

with the GTX team. Jason Norris will be joining the NCSU team in January of 2003. Jason 

obtained his Master of Science degree in Aerospace Engineering from NCSU in 1997and has 

been employed by Pratt & Whitney for the past five years. Jason will pursue a Ph.D in the 

general area of high-speed aeropropulsion, and it is hoped that his work might be funded under 

the present contract. 

References 

[1] Trefny, C.J. “An Air-Breathing Launch Vehicle Concept for Single-Stage-to-Orbit” 

NASA/TM—1999-209089/AIAA Paper 99–2730, May, 1999. 

[2] Roy, C.J. and Edwards, J.R. “Numerical Simulation of a Three-Dimensional Flame/Shock 

Wave Interaction,” AIAA Journal, Vol. 38, No. 5, 2000, pp. 745–753. 

[3] McDaniel, K.S. and Edwards, J.R. “Simulation of Thermal Choking in a Model Scramjet 

Combustor,” AIAA Paper 99–3411, June, 1999. 

[4] McDaniel, K.S. and Edwards, J.R. “Three Dimensional Simulation of Thermal Choking in a 

Model Scramjet Combustor,” AIAA Paper 2001–0382, Jan. 2001. 

[5] Bond, R.B. and McRae, D.S., “Testing of an Interblock Communication Algorithm for 

Dynamically Discontinuous Interfaces in 3-D Flow Fields, “Proceedings, 7th International 

Conference on Numerical Grid Generation in Computational Field Simulation, Honolulu, Hawaii, 

June 2–6, 2002. 

[6] Choi, Y.H., and Merkle, C.L. “The Application of Preconditioning in Viscous Flows,” 

Journal of Computational Physics, Vol. 105, pp. 207–223, 1993. 

[7] Weiss, J.M. and Smith, W.A. “Preconditioning Applied to Variable and Constant Density 

Time-Accurate Flows on Unstructured Meshes,” AIAA Paper 94–2209, June, 1994. 

[8] Edwards, J.R. “Towards Unified CFD Simulation of Real Fluid Flows,” AIAA Paper 2001–

2524, June, 2001. 

[9] Steffen, C.J. and Yungster, S. “Computational Analysis of the Combustion Processes in an 

Axisymmetric RBCC Flowpath”, JANNAF 2000 APS–CS–1B5, November, 2000 

[10] Jachimowski, C.J. “An Analytical Study of the Hydrogen-Air Reaction Mechanism with 

Application to Scramjet Combustion,” NASA TP–2791, Feb. 1988. 
This publication is available from the NASA Center for AeroSpace Information, 301–621–0390.

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13

Three Dimensional Numerical Simulation of Rocket-Based Combined-Cycle

Engine Response During Mode Transition Events

Jack R. Edwards, D. Scott McRae, and Ryan B. Bond

Ramjet engines; Computational fluid dynamics; Rocket-based combined-cycle engines

Unclassified -Unlimited

Subject Categories: 07, 20, and 34 Distribution: Nonstandard

North Carolina State University

Raleigh Main Campus

Raleigh, North Carolina 27695

Project Manager, Christopher Steffan, Turbomachinery and Propulsion Systems Division, NASA Glenn Research Center,

organization code 5880, 216–433–8508.

The GTX program at NASA Glenn Research Center is designed to develop a launch vehicle concept based on rocket-based combined-cycle (RBCC) propulsion. Experimental testing, cycle analysis, and computational fluid dynamics modeling have all demonstrated the viability of the GTX concept, yet significant technical issues and challenges still remain. Our research effort develops a

unique capability for dynamic CFD simulation of complete high-speed propulsion devices and focuses this technology toward

analysis of the GTX response during critical mode transition events. Our principal attention is focused on Mode 1/Mode 2 operation,

in which initial rocket propulsion is transitioned into thermal-throat ramjet propulsion. A critical element of the GTX concept is the

use of an Independent Ramjet Stream (IRS) cycle to provide propulsion at Mach numbers less than 3. In the IRS cycle, rocket thrust

is initially used for primary power, and the hot rocket plume is used as a flame-holding mechanism for hydrogen fuel injected into the

secondary air stream. A critical aspect is the establishment of a thermal throat in the secondary stream through the combination of

area reduction effects and combustion-induced heat release. This is a necessity to enable the power-down of the rocket and the

eventual shift to ramjet mode. Our focus in this first year of the grant has been in three areas, each progressing directly toward the key

initial goal of simulating thermal throat formation during the IRS cycle: CFD algorithm development; simulation of Mode 1

experiments conducted at Glenn's Rig 1 facility; and IRS cycle simulations. The remainder of this report discusses each of these

efforts in detail and presents a plan of work for the next year.