NASA/TM--2001-210679

Computational Analysis of the Combustion

Processes in an Axisymmetric, RBCC Flowpath

Christopher J. Steffen, Jr.

Glenn Research Center, Cleveland, Ohio

Shaye Yungster

Institute for Computational Mechanics in Propulsion, Cleveland, Ohio

Prepared for the

37th Combustion Subcommittee, 25th Airbreathing Propulsion Subcommittee, and

19th Propulsion Systems Hazards Subcommittee Joint Meeting

cosponsored by the Joint Army-Navy-Air Force Interagency Propulsion Committee

Monterey, California, November 13-17, 2000

National Aeronautics and

Space Administration

Glenn Research Center

February 2001
This report is a formal draft or working

paper, intended to solicit comments and

ideas from a technical peer group.

This report contains preliminary

findings, subject to revision as

analysis proceeds.

Available from

NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076

Price Code: A03

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22100

Price Code: A03

Available electronically at http: //gltrs.grc.nasa.gov/GLTRS
COMPUTATIONAL ANALYSIS OF THE COMBUSTION

PROCESSES IN AN AXISYMMETRIC, RBCC FLOWPATH

Christopher J. Steffen, Jr.*

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Shaye Yungster "_

Institute for Computational Mechanics in Propulsion

Brook Park, Ohio 44135

ABSTRACT

Computational fluid dynamic simulations have been used to study the combustion processes within an

axisymmetric, RBCC flowpath. Two distinct operating modes have been analyzed to date, including the

independent ramjet stream (IRS) cycle and the supersonic combustion ramjet (scramjet) cycle. The IRS

cycle investigation examined the influence of fuel-air ratio, fuel distribution, and rocket chamber

pressure upon the combustion physics and thermal choke characteristics. Results indicate that

adjustment of the amount and radial distribution of fuel can control the thermal choke point. The

secondary massflow rate was very sensitive to the fuel-air ratio and the rocket chamber pressure. The

scramjet investigation examined the influence of fuel-air ratio and fuel injection schedule upon

combustion performance estimates. An analysis of the mesh-dependence of these calculations was

presented. Jet penetration data was extracted from the three-dimensional simulations and compared

favorably with experimental correlations of similar flows. Results indicate that combustion efficiency

was very sensitive to the fuel schedule.

INTRODUCTION

BACKGROUND

NASA is presently studying several advanced propulsion systems that promise to provide affordable access

to space. The John H. Glenn Research Center is focusing on the development and demonstration of several

low-risk approaches to Air-Breathing Launch Vehicle technologies. One concept, the reusable SSTO

"GTX", is based upon Rocket Based Combined Cycle (RBCC) propulsion. A three-view schematic is

shown in Figure 1. Vehicle propulsion is the critical technology for GTX. However, design simplicity is

the key attribute. Therefore, a nearly axisymmetric engine design has been created. Structural and

analytical simplicity results.

The RBCC concept considered here is defined by four separate modes in a single-stage-to-orbit

configuration. First, the engine functions with the rocket ignited in a unique Ejector-Ramjet cycle _ (mode

1). Then the rocket engine is switched off and subsonic combustion is present in the ramjet (mode 2). As

the vehicle continues to accelerate, supersonic combustion occurs in the Scramjet (mode 3). The rocket is

eventually re-ignited (mode 4) for the final ascent into orbit in an all-rocket configuration. Further details

on the operation of this propulsion cycle are available in reference".

A single flowpath is used throughout the four propulsion modes. This geometric simplicity presents a

complex design challenge for the air-breathing combustor. Location of the fuel injection ports must

optimize the performance of the entire air-breathing portion of the trajectory. CFD offers an efficient

analysis method, when coupled with ongoing experimental efforts, to estimate combustor efficiencies and

generate 3D design-specific fluids analysis. The current work discusses the computational combustor

*Engine Systems Technology Branch, c.j.steffen@grc.nasa.gov

_'shaye.yungster@ grc.nasa.gov

NASA/TM--2001-210679 1
analysisforMode1andMode3. In turn,thisanalysisguidesustowardmoreaccurateID combustion

modelingforcycleanalysisandtrajectoryoptimization.

Thepresentstudyispresentedintwodistinctphases, definedbytheseparateoperatingmodes.Thefirst

sectionof thispaperdealswitha computational analysisof thelow speed(mode#1)combustor. The

numerical modelsandresultsapplicabletomode#1analysisarepresentedtogetherin onesection.The

secondsectionof thispaperdealswiththeanalysisandresultsapplicabletothehighspeed(mode#3)

combustor. Thissecondsectionincludesaseparatepresentationfthenumerical modelsandresults.This

workrepresentsanoverviewof thecomputational combustionanalysisthatiscurrentlyunderwaywithin

theGTXprogram.

LOW SPEED COMBUSTOR ANALYSIS

MODE 1: EJECTOR-RAMJET MODE (IRS CYCLE)

The Independent Ramjet Stream (IRS) cycle, a variation of the conventional ejector-ramjet, is currently

being evaluated for use as the low speed propulsion mode of GTX. This propulsion mode typically covers

the speed range from lift-off to a maximum around Mach 3. In a conventional ejector-ramjet, a fuel-rich

rocket exhaust is mixed and burned with air captured by the inlet. The rocket provides all of the fuel needed

for combustion with the entrained air. The internal flowpath is designed to produce thermal choking where

mixing is complete. The main disadvantage of this concept is the relatively long duct required to achieve

complete mixing of the air and rocket streams. In order to overcome this difficulty, a modification of the

conventional ejector-ramjet was proposed in which the requirement for complete mixing of the two streams

is removed. Removing the requirement for mixing can shorten the towpath considerably, with a

corresponding reduction in structural weight and wetted area. Another benefit is a reduction in risk and

complexity since a single rocket element can now be used without regard for mixing length. Also, higher

thermodynamic performance is possible in other modes where a shorter mixing duct would reduce

expansion process losses.

In the IRS cycle, the airstream is fueled independently using the ramjet and scramjet mode fuel injectors

located in the inlet diffuser, as shown in Figure 3. The rocket serves as a pilot for the fueled airstream. This

can be accomplished upstream, since the air stagnation temperatures during this mode are not high enough

to cause autoighition. When the premixed fuel-Mr stream makes contact with the rocket plume, it is ignited

(see Figure 3) and a flame propagates across the combustor duct forming a thermal throat. The length of the

towpath is now determined by the flame propagation speed. Since the rocket is not the fuel source for the

airstream, the rocket oxidizer-to-fuel ratio (O/F) can be fixed at an optimum value for best system

performance. An additional advantage of the IRS cycle is that the fuel injectors provide the means to

control the location of the thermal throat by adjusting the amount and radial distribution of the fuel injected

into the airstream.

The goal of this mode 1 study is to conduct a CFD investigation of the IRS cycle on an axisymmetric

engine configuration having the same area distribution as the GTX engine flowpath. The objective is to

understand the flow and combustion physics, thermal choke characteristics, and the effects of airstream

fuel-air ratio, mixture distribution, and rocket chamber pressure on flame propagation and stability.

NUMERICAL METHOD

The analysis of the IRS cycle is carried out using a specialized CFD code developed in-house for

computing reacting flows, and is described in Yungster and Radhakfishnan 3. It solves the axisymmetric

Navier-Stokes equations including finite-rate chemistry and real gas effects using an implicit, total

variation diminishing (TVD) algorithm. It includes a generalized detailed chemistry capability, various

options for turbulence models, and steady-state or time accurate marching algorithms. In particular, the

Spalart-Allmaras 4 one-equation turbulence model was used in this study.

The chemical reaction mechanism for hydrogen-air combustion was based on Jachimowski's model 5,

except reactions involving N2, HO2 and H202 are not considered. Nitrogen reactions become important

only at higher Mach numbers than considered here, and reactions involving HO2 and H202 are of

secondary importance for this application. The simplified reaction mechanism, consisting of 8 elementary

reactions among 6 reacting species and the inert species N2, results in significant savings in CPU time.

NASA/TM--2001-210679 2
Thenumerical methodusedforsolvingtheNavier-Stokes andspeciestransport equationsi described in

detail in reference 3 and briefly summarized below. The equation set is discretized using the backward

differentiation formula (BDF) method, because its accuracy and efficiency in solving the differential

equations arising in combustion chemistry have been well established 6.

The numerical fluxes are discretized using Yee's second order total variation diminishing (TVD) scheme 7.

The resulting equation is then linearized in a conse_'ative manner and solved iteratively, by using a lowerupper relaxation procedure consisting of successive Gauss-Seidel (LU-SGS) sweeps.

The inversion of large matrices is avoided by partitioning the system into reacting and nonreacting parts.

Consequently, the matrices that have to be inverted are of the same size (NxN), where N is the number of

reacting species as those that arise in the commonly used point implicit methods. An important advantage

of the present method is that, because it is fully implicit, it is stable for large values of the CFL number,

thereby enabling the use of relatively large time steps to minimize computational cost. Steady state was

achieved when the mass flux was resolved to within 1% across the domain.

RESULTS

In this paper, we present results from several numerical simulations of the IRS cycle that illustrate the

effects of one particular parameter (at a given Mach number) on the flow and combustion characteristics of

a specific axisymmetric engine configuration, which is shown in Figure 2. The area distribution was

selected to correspond to that in the engine flowpath of the GTX vehicle. A plug nozzle rocket

configuration is used to provide pressure compensation as the rocket is throttled down and ram pressure

increases with Mach number.

The boundary conditions are as follows: For the inflow plane of both the primary (rocket) and secondary

tairflow) streams the total pressure and total temperature were specified. Adiabatic walls were assumed,

and the exit plane used a mixed subsonic/supersonic boundary condition. When the local Mach number

exceeded one, all variables were extrapolated. For regions of subsonic flows, an exit pressure was

specified. In all the calculations, the rocket operated at an oxygen-fuel ratio of six.

The IRS propulsion mode covers the speed range from lift-off to a maximum around Mach 3. Results are

presented for Mach numbers of 1.0, 1.5 and 2.0. For the M=I conditions, two different secondary flow

models are investigated as discussed below. At the M=I.5 flight condition we studied the effects of

secondary flow equivalence ratio (¢_), and at M =2 we show the effects of rocket chamber pressure on the

flowfield.

Figure 4 and Figure 5 show the results for M = 1. Figure 4 shows the results of a computation that assumes

the secondary stream consists of a hydrogen-air gas mixture at an equivalence ratio, ¢=0.6. That is, we are

assuming that hydrogen injection occurred further upstream, and a premixed hydrogen-air secondary

stream is flowing into the combustor. In order to examine the effects of nonuniform mixing, we carried out

a computation in which hydrogen is injected through two axial sonic injectors. The results of this

simulation are shown in Figure 5. The equivalence ratio was (¢_=0.4) for this case.

The results shown in Figure 4 and Figure 5 are presented in the form of 02 mass fraction, nondimensional

temperature and pressure, and Mach number contours. The 02 plot clearly shows the flame front

propagating across the secondary stream, and, in the case of Figure 5, shows the hydrogen injection as

regions of lower 02 concentration. The black colored region indicates the rocket exhaust, which has no

excess oxygen. The temperature plot also shows the flame front and the mixing region. This region, located

between the rocket exhaust and the flame front, is characterized by a higher temperature due to the

combustion of the excess hydrogen in the rocket stream, which has been mixed with secondary air. The

pressure plot shows the high pressure produced in the front part of the combustor due to the thermal

choking. Also, at these M=I conditions, there is not sufficient pressure differential across the combustor to

drive the secondary flow completely supersonic, and as a result a shock wave forms near the exit of the

combustor. The final two plots in Figure 4 and Figure 5 show Mach number contours. The fourth pair of

images shows the overall Mach number range, while the fifth and final pair show only the subsonic flow

regions.

The thermal choke mechanism can be clearly seen from this (and subsequent) figures. The flame

propagating across the secondary stream creates an aerodynamic throat that forces the remaining unburned

NASA/TM--2001-210679 3
secondaryflowto choke. As the velocity of the secondary stream increases, the flame angle decreases and

in fact the flame never reaches the top wall. Note also that near the exit of the combustor the secondary

stream shocks down to subsonic speeds and the flame angle increases slightly but not enough to reach the

top wall before the end of the combustor. Note also that the thermal throat location occurs further

downstream in Figure 5 as compared to Figure 4. This indicates that by adjusting the amount and radial

distribution of fuel it is possible to control the location of the thermal throat and therefore, to control the

combustor pressure and secondary airflow.

The remaining cases (for M=l.5 and M=2) have all been computed assuming a premixed hydrogen-air

secondary stream. Figure 6 shows results for M=I.5 conditions and for three different values of the

secondary flow equivalence ratio, (0=0.6, 0.7, & 0.8). This figure plots contours of the subsonic flow

region and temperature contours. Note that by increasing _, the flame penetrates deeper into the secondary

stream, and the flame becomes steeper in its initial portion. It subsequently flattens out due to the increased

velocity in the secondary stream. The flame does not reach the combustor wall in any of these cases. The

airflow is very sensitive to increases in equivalence ratio, since as $ is increased and more heat is released,

the airflow decreases resulting in lower velocities in the secondary stream. As a result of the lower

velocities, the flame can propagate deeper across the combustor and reduce airflow even more. The

aerodynamic throat occurs approximately at the same axial location, but the available area of the

nonreacting flow decreases with increasing _. As a result the amount of airflow decreases. The parameter fl

represents the secondary-to-primary total mass flow ratio. The mass flow ratio decreases from fl=2.74 for

¢_--0.6 to fl=2.00 for 0=0.8. Note also that for the conditions at M=l.5, the entire flow is supersonic at the

exit plane. (The white areas in the Mach number plots in Figure 6 represent Mach number values higher

than one).

Figure 7 shows three cases for the M=2 conditions. These calculations were made with a secondary flow

equivalence ratio of (0=0.6), but for three different values of the rocket chamber pressure, Pc. This figure

shows that when Pc is reduced from 1393 psi to 1000 psi, the rocket exhaust expansion is lower as

expected. As a result, the flame penetration into the secondary flow is also reduced and therefore more air

can flow through the engine. As Pc is reduced further to 700 psi, the secondary stream goes supersonic

shortly after the constant area section. This short supersonic region is followed by a normal shock. The

flow then thermally chokes in a manner similar to the previous cases. Therefore, at Pc=700 psi more fuel is

needed in order to push out the normal shock out of the domain.

HIGH SPEED COMBUSTOR ANALYSIS

MODE 3: SCRAMJET

The GTX vehicle is expected to operate in the Scramjet mode from about Mach 6-11. The fuel injectors

have been laid-out to maximize combustion efficiency. This is achieved by properly locating the

combustion process along the fiowpath with an optimal fuel schedule. A combination of axial and normal

injectors have been specified as shown in Figure 8. The engine configuration specified for these

simulations corresponds to an inlet contraction ratio of 12. At this contraction ratio, the inlet throat is

defined by the alignment of two backward-facing steps at the same axial location, one each for the

centerbody and cowl surfaces. The axial fuel injectors supply a small amount of hydrogen in the flame

holding regions of the backward facing steps. Just downstream of the flameholding region, the second row

of injectors has been located and oriented to inject fuel into the stream through transverse ports. Strict

normal injection from the centerbody yielded a small, positive axial component. Strict radial injection from

the cowl has been specified to avoid the negative axial component of velocity. Thus, all cowl injectors have

been slightly inclined into the streamwise direction.

The axial injectors have been placed with a 3-degree pitch between adjacent ports. The second and third

rows of injectors have been placed at a 6-degree pitch, while the fourth row has been placed at a 12-degree

pitch. The CFD simulation takes advantage of the symmetry conditions as much as possible to minimize

the computational effort required. For the first two simulations executed, a 6-degree pitch dictated the

symmetry condition of a 3-degree domain. The third simulation required the resolution of the 12-degree

pitch, so that a 6-degree domain was specified. This was accomplished by simply doubling the

computational mesh in size. Thus a similar mesh density was used for all cases. Note that the use of

NASA/TM--2001-210679 4
symmetryplanesimpliesthesimulationof afull 360-degreeengine.ThisdiffersfromtheactualGTX

referencevehiclegeometry, whichiscomprisedofanapproximately 215degreesectorwithsidewalls.

Thegoalof thismode#3studywasto performa seriesof 3Dcalculationsof thescramjet combustion

processthatcanbe(1)analyzedformeshdependence oftheperformanceresults(CFDverification)and(2)

comparedtotheperformanceresultsofupcomingfree-jettestsICFDvalidation). Thecurrentsimulations

havebeenconductedatafixedinflowcondition.Threedifferentfuelscheduleshavebeenexamined, at

_/_=0.6,0.8 and1.0.Thecalculationsat0=0.6 have been repeated with a fine mesh that is doubled in each

coordinate direction (eight times as many grid points) to enable an assessment of the mesh dependency of

the calculations.

NUMERICAL MODELS

The flow solver GASP v3.28 from Aerosoft, Inc. was used to conduct the analysis. The solver was

configured to the following specifications:

• Third-order-accurate upwind biased scheme

• Minmod limiting strategy

• Roe's approximate Reimann solver

• Two-factor ADI algorithm

• Low Ret k-o) turbulence model

• Drummond et al9 model for air/H2 chemical kinetics (9 species/18 reactions)

• Thermodynamic equilibrium assumed for translational, rotational, and vibrational energy modes, using

the LeRC curve fits _°

The mesh was developed with Gridgen nl software from Pointwise, Inc. The mesh consisted of 260(axial) x

152(radial) x 32(spanwise) cells over a three-degree annular sector. For the six-degree mesh, the

dimensions were (260x152x64). This mesh density corresponded to the "fine mesh" resolution. By

eliminating every other mesh point in all three directions, a "coarse mesh" was generated. This coarse mesh

resolution was used for both convergence analyses of the fine mesh results, as well as a cost/benefit study.

The increased accuracy of the fine mesh (1.26M cells) comes at a significant computational cost, versus the

coarse mesh (1.58k cells). All results have been iteratively converged approximately 4 orders of magnitude

for the L2 norms. The coarse mesh results exhibit a mass flow consistent to within +-1.0% while the fine

mesh exhibits a massflow consistent to within +-0.6%.

The upstream boundary condition for the combustor calculation was created from an axisymmetric inlet

calculation that resolved the flowfield from station #1 to station #2 (see Figure 8). The Mach number of the

incoming flow was supersonic everywhere except for the nearwall portion of the boundary layer. Thus, the

specification of this radial profile as fixed inflow condition to the 3D combustor was a justifiable

simplification. Earlier studies of the isolation of downstream pressure disturbances was demonstrated (see

DeBonis et al n2) for this type of geometry. The supersonic outflow boundary condition at station #3 was a

simple extrapolation.

The shape of the injector ports was modified so as to simplify the mesh generation process. The

experimental rig has gaseous hydrogen lines that supply gaseous H2 to combustor injection ports of a given

diameter. The H2 supply is such that a discharge coefficient of 70% has been observed. The computational

model has altered the round injector holes by (a) creating an equivalent area square port, and (b) reducing

the area to account for the discharge coefficient. The fuel is specified as a sonic, top-hat profile that entered

the domain at a mesh boundary that lies flush with the combustor wall. Additionally, a trace amount of

atomic Hydrogen (H) was added to the axial jets to ignite the flame-holding region. This amounted to an

equivalence ratio for the atomic hydrogen of 0.01, included for all cases presented here. The remaining

boundary condition surfaces were specified as either iso-thermal, no-slip walls (1000R) or as symmetry

planes.

The three dimensional results of the combustor ftowfield are analyzed in the following section. First the

dataset is one-dimensionalized in a fashion similar to the stream-thrust-averaging (STA) approach

described in Riggins and McClinton 13. This procedure can yield a great deal of information about the

progress of the combustion process. However, care must be taken to properly account for the species mass

NASA/TM--2001-210679 5
fluxvalues in regions of reverse flow. The combustion efficiency (rio) is stated as the percent of H2 that is

present in the form of H20. In other words, rio is the portion of fuel that is fully combusted.

RESULTS AND DISCUSSION

_=.6 DATA: COARSE & FINE MESH RESULTS:

Table 1 shows the state of the inlet flow at the entrance of the combustor domain. Keep in mind that the

combustor-inflow boundary condition was applied as a radial profile; Table 1 contains a 1D stream-thrustaverage of the incoming state for reference purposes only. Table 2 indicates the fuel schedule for this

simulation. The results of this calculation appear in the following figures. Figure 9 shows the 1D results

and their associated sensitivity to mesh resolution. Note that we can see that there is a measurable

difference between the two results for both the ID Mach number and ID combustion efficiency. Figure 10

shows a 3D view of the water mole fractions at six cross sections throughout the domain. The coarse and

fine mesh results compare quite favorably throughout the constant area section of the combustor. The

results begin to diverge throughout the downstream portion of the combustor, differing by 4% at the exit

plane. The Mach number profiles look quite similar throughout. Note that as the 1D Mach number

approaches unity, a practical limit for upstream fuel injection is approached.

The coarse mesh solution converges in approximately 3000 iterations on four SGI R12000 processors at a

wall clock time of about 3.5 days. The fine mesh, (eight times larger) converges after approximately 1500

additional iterations in about two weeks, due to the advantages of mesh sequencing.

The STA data and 3D graphics help to give a feel for the injection strategy employed during this analysis.

The presence of H20 clearly indicates the degree to which combustion has occurred. For the 0=0.6 case

shown in Figure 9 and Figure 10, the burning occurs primarily in the constant area section between the first

and second rows of normal injectors. The upstream injectors function quite well and manage to burn the

first ¢_---0.4 of fuel in the constant area portion of the combustor. The next ¢=0.2 of injected fuel seems to

take the remainder of the combustor length to burn, but does indeed reach combustion efficiencies in the

90%+ range. However, the flow at the exit of the combustor is rather stratified. A contour plot of oxygen

mole fraction (not shown) reveals that a region of oxygen depleted flow sits along the combustor walls on

both cowl and centerbody. In order to effectively burn more fuel, we will need to gain access to the

oxygen-rich core flow, without approaching the sonic limit for supersonic combustion. The 1D Mach

number has dipped to approximately 1.25 with this fuel schedule.

_=.8 DATA: COARSE MESH RESULTS:

The fuel schedule for the 0=0.8 condition is given below in Table 3. The difference between 0=.6

calculation and 0=.8 calculation was that the last row of ports have injected a total of 0=0.4, as opposed to

0=0.2. Figure 11 is another 3D depiction of the water mole fraction and Figure 12 shows the associated 1D

combustion efficiency and Mach number. (Note that the results for the stoichiometric case will be

discussed below.) At the exit of the combustor, the combustion efficiency was 88%. For the 0=0.6 case, we

have completely burned approximately 54% of the available oxygen, while for the 0=0.8 case, we have

burned approximately 70% of the available oxygen. The minimum 1D Mach number has approached even

closer to the sonic limit. It appears from Figure 11 that the increased injector pressure has not only pushed

more fuel into the combustor, but improved the jet penetration.

_=1.0 DATA: COARSE MESH RESULTS:

The fuel schedule for the 0=1.0 case is given below in Table 4. Note that the only difference from the 0=0.6

case was the addition of fuel through the third station of normal injectors. These injectors add an additional

0=0.4 of fuel to the combustor flow. This injection occurs in an expansion region and thus the minimal

value of Mach number still occurs upstream in the constant area flow. Figure 12 indicates that the

combustion efficiency at the exit plane has dropped considerably, as compared to the earlier fuel schedules.

The results indicate that we have burned approximately 68% of the available oxygen. Surprisingly, the

0=1.0 and the 0=0.8 have consumed about the same amount of oxygen. However, for 0=1.0, there's a

significantly larger lost-thrust-potential due to incomplete combustion.

NASA/TM---2001-210679 6
AfterconsideringtheresultsdepictedintheFigure13,thereadernoticesthattheflowhasstratifiedrather

thaneffectivelymixed.Theexpansionregionof thisannularcombustor canberoughlydividedintothirds

intheradialdirection,withanoxygen-richcore,surroundedbyfuelrichregions.It appearsthatforthe

combustor toeffectivelyburntheremainder of thefuelinjectedintotheexpansionregion,moremixing

mustbegenerated, orthefuelmustbeinjectedin sucha fashionasto penetratehroughtheoxygendepletedregionsalongbothcowlandcenterbodywalls.

Thisquestionofjet penetrationhasbeenstudiedforseveral decades, andprovidesareasonablemeansof

checkingoneaspect of theCFD.PovineltiandPovineili 14havepublishedacorrelationforthepenetration

distanceof normal jet injectionintoasupersonicfreestream. Theexperimental studyinvolvedinertgas

injectionintoaconstant areaflow.However, correlationcanbeexpectedto berelevanttothenear-field

analysis(i.e.firsttwentyjet diameters, d*) of our hydrogen injectors in a region of nearly constant area

ratio. This is due to the fact that the mixing limited combustion has not consumed much of the fuel stream

in the near-field region. The boundary of the fuel jet penetration can be defined as a peak in the thin (OH)

layer, along the jet centerline. The mesh resolution of this edge will dictate how accurately we can extract

the penetration depth. Consequently, the penetration data has been presented with uncertainty bounds that

reflect the local radial cell size. With this definition, we can compare the penetration valuespredicted with

the experimental correlation (y '/d*) e°_'and the values calculated from the CFD results (y '/d*) cr°.

You can see from Figure 14 that the injectors from the 0=0.6 and 0=0.8 cases have very different

penetration values over the first twenty diameters. Despite these differences, the correlation demonstrates

that these penetraion values are consistent with the aforementioned experimental data. This is shown in the

pitt of Figure 15. Notice that the CFD data lie within a +-15% uncertainty bound of the experimental

correlation. This (+-15%) bound is representative of the spread in the experimental data from which this

correlation is derived. In lieu of a strict validation for this combustor flowpath prediction, the above

comparison with experimental data is encouraging. An ability to reliably model the 3D jet injection process

will prove to be a significant compliment to our upcoming experimental free-jet data.

SUMMARY AND CONCLUSIONS

We have endeavored to present an overview of the computational combustion research that is currently

underway within the GTX program. Detailed computational fluid dynamic simulations for two distinct

propulsion modes have been presented. An axisymmetric RBCC engine fiowpath was the basis for both

sets of CFD analyses.

The numerical simulations of the Independent Ramjet Stream cycle have demonstrated that a flame can be

stabilized in the secondary stream, and that the airflow (and therefore the engine pressure) can be adjusted

by changing the fuel injection scheme. This ability to control the amount of airflow is essential in order to

keep the inlet operating at optimum conditions through the entire Mach number range. The calculations

have also allowed us to gain insight into the thermal choke mechanism. In the IRS cycle, the flame

propagating across the secondary stream creates an aerodynamic throat that forces the remaining unburned

flow to choke.

The scramjet combustor simulations to date have concentrated on Mach 6 freestream flow. The simulations

allow for a variety of fuel schedules to be examined quickly in order to optimize the combustor

performance. Relatively high combustion efficiencies have been achieved thus far with lean fuel mixtures.

The coarse mesh results for combustion efficiency differ by as much as 4% from the fine mesh results. The

mesh dependence study indicated that large performance differences (i.e 10% or more) can be analyzed

with the coarse mesh density, but relatively fine scale comparisons (i.e. 5% or less) require the more costly

fine mesh resolution. Fuel schedule optimization for stoichiometric conditions is currently underway. Both

coarse and fine mesh predictions of the normal fuel-jet penetration correlated with similar experimental

data to within (+-15%).

NASA/TM--2001-210679 7
Table 1 Inlet flow conditions

variable Station #1 Station #2

Ps(psf)

Ts (R)

M

UaxiaI (ft/sec)

Wtadial

74.12 4816

390 1454

6 2.38

5844 4275

0. -966

Table 2 Fuel schedule for #J=0.6 simulation

Fuel Schedule:

cp=0.6 simulation

Ps (psf)

Ts (R)

M

UaxiaI (ft/sec)

Uradial

0 a2

A._ial Injector

#1

Transverse

Injector #2

Transverse

Injector #3

cbdv cowl cbd), cowl cbdv cowl

6739 6739 7964 7964 7964 7964

433 433 433 433 433 433

1 1 1 1 1 1

3798 3798 835 --- 835 ---

-835 -835 3798 -3888 3798 -3888

0.1 0.1 0.1 0.1 0.1 0.1

0.01 0.01 ............

chdv Ci) i',//

Table 3 Fuel schedule for ¢_-0.8 simulation

Fuel Schedule:

_=0.8 simulation

Ps (psf)

Ts (R)

M

U_iaj (ft/sec)

Uradial

Axial Injector

#1

Transverse

Injector #2

Transverse

Injector #3

cbdy cowl cbdy cowl cbdy

6739 6739 7964 7964 18100 18100

433 433 433 433 433 433

1 1 1 1 1 1

3798 3798 835 --- 835 ---

-835 -835 3798 -3888 3798 -3888

0.1 0.1 0.1 0.1 0.2 0.2

0.01 0.01 ............

cowl c_,dv cc,w_

NASA/TM--2001-210679 8
Table 4 Fuel schedule for 0=1.0 simulation

Fuel Schedule."

(9=1.0 simulation

Ps (psf)

Ts (R)

M

Ua×iaI (ft/sec)

Wradial

Axial Injector Transverse Transverse Transverse

#1 Injector #2 Injector #3 ln iector #4

cbdv cowl cbdv cowl

6739 6739 7964 7964

433 433 433 433

1 1 1 1

3798 3798 835 ---

-835 -835 3798 -3888

0.1 0.1 0.1 0.1

0.01 0.01 ......

cbdv cowl cbdy cowl

7964 7964 9479 9479

433 433 433 433

1 1 1 1

835 --- 835 ---

3798 -3888 3798 -3888

0.1 0.1 0.2 0.2

/

"\\

Figure 1. GTX vehicle schematic Figure 2. Computational Grid

Fuel injection and

premixing IMo>0) Flame Front Thermal Throat

Rock¢| ¢xhaus_ r _ .

Figure 3. Cross-sectional view of the GTX engine: schematic of the IRS propulsion mode

NASA/TM--2001-210679 9
FlowconditionsatM=I :

Altitude= 10918.7ft; Freestreampressure= 1408.4psf: Inlet recovery = 0.95; Rocket chamber pressure = 2000 psi

Secondary stream total pressure = 2532.7 psf ; Secondary stream total temperature = 575.5 R

a) a)

c_

e)

Figure 4. IRS cycle computation at M=I conditions for

a hydrogen-air premixed secondary stream at ¢--0.6.

(Tref=_3 R; Pref=3133 psf)

Figure 5. IRS cycle computation at M=I conditions

for two axial hydrogen injectors at ¢--0.4. (Legends are the

same as in Fig. 4)

NASA/TM--2001-210679 10
FlowconditionsatM=I.5:

Altitude=20446.0ft; Freestreampressure=957.9psf;Inletrecovery=0.925;Rocketchamber pressure= 1393psi

Secondarystreamtotalpressure=3252.8psf ;Secondarystreamtotaltemperature=648.0R

,--0.6 [3=2.74

_=0.7 13=2.33

13=2.00

Figure6.IRScyclecomputationatM=l.5conditionsforthreedifferentequivalenceratios.(Tref=403R)

NASA/TM--2001-210679 11
(.q

II

O

O

O

H

O

.=

,,.a

e-.

._ t_

2

E

O

O

,,6

¢",1

e'_ t"q

¢,e,_

E II

¢.e5

|

t-...-

H

H

e_

H

,fi

¢,d. ¢_,

-=

e,d,

NASA/TM--2001-210679 12
_ Station#1 _k Station#2

Figure 8 Cross-sectional view of the GTX engine: schematic of the Scram jet propulsion mode

[ /

- - Fine Mesh

Coarse Mesh

-0.8 -0.6 -0.4

Figure 9 Mesh sensitivity of ID results: Mach

Number and combustion efficiency for ¢=0.6

Phi-0.6 O.52O

O.256

............ 0.192

0.128

O.O64

0.000

Figure 10 ¢=0.6 Simulation: H20 mole

fraction contour

Figure 11 ¢=0.8 Simulation: H20 mole

fraction contours

1

Mach

!

L , I _ i '

/'

i

L i T

i -- ¢=0.6

: ---- ¢,=08

i' z

i i i

-1.0 -0.8 -0.6 -0.4 -0.2

1.0

0.9

0.8

0.7

0.6 0.5

0.4 |

0.3 _-

0.2

0.1

0.0

0.0

Figure 12 Mach number and combustion

efficiency for ¢=0.6, 0.8 & 1.0

NASA/TM--2001-210679 13
Phi=l.O ,0.520

0.256

Figure 13 ¢=1.0 Simulation: H20 mole fraction contours

Jet Penetration

6.0 .........

5.0

4.0

-16

3.0

2.0

1.0

0.0

0

t

i

• q_--0.6injector #3

• 0=0.8 injector #3

, I

5 10 15

x'/d*

Figure 14 Axial location versus Jet

Penetration for CFD data

6 -- i

"I

5

x

: 4

q

2

1

20

Fuel Jet Penetration

y'/d*Ipo,_e|li

Figure 15 Jet Penetration: experimental

correlation versus CFD prediction

NASA/TM--2001-210679 14
REFERENCES

Yungster, S., and Trefny, C. J., "Analysis of a New Rocket-Based Combined-Cycle Engine Concept at

Low Speed," AIAA 99-2393, , 35 _hAIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit,

June 20-24, 1999.

2 Trefny, C. J. "An Airbreathing Launch Vehicle Concept for Single Stage to Orbit," AIAA 99-2730, 35 th

AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, June 20-23, 1999

3 Yungster, S. and Radhakrishnan, K., "A Fully Implicit Time Accurate Method for Hypersonic

Combustion: Application to Shock-Induced Combustion Instability," Shock Waves, Vol. 5, 1996, pp. 293-

303.

Spalart, P.R. and Allmaras, S.R., "A One-Equation Turbulence Model for Aerodynamic Flows," La

Recherche Aerospatiale, Vol 1, 1994, pp. 5-21.

-_Jachimowski, C.J., "An Analytical Study of the Hydrogen-Air Reaction Mechanism with Application to

Scramjet Combustion," NASA TP-2791, Feb. 1988.

6 Radhakrishnan, K., "LSENS-A General Chemical Kinetics and Sensitivity Analysis Code for

Homogeneous Gas-Phase Reactions. I. Theory and Numerical Solution Procedures," NASA RP-1328,

1994.

7 Yee, H.C., "Construction of Explicit and Implicit Symmetric TVD Schemes and Their Applications,"

Journal of Computational Physics, Vol. 68, 1987, pp. 151-179.

8GASP Version 3, User's Manual, ISBN 0-9652780-0-X, Aerosoft, Inc., 1996, Blacksburg, VA

9 Drummond, J. P., Rogers, R. C., and Hussaini, M. Y., "A Detailed Numerical Model of a Supersonic

Reacting Mixing Layer," AIAA 86-1427, AIAA/ASME/SAE/ASEE 22 °d Joint Propulsion Conference,

July, 1986

_0Gordon, S. and McBride, B. J., "Computer Program for Calculation of Complex Chemical Equilibrium

Compositions and Applications; Part I, Analysis," NASA Reference Publication 1311, October 1994,

Cleveland, OH

1_Gridgen Version 13, User Manual, Pointwise, Inc., 1998, Bedford, Texas.

t2 Debonis, J. R., Trefny, C. J. and Steffen, C. J. Jr., "Inlet Development for a Rocket Based Combined

Cycle, Single Stage to Orbit Vehicle Using Computational Fluid Dynamics," AIAA 99-2239, 35 th

AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, June 20-24, 1999

13Riggins, D. W., and McClinton, C. R., "Analysis of Losses in Supersonic Mixing and Reacting Flows,"

AIAA 91-2266, 27 thAIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, June 24-26, 1991

14 Povinelli, F. P., and Povinelli, L. A., "Correlation of secondary sonic and supersonic gaseous jet

penetration into supersonic crossflow," NASA TN D-6370, June, 1971.

NASA/TM--2001-210679 15
REPORT DOCUMENTATION PAGE FormApproved OMB No. 0704-0188

Public reporting burden for this coUection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources,

gathering and maintaining the dala needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this

collection of information, including suggestions for reducing this burden, to Washington Headquarters Services. Directorate for Information Operations and Reports. 1215 Jefferson

Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washinglon, DC 20503.

1. AGENCY USE ONLY (Leave blank) i2. REPORT DATE

February 2001

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

Computational Analysis of the Combustion Processes in

an Axisymmetric, RBCC Flowpath

6. AUTHOR(S)

Christopher J. Steffen, Jr. and Shaye Yungster

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

John H. Glenn Research Center at Lewis Field

Cleveland, Ohio 44135-3191

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

3. REPORT TYPE AND DATES COVERED

Technical Memorandum

WU-708-65-13-00

8. PERFORMING ORGANIZATION

REPORT NUMBER

E- 12606

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

NASA TM--2001-210679

11. SUPPLEMENTARY NOTES

Christopher J. Steffen, Jr., NASA Glenn Research Center, and Shaye Yungster, Institute for Computational Mechanics in

Propulsion, Cleveland, Ohio. Prepared for the 37th Combustion Subcommittee, 25th Airbreathing Propulsion Subcommittee, and 19th Propulsion Systems Hazards Subcommittee Joint Meeting cosponsored by the Joint Army-Navy-Air Force

lnteragency Propulsion Committee, Monterey, California, November 13-17, 2000. Responsible person, Christopher J.

Steffen, Jr., organization code 5880, 216--433-8508.

12b. DI_iHtBUTION CODE 12a. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified - Unlimited

Subject Categories: 64 and 34 Distribution: Nonstandard

Available electronically at http://gltrs.gc.n_sa.gov/GLTRS

This publication is available from the NASA Center for AeroSpace Information. 301-621-0390.

13. ABSTRACT (Maximum 200 words)

Computational fluid dynamic simulations have been used to study the combustion processes within an axisymmetric,

RBCC flowpath. Two distinct operating modes have been analyzed to date, including the independent ramjet stream (IRS)

cycle and the supersonic combustion ramjet (scramjet) cycle. The IRS cycle investigation examined the influence of fuelair ratio, fuel distribution, and rocket chamber pressure upon the combustion physics and thermal choke characteristics.

Results indicate that adjustment of the amount and radial distribution of fuel can control the thermal choke point. The

secondary massflow rate was very sensitive to the fuel-air ratio and the rocket chamber pressure. The scramjet investigation

examined the influence of fuel-air ratio and fuel injection schedule upon combustion performance estimates. An analysis of

the mesh-dependence of these calculations was presented. Jet penetration data was extracted from the three-dimensional

simulations and compared favorably with experimental correlations of similar flows. Results indicate that combustion

efficiency was very sensitive to the fuel schedule.

14. SUBJECT TERMS

Combustion; Propulsion

17. SECURITY CLASSIFICATION

OF REPORT

Unclassified

NSN 7540-01-280-5500

18. SECURITY CLASSIFICATION

OF THIS PAGE

Unclassified

19. SECU_iTIf CLASSIFICATION

OF ABSTRACT

Unclassified

15. NUMBER OF PAGES

21

16. PRICE CODE

A03

20. LIMITATION OF ABSTRACT

Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. Z39-18

298-102