large eddy simulations of the hifire scramjet using a ... · rate for consistency with the local...

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Proceedings of the Combustion Institute 35 (2015) 2163–2172

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of the

CombustionInstitute

Large eddy simulationsof the HIFiRE scramjet using a compressible

flamelet/progress variable approach

Amirreza Saghafian, Lee Shunn ⇑, David A. Philips, Frank HamCascade Technologies Inc., Palo Alto, CA 94303, USA

Available online 8 November 2014

Abstract

In this study, large eddy simulations (LES) of supersonic combustion using a compressible flamelet/pro-gress variable (CFPV) approach are performed for the HIFiRE scramjet at Mach 8 flight conditions. TheLES results show good agreement with the ground test experimental measurements. The combustionmodel is based on an efficient flamelet approach, where compressibility corrections are devised based onassumed functional forms of important thermo-chemical quantities. Specifically, the source term of theprogress variable is rescaled with the local density and temperature in the LES, leading to improved pre-dictions relative to existing flamelet models. A modified equilibrium wall-model, capable of predicting theviscous heating, is used in the viscous near-wall region. Temperature near the wall increases significantlydue to viscous heating, enhancing the reaction rate and heat-release. This is shown to be a crucial stepfor accurately predicting the pressure rise in the combustor.� 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Keywords: Supersonic combustion; Turbulent combustion; Compressible flow; Scramjet; Large eddy simulation

1. Introduction

Scramjet engines have the potential to provideeconomical air-breathing propulsion at high Machnumbers for applications such as transportation,reusable launch vehicles, and hypersonic cruisemissiles. Designing stable high-speed combustionsystems remains a major challenge for scramjet

http://dx.doi.org/10.1016/j.proci.2014.10.0041540-7489/� 2014 The Combustion Institute. Published by El

⇑ Corresponding author at: Cascade Technologies,Inc., 2445 Faber Pl., Suite 100, Palo Alto, CA 94303-334, USA. Fax: +1 (650) 521 0679.

E-mail address: [email protected](L. Shunn).

propulsion, where fuel must be mixed, ignited,and burned to completion all within a few millisec-onds. The large scale and extreme thermodynamicconditions in hypersonic flight vehicles makeexperiments costly and challenging [1]. Data areoften limited to relatively sparse measurements ofpressure, temperature, thrust, or combustion effi-ciency using conventional instrumentation. Vali-dated numerical models are the most promisingoption to bridge the gap between sub-scale groundtesting and full-scale flight-testing.

The vast majority of computational work insupersonic turbulent combustion has relied onsimplified/reduced chemistry mechanisms andthe explicit transport of the involved species [2].

sevier Inc. All rights reserved.

2164 A. Saghafian et al. / Proceedings of the Combustion Institute 35 (2015) 2163–2172

Such approaches require the closure of the chem-ical source term in the species transport equationsdue to nonlinear interactions with the turbulentflow field. Although many types of closure modelshave been investigated [3–10], research is ongoingto construct models that describe fundamentalphysics, reduce computational expense, andincrease accuracy and robustness of simulationtools.

Flamelet models present an alternative to tra-ditional finite rate chemistry approaches forCFD. The approach is based on the flamelet con-cept [11,12], which assumes that the chemical timescales are shorter than the turbulent time scales,such that the flame can be approximated as anensemble of laminar flamelets. The flameletapproach allows the chemistry to be computedindependently of the flow simulation and storedin tabulated form as a function of a small numberof scalars. During the CFD simulation, thermo-chemical quantities are interpolated from thechemistry table, thus, dramatically decreasingthe overall computational cost and allowing theuse of complex chemical mechanisms.

In this study, a computationally efficient flam-elet combustion model is developed for high-speedflows. Flamelet-based models that are currentlyused in low-Mach applications are extended andvalidated for hypersonic conditions. The targetconfiguration is the HIFiRE Direct-Connect Rigexperiments from the NASA Langley Arc-HeatedScramjet Test Facility [13].

2. Mathematical model

In this section, the filtered transport equationsfor LES of compressible reacting flows are pre-sented, the combustion model based on the flam-elet/progress variable approach is described, andthe wall modeling approach is summarized.

2.1. Governing equations

The Favre averaged or filtered variables (indi-

cated by ~: and �:, respectively), �q; �qeui; �qeE; �qeZ ;�qgZ 002 , and �qeC are solved in the conservative form,where �q is the density, eui the components of thevelocity vector, eE the total energy (including thechemical energy), eZ the mixture fraction, gZ 002 thevariance of the mixture fraction, and eC a reactionprogress variable [14].

The mixture composition depends directly oneZ ; gZ 002 , and eC . In order to close this system, thepressure and the temperature need to be deter-mined. This is achieved by using an equation ofstate and the energy of the mixture as explainedin the following section. For the current study,

the progress variable is defined asC ¼ Y H2O þ Y H2 þ Y CO2 þ Y CO.

2.2. Combustion model

The combustion model used in this study isbased on the compressible flamelet/progress vari-able approach (CFPV) [15,14]. In the CFPVapproach, flamelet equations are solved in a pre-processing step using detailed kinetic mechanisms(GRI 3.0 mechanism [16] in this study) and storedin a chemistry table. Appropriate compressibilitycorrections are introduced [14] to decrease the sizeof the chemistry table. The CFPV model has beenextensively validated in a priori and a posterioristudies using direct numerical simulation data[14]. In this section, the CFPV approach is brieflyexplained, and the compressibility corrections aresummarized.

The CFPV approach is designed to account forvariations due to compressibility, while maintain-ing roughly the same computational efficiency asits low-Mach-number counterpart. In thisapproach, the thermochemical state of the com-pressible flow is approximated as a perturbationabout nominal low-Mach-number flamelet solu-tions. Appropriate expressions are derived fromthe physical behavior of each variable, and areused to correct the value from the low-Mach-number flamelet library.

Quantities of interest that are necessary toclose the transport equations include the gas con-stant, specific heat ratio, temperature, pressure,molecular viscosity and thermal diffusivity. Cor-rections that account for the effects of compress-ibility on these quantities are described in detailin Refs. [14,17].

The source term of the progress variable is verysensitive to perturbations in temperature and con-centration. A rescaling of this term is applied as

�_xC�_xC0¼ �q

�q0

� �aqexp �T a

1eT � 1eT 0� ��

; ð1Þ

where �_xC0 is the tabulated source term computedat a background pressure p0. This equation is thedimensionless ratio of the progress variable sourceterm from the LES to its value from the chemistrytable. It is used to adjust the tabulated productionrate for consistency with the local temperatureand density in the LES. The values of the baselinedensity �q0, the density exponent aq, and the acti-vation temperature T a are computed in a prepro-cessing step to describe the dependency of thesource term on the mixture temperature and pres-sure, and are then tabulated as a function ofeZ ; gZ 002 , and eC . The form of this equation is moti-vated by the Arrhenius behavior of elementaryreactions, where density (to some order) appearsin the species concentration terms. For hydrocar-

A. Saghafian et al. / Proceedings of the Combustion Institute 35 (2015) 2163–2172 2165

bon fuels, the value of aq is close to two, becausethe majority of reactions are bimolecular. Thevalue of T a, in general, depends on the chemicalmechanism. For the conditions studied in thiswork, T a at stoichiometric conditions is approxi-mately 15,000 K.

It should be noted that all of the variables withthe “0” subscript are obtained directly from thebase-state flamelet data, while the other parame-ters, aq and T a, are determined by local data fit-ting using flamelet solutions at perturbedconditions. All of the parameters are tabulated

as functions of eZ ; gZ 002 , and eC in the chemistrytable. The functional form of the compressibilitycorrections are general and can be used for differ-ent conditions and fuels (e.g., see [14] for hydro-gen fuel). However, most of the compressibilitycoefficients are not universal (e.g., T a), and are

precomputed as functions of eZ ;gZ 002 , and eC forthe chemistry and conditions of interest. For moredetails on the CFPV model along with validationsof the above expressions refer to Refs. [15,14].

2.3. Wall modeling

Wall-resolved LES of scramjets is not practicalwith the current computational resources [18],therefore, a wall model for the wall shear stressand heat flux is applied. The unstructured LESgrid extends all the way to the wall and is designedto resolve outer-layer scale motions of the bound-ary layer [19]. The wall model then solves the com-pressible equilibrium boundary layer equationsfor momentum and energy as described in Refs.[20,21]. In the current work, the manner ofexchanging data between the LES and wall modelhas been modified from Bodart and Larsson [20]to use an integral constraint based on the wall-adjacent LES cell. The following equations,

1

d

Z d0

ujjdg ¼ eu; 1dZ d

0

Tdg ¼ eT ; ð2Þare solved iteratively at each wall-adjacent LEScell, ensuring that the average streamwise velocityand temperature from the wall model match thefiltered values from the LES. The wall-shear stresscomputed by the wall-model is applied as a flux inthe LES momentum equation. This integralapproach allows for the wall-modeled viscousheating to be passed as a source term to theLES energy equation. In prior wall-modeling

Fig. 1. Schematic of H

implementations, thermal feedback to the LESsolution was limited to the wall heat flux andwas simply zero in the adiabatic case.

3. HIFiRE simulations

Figure 1 shows the HIFiRE Flight 2 (HF2)scramjet [22] with relevant dimensions shown. Ateach streamwise fuel injection station shown inFig. 1, there are four injectors (spaced equally inthe spanwise direction) on the body side (uppersurface) and four injectors on the cowl side (lowersurface). The primary injectors have a diameter of3.175 mm, and are canted at 15� relative to thecombustor wall. The secondary injectors are nor-mal to the combustor wall with a diameter of2.388 mm. For more details on the HF2 geometryrefer to Ref. [23].

The fuel is a JP-7 surrogate with molar compo-sition of 64% ethylene and 36% methane. Thetotal equivalence ratio is 1.0, where 40% of thefuel by mass is injected from the primary injectorsand the balance from the secondary injectors [23].

The experimental measurements [13] of thefull-scale HIFiRE scramjet are conducted atNASA’s Arc-Heated Scramjet Test Facility [24].In this study, the experimental results correspond-ing to the highest Mach number are considered,where the Mach number at the isolator inlet is3.46 (equivalent to the Mach 8 HF2 flight test).

3.1. Boundary conditions

The LES is performed on one-quarter of theHF2 domain (including the cowl-side surfaceand one side wall), with symmetry boundary con-ditions applied at the mid-plane in both the span-wise and lateral directions. The use of symmetryboundary conditions reflects a compromisebetween computational costs and the need to pro-vide adequate resolution in boundary layers, shearlayers, and reaction zones. Unfortunately, the res-olution requirements of the HF2 configurationmade it infeasible to simulate the entire domainwith the computational resources that were avail-able. The symmetry boundary condition is obvi-ously an approximation to the physicalcombustor and carries implications for the overallfidelity that can be achieved. Despite this, it is areasonable concession given the cost constraintsand has been used in other investigations [25,26].Simulations of the full HF2 domain (i.e., no

IFiRE 2 scramjet.

Table 1Inflow boundary condition parameters.

Inflow boundary Pressure[kPa]

Temperature[K]

Machnumber

Isolator 40.3 736.2 3.46Primary injector 105.7 293.3 1.0Secondary injector 290.7 301.1 1.0

X [m]

P [

kPa]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

100

200

300

400

500LESLES - no source term compressibility correctionLES - no wall modelLES - fineExperiment (cowl)Experiment (body)

Fig. 2. Wall pressure along the centerline between theinjectors. LES results (lines) are compared with theexperimental measurements (symbols). Black line: LESwithout progress variable source term corrections (i.e.,Eq. (1) is deactivated); Red dot-dash line: LES resultswithout wall model; Green line: LES on coarse mesh;Blue dotted line: LES on fine mesh. (For interpretationof the references to color in this figure legend, the readeris referred to the web version of this article.)


symmetry boundary condition) are planned asfuture work; however, results are not availablefor the current paper.

Specific inflow boundary conditions of the iso-lator, primary injectors, and secondary injectorsare shown in Table 1. At the isolator inlet, syn-thetic turbulence is generated using a digital filter-ing approach [27,28]. Profiles of the Reynoldsstress tensor from the boundary layer DNS dataof Wu and Moin [29] are rescaled and used asinputs. As the turbulent conditions inside theHIFiRE isolator are not well characterized[23,22], the objective of this approach is simplyto develop a fully turbulent boundary layer priorto the primary fuel injectors. This is similar tothe approach taken in Brès et al. [30], where forpractical design studies the synthetic turbulenceinside a jet nozzle is prescribed in a manner toensure realistic turbulence levels at the nozzle exit.Simulation of the full isolator provides a suffi-ciently long development length for the boundarylayer to equilibrate before reaching dynamicallyimportant regions of the flow. All of the wallsare assumed to be adiabatic due to the long dura-tion of the experiment [13], and wall modeling isapplied to all surfaces. Characteristic boundaryconditions are applied at the outflow boundary.

3.2. Numerical implementation

The unstructured finite volume LES solver“Chris” developed at Cascade Technologies, Inc.[31] is employed in this study. Numerical stencilsbased on higher-order polynomial expansionsare used to minimize numerical dissipation. Thespatial discretization relies on a second-orderhybrid central/ENO method, in which a shocksensor is used to identify the cells where theENO scheme should be applied. An explicitthird-order Runge–Kutta scheme is used for tem-poral integration. All sub-grid turbulent quanti-ties are modeled using the dynamic procedure[32,14].

A body-fitted, block-refined, unstructuredmesh [31] is used for all of the simulations in thisstudy. Several embedded zones of refinement aredefined to provide sufficient resolution in regionswhere gradients are large, e.g., in boundary layers,fuel/air mixing layers, and the cavity. The simula-tions are performed using a coarse mesh with21 M cells, and a fine mesh with 96 M cells to

evaluate the grid independence of the solution.For the fine case, grid spacing in the wall normaldirection near the primary injectors is approxi-mately 100 wall units and is around 3% of thediameter of the primary injectors in the mixinglayer of fuel and air. Grid spacing is approxi-mately 35% larger in the coarse mesh. Althoughthe coarse mesh includes the full length of theHF2 geometry, the fine mesh utilizes a shortenedisolator in order to reduce the cost of the simula-tions. The impact of these decisions on the resultsare discussed below.

3.3. Results

Figure 2 shows the LES wall pressure distribu-tion in the symmetry plane normal to the spanwisedirection (centerline between the injectors). Exper-imental measurements on the body and cowl sidesare also plotted for comparison. Statistics fromthe LES are obtained by time-averaging instanta-neous flow-fields after 10 flow-through times(when the LES results are statistically steady). Aschematic of the HF2 domain is shown on the plotfor reference.

Comparisons with the experimental measure-ments show relatively good agreement. Combus-tion heat-release causes a sharp pressure risebeginning just upstream of the primary injectors.The pressure reaches a plateau in the cavity, andrises again due to compression on the ramp wallof the cavity. Strong turbulent mixing producesa relatively homogeneous flow in the cavity, and


nearly constant pressure in this region. The coarseLES under-predicts the pressure in the cavity byabout 4.5%, while the fine LES attains the correctpressure levels. The pressure drops suddenly asthe supersonic flow expands at the end of theramp wall. The pressure is under-predicted inthe expansion region downstream of the second-ary injectors on both the fine and coarse mesh;however, experimental uncertainty is uncharacter-istically high in this region for reasons that are notexplained in Ref. [13]. For example, note the largevariations in the experimental measurements onthe body and cowl sides around the secondaryinjectors. For this reason, the LES results arebelieved to be in the range of experimentaluncertainties.

There are notable differences between the fineand coarse LES results in Fig. 2. The fine meshoutperforms the coarse grid in predicting trendsand peak pressures in the cavity, ramp, and sec-ondary injection regions. The coarse mesh, how-ever, seems to better predict the initial pressurerise around the primary injectors. This discrep-ancy is most likely the result of the truncated iso-lator that was used in the fine grid simulations.The shorter development length resulted in jet/boundary-layer interactions that were sufficientlydifferent from the coarse mesh to suppress mixingand combustion until the cavity. These differenceswill be clarified in future simulations.

It should be noted that the current combustionmodel uses a single mixture fraction that cannotfully represents the interactions between the pri-mary and secondary fuel jets. Properly modelingthis interaction could enhance the combustionaround the secondary injectors, and increase thepressure in this region. The addition of a secondmixture fraction and modeling of cross-dissipation

Fig. 3. Contours of the mixture fraction on sixx1 ¼ 0:25; 0:3; 0:35; 0:4; 0:45, and 0.5 m. Combustor wall is

effects in the flamelet equations are the subjectsof ongoing research. Using a multi-stream modelcould potentially improve the results in theregions after the secondary injectors.

Figure 3 shows the mixture fraction contoursand the pressure rise on the combustor walls(the isolator wall is excluded for clarity). The pri-mary jets are confined near the wall by the rela-tively strong cross-flow. The secondary jets,which are injected normal to the cross-flow andhave a higher momentum flux ratio, penetratemore deeply into the combustor interior. Figure4 shows the iso-surface of the stoichiometric mix-ture fraction colored by the progress variable.Upstream of the cavity, the primary jets burnmostly in the low speed boundary layer, and themixing region between the injectors. In fact,Figs. 3 and 4 indicate that the fuel streams mergebefore entering the cavity. Mixing is enhanced inthis region as the boundary layer separates justprior to the cavity due to the strong adverse pres-sure gradient (see Fig. 2). This can be clearly seenin Fig. 5a, where a small recirculation zone is vis-ible between the primary injectors and the cavitystep.

Contours of the progress variable near the pri-mary injectors are plotted in Fig. 6a. The oxidizerstream in the mixing layer has low velocity andhigh temperature due to conversion of the kineticenergy to thermal energy. This provides favorableconditions for the mixture to ignite [14]. Auxiliarysimulations were also performed to independentlyevaluate the effect of the source term correctionoutlined in Eq. (1), and the effects of the wallmodel. Figure 2 compares the pressure distribu-tion from the full CFPV model with a secondLES where the source term correction was notapplied. It is clear from the delayed pressure

slices normal to the streamwise direction atcolored by pressure.

Fig. 4. Iso-surface of the stoichiometric mixture fraction colored by the progress variable.


response in the case with no correction term thatEq. (1) is an indispensable step in the CFPVapproach. Contours of the progress variable fromthese two cases are plotted in Fig. 6b and c, whichshows that combustion cannot be sustained at theprimary injectors without correcting the progressvariable source term for compressibility. A thirdLES simulation was performed that included thesource term correction but did not apply the wallmodel. Comparing Fig. 6a and c shows that theviscous heating provided by the wall model isequally important in stabilizing the flame at theprimary injectors. The viscous heating in the isola-tor boundary layer transfers the kinetic energy ofthe flow into sensible energy. The correspondingincrease in the fluid temperature enhances thereactions and stabilizes the flame near the primaryinjectors. Equation (1) provides a mechanism tocouple these two phenomena in the CFPV model.

4. Analysis and discussion

Flamelet models assume that a turbulent react-ing flow can be approximated by asymptotically-thin laminar flame structures embedded in a tur-bulent flow field [11]. Implicit in this model isthe assumption that the chemical length and timescales of the flamelet are much smaller than therepresentative turbulent scales. Also, becauseflamelet manifolds are derived from collectionsof canonical flame structures, the target systemmust persist more or less within the prescribedmixing and turbulence regimes for the approachto be valid. In this section, the results from theHF2 simulations are evaluated in terms ofassumptions common to the flamelet paradigm.

The CFPV model presented in Section 2.2 isbased on non-premixed diffusion flamelets. It is

instructive to compare characteristic flame struc-tures from the compressible LES to the originalincompressible flamelet solutions. Figure 7 showsa scatter plot of instantaneous temperature versusmixture fraction from the HF2 simulation. Datafrom two separate z-planes are shown — the darksymbols represent data from a slice along the cen-terline of the fuel injectors, and the lighter sym-bols show data from midway between the twojets. Laminar flamelet solutions depicting isenthal-pic mixing (vst ¼ 500 s�1) and near equilibriumchemistry (vst ¼ 1� 10�4 s�1) are also presentedfor reference.

Deviations from the incompressible flameletmanifold due to compressibility are immediatelyapparent in Fig. 7. Differences of over 1000 K rel-ative to the baseline flamelets are observed in andaround the reaction zone, with even larger tem-perature excursions near the lean boundary. Thesehigh temperatures arise from the shocked air flowsin the isolator upstream of the primary mixers.Data sampled from the fuel jets (dark symbols)show temperature fluctuations around the base-line fuel inlet condition and a variety of reactingand intermediate states in the interior of the flam-elet. Data sampled from between the fuel injectors(lighter symbols) suggest a more consistent transi-tion to burning, as hot air is entrained with burn-ing gases in this highly unsteady region. Profileswith similar flame structure and temperaturerange have been reported in previous RANS [33]and LES [25] studies of this configuration.

Although the global flame structure in Fig. 7appears to have significant non-premixed charac-ter, more careful analyses are required to evaluatethe suitability of the diffusion flamelet approachfor the HF2 combustor. The Takeno FlameIndex [34] is a useful indicator for identifyingmixing regimes in reacting flows. It assumes that

(a) Streamwise velocity (white line indicates the u1 = 0 boundary)

(b) Pressure

(c) Scalar dissipation rate, χ (logarithmic scale)

(d) Takeno Flame Index, GFO

(e) )elacscimhtiragol(rebmunrelhökmaD

Fig. 5. Flow variables from LES of the HIFiRE scramjet.


gradients in the fuel and oxidizer fields arealigned in premixed flames and anti-aligned innon-premixed flames

GFO ¼reY F � reY OjreY F jjreY Oj ; ð3Þ

so that non-premixed regimes are characterized bynegative values of GFO and premixed regimes areidentified by positive values of GFO. Contours ofGFO are shown in Fig. 5d. Non-premixed combus-tion modes are widespread in shear layers and thecavity; however, pockets of premixed combustionare peppered throughout the flow.

(a) with source term correction, with wall model

(b) without source term correction, with wall model

(c) with source term correction, without wall model

Fig. 6. Contours of the progress variable from C ¼ 0 (black) to C ¼ 0:3 (white).

Fig. 7. Scatter plot showing temperature eT from theLES as a function of mixture fraction eZ . Representativesolutions from the laminar flamelet library are shown forcomparison.

Fig. 8. Iso-surfaces showing regions of intense reactionand heat release, colored by values of the Flame Index,GFO.


With the diverse range of flame states shown inFig. 5d, it is interesting to consider which struc-tures are contributing most strongly to the com-bustion. Figure 8 shows an iso-surface ofprogress variable reaction rate, a quantity that isclosely correlated with heat release. The surfacesare colored according to the local value of the

Flame Index. Non-premixed combustion isobserved in the shear layer rollup at the windwardbase of the injectors, but there appears to be sig-nificant premixed zones in entrainment regionsof the jet-in-crossflow vortex systems.

A time-scale analysis is used to examine thesereactive zones in more detail. The analysis is basedon estimates of the local Damköhler number,


Da ¼ sflow=schem. For non-premixed combustion,the scalar dissipation rate provides an inverse timescale for mixing. We use the equilibrium model forscalar dissipation rate proposed by De BruynKops et al. [35]

1

sflow¼ ev ¼ em

Peþ mt

Sct

� �jreZ j2; ð4Þ

with the primary jet diameter as a representativelength scale in the Peclet number. The computeddissipation rates are shown in Fig. 5c and are lar-gely insensitive to the choice of length scale due tolarge contributions from the SGS term mt=Sct. Thecharacteristic chemical time scale for the CFPVmodel is

schem ¼�qeC�_xC

: ð5Þ

Contours of Damköhler number based on Eqs. (4)and (5) are shown in Fig. 5e.

The flamelet assumptions are valid for Da� 1,a criteria that can be loosely interpreted asDa > 10. The regions shown in Fig. 8 are evaluatedusing this criteria in conjunction with the FlameIndex to determine the suitability of the CFPVmodel for the HF2 case. Figure 9 shows the vol-ume-weighted joint PDF of Damköhler numberand Flame Index for the heat release regionsshown in Fig. 8. The Da ¼ 10 line is representedby the horizontal dashed line and the non-pre-mixed (GOF < 0) and premixed (GOF > 0) regionsare divided by the vertical dashed line. A substan-tial fraction of the heat release region (67%) lies inthe upper left quadrant, where the flameletassumptions are valid and diffusion flamelets prop-erly characterize the combustion regime. A non-negligible fraction (26%) of the heat release regionfalls in the upper right quadrant, indicating that

Flame Index

log 1

0(D

a)

−1 −0.5 0 0.5 1−5

0

5

10

0

0.5

1

1.5

2

2.5

3x 10

−3

Fig. 9. Volume-weighted joint PDF of Damköhlernumber and Flame Index for the heat release regionsshown in Fig. 8.

time scale ratios are amenable to flamelet modelingbut that the combustion model should considerpremixed flame structures as a basis. The remain-ing 7% of the heat release region lies below theDa ¼ 10 line, suggesting that flamelet methodsare unlikely to properly describe all of the impor-tant reaction phenomena under these conditions.

5. Conclusions

Large eddy simulations using the CFPV com-bustion model are reported for the HIFiREscramjet at Mach 8 flight conditions. Results arecompared with experimental measurements fromthe HIFiRE Direct-Connect Rig at NASA Lang-ley. The CFPV model utilizes functional correc-tions to a nominal flamelet solution to accountfor compressibility, thus providing an efficientdescription of high-speed combustion with a lowmemory footprint. Turbulent wall modeling ofthe viscous near-wall region is used to accuratelypredict the wall shear stress and heat flux in theLES. The numerical results show good agreementwith the experiment when both compressibilityand wall effects are modeled. Neglecting eitherof these factors, however, leads to reduced com-bustion and poor prediction of the pressure trendsobserved in the experiment. Corrections to theprogress variable source term are particularlyimportant, as they provide strong couplingbetween the combustion chemistry and compress-ible phenomena such as shocks, expansions, andviscous heating. The present results also suggestthat jet/boundary-layer interactions are importantin sustaining proper mixing and combustion in thenear field of the primary injectors. All of theseeffects must be considered to stabilize combustionin the proper location. A time-scale analysisshowed that assumptions about flamelet timescales are valid throughout a large fraction ofimportant heat release regions of the HIFiREcombustor. However, analysis of the mixingregime suggested that premixed combustion playsa non-negligible role in this flow and should beconsidered in future simulations.

Acknowledgments

An award of computer time was provided bythe Innovative and Novel Computational Impacton Theory and Experiment (INCITE) program.This research used resources of the Argonne Lead-ership Computing Facility at Argonne NationalLaboratory, which is supported by the Office ofScience of the U.S. Department of Energy undercontract DE-AC02-06CH11357. Additional sup-port was provided by the Air Force Research Lab-oratory STTR program under project numberFA8650-12-C-2246.


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large eddy simulations of the hifire scramjet using a ... · rate for consistency with the local...

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