Available online at www.sciencedirect.comProceedings

Proceedings of the Combustion Institute 32 (2009) 2413–2420

www.elsevier.com/locate/proci

of the

CombustionInstitute

Large-eddy simulation of equilibriumplasma-assisted combustion in supersonic flow

Kenji Miki, Joey Schulz, Suresh Menon *

School of Aerospace Engineering, Georgia Institute of Technology, 270 Ferst Drive, Atlanta, GA 30332-0150, USA

Abstract

A large-eddy simulation (LES) model with a new localized dynamic subgrid closure for the magnetohy-drodynamics (MHD) equations is used to investigate plasma-assisted combustion in supersonic flow. A 16-species and 74-reactions kinetics model is used to simulate hydrogen-air combustion and high-temperatureair dissociation. The numerical model is validated with experimental data for non-reacting and reactingsupersonic flow over a rearward-facing step. The creation of a plasma source near the step corner is shownto have a strong localized effect with the high temperature region resulting in an increase of the radical spe-cies concentration in the mixing region. This has the potential for enhancing combustion. In addition,downstream fuel–air mixing is improved, primarily by the creation of a strong baroclinic torque effectin the near field of the plasma source. Furthermore, by adding an uniform external magnetic field, the Lor-entz force effect helps to further enhance mixing by lifting the shear layer and increasing fuel penetration byapproximately 20%.� 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Keywords: Supersonic flow; Plasma-assisted combustion; Mixing enhancement; Flameholding

1. Introduction

Bluff-body stabilization of flames in combustorsis a well-established approach in both subsonic andsupersonic flows. In supersonic combustion, as in ascramjet engine, fuel (gaseous or liquid) is injectedboth upstream of and behind a rearward facingstep. The recirculating hot products create an effec-tive re-ignition and flame-holding mechanism [1–6]. For stable combustion, however, the location(s)of the injectors and the scale of the combustorgeometry may need to be optimized for the Machnumber and the temperature of the inflow air.

1540-7489/$ - see front matter � 2009 The Combustion Institdoi:10.1016/j.proci.2008.06.131

* Corresponding author. Fax: +1 404 894 2760.E-mail addresses: suresh.menon@ae.gatech.edu,

suresh.menon@aerospace.gatech.edu (S. Menon).

Practical constraints limit major changes to thestructure of the combustor, and therefore, as thecombustor inlet Mach number increases (e.g.,Ma > 3:5), fuel–air mixing and flame holdingbecome problematic or even unattainable.

Flow assisted flame holding mechanisms thatcan adapt to changing inflow conditions are there-fore being explored. Among them, plasma-assisted combustion has demonstrated a potentialfor improving or enhancing combustion perfor-mance. In a recent study [7], the capability of aplasma source to sustain premixed hydrogen andethylene combustion over a rearward-facing stepat Ma ¼ 2 was demonstrated. In their experiment,the electrical arc near the step corner was shownto create a non-equilibrium plasma inside therecirculation region, which increased the shearlayer width and the turbulent intensity. Other

ute. Published by Elsevier Inc. All rights reserved.

2414 K. Miki et al. / Proceedings of the Combustion Institute 32 (2009) 2413–2420

studies (e.g., [8]) also seem to suggest that aplasma may create a high temperature radical richstream that provides an active ignition source. Ifthe location and the quality of this source canbe controlled then it may be possible to create avirtual flameholder in the fuel–air mixing region,and thus, provide a mechanism for flameholdingin high Ma flows.

Numerical studies of plasma-enhanced com-bustion are sparse, with only steady-state analysisreported (e.g.,[7]). Since fuel–air mixing and flamedynamics are unsteady, large-eddy simulation(LES) may offer a more comprehensive analysisapproach. In order to establish a plasma-LESmodel, many issues need to be resolved, includingsubgrid closures for the magnetohydrodynamic(MHD) equations and modeling of the plasma.Recently, we described a new subgrid closuremodel for MHD turbulence [9] and a numericalmethod to simulate an electric discharge in super-sonic flows [10,11]. In the current paper, we com-bine these capabilities and apply it to the studyplasma-assisted combustion in a typical scramjetgeometry.

2. Governing equation

The MHD-LES equations are obtained byspatially Favre-filtering (using a box filter ofgrid filter-width D) the unsteady, compressibleNavier–Stokes equations, the magnetic induc-tion equation, the species equation, and thestate equation for an electrically conductingfluid [11]:

o�qotþ o

oxjð�q~ujÞ ¼ 0

o�q~ui

otþ o

oxjð�q~ui~uj þ �pdij � �sij � T ij þ ssgs

ij þ T sgsij Þ ¼ 0

o�qeEotþ o

oxi½ð�qeE þ �pÞ~ui � �j

oToxi� ~uj�sij � ~ujT ij

� H sgsi � rsgs

i þ �qsgsi � ¼ S þ Osgs

oBi

otþ o

oxjð~ujBi � Bj~ui � �k

oBi

oxjþ ssgs;b

ij � dsgs;bij Þ ¼ 0

o�qeY m

otþ o

oxjf�qeY mð~uj þ ~V j;mÞ þ Y sgs

j;m þ hsgsj;mg ¼ �_wm

�p ¼ �qRT ð1Þ

Here, all Favre-filtered quantities are definedas ~f ¼ qf =�q, and all terms with superscript‘‘sgs” indicate subgrid scale terms that need tobe closed. In the above equations, q, ui, p, R,T, and Bi represent the density, velocity compo-nents, pressure, gas constant, temperature, andmagnetic field components, respectively. In themomentum equation, sij is the viscous stress ten-sor and T ij is the magnetic stress tensor defined

asoT ij

oxj¼ o

oxjfBiBj

l0� Bk Bk

2l0dijg, where l0 is the mag-

netic permeability. The magnetic stress tensorT ij is analogous to the viscous stress tensor,sij, and is related to the Lorentz force (~J �~B),where ~J is the current density. E is the sum ofthe kinetic and internal energies per unit mass,j is the thermal conductivity, and the term S is:

S ¼ o

oxið��k�ijkJ jBkÞ � Rd þ

5kbJ j

2ecp

oeToxj

ð2Þ

Here, kb, cp, and e are the Boltzmann con-stant, the specific heat, and the electronic charge,respectively. The electric heat flux is a resistiveheating term. In Eq. (2), since the assumptionof neglecting the Hall current is reasonable as aresult of the large collision frequency [11], thusthe resistive heating term simplifies to the firstterm on the right-hand side. Rd is the energy lostto radiation, and the last term reflects the energytransfer due to electron mobility in an electricfield. In the induction equation and in Eq. (2),k is the magnetic diffusivity (k ¼ ðrl0Þ

�1), wherer is the electrical conductivity. Note that theelectric field has not been neglected even thoughit does not appear specifically in the MHD gov-erning equations. The MHD equations aremanipulated in order to eliminate the electricfield so that only the current density (J i) andmagnetic field (Bi) are variables. In the speciesequation, the individual species mass fraction,diffusion velocities, and mass reaction rate perunit volume are Y m, V j;m, and _wm, respectively.The calculation of V j;m is given by Menon andPatel [13].

The subgrid terms in the above LES equationsare defined as: ssgs

ij ¼ �qguiuj � �q~ui~uj, T sgsij ¼

BiBj�BiBj

l0� Bk Bk�Bk Bk

2l0

� �dij, H sgs

i ¼ ð�qgEui � �qeE~uiÞþ

pui��p~ui, �qsgsi ¼

P16m¼1hmDm

oY moxi�~hm

eDmoeY moxi

, rsgsi ¼gujsij� ~uj�sij, ssgs;b

ij ¼ðujBi�uiBjÞ�ð~ujBi� ~uiBjÞ,dsgs;b

ij ¼koBioxj��koBi

oxj,

Osgs ¼ oð�k�ijk J jBkÞoxi

� oð��k�ijk J jBkÞoxi

þ 5kb2e

Jj

cp

oToxj

� �� 5kb

2eJj

cp

oToxj

, Y sgsj;m ¼ �qðgujY m� ~uj

eY mÞ, and hsgsj;m ¼

�qð gV j;mY m � ~V j;meY mÞ.

Here, hm and Dm are the mth species enthalpyand molecular diffusion coefficient, respectively.Some of these terms (e.g., ssgs

ij , H sgsi , and Y sgs

j;m)appear even in non-MHD flows, and their closurehas been adopted from previous efforts. For thepresent study, we neglect rsgs;v

i , �qsgsi , and hsgs

j;m, asdone in earlier non-MHD flows [12,13]. Of theMHD subgrid terms, dsgs;b

ij and Osgs are neglected,but the validity of this assumption still needs to beaddressed in the future. The other terms are mod-eled using transport models for the subgrid kineticenergy ½ksgs ¼ 1

2ðgukuk � ~uk~ukÞ� and the subgrid

magnetic energy ½ksgs;b ¼ 12l0ðBkBk � BkBkÞ� [11]:

o�qksgs

otþ o

oxi�qksgs~ui ¼

o

oxið�q me

Prt

oksgs

oxiÞ � ssgs

ijo~uj

oxi� T sgs

ijo~uj

oxi� �qC�

�4ðksgsÞ

32

oksgs;b

otþ o

oxið~uik

sgs;bÞ ¼ o

oxkð�k oksgs;b

oxkÞ þ ksgs;b o~ui

oxiþ 1

l0

ssgs;bij

oBi

oxj� C�;b

�4 ffiffiffi�qp ðksgs;bÞ

32

ð3Þ

Fig. 1. Three dimensional geometry and electric nodelocations. The step height H ¼ 3:1 mm. The transversesonic injection is set at the bottom surface (3H � 9 mmdownstream from the step). The second injection forCase 2 is 7H � 22 mm downstream. The grid resolutionis 229� 69� 65 and clustered around the step and thefuel injector.

K. Miki et al. / Proceedings of the Combustion Institute 32 (2009) 2413–2420 2415

The ksgs model is a well established non-MHDclosure, and the assumptions and simplificationsmade for this closure are carefully examined in[12]. The present model contains a new produc-tion term due to MHD effect.

An eddy viscosity type closure is employedto close the major SGS terms. Thus, forexample, ssgs

ij ¼ �2�qmtðeSij � 13eSkkdijÞ þ 2

3�qksgsdij

and T sgsij ¼ �2mT ð �Mij � 1

3�MkkdijÞ � 1

3ksgs;bdij. Here,

mt ¼ Cm

ffiffiffiffiffiffiffiksgsp

�4 is the eddy-viscosity, and

mT ¼ CTm

ffiffiffiffiffiffiffiksgs;b

l0

q�4 is the magnetic eddy diffusivity.

eSij and Mij are the resolved rate of strain tensors

defined as eSij ¼ 12

o~uioxjþ o~uj

oxi

� �and Mij ¼ 1

2oBioxjþ

�oBj

oxiÞ,

respectively.The closure of the subgrid magnetic flux, ssgs;b

ij ,in the induction equation is obtained using thetwo-scale direct interaction approximation(TSDIA) [14]. All the model coefficients (C�,C�;b, Cm, CT) are obtained using a localizeddynamic closure [11,12]. For estimation of theradiation loss Rd , empirical data for high-temper-ature air at atmospheric pressure is used [15].

A 16 species (H2O, H2, O2, N2, H, O, N, OH,NO, Hþ2 , Nþ2 , Hþ, Oþ, Nþ, NOþ, e�), 74 reactionskinetics hydrogen-air combustion and high tem-perature air dissociation model is employed. Thehydrogen combustion kinetics are based on a 7-step and 7-species mechanism [16]. The remainingspecies and reactions are based on a high-temper-ature dissociation mechanism [17]. At present, theplasma is assumed to be in local thermodynamicequilibrium, therefore, it is not necessary to solvethe electron energy equation, and because ofquasi-neutrality, the electron density ne is givenby ne ¼

P6m¼1Zmnm, where Zm is charge number

and 6 denotes the number of positive ions(Hþ2 ;N

þ2 ;H

þ;Oþ;Nþ;NOþ).In the current model, a subgrid eddy breakup

model called EBU-LES [13] is used to obtainedthe filtered reaction rates. Such a closure is consid-ered simplistic but computationally efficient and isused here as an initial effort. However, in thefuture a more comprehensive subgrid scalar clo-sure [13,18] will be considered. The total magneticfield, Bi, is the sum of all external fields and theinduced magnetic field. Similarly, the total currentdensity, J i, is the sum of the current resulting froman electric potential, /, difference between thecathode and anode and the induced current den-sity. The induced fields are determined from themagnetic induction equation and Amp�ere’s law.The external current density is calculated fromthe scalar potential by: J ex;i ¼ ��r o�/

oxi. The external

magnetic field is determined by Bex;i ¼ �ijko�Akoxjþ

B0;i, where �Ak is the vector potential of the mag-netic field [11,19]. The first term results from anelectric potential difference and the second termaccounts for any applied external fields.

3. Numerical formulation

The MHD-LES equations are solved using afinite volume scheme that employs an approxi-mate MHD Riemann solver using a Harten,Lax, and van Leer (HLL) approach for MHD[20]. The Monotone Upstream-Centered Schemefor Conservation Laws (MUSCL) method is usedwith the monotized-central (MC) slope limiter inorder to maintain second-order spatial accuracy[21]. The near-zero divergence of magnetic fieldis achieved by using a constrained transport scheme[22]. Second-order accurate explicit time-integra-tion is employed, and this requires the time-stepto be limited by the minimum time-scale.

In the MHD problem, there are wide rangeof characteristic time scales: viscous diffusion,Dtd;le

� 10�5s, convection, Dtc � 10�8s, electricalpotential diffusion, Dtd;�r � 10�9s � 10�12s, andmagnetic diffusion, Dtd;�k � 10�12s � 10�15s. Here,dual time stepping is used to solve the electricalpotential evolution equation, and an implicitscheme is used to determine the magnetic diffusionflux [11]. Tzhis allows the simulation to be carriedout using the convection time-step constraint. Thebaseline LES code is a well-established parallelsolver that has been validated extensively andapplied to many reactive flow problems [18] usinga similar time-step restriction.

Figure 1 shows the computational domain andother reference parameters. The cathode is locatedupstream of the step, and the anode is positioned

2416 K. Miki et al. / Proceedings of the Combustion Institute 32 (2009) 2413–2420

on the bottom wall aft of the step. Location forthe anode and cathode were chosen based onexperiments [7], and the practical considerationthat sustaining an equilibrium arc anywhere butin the re-circulation zone would be highly improb-able. Fuel is injected perpendicularly upwardsfrom the bottom wall. The top wall is a slip wall,and no-slip wall boundary conditions are usedelsewhere. Adiabatic wall conditions are usedeverywhere except at the anode and cathodewhere the wall temperature is held at a constanttemperature (T wall ¼ 3500 K) [19]. At the cathodeand the anode surfaces, the electric potential, /, isdetermined by specifying the current in the nor-mal direction as JwallðlÞ ¼ J maxexpð�blÞ, whereJmax ¼ 1:4� 108 Am�2, b ¼ 2000 for an input cur-rent of 200A, and l is measured from the center ofthe electrical node. The current density in the tan-gential direction is set to zero at the conductingsurfaces. Everywhere else the scalar electric poten-tial and vector magnetic potential are required tohave zero normal gradients.

The inflow conditions for the supersonic airand the jet are summarized in Tables 1 and 2.Cases 1 (no fuel injection) and 2 (two fuel injec-tors) are simulated to compare with non-reactingdata [23], while Case 3 with a single fuel injectionis a reacting case [1]. These cases serve to validatethe current baseline setup. Cases 4-8 studyplasma-assisted combustion at Ma ¼ 1:4 (Cases 4and 5) and Ma ¼ 3:5 (Cases 6-8). In Case 8, anuniform external magnetic field (B0;z) is appliedin the z-direction with a strength of B0;z ¼ 3T ,which is thought to be practical with current tech-nology. The grid is chosen based on past

Table 1Free-stream flow conditions

Case Ma Gas T in½K� P in½kPa� Arc [A]

1 2.0 N2 167 35 –2 2.0 N2 167 35 –3 1.4 O2=Ar 2200 40 –4 1.4 Air 1300 32 –5 1.4 Air 1300 32 406 3.5 Air 1300 32 –7,8 3.5 Air 1300 32 200

For Case 8, an uniform magnetic field of 3 Telsa isapplied in the z-direction. The concentration of O2 forCase 3 is 21%.

Table 2Jet flow conditions

Case Fuel T in½K� P in½kPa�1 No injection2 O2, two jets 250 1393 1%NO;19%CO=H2 221 1624–8 H2 221 162

For all cases, Majet ¼ 1.

experience and a limited number of grid refine-ment studies for this configuration. The current229� 69� 65 resolution gives around 10-15points in the separating shear layer region. Theprevious works [12,13,18] for non-MHD flowsdemonstrate that the dynamic sub-grid closurefor the sub-grid kinetic energy recovers inertialrange spectra in high turbulence region with rela-tively low grid resolution. The grid resolutionused in this paper is considered adequate, andthe grid resolution requirement for modelingMHD turbulence is relaxed in this calculationdue to the high magnetic diffusivity. This will bediscussed further in the results section.

4. Results and discussion

Many validation studies have been performedto establish the MHD numerical algorithm andthe MHD-LES approach. Earlier, the classicalOrszag-Tang vortex, which is routinely used as atwo-dimensional validation for MHD schemes,was simulated and compared to past predictionswith very good agreement [11].

Additional validation studies include MHD-DNS and MHD-LES of forced, decaying, androtating isotropic turbulence with and withoutan external magnetic field [9]. Due to space con-straint, we focus only on the scramjet configura-tion related validations and applications.

4.1. Non-reacting and reacting flows withoutplasma

The normalized (by inflow conditions) pres-sure, temperature, U velocity, and V velocitywall-normal profiles for Case 1 are compared withdata [23] at two locations downstream of the stepin Fig. 2a and b. At both locations the current

Fig. 2. Comparison of experimental data [1] and LESpredictions for non-reacting Case 1. All quantities arenormalized by the inflow condition of the free-stream.

Fig. 3. Comparison of experimental data [23] and LESprediction of mole fraction of O2 for Case 2.

K. Miki et al. / Proceedings of the Combustion Institute 32 (2009) 2413–2420 2417

LES shows very good agreement with data.Figure 3 shows Case 2 with two non-reactinginjectors. The over-expanded fuel jets create shockbubbles that becomes bent by the oncoming flow.Multiple recirculation regions are formed behindthe step and in the wake of the jets, and they resultin a relatively high fuel mass fractions near thebottom wall. The fuel penetration distance is ingood agreement with experiment, and thus thestructure of the shock bubble and turbulent mix-ing of the flow are assumed to be captured accu-rately by the current LES.

The reacting case (Case 3) McMillin et al.obtained temperature data using NO and OH asthe temperature tracers. Figure 4 compares thisdata with the numerically predicted time-averagedplume temperature. The agreement is acceptableconsidering that the measurements were reportedto have a large degree of uncertainty (see figurecaption). These non-reacting and reacting super-sonic flows serve to establish additional validityof the LES solver to simulate non-MHD super-sonic combustion.

Fig. 4. Time-averaged temperature variation in thewake of the dual injector [1] for Case 3. Fothe experimental NO measurement (in the near-field othe injector), the shot-noise temperature uncertaintyranges from � 4–20% over the temperature range 300–1500 K. For OH, the temperature uncertainty range i� 13–30%. For the numerical results, the temperature iaveraged in the regions of the x–y plane where theconcentration of NO and OH is more than 0.01% and0.1% in the plume region, respectively.

Fig. 5. Simulated electromagnetic fields for Case 7 withan input current of 200 A (a) current density (j~J j)contours and vector field (dark lines), and (b) magneticfield magnitude contours (j~Bj) and its vector field (dark

rf

ss

Earlier validation efforts [11] for non-reactingMHD turbulent flows and the earlier well estab-lished accuracy of the LES solver for both non-reacting and reacting flows serve to complete thevalidation of the solver for these various applica-tions. In the following, we discuss plasma-assistedcombustion in supersonic flow.

4.2. Plasma-assisted combustion

Plasma-assisted combustion is investigated attwo different Mach numbers, Ma ¼ 1:4 andMa ¼ 3:5, using pure hydrogen as the fuel. Thelower Ma case is perhaps not that interesting sincesupersonic combustion is known to occur for thisMa even without plasma-assistance. The secondcase is chosen since for a vehicle flight Ma ¼ 10,the combustor inlet Ma is estimated to be around3.5 with a static temperature of 1300 K [2]. It isobserved that at these high Ma, the same rear-ward-facing step is not sufficient for flame stabilityand very little fuel–air mixing occurs. Unfortu-nately, little experimental data exists at these highMa.

Figure 5a shows the iso-contour of the mag-nitude of the current density, j~J j, and the cur-rent vector lines for Case 7. It is observed thatthe current density is swept downstream by theflow, but still remains localized around the elec-trical nodes due to the high temperature depen-dence of the electrical conductivity r. Theseresults mirror those observed in experiments[7]. Figure 5b shows the corresponding iso-con-tours of the magnetic field, j~Bj, and the mag-netic vector lines. The magnetic field achievesa maximum strength (0:002T ) near the step.The induced magnetic field for all cases is morethan four orders of magnitude smaller than themagnetic field associated with the arc currentdue to the large magnetic diffusivity, k. Thisobservation is consistent with the fact the mag-netic Reynolds number defined as Rm ¼ U inh=kbased on the channel height and the inflowvelocity is much less than unity.

Figure 6a and c show two representative snap-shots of the density field for different Ma withoutan arc (Cases 4 and 6, respectively). With increase

lines).

Fig. 6. Comparison of density contours for Ma ¼ 1:4and Ma ¼ 3:5 without/with/arc (a) Case 4, (b) Case 5, (cCase 6, and (d) Case 7.

Fig. 7. Comparison of temperature contours for Cases6–8. The inset figures show the velocity vector fieldaround the step.

2418 K. Miki et al. / Proceedings of the Combustion Institute 32 (2009) 2413–2420

)

Fig. 8. Comparison of OH mass fraction contours in thex–y cross section for Cases 6–8.

in Ma, the flow in the recirculation zone betweenthe fuel injector and the step changes in magni-tude, the leading shock angle (in front of the injec-tor) is reduced and fuel penetration is decreased.The corresponding cases with the arc on Fig. 6band d show qualitatively similar overall features,with some significant near-field differences thatare discussed further below. The plasma sourceenhances combustion by increasing the local tem-perature and by creating a radical pool in therecirculation zone near regions of high currentdensity.

This high temperature and radical rich regioncan be seen in the temperature and OH contoursin Figs. 7–9(a–c). The effect of the plasma source(Case 7) is limited to a small region in the recircu-lation zone and the flow field (inset vector plots) isnot significantly affected (Fig. 7a and b). How-ever, when a uniform magnetic field is applied(Case 8), it creates a significant body force effectthat changes the flow field (Fig. 7c, inset). Itappears that the shock strength is weakened andtherefore, fuel penetration and fuel–air mixingincreases. The spanwise views (Fig. 9a–c) clearlyshow increased concentration of OH (also otherradicals, not shown) with the arc turned on, andeven more formation when the external magneticfield is included.

To explain these observations, Fig. 10 shows aschematic of the various processes and forces(albeit in a time-averaged sense) based on the inter-pretation of the current results in order to empha-size the MHD flow control aspect of this case. Dueto the curvature of the electric current, the

Fig. 9. Comparison of OH mass fraction contours onthe x–z cross section at Y =H ¼ 0:33 for Cases 6–8.

Fig. 10. Schematic of the flow around the step cornewith an applied magnetic field and electrical dischargewith the resulting Lorentz forces.

K. Miki et al. / Proceedings of the Combustion Institute 32 (2009) 2413–2420 2419

r

Fig. 11. (a) OH mass fraction and (b) magnitude obaroclinic torque at various downstream locationsSection A–A: x ¼ 1 mm, Section B–B: x ¼ 7:5 mm, andSection C–C: x ¼ 12:5 mm.

direction of the Lorentz force changes and it cre-ates a recirculation bubble upstream of the stepcorner acting with an upward force to shift theshear layer upward (inset Fig. 7c). By shifting theshear layer, the fuel penetration depth increasesby approximately 20%, and more of the freestreamair is mixed with the fuel leading to increased com-bustion and heat release. Increase in T and radical

concentration (e.g., OH) in the recirculation zone(Figs. 7, 8c), as well as further downstream(Fig.11a) can be clearly seen. MHD effect mani-fests itself as a strong local baroclinic torque(rp �rq=q2) in the near field shear layer, asshown by the time-averaged profiles of its magni-tude in Fig. 11b. It is well known that this forceeffect can increase vorticity strength and hencecan impact turbulent mixing.

Finally, Fig. 12 shows the mole fractions ofminor species along the centerline at the step heightfor Case 8. The large concentration of electronsindicates the location of the plasma source. Anincrease in charged species is seen, which recombineinstantly downstream. The region of zero H speciescorresponds to the location of the fuel injection.

The non-zero NO radical mole fractionslocated behind the fuel injector is a result of span-wise entrainment of hot products. From thesesimulations, an insight into plasma-assisted mix-ing and combustion can be obtained. Overall,the effect of the plasma (as simulated here) islimited to the near-field of the plasma source withsignificant impact on fuel–air mixing and combus-tion. Further studies are still needed to fully inves-tigate the plasma effect for a range of Ma and isdeferred to a future effort. Studies are alsorequired with improved subgrid closure for thereaction kinetics to confirm these observations.However, the current results are consistent with

f,

Fig. 12. Mole fractions of minor species along thecenterline at Y =H ¼ 1:0 for Case 8.

2420 K. Miki et al. / Proceedings of the Combustion Institute 32 (2009) 2413–2420

past experimental observations and therefore,provides confidence that simulations such as thesecould be used to understand the physics ofplasma-assisted combustion in supersonic flow.

5. Conclusions

Operational scramjet at high flight Ma willrequire efficient fuel–air mixing and combustionat high combustor Ma much larger than whathas been demonstrated in the laboratory. Sincephysical modifications of the combustor and/orfuel injection strategy as a function of Ma toachieve optimal performance is not practical, avirtual approach is explored here. In particular,a LES study of a plasma source in the recirculat-ing zone to control and enhance fuel–air mixing isreported here using a new MHD-LES approachthat has no ad-hoc adjustable constants. It isobserved that an electrical discharge creates a hightemperature and a radical rich concentrationregion in the recirculation zone that aids in igni-tion and flame-holding. When an uniform mag-netic field is applied, mixing is significantlyenhanced since the shock structure ahead of thefuel jet is weakened and fuel penetration into theair crossflow is increased. Further studies on thedependence of the location, intensity and type ofelectrical discharge on scramjet combustion per-formance will be reported in the future.

Acknowledgments

This research is supported by NASA/GRCand U.S. Air Force Office of Scientific Research.The second author is supported by the National

Science Foundation under a Graduate ResearchFellowship.

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