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Direct numerical simulation of turbulence/radiationinteraction in premixed combustion systems

Y. Wua, D.C. Hawortha,*, M.F. Modesta, B. Cuenotb

a Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, PA, USAb Centre Europeen de Recherche et de Formation Avancee en Calcul Scientifique, Toulouse, France

Abstract

An important fundamental issue in chemically reacting turbulent flows is turbulence/radiation interac-tion (TRI); TRI arises from highly nonlinear coupling between temperature and composition fluctuations.Here, a photon Monte Carlo method for the solution of the radiative transfer equation has been integratedinto a turbulent combustion direct numerical simulation (DNS) code. DNS has been used to investigateTRI in a canonical configuration with systematic variations in optical thickness. The formulation allowsfor nongray gas properties, scattering, and general boundary treatments, although in this study, attentionhas been limited to gray radiation properties, no scattering, and black boundaries. Individual contributions

to emission and absorption TRI have been isolated and quantified. Of particular interest are intermediatevalues of optical thickness where, for example, the smallest hydrodynamic and chemical scales are opticallythin while the largest turbulence scales approach an optically thick behavior. In the configuration investi-gated, the temperature self-correlation contribution (emission) is primarily a function of the ratio ofburned-gas temperature to unburned-gas temperature, and is the dominant contribution to TRI only inthe optically thin limit. Even in the most optically thin case considered, the absorption coefficientPlanckfunction correlation and absorption coefficientintensity correlation are not negligible. At intermediate val-ues of optical thickness, contributions from all three correlations are significant. 2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Keywords:Turbulence/radiation interaction; Direct numerical simulation; Photon Monte Carlo method

1. Introduction

Thermal radiation often is a dominant mode ofheat transfer in practical turbulent combustionsystems. By contrast to conduction and convec-tion, consideration of thermal radiation leads toan integral equation in up to six independent vari-ables; radiative heat transfer rates vary stronglywith temperature differences (to the fourth or

higher power); and the radiation properties ofcombustion gases exhibit strong and irregularvariations with wavenumber[1]. For these reasonsand others, radiation has often been neglectedaltogether or has been treated using simple models(e.g., an optically thin approximation) in combus-tion applications.

The importance of interactions between turbu-lence and thermal radiation (turbulence/radiationinteractionTRI) has long been recognized[26].

TRI arises from highly nonlinear coupling be-tween temperature and composition fluctuationsin both nonreacting and reacting turbulent flows.

1540-7489/$ - see front matter 2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved.doi:10.1016/j.proci.2004.08.138

* Corresponding author. Fax: +1 814 865 3389.E-mail address:[email protected](D.C. Haworth).

Proceedings of the Combustion Institute 30 (2005) 639646

www.elsevier.com/locate/proci

Proceedingsof the

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In this respect, it is akin to the turbulence/chemis-try interaction[7] that has been the subject of in-tense research for many years. It has been shownto result in significant increases in overall heattransfer, significant reductions in local tempera-ture, and consequently in significant changes in

key pollutant species (particularly NOx and soot)in both luminous and nonluminous turbulentflames (e.g.,[4,6,816]). TRI effects can be compa-rable to those resulting from turbulence/chemistryinteraction. Yet, TRI modeling has received rela-tively little attention to date.

Direct numerical simulation (DNS) hasbecome an accepted tool for generating new fun-damental insight into turbulence/chemistry inter-action (e.g., [17,18]). Here, DNS is used toexplore turbulence/radiation interaction in ideal-ized systems. The goals are to develop new funda-mental physical insight and to provide guidancefor model development. The nature of turbu-lence/radiation interaction is discussed in Section2. The model problem is outlined in Section 3.Numerical methods are briefly described in Sec-tion 4, and results and discussion are providedin Section 5. Conclusions and next steps are sum-marized in the final section.

2. Turbulence/radiation interaction in chemicallyreacting flows

The radiation source term in the instantaneousenergy equation can be expressed as the diver-gence of the radiative heat flux~qrad,

r ~qrad

Z 10

jg 4pIbg

Z4p

Ig dX

dg

4jPrT4

Z 10

Z4p

jgIg dXdg; 1

where

jP R1

0 jgIbg dgR10 Ibg dg

p

rT4Z

1

0

jgIbg dg 2

is the Planckmean absorption coefficient and r isthe StefanBoltzmann constant. Here, g denotesthe wavenumber, X is the solid angle, jg is thespectral absorption coefficient, Ibg is the Planckfunction (a known function of local temperatureand wavenumber), and Ig is the spectral radiativeintensity. Intensity is determined from the radia-tive transfer equation (RTE)[1]:

dIgds

s rIg jgIbgbgIg

rsg

4p

Z4p

IgsiUgsi;s dXi: 3

Here, sand si denote unit direction vectors, rsgisthe spectral scattering coefficient, bg=jg+rsg isthe spectral extinction coefficient, and Ugsi;s

denotes the scattering phase function; the latterdescribes the probability that a ray from incidentdirection si is scattered into direction s. The localvalue ofIg depends on nonlocal quantities, direc-tion s, and wavenumber.

The first term on the right-hand side of Eq.(1)

corresponds to emission and the second toabsorption. TRI is brought into evidence by tak-ing the mean of Eq.(1):

hr ~qradi

Z 10

4phjgIbgi

Z4p

hjgIgi dX dg

4rhjPT4i

Z 10

hjgGgi dg; 4

where, angled brackets denote mean quantities,

and the direction-integrated incident radiationGg R

4pIg dX has been introduced.

In the emission term, TRI appears as a correla-tion between the spectral absorption coefficientand the Planck function or, equivalently, betweenthe Planckmean absorption coefficient and thefourth power of temperature: hjPT

4i hjPihT

4i hj0P T40i, where, a prime denotes a

fluctuation about the local mean. Emission TRIcan be decomposed to consider separately thetemperature self-correlation (T4 T4) and theabsorption coefficientPlanck function correla-tion. Radiative emission including TRI appearsin closed form in one-point probability densityfunction (PDF) approaches[11,12]. Li and Mod-est[12]used a PDF method to examine individualcontributions of various correlations to TRI inturbulent nonpremixed flames.

In the absorption term, TRI appears as a cor-relation between the spectral absorption coeffi-cient and the spectral intensity (or incidentradiation),hjgGgi hjgihGgi hj

0gG

0gi. A dimen-

sionless optical thickness is introduced, jgL,where, L is a length scale. In the optically thineddy approximation (jgL1), fluctuations injg (a local quantity) are assumed to be uncorre-lated with those in Gg (a nonlocal quantity), sothat jgGgjg Gg. At the other extreme(jgL1), the optical thickness may be largecompared to all hydrodynamic and chemicalscales. In that case, fluctuations in intensity aregenerated locally and would be expected to be cor-related strongly with those of the absorption coef-ficient. Between these extremes are cases where,the smallest scales (Kolmogorov microscalesand/or flame thickness) are optically thin whilethe largest (integral scales) are optically thick.

The physics and modeling of optically thick ed-dies is an outstanding issue in TRI and is a pri-mary motivation for this research.

Experimental measurements (e.g., [8,9]), theo-retical analysis (e.g., [10]), and computationalstudies (e.g.,[4,1115]) have quantified the impor-

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tance of TRI in several turbulent reacting flows. Ithas been shown that radiative emission from aflame can be 50% to 200% higher than would beexpected based on mean values of temperatureand absorption coefficient, and that local gas tem-peratures can be reduced by as much as 200 C

with TRI compared to radiation heat transferwithout TRI. Until recently, it had generally beenaccepted that TRI effects should be small innonsooting flames. However, recent studies haveshown significant influences on temperature andheat transfer even in nonluminous flames. Forexample, Li and Modest [12]reported a decreasein computed peak temperature of over 100Cwith TRI for an atmospheric-pressure laborato-ry-scale nonpremixed methaneair flame, andCoelho [14] reported a nearly 50% increase incomputed radiative heat loss due to turbulent fluc-tuations for a similar flame configuration.

In the present study, we explore TRI in a sta-tistically one-dimensional turbulent premixed sys-tem using DNS. The principal quantitiesexamined are the normalized means RT4 , RjIb ,and RjG,

RT4 hT4i

hTi4; RjIb

hjgIbgi

hjgihIbgi;

RjG hjgGgi

hjgihGgi; 5

and the correlation coefficients qjIb

and qjG,

qjIb hj0gI

0bgi

hj02gihI02bgi

h i1=2;

qjGhj0gG

0gi

hj02gihG02gi

h i1=2: 6In the absence of TRI, RT4 , RjIb , and RjGwouldbe equal to unity while qjG would be equal tozero. The departures of each quantity from thesevalues allow different contributions to TRI to be

isolated and quantified.

3. Physical models and computational configuration

A turbulent, compressible, chemically reacting,and radiatively participating ideal-gas mixture isconsidered. The continuity, linear momentum,chemical species, and energy equations have thesame form as in[17],with the addition of a thermalradiation source term in the energy equation. Thus,

oqetot

r qet p~uo

uisijoxj

r krT

Q _w r ~qrad: 7

Here,~u is the fluid velocity vector, q is the fluidmass density, p is the thermodynamic pressure,

sijare the components of the viscous stress tensor,Q is the heat of reaction per unit mass of freshmixture, and qet is the total energy density perunit volume, qetq~u~u=2p=c1, where, cis the (constant) ratio of specific heats.

Single-step irreversible finite-rate Arrhenius

chemistry is considered. The reaction rate is _

wBq~YRexp b1H=1a1H f g, where, His the reduced temperature, H= (TT1)/(T2T1), and subscript 1 refers to the freshgases and 2to the burned products (T2is the con-stant-pressure adiabatic flame temperature). Thecoefficients B, a, and b are, respectively, the re-duced pre-exponential factor, the temperature fac-tor, and the reduced activation energy, and ~YRis anormalized reactant mass fraction that variesfrom unity in the fresh gases to zero in the burnedgases. Standard molecular transport models(Newtonian viscosity, Fourier conduction, andFickian species diffusion) are employed where,the molecular transport coefficients (viscosity l,thermal conductivityk, and species diffusion coef-ficient D) are set such that the Prandtl number Prand Lewis numberLeare constant. Soret and Du-four effects are not included.

Here, the divergence of the radiation heat fluxis determined by solving the RTE, Eq.(3), using aphoton Monte Carlo method (Section 4). Radia-tion properties correspond to a fictitious graygas with Planckmean absorption coefficient,

jP CjYPY

c0 c1A

T

c2

A

T

2" c3

A

T

3c4

A

T

4c5

A

T

5#;

8

where,YP 1 ~YR is a normalized reaction pro-gress variable. Coefficients A and c0c5have beentaken from a radiation model suggested for watervapor [19], with the temperature rescaled to thecomputational temperature range. Here, Y is anarbitrary, small, positive threshold to ensure thatjP is nonzero everywhere, and Cj is a coefficient

that allows the optical thickness to be varied sys-tematically and independently of other parame-ters. For fixed values ofCj and YP, jP varies bymore than a factor of 10 over the temperaturerange of interest.

The governing equations are solved for astatistically one-dimensional turbulent premixedsystem. The configuration is periodic in the

y- and z-directions, and x is the direction of(mean) flame propagation (Fig. 1). An initial tur-bulence spectrum is prescribed using methods thathave been developed for earlier DNS studies

[17,20]. A one-dimensional premixed laminarflame profile is superposed on the initial turbu-lence field, and the system is allowed to evolvein time. Key parameters are the thermochemicalquantities (B, a, b, Pr, Le, c, and jP), the initialturbulence integral length scale l0 (the two-point

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longitudinal integral length scale,l11, or the wave-length of the most energetic eddies in the initialturbulence spectrum, Li[17]) and rms turbulencelevel u00, and the undisturbed steady one-dimen-sional laminar flame speed sland flame thicknessdl. Here,d lis based on the maximum temperaturegradient: dl(T2T1)/(dT/dx)max. Key dimen-sionless parameters are a turbulence Reynoldsnumber Re0 q1u

00l11=l1, the ratios u

00=sl and L i/

dl, and a Damkohler numberDa BD=s2lexpb=a. The values specified forthese quantities are similar to those used in [17]

(Table 1). A new dimensionless parameter is intro-duced to characterize thermal radiation: jP, 2 l11,the optical thickness based on burned-gas proper-ties and the initial turbulence integral length scale.

As the system evolves, u0 decays while l in-creases. For two-dimensional cases, the turbu-lence Reynolds number q1u

0l/l1 increases withtime. From earlier studies [17], it is known thatflame statistics become approximately stationaryafter two to three eddy-turnover times. Here thesystem is allowed to evolve for three eddy-turn-over times before the radiation model is activated.

The system then evolves for one additional turn-over time. Mean quantities are estimated by aver-aging over the y- and z-directions; these are thendisplayed as functions ofYP through the turbu-lent flame brush.

The present study follows earlier DNS workfor turbulence/chemistry interaction (e.g., [17])both in spirit and in form. Most of the simulationsare spatially two-dimensional. Previous studieshave shown relatively small differences betweentwo- and three-dimensional statistics when the fo-cus is on flame/turbulence interaction. This issuehas been discussed by Haworth and Poinsot [17].One three-dimensional case is included for com-parison (Table 1). The focus is on quantities[Eqs.(5) and (6)] that are expected to weakly de-pend on the specific configuration (initial and

boundary conditions, spatial two-dimensionality).The model problem is designed to allow system-atic variation in key dimensionless parameters(e.g.,Re0,Da, andjP, 2l11) and isolation of genericphysical effects.

4. Numerical methods

4.1. DNS of chemically reacting turbulent flows

Dimensionless forms of the conservation equa-

tions are solved. Temporal integration is per-formed with a RungeKutta method of orderthree; for spatial discretization, a compact schemeof order six is used in the interior of the computa-tional domain with various noncentered schemesnear boundaries[21]. Nonperiodic boundary con-ditions are enforced using the NavierStokesCharacteristics Boundary Conditions method[22]. Details of the equations, normalizations,and numerical methods (in the absence of thermalradiation) can be found in[20].

4.2. A photon Monte Carlo method for the solutionof the RTE

The RTE is solved by following the trajectoriesof a large number of representative photon bun-dles generated using statistical sampling tech-

Fig. 1. The computational configuration. (A) Instantaneous temperature isocontours after four eddy-turnover times forCase 4. The x boundary is a cold radiation boundary, and the +x boundary is a hot radiation boundary. (B)Instantaneous heat release Q _wafter four eddy-turnover times for Case 1.

Table 1Simulation parameters

Case Grid jP, 2l11 u00=sl Li/dl Re0

0 4512 0.0a 15.2 8.9 65.1 4512 0.1 15.2 8.9 65

2 4512 1.0 15.2 8.9 653 4512 10.0 15.2 8.9 654 1443 1.0 37.5 6.0 125

In all cases: Da50, a= 0.75, b= 8.0, Pr= 0.75,Le= 1.0, and c= 1.4.

a Baseline case without thermal radiation.


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niques. A general formulation has been imple-mented that allows for nongray gas properties,scattering, and a variety of boundary conditions.In the present study we limit our attention to grayradiation properties, no scattering, and blackboundaries. The general spectral formulation is

outlined as follows. A photon Monte Carlo meth-od for a participating medium consists of twoparts: an emission stage and a tracing/absorp-tion/scattering stage. Additional considerationsare required at boundaries of the computationaldomain. The approach that has been implementedessentially follows the method outlined in Chapter20 of Modest [1]. High-order schemes havingaccuracy commensurate with that of the underly-ing DNS code (up to sixth order in space) havebeen employed throughout.

4.2.1. EmissionEach photon bundle represents a specifiedfraction of the total emitted radiant energy, EV,and is characterized by six quantities: an emissionlocation (three spatial coordinates for volumeemission, two for surface emission), an emissiondirection (azimuth angle w, polar angle h), anda spectral variable (wavenumber g). These prop-erties are determined based on the probabilitiesof events in the reacting gas mixture. As anexample, emission locations are determined asfollows. First, the local Planckmean absorption

coefficient jP (a function of local temperature,pressure, and composition) is computed at eachgrid point. The total emission from the gas vol-ume V is then

EV

ZV

4jPrT4 dV

Z Lx0

Z Ly0

Z Lz0

4jPrT4 dzdydx: 9

The cumulative distribution functions (CDFs) ofemission along thex,y, andz directions are deter-mined sequentially as[1],

Rx

Rx0

RLy0

RLz0

4jPrT4 dzdydx

EV;

Ry

Ry0

RLz0

4jPrT4 dzdyRLy

0

RLz0

4jPrT4 dzdy

;

Rz

Rz04jPrT

4 dzRLz0

4jPrT4 dz

;

10

so that Rx, Ry, and Rz each lie between zero andunity. Inversion of Eq.(10)yields the emission po-

sition with Rx, Ry, and Rzeach sampled indepen-dently from a uniform distribution on [0, 1]:x= x (Rx), y= y (Ry, x), and z =z (Rz, x,y).

The emission wavenumber and propagationdirection are determined in a similar manner.Details can be found in [1,23].

4.2.2. Tracing, absorption, and scatteringThe energy of each photon bundle is attenu-

ated by volumetric absorption in the gas and byinteraction with surfaces; its direction may changeas a result of scattering. An energy-partitioningscheme [1] is employed for absorption, whereby

each bundles energy is attenuated along its trajec-tory until the energy becomes negligible or the

bundle hits a wall; bundles that strike a wallmay be partially reflected, partially transmitted,and partially absorbed. The absorbed energy is as-signed to computational grid points using high-or-der interpolation; this provides the radiationsource term in the energy equation. On scattering,a new propagation direction is determined fromthe CDFs of all possible directions.

4.2.3. Boundary conditions

In this study, three types of boundaries areconsidered for radiation (Fig. 1): periodic, cold,and hot. When a photon bundle reaches a peri-odic boundary, it re-enters the computational do-main through the opposite side with no change inproperties. A bundle that arrives at a cold bound-ary is absorbed; no photon bundles are emittedfrom a cold boundary. A hot boundary is treatedas a black surface: a bundle that arrives at a hotboundary is absorbed. Emission from a hotboundary is also considered using a two-dimen-sional analog of Eqs. (9) and (10).

4.2.4. Computational considerationsNumerical evaluation of Eqs. (9) and (10) in-

volves extensive spatial interpolation; and thisinterpolation dominates the computational effort.The interpolation order is determined locally andadaptively. For example, low-order interpolationsuffices in the reactants well ahead of the flameand in the burned gases well behind the flame.Spatial and temporal accuracy, statistical error,parallelism, adaptivity, and other computationalaspects are addressed in[23].

The computational effort increases in propor-tion to the number of photon bundles and theaverage distance that a bundle travels before beingabsorbed. For the cases reported here, radiationrequires approximately ten times the CPU timeof the underlying simple-chemistry DNS code.While this is significant, it is important to keepin mind the following. First, the photon MonteCarlo method provides an exact solution tothe RTE that is compatible with the philosophyof DNS. Alternative methods including sphericalharmonics and discrete ordinates invoke approx-

imations [1], and may prove to be equally inten-sive computationally to achieve the level ofaccuracy that is required for DNS. Second, con-sideration of more detailed chemistry (e.g., [24])implies little additional computational effort forradiation, while the CPU time for the underlying


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hydrochemical DNS would increase dramatically;chemical kinetics would then dominate the CPUrequirements. And third, the implementation isquite general. Nongray radiation properties, scat-tering, and solid particle (soot) radiation can beincluded with little additional computational

overhead.

5. Results and discussion

Emission TRI is examined first. The tempera-ture self-correlation factor RT4 is plotted as afunction of normalized mean reaction progressvariableYPinFig. 2. Results for the four two-di-mensional cases (Table 1) are essentially the same.Here, and in the following, mean profiles for two-dimensional cases have been smoothed slightly tocompensate for the limited information in one-di-mensional averages. While temperature self-corre-lation is considered to be a part of TRI, RT4 doesnot directly depend on radiation properties in thisconfiguration. In the limit of an infinitesimally

thin flame sheet, the probability of encounteringburned gases at any x location is YP (x), andthe probability of encountering unburned gasesis 1YP (x). In that case, T

4/T4 is given by,

RT4sheet hYPiT2=T1

4 1 hYPi

hYPiT2=T1 1 hYPi 4: 11

This quantity has been plotted as a function oftemperature ratio T2/T1 in Fig. 2. As T2/T1 in-creases from unity, the peak in RT4 sheet increasesand shifts toward the leading edge of the flame(smaller values of YP). The simulated flames(T2/T1= 4) have nonzero thickness and thereforelower values ofRT4 compared to those given byEq.(11). The two-dimensional DNS results lie be-tween the flamesheet results for T2/T1= 3 and T2/T1= 4; the three-dimensional DNS results (smal-ler Li/dl, Table 1) are close to the flamesheet re-

sults for T2/T1= 3.The quantities RjIb andqjIb are plotted inFig.

3. For the three two-dimensional cases (Cases 13), the values of these normalized quantities areessentially the same for all values of the opticalthickness; the small differences are not statisticallysignificant. That is because the values ofjP= jP (YP, T) for these three cases differ simplyby a multiplicative constant [Cj, Eq.(8)]. Largerdifferences result from changing the functionalform of jP (YP, T) (not shown). The peak valueofRjIb is between 7 and 8, and occurs close to

the leading edge of the turbulent flame brush; itthen decreases monotonically to unity throughthe flame. At the leading edge, qjIb jumps to unityfor all values of jP, 2l11 (perfect correlation be-tween jP and Ib); the correlation then decreasesmonotonically through the flame brush. Thus,even in the most optically thin case examined,the absorption coefficientPlanck function contri-bution to TRI is not negligible. Three-dimensionalresults (Case 4) are qualitatively similar to thetwo-dimensional results.

Absorption TRI is examined next (Fig. 4). The

approximation jPGjP G improves with

Fig. 2. Temperature self-correlation RT4 , Eq.(5), versusmean progress variableYPfor 2D Case 2 (dashed line)and 3D Case 4 (solid line). Also shown are valuespredicted using a flamesheet approximation [RT4sheet, Eq.

(11)] for several values ofT2/T1 (lines with symbols).

Fig. 3. Absorption coefficientPlanck function correlation factor RjIb (A) and correlation coefficient qjIb (B) versusmean progress variable YP for three values of the optical thickness.


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decreasing optical thickness, as expected. How-

ever, even in the most optically thin case examinedRjGranges from 0.8 to 1.1 through the flame brush.The correlation coefficient qjGgoes to zero in theburned gas and in the unburned gas for all valuesofjP, 2l11. The variation ofqjGthrough the flamebrush is essentially the same for the intermediateand large optical thicknesses; values are systemati-cally lower, but still nonnegligible, for the opticallymost thin case. Three-dimensional results (Case 4)are similar to two-dimensional results (Case 2) forthe same dimensionless optical thickness.

The present simulations are limited to low Reand a correspondingly narrow dynamic range ofscales. This is a fundamental limitation of finite-rate-chemistry DNS with heat release. While onemust exercise caution in extrapolating results topractical combustion systems, the favorable com-parison between DNS results and a simple flame-sheet model (Eq. (11), Fig. 2) suggests that thepresent DNS results should be relevant for highRe, high Dasystems.

6. Conclusion

Direct numerical simulation has been used toexplore turbulence/radiation interaction in an ide-alized premixed system. Three contributions toTRI have been isolated and quantified as a func-tion of optical thickness: temperature self-correla-tion, absorption coefficientPlanck functioncorrelation, and absorption coefficient-intensitycorrelation. Key findings are as follows:

Temperature self-correlation is primarily afunction of the temperature ratio in thisconfiguration.

Temperature self-correlation is the dominantcontribution to TRI only for the most opticallythin case. Even in that case, the absorptioncoefficientPlanck function correlation andabsorption coefficient-intensity correlation arenot negligible.

At intermediate values of optical thickness,

contributions from all three correlations aresignificant.

The importance of TRI and other radiationphenomena (e.g., nongray effects [13,25]) isbecoming increasingly evident for practical com-bustion systems. Here, a first step has been takentoward systematically isolating and quantifyingTRI effects using DNS. As always, one must exer-cise caution in extrapolating DNS results to apractical combustion systems. The model problemis highly idealized; in particular, the dynamicrange of length scales is small. DNS will continueto map out the influence of key dimensionlessparameters (e.g., Re, Da, and jL), to study theinfluence of the functional form of jP (YP, T), toexplore nongray-gas effects and soot radiation,to study alternative configurations (nonpremixedsystems, detailed chemistry, and transport), andultimately to assess and to calibrate models suit-able for engineering applications.

Acknowledgments

This work has been supported by the NationalScience Foundation under Grant No. CTS-0121573 and by the Air Force under Grant No.F49620-99-1-0290.

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Fig. 4. Absorption coefficientintensity correlation factor RjG (A) and correlation coefficient qjG (B) versus meanprogress variable YPfor three values of the optical thickness.


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Comment

S. Kumarau, Cabot Corporation, USA.The T-correc-tion induced by radiation inclusion in the DNS signifi-cantly changes the local burning velocity. What is theactual reduction in the burning velocity? What are theeffective burning rates across the flame front?

Reply. Radiative heat transfer modifies the temper-ature field, and thereby the local and global burning

velocities of the flame. In this initial DNS study, wehave not examined the effect of radiation on burningvelocity, but rather have focused on quantities ofinterest in modeling turbulence-radiation interaction.Ongoing DNS work will quantify the changes in tem-

perature and burn rates, among other local and glo-bal quantities of interest.

http://www.ca.sandia.gov/TNF/radiation.htmlhttp://www.ca.sandia.gov/TNF/radiation.html

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