A numerical method for DNS of turbulent reacting flows using complex chemistry

Transcription

1 4nd AIAA Fluid Dnamics Conference and Ehibit 5-8 June 01, New Orleans, Louisiana AIAA A numerical method for DNS of turbulent reacting flows using comple chemistr Rajapandian Asaithambi, Suman Muppidi and Krishnan Mahesh Aerospace Engineering and Mechanics, Universit of Minnesota, Minneapolis, MN , USA A novel compressible Navier-Stokes solver for chemicall reacting flows is proposed with an eplicit Navier-Stokes predictor step and a semi-implicit corrector step for stiff chemical source terms. A modular code to read chemical mechanisms in the Chemkin format is coupled to the solver allowing the abilit to simulate multiple fuels with minimal effort. This segregated approach allows the independent modification of the Navier-Stokes solver and the chemical source term integration algorithm. Validation of a well-stirred reactor, an unstead unstrained diffusion flame, and results from a lifted non-premied flame in vitiated coflow in two and three dimensional configurations are presented. I. Introduction Combustion is central to man applications, including automotive and gas turbine engines, and various burners. These applications involve turbulent transport of various species which directl affects the chemical process and it is imperative that accurate numerical simulations reliabl capture this interaction. The design of the net generation of engines aimed at efficient combustion and reduced pollutants such as NO can benefit from these high-fidelit computations. Simulations of combustion using Renolds Averaged Navier Stokes (RANS) equations are computationall efficient but ma not be accurate enough for turbulent reacting flows. 1 Large Edd Simulations (LES) and Direct Numerical Simulations (DNS) are ver accurate but require suitable numerical techniques while also being computationall epensive. We are developing the capabilit to perform DNS/LES of turbulent reacting flows in comple geometries. The challenge in simulating turbulent reacting flows arises from the stiffness imposed b chemical time scales in addition to the turbulent length scales and etra species equations. In Doom, Hou and Mahesh the species source term was linearized and made semi-implicit which allowed the stiffness from chemistr to be vastl reduced, allowing the reduction of the time step t b a factor of 10 5 for hdrogen chemistr. The algorithm was then applied to autoignition of hdrogen vorte rings in Doom & Mahesh. 3 The solver is an implicit projection-based method for all Mach numbers. An unstructured eplicit solver derived from Park & Mahesh 4 has been used in ver large comple geometries, includes a robust modified least squares flu reconstruction, a shock-capturing scheme and subgrid-scale modelling. We propose a hbrid densit based approach where we retain the eplicit method of Park & Mahesh 4 for advection and diffusion and integrate the chemical source term using the semi-implicit method of Doom, Hou & Mahesh. The species equation is solved in two steps with advection-diffusion being the eplicitl advanced predictor step. The linearized chemical source terms are solved implicitl in the corrector step b iterating till convergence is obtained. The implicit step does not affect an spatial operator and therefore does not suffer from the computational overhead that full implicit methods do. This algorithm is suited for high speed subsonic reacting flows where the viscous wall limitations are not encountered such as jets. In addition, a new chemistr module is designed to read in detailed Chemkin input files and automaticall linearize source terms. This allows us to plug in arbitrar reaction mechanisms to the code and obtain results for various fuel/oidizer combinations. With access to tabulated thermodnamic properties, chemical species can have realistic heat capacities as a function of temperature. Graduate Research Assistant, Aerospace Engineering and Mechanics, Universit of Minnesota, AIAA Student Member Research Associate, Aerospace Engineering and Mechanics, Universit of Minnesota, AIAA Member Professor, Aerospace Engineering and Mechanics, Universit of Minnesota, AIAA Associate Fellow 1 of 1 Copright 01 b Rajapandian Asaithambi. Published b the, Inc., with permission.

2 To demonstrate the algorithm we simulate a categor of flames that has been the focus of etensive eperimental and numerical stud. The eperimental flames designed b Cabra et al., 5 Dall et al., 6 Mastorakos et al. 7 and Oldenhof et al. 8 autoignite, where no eternal heat source is necessar to initiate combustion. These eperiments were inspired b compression engines, where there is a need to understand the ignition of fuel jets when injected into a hot oidizer. These flames pose a challenge to current modelling techniques 9 and DNS of such flames could help better understand the turbulence-chemistr interaction and aid the development and validation of models. II. Numerical Details II.A. Governing Equations The governing equations for an ideal thermall perfect gas are written down below. The energ equation is written for the total chemical energ and therefore the equation does not have an eplicit chemical heat release term. ρ d t d + ρud j d j = 0 (1) ρ d Y k t d + ρd Y k u d j d j ( ) = d ρ d Dk d Y k j d + ω k d () j where g d i t d + gd i ud j d j = pd d j ρ d Et d t d + ( ρ d d Et d + p d) u d j = τ ij d ud i j d j τ d ij = µ d ( u d i d j + ud j d i + τ d ij d j ( ) + d k d T d j d j ) u d k 3 d δ ij k (3) (4) (5) E d t = e d t + ud i ud i = h d t p d /ρ d + ud i ud i (6) h d t = T d T d o c d p(y k, T d )dt d + n h o f,kd Y k (7) The superscript d is used to denote dimensional quantities. We can non-dimensionalize these equations with reference quantities denoted with the subscript r as follows: t = td, = d, ρ = ρd, u i = ud i, g i = L r /u r L r ρ r u r k=1 gd i, µ = µd, p = pd ρ r u r µ r ρ r u, T = T d, ω k = r T r L r ρ r u r ω d k (8) R = Rd, W = W d, c p = cd p, h = hd, M r = u r, p r = ρ r R r T r, R r = R univ, c r = γ r R r T r (9) R r W r R r R r T r c r W r Re = ρ ru r L r, Sc k = µd µ r ρ d Dk d, P r = µd c d p k d (10) The reference quantities that need to be chosen are a length scale L r, a velocit scale b choosing M r and the thermodnamic properties: pressure p r, temperature T r, and viscosit (b choosing Re) based on a reference miture Y kr. The non-dimensional form of the equations are now written down: of 1

3 II.B. ρe t t ρy k t ρ t + ρu j = 0 j (11) + ρy ( ku j 1 = µ Y ) k + ω k j ReSc k j j (1) g i t + g iu j j + j (ρe t + p) u j = The non-dimensional equation of state is: Numerical Method = p + 1 τ ij (13) j Re j 1 τ ij u i 1 + Re j γ r Mr ReP r j ( µc p T j ) (14) ρt = γ r M r pw (15) The algorithm is a second order scheme in space and time, and colocated allowing the method to be applied for a structured or unstructured finite volume grid. Smmetric average flu reconstruction, as described b Park & Mahesh, 4 of cell centered variables is used to obtain the values at faces in the structured solver whereas the unstructured solver uses the modified least-square method. Time advancement of the equations is dealt with a two step predictor-corrector method. The advection and diffusion terms are advanced using a second-order eplicit Adams-Bashforth scheme. The stiff chemical source terms emplo a second-order semi-implicit discretization as described in Doom & Mahesh. The following equations are eplicitl solved in the predictor step: ρe t t ρy k t g i t = 1 V f = 1 V f faces ρ t = 1 V f = 1 V f faces faces faces ρ f v n A f (16) [ ρf Y k,f v n + J k,f n k ] Af (17) [g i,f v n + p f n i 1Re τ ik,f n k ] A f (18) [(ρe t + p) v n 1Re τ ik,f u i,f n k Q k,f n k ] A f (19) These equations are solved with the following Adams-Bashforth time discretization and we get the densit ρ, mass fractions Ŷk, momentum g i and total chemical energ ρe t for all the cells at time (t + 1). q n+1 = q n + t [ 3 rhs n (q) rhs n 1 (q) ] (0) Note that the species equation is solved without the source term ω k and thus the eplicit step gives us ρŷk. This predicted species densit has to be corrected to include the effect of chemical reactions from the source term ω k. The stiff chemical source terms are linearized to make this term implicit which is then iterativel solved. The source term onl affects the species equations; the mass, momentum and energ are not affected and this allows us to decouple the source term in a special wa. Since the quantities ρ t+1, g t+1 i and Et t+1 are alread known, we can obtain the chemical energ e t+1 t. The change in species concentrations due to the chemical source terms therefore is an ordinar differential equation with the constraint e t+1 t that the new mass fractions Y t+1 k and T t+1 have to obe. The correction for source terms is written: (ρy k ) t+1,p (ρŷk) t+1 ) t = ω k ((ρy k ) t, (ρy k ) t+1,p, (T ) t, (T ) t+1,p ) = ( ω k ) L (ρy k ) t+1,p + ( ω k ) R (1) 3 of 1

4 The linearization of ω k is done in a separate code module which parses Chemkin mechanism and thermodnamic data files and computes linearized source terms. The two equations we need to iterativel solve in the corrector step are: (ρy k ) t+1,p = (ρŷk) t+1 + t( ω k ) R 1 + t( ω k ) L () T t+1,p = f 1 (e t t+1, Y k t+1,p ) (3) This step ields the final species mass fractions and temperature at the new time step (t + 1). The enthalp necessar to calculate e t is obtained directl from thermodnamic propert tables as a function of temperature and species concentrations. Since e t and h t are both purel functions of temperature and species composition and we are tring to estimate the temperature from equation 3, this step involves a mutlivariate root finding method. Halle s method is used for its faster convergence as compared to Newton-Raphson. III. Results The algorithm is applied to four closel related problems with a logical progression in compleit. The first is a well-stirred reactor, without an spatial variations: a zero-dimensional problem with evolution in time onl. The equations reduce to a set of ordinar differential equations and this serves as a validation for the chemical source terms. The results are compared with Chemkin for two different fuels. The second problem is an unstead unstrained one-dimensional diffusion flame which couples chemistr with spatial variation. The last two problems are a two-dimensional jet flame and a three-dimensional round jet flame. The two-dimensional jet serves as a useful tool to understand and evaluate the behavior of various fuels and is computationall cost-effective. The three-dimensional round jet can however directl address eperimental studies. Note: All problems in this paper implicitl take the fuel inlet conditions to be the reference miture at Mach number, M r = 1, temperature T r = 98K and pressure p r = 1atm. The reference length scale is L r = 0.005m which is representative of the problems that will be presented below. The jet diameter (for D and 3D) is thus taken to be 5mm. All quantities are non-dimensional unless units are eplicitl noted. III.A. Well Stirred Reactor Temperature H Temperature CH E-05 4E-05 6E-05 8E time(s) E-06 1E E-05 Time (s) Figure 1. H Air Mueller Mechanism. Figure. CH 4 Air GRI-Mech. The well-stirred reactor (0D combustion) is a temporall accurate solution to a set of initial conditions and the miture reaches an equilibrium temperature. A hdrogen-air miture at 1500K and a methaneair miture at 500K, both at stoichoimetric ratios and atmospheric pressure, are simulated. In figures 1 and, the results obtained (straight lines) are compared with Chemkin (dots) where we are able to get 4 of 1

5 ecellent agreement. The simulations use detailed reaction mechanisms for both fuels: hdrogen, which uses a 9 species, 19 reaction Mueller et. al. mechanism 10 and methane, which uses the full GRI-Mech mechanism with 53 species and 35 reactions. This demonstrates the black-bo abilit of the chemistr module to solve a wide range of chemical mechanisms. In the jet flames described further below we use this fleibilit to stud three different fuels in the same configuration. III.B. One-dimensional unstead unstrained diffusion flame (a) Temperature (b) Y O (c) Y HO Figure 3. Comparison of 1D unstrained diffusion flame results from the structured ( ) and unstructed ( ) solvers. An unstead unstrained one-dimensional diffusion flame with cold fuel (H /N at T = 1) and hot oidizer (Air at T = 4) on either ends allows autoignition of fuel at the interface. No numerical spark is needed to start the combustion, which quickl stabilizes into a diffusion flame and slowl evolves. The initial temperature and miture fraction curve is a profile given b: T () = T [ ( )] f T o 1 tanh + T o (4) 0.1 ζ() = ζ f ζ o [ 1 tanh ( 0.1 )] + ζ o (5) Table 1. Fuel T fuel T air Y fuel Y O Re H Initial conditions for the unstead one-dimensional flame. In figure 3, the red lines are the initial profiles and blue lines are the profiles at 0.1s. The initial mass fractions are 0.09 for hdrogen on the cold fuel end (left half) and 0.33 for ogen of the hot oidizer end (right half) and the rest filled up with nitrogen (Table 1). The mass fraction of H O peaks at 0.1 for the diffusion flame at t = 0.1s. After the autoignition phase, the production of H O is limited b diffusion of fuel and oidizer into the flame, thus slowl losing heat while epanding in thickness. III.C. Two-dimensional unstead reacting jet Etending the idea of an autoigniting flame to two dimensions leads to a jet in place of a diffusion flame. Cold nitrogen diluted fuel is injected into hot ambient air and this problem has practical applications from compression ignition engines to various combustors with hot product recirculation. The vitiated coflow burner 5 and the jet in hot coflow 6 burner are model flames to stud such applications. A cold fuel jet at M jet = 0.3 issues into heated air with a coflow at M co = 0.1. Three fuels: hdrogen, methane, and ethlene are simulated in a D slot-jet like geometr. The hdrogen jet uses the 9 species Mueller et. al. mechanism, 10 a 17-species skeletal mechanism 1 for methane and a -species reduced mechanism 13 for ethlene are chosen. Table below lists the inlet conditions for the jet and the coflow. The 5 of 1

6 jet and coflow velocities are same across the different fuels. The inlet velocit profile is given b the following equation with thickness δ = 0.01H: u in = u [ ( )] jet u coflow H/ 1 tanh + u coflow (6) δ Non-reflecting far field boundar conditions 14 are applied at the other three boundaries. The domain is 40D 40D in the stream-wise and span-wise direction. Figure 4 is a temperature contour plot of the three jets with a part of the domain is shown. The fuels show different behavior with hdrogen sustaining a stable lifted flame whereas the hdrocarbons onl ehibit small kernels of autoignition. The hotter coflow needed to ignite the hdrocarbons has the effect of reducing the coflow densit, which leads to thicker shear laers with reduced reaction rates. This effect was the reason to increase the Renolds number of the hdrocarbon jets to 700 from the original 3600 which increased roll-up and miing along the shear laer. Fuel T fuel T air Y fuel Y O Re U jet U c H CH C H Table. Fuels and their respective inlet conditions. In figure 5, an autoigniting kernel in each fuel jet is shown. The temperature contours (labelled T) identif the flame with a temperature much hotter than both the fuel and oidizer streams. Y OH, a species that can be measured in eperiments, is a much better indicator of the flame location. Similar correlation with the flame is also observed for the major combustion products Y HO, Y CO. Y CO is shown for the ethlene flame as it also a species measured in eperiments and plas a role in hdrocarbon oidation. The fuel contours show a local depletion at the flame location. Y HO for the hdrogen kernel has high concentrations surrounding the kernel but not inside it, this species breaks down in high temperature zones but plas an important role b aiding formation of intermediates at lower temperatures. For the hdrogen-air jet, a scatter plot of temperature against the miture fraction (at ever computational volume) over different regions of the computational domain is shown in figure 6. Towards the left half of the domain, < 0H, figure 6(a) shows the absence of an chemical reaction. Figure 6(b) roughl corresponds to the location of contours shown in figure 5 (a) depicting the autoignition of fuel; note that autoignition appears to begin at lean, relativel hotter regions of the flow, the most reactive miture fraction ζ mr, 15 and the reaction then spreads to the fuel-rich regions (as observed in figure 6(c)). Figure 6(d), corresponding to the right half of the domain, indicates that the lean miture is completel burnt (noted b high temperature) and that the domain contains a significant amount of unburnt, fuel-rich region. An interesting aspect of this lifted flame is the flame base dnamics at the center of the domain. Here, the flame front appears to leapfrog a vorte pair upstream of it, and while it grows hotter it also gets advected downstream before it makes the jump again over the net pair of vortices. Figure 7 illustrates this process with a sequence of frames from τ j = 180 to τ j = 195, where τ j is the non-dimensional time taken for the jet to cover one jet diameter. The corresponding Y HO contours reveals more about this peculiar leapfrogging. There is a high concentration of Y HO radicals, an indicator of autoignition, 9 along the shear laers of the jet well. This is well ahead of the temperature rise from the flame. This indicates that the isothermal chemical runawa process has begun but the thermal runawa is simpl waiting to happen. The high shear along the vortices edges epose these radicals to the much hotter coflow which could initiate thermal runawa. The scatter plots from figure 6 are consistent with this eplanation that leads to the lean hot mitures igniting first. A similar mechanism was found to pla a role in a turbulent autoigniting lifted slot jet simulation. 16 III.D. Reacting round jet The round jet is ubiquitous and a reacting round jet finds its place in a lot of applications, from Bunsen burners and blowtorches to fuel injectors in various combustion chambers. Hence the abilit to perform round jet simulations is essential to address most real flames. The eperiment b Cabra et. al. 5 serves as a reference for the following simulation which was carried out at a lower Renolds number. The jet inlet velocit is specified with the hperbolic tangent function given b 6 of 1

7 H (a) CH 4 (b) C H 4 (c) Figure 4. Normalized temperature contours for (a) H, (b) CH 4, and (c) C H 4 ranging from 1 to 8, corresponding to blue and red respectivel. The bo highlighting autoigniting flame kernels is shown in detail in Figure 5. 7 of 1

8 T YOH YH YH O YHO T YOH YCH4 YCO YH O T YOH YC H4 YCO YCO (a) (b) (c) Figure 5. Autoigniting flame kernels for (a) H, (b) CH4, and (c) C H4. (a) = [0, 0] (b) = [0,.5] (c) = [.5, 5] (d) = [5, 40] Figure 6. Scatter plot of temperature against miture fraction at various intervals of (in units of jet width H). The autoignition of H at lean conditions is evident in (b) and (d) indicates that the lean mitures have completel burnt, while there is still unburnt rich fuel indicated b the thick line at the bottom right corner. 8 of 1

9 τ j = 180 τ j = 183 τ j = 186 τ j = 189 τ j = 19. τ j = 195 (a) Figure 7. Temporal evolution of (a) temperature and (b) Y HO at the base of the lifted H Air flame from τ j = 180 to τ j = 195. (b) 9 of 1

10 u in = u [ jet u coflow 1 tanh ( r D/ δ )] + u coflow (7) For this calculation, δ = 0.01D. The Renolds number of the jet is Re jet = 700 and the domain size is 40D 40D 40D. Non-reflecting boundar conditions 14 are applied at the side and eit boundaries. Turbulent fluctuations (in the form of homogeneous isotropic turbulence) are not added to the inlet, as is commonl done in DNS studies of turbulent autoigniting flames. 16 Improved transport properties are taken into account with viscosit modified b temperature, modelled with a power law, µ/µ = (T/T ) 0.67, and the different species are allowed to have different Schmidt numbers. 17 The effect of Lewis numbers on hdrogen flames is important and can affect autoignition times and intensities. 3, 18 This simulation took a total of 0.3 million cpu-hours and was run on 104 cpu-cores for 1.5 das for 1 flow-through time of the domain. At these conditions, a laminar flame close to the inlet is observed. Figures 8(a) and 8(b) show the contours of temperature and Y OH which are correlated with a lifted flame height of = 4D. Y HO in 8(c) however is leading the flame b almost one jet diameter, again indicating an autoignition based flame stabilization. Figure 9 illustrates an instantaneous cutawa of isosurfaces and we can see the substantial buildup of Y HO radicals followed b the temperature increase. A plausible reason for this flame remaining laminar in spite of the high Renolds number can be down to the high viscosit of the hot coflow. The effect of hdrogen s low Lewis number also leads to faster ignition 3 and further increases the temperature and hence viscosit downstream of the flame. This effect is also clear in figure 8(d) where the miture fraction shows increased diffusion downstream of the flame anchor location. (a) (b) (c) (d) Figure 8. Contour plots of (a) Temperature, (b) Y OH, (c) Y HO, and (d) Miture fraction ζ for the round jet. Flow Figure 9. Flame cutawa superposing the two sets of isosurfaces, the bluish-gra isosurfaces of Y HO positioned below the orange temperature isosurfaces indicate that the flame is stabilized b autoignition. 10 of 1

11 IV. Summar and future work Ongoing work on the development of an algorithm to solve turbulent reacting flows is presented. The semi-implicit source term discretization mollifies the stiffness associated with the chemical source terms while simultaneousl allowing eplicit methods for advection and diffusion. This segregated formulation allows us to independentl modif the compressible Navier-Stokes, species and chemical source term parts of the complete solver. Colocated variable storage allows this algorithm to be etended to structured and unstructured formulations seamlessl. The chemical mechanism module allows us to simulate multiple fuels easil and the simulations in this paper demonstrate this capabilit. Future work includes the simulation of the eperimentall observed autoigniting flames at identical laborator conditions. The unstructured solver 4 has been used for preliminar non-reacting simulations of a scramjet inlet geometr (figure 10, based on the eperiments b Gamba et al 19 ). High fidelit simulations of (detailed-chemistr) reacting turbulent flow in this geometr will provide ver useful understanding of issues pertinent to scramjet engines. (a) (b) Figure 10. (a) Isometric visualization of non-reacting flow in a scramjet inlet geometr at M =.9. Figure shows the computational domain, and contours of ω z on the top and bottom walls, contours of vorticit magnitude on the end planes. (b) Contours of (top) temperature, and (bottom) passive scalar concentration on the smmetr plane. Note that the flow features include a jet in crossflow, shock-boundar laer interaction, and a transition to turbulence. Acknowledgements Computer time for the simulations was provided b the Minnesota Supercomputing Institute (MSI). References 1 Vervisch 1, L., Hauguel, R., Domingo, P., and Rullaud, M., Three facets of turbulent combustion modelling: DNS of premied V-flame, LES of lifted nonpremied flame and RANS of jet-flame, Journal of Turbulence, 004, pp. N4. Doom, J., Hou, Y., and Mahesh, K., A numerical method for DNS/LES of turbulent reacting flows, Journal of Computational Phsics, Vol. 6, No. 1, 007, pp Doom, J. and Mahesh, K., Direct numerical simulation of auto-ignition of a hdrogen vorte ring reacting with hot air, Combustion and Flame, Vol. 156, No. 4, 009, pp Park, N. and Mahesh, K., Numerical and modeling issues in LES of compressible turbulent flows on unstructured grids, AIAA Paper 007 7, Cabra, R., Mhrvold, T., Chen, J. Y., Dibble, R. W., Karpetis, A. N., and Barlow, R. S., Simultaneous laser ramanraleigh-lif measurements and numerical modeling results of a lifted turbulent H/N jet flame in a vitiated coflow, Proceedings of the Combustion Institute, Vol. 9, 00, pp Dall, B. B., Karpetis, A. N., and Barlow, R. S., Structure of Turbulent Nonpremied Jet Flames in Hot Dilute Coflow, Proceedings of the Combustion Institute, Vol. 9, 00, pp of 1

12 7 Mastorakos, E., Markides, C., and Wright, Y. M., Hdrogen autoignition in a turbulent duct flow: Eperiments and Modelling, Conference on Modelling Fluid Flow, Oldenhof, E., Tummers, M., van Veen, E., and Roekaerts, D., Ignition kernel formation and lift-off behaviour of jet-inhot-coflow flames, Combustion and Flame, Vol. 157, No. 6, 010, pp Mastorakos, E., Ignition of turbulent non-premied flames, Progress in Energ and Combustion Science, Vol. 35, No. 1, 009, pp Mueller, M. A., Kim, T., Yetter, R. A., and Drer, F. L., Flow Reactor Studies and Kinetic Modeling of the H/O Reaction, International Journal of Chemical Kinetics, Vol. 31, 1999, pp Smith, G. P., Golden, D. M., Frenklach, M., Moriart, N. W., Eiteneer, B., Goldenberg, M., Bowman, C. T., Hanson, R. K., Song, S., Gardiner, W. C., Jr., V. V. L., and Qin, Z., mech/. 1 Sankaran, R., Hawkes, E., Chen, J., Lu, T., and Law, C., Structure of a spatiall developing turbulent lean methane air Bunsen flame, Proceedings of the Combustion Institute, 007, pp Wang, H., Personal communication, Poinsot, T. J. and Lele, S. K., Boundar conditions for direct simulations of compressible viscous flows, Journal of Computational Phsics, Vol. 101, 199, pp Mastorakos, E., Baritaud, T., and Poinsot, T., Numerical simulations of autoignition in turbulent miing flows, Combustion and Flame, Vol. 109, No. 1, 1997, pp Yoo, C. S., Sankaran, R., and Chen, J. H., Three-dimensional direct numerical simulation of a turbulent lifted hdrogen jet flame in heated coflow: flame stabilization and structure, Journal of Fluid Mechanics, Vol. 640, 009, pp Hawkes, E. R. and Chen, J. H., Direct numerical simulation of hdrogen-enriched lean premied methane-air flames, Combustion and Flame, Vol. 138, 004, pp Doom, J. and Mahesh, K., DNS of auto-ignition in turbulent diffusion H /air flames, Gamba, M., Miller, V. A., Mungal, G., and Hanson, R. K., Ignition and Flame Structure in a Compact Inlet/Scramjet Combustor Model, AIAA Paper , of 1