Abstract It is of great theoretical interest to investigate the interaction between flames and vortices as a model problem to study turbulent combusti

Transcription

1 Reduced Kinetic Mechanisms in Time Dependent Numerical Simulations of Nonpremixed Flames JOSHUA HSU 1 and SHANKAR MAHALINGAM Joint Center for Combustion and Environmental Research Department of Mechanical Engineering University of Colorado at Boulder, Boulder, CO Paper 00S-12 March 13-14, 2000 Spring Meeting of the Western States Section of the Combustion Institute Colorado School of Mines, Golden, Colorado 1 Corresponding author: Department of Mechanical Engineering, University of Colorado at Boulder, Boulder, CO Phone: Fax: hsuj@colorado.edu

2 Abstract It is of great theoretical interest to investigate the interaction between flames and vortices as a model problem to study turbulent combustion because a field of turbulence can be considered as an ensemble of vortices of various length and time scales. Interaction between flames and vortices governs the rate of combustion and results in different types of instabilites. The goal of this study is to understand the limits of applicability of progressively more accurate reduced kinetic schemes for methane-air flames using time dependent numerical simulations in a two dimensional flow field. Nonpremixed one, three and four step reduced kinetic methane air flame structure and flame response to interaction between a pair of counter rotating vortices with an initially laminar unstrained flame is studied. Different combinations of sizes and strengths for the vortex pair are selected such thatvarious regimes on a typical flame vortex interaction map (Cuenot and Poinsot, [1]) are covered. From the numerical experiments, continuous burning regime for all three reduced kinetic schemes are observed. Simulations in which local extinction of the flame by the vortex pair has been observed for one and three step reduced kinetic mechanisms to date. Results how that chemical kinetics plays a major role in the extinction dynamics of a methane-air flame simulated with a three-step reduced scheme. The precise mechanism by which it is quenched is currently being investigated. ii

3 Introduction Non premixed flames are those in which the fuel and oxidizer are initially separated, and react upon mixing. The reaction is predominantly mixing controlled since the chemical reaction time scale is usually several orders of magnitude smaller than the smallest turbulence time scale. When the flow field is turbulent, the flame can be considered to be interacting with an ensemble of vortices of various sizes and strengths. Thus, the interaction of a flame with an individual, or pairs of vortices is of significant theoretical interest. There have been many analytical and asymptotic studies [2, 3, 4, 5, 6, 7, 8, 9, 10] in which the structure of diffusion flames were investigated. Thus far, the majority of numerical studies of flame vortex interaction have either employed simple, irreversible, infinitely fast chemistry or detailed chemistry which describes the combustion processes using many species and reversible reactions. Laverdant and Candel [11] used infinitely fast chemistry to validate the experimental results of combustion enhancement due to vortex interacting with the flame. Thevenin and Candel [12] used finite rate chemistry to investigate ignition of diffusion flame rolled up in a vortex. Using one step chemistry, Poinsot et al. [13] studied extinction regimes for premixed flames. Rutland and Ferziger [14] performed similar investigation to study the flame structure. Cuenot and Poinsot [1] utilized simple chemistry to examine non premixed combustion. The validation of the limits of laminar flamelet model assumption was carried out in detail in their study. Simplified chemistry was used in the analytical study of the reaction zone structure of a diffusion flame in a vortex [15]. Takahashi and Katta [16] used infinitely fast chemistry in their study of diffusion flames. Recently, advancement in parallel computing has enabled the implementation of detailed chemistry in numerical studies. Thévenin et al. [12, 17] investigated extinction processes using detailed chemistry (9 species and 19 reversible reactions) for non premixed flame vortex interactions. More recently, Katta et al. [18] also employed detailed chemistry (13 species and 74 elementary reactions) to study quenching patterns of a vortex interacting with a flat flame. Reduced chemical kinetic schemes for several hydrocarbon flames have already been derived and are well documented [7, 19]. In this approach, steady state and partial equilibrium assumptions are applied to a set of elementary reactions. The result is a reduction in the number of elementary reactions with algebraic equations 1

4 used to relate species concentrations. In order to understand the physics of turbulent reacting flows, Direct Numerical Simulations (DNS) have been employed in many studies. These simulations are three dimensional with all length and time scales fully resolved. When complex chemistries are implemented, the computational costs are exceptionally expensive. To minimize the cost, several modeling approaches have emerged to treat the chemistry involved in DNS calculations. Computational Singular Perturbation (CSP) technique by Lam and Goussis [21] groups a large number of complex, physically meaningful elementary reactions into separate reaction groups, each identified with a single characteristic time scale. The Intrinsic Low Dimensional Manifolds (ILDM) method developed by Maas and Pope [22] determines the state properties of a given simplified system automatically by the number of degrees of freedom in the simplified scheme. The most recent approach due to Bédat et al. [23] is the Integrated Combustion Chemistry (ICC) method in which it utilizes a minimal number of species and reactions with parameters derived to match a number of flame properties. These approaches strive to accurately integrate the combustion processes into the DNS with simplified chemistry while efficiency is not sacrificed, and retaining both detailed and overall flame properties. Currently, a systematic investigation on combustion processes using flame vortex interaction studies with implementation of different degrees of reduced kinetics is lacking. The goal of this study is to examine progressively more complex reduced chemical kinetic schemes on the flame structure and response. Specifically, we consider one, three and four step reduced kinetic mechanisms for methane air combustion to model the flame. The flame interacts with a pair of counter rotating vortices initiated on the fuel side. We begin by documenting the flame structure and extinction characteristics under a steady flow condition in a one dimensional Tsuji burner configuration for the three kinetic mechanisms. Then we utilize time dependent numerical simulations to study two dimensional, unsteady flame vortex interaction. The treatment of the transport mechanisms, such as viscosity, heat capacity, thermal diffusivity and species diffusion coefficients, are the same in both steady Tsuji configuration and unsteady time dependent calculation. The time dependent flame structure, its response to increasing levels of unsteady strain are then examined systematically. This is accomplished by 2

5 varying the strength and size of the vortices. Continuous burning and conditions leading to local extinction are studied in detail. In this paper, we focus on results obtained from the one step and three step mechanisms. We then highlight ourfindings for the two reduced kinetic schemes, focusing on the differences, and draw conclusions on the general value of reduced kinetic schemes when applied to other flames. Methodology Reduced Kinetic Mechanisms Reduced one, three, and four step kinetic mechanisms for methane air combustion are used in both the steady, one dimensional laminar flame in a Tsuji configuration and the two dimensional, unsteady flame vortex interaction study. This choice is motivated by the fact that extensive work has been done on developing reduced kinetic schemes for methane air flames [3, 4]. The global one step reduced mechanism for methane air combustion is as follows: CH4 +2O2! CO2 +2H2O (I) The three step reduced kinetic mechanism given in [3] is: CH4 +O2! CO + H2 +H2O (I 0 ) CO + H2O Ω CO2 +H2 (II 0 ) O2 +2H2! 2H2O (III 0 ) Lastly, the four step reduced kinetic scheme used in the simulation is [4]: CH4 +2H+2H2O! CO + 4H2 (I 00 ) CO + H2O Ω CO2 +H2 (II 00 ) 2H + M! H2 + M (III 00 ) O2 +3H2 Ω 2H + 2H2O (IV 00 ) At sufficiently high pressures, the pressure dependence of the recombination step (III 00 ) in the four step mechanism causes a reduction in the H atom concentration to a point at which its steady state 3

6 balance becomes accurate. As a consequence of this additional steady state approximation, the four step mechanism can be reduced to the three step mechanism. Computational Technique A one dimensional code, set up to solve the Tsuji burner laminar diffusion flame problem is used in the investigation of laminar flame structure and extinction limit. The governing equations are the steady, compressible boundary layer equations: dv dy + ρau =0; (1) V du dy + d μ du a(ρ 1 ρu 2 )=0; (2) dy dy V dy k dy + d dy (ρy kv k ) _! k =0; k =1;:::;N (3) c p V dt dy d dt + dy dy NX k=1 dt X N ρy k V k c pk dy + _! k h k =0 (4) k=1 where ρ, T, a and N denote mixture density, temperature, strain rate and number of species excluding N2, V ρv and U u=u 1 are the mass flux and dimensionless free stream velocity and density are given by u 1 = ax and ρ 1 respectively, and y denotes the distance from the burner surface, while x is the coordinate perpendicular to y. The symbols Y k, _! k, c pk and h k denote mass fraction, mass production rate per unit volume, molecular weight, specific heat and specific enthalpy of the k th species. Diffusion velocities are given by V k = D k ry k, where D k is the diffusion coefficient for the k th species. The symbols c p, μ and are the mixture specific heat, viscosity and thermal conductivity. The symbol y denotes the distance from the burner surface, while x is the coordinate perpendicular to y. Pressure, density and temperature are related through the ideal gas equation of state. A two point boundary value problem solver TWOPNT, originally developed by Grcar [24], is used to obtain a converged solution. If the grid is not adequate to obtain a stable solution, the number of points is increased in order to ensure convergence. A three dimensional, viscous, compressible direct numerical simulation code developed by Baum and Poinsot [25], subsequently used by Mu and Mahalingam [26] to study acoustics, was 4

7 modified for our investigation. The governing equations solved are the fully compressible mass, momentum, and energy j) =0; iu j i j ; [(ρe t + p)u j i (u j fi ij j + _! T ; (7) where u j, p, e t denote the j th velocity component, pressure, and total energy, fi ij the shear stress tensor, q j the heat flux vector, and _! T the rate of energy released per unit volume. The species conservation equations describes methane air combustion with the respective reduced chemistry ku j j kv kj j + _! k ; k =1;:::;N (8) where V kj denotes the diffusion velocity ofthek th species in the j th direction. All the kinetic and thermal diffusive parameters are obtained from [27]. The system of equations are solved using a sixth order accurate compact finite differencing scheme for evaluating spatial derivatives [28], and time advancement isachieved through a third order accurate Runge Kutta scheme. The Courant Friedrichs Lewy (CFL) criterion is used for variable time stepping. Domain Description, Boundary Conditions The flame vortex interaction problem depicted in Figure 1 is solved with the two dimensional time dependent numerical code described above. The domain size is 7:02 cm 4:00 cm. The Navier Stokes Characteristic Boundary Condition (NSCBC) procedure developed by Poinsot and Lele [29] is used to implement boundary conditions at the lateral and stream wise edges of the computational domain. At a non reflecting boundary, the incoming wave amplitude variation is set to zero to ensure that no waves re enter the domain. In this problem, periodic conditions are prescribed on the top and bottom boundaries and non reflective conditions on the other two boundaries. Mixture Fraction and Scalar Dissipation Rate 5

8 In order to identify the location of the flame surface, the mixture fraction Z, is defined as [30]: Z 2Z C=W C +1=2 Z H =W H +(Z O;O Z O )=W O 2Z C;F =W C +1=2 Z H;F =W H + Z O;O =W O (9) where px Z C k=1 nw C W k Y k;c ; Z H qx k=1 nw H W k Y k;h ; Z O rx k=1 nw O W k Y k;o (10) and Y k;c, Y k;h and Y k;o denote the mass fractions of the k th species in the system that contains either C, H or O, W C, W H and W O are the atomic weights of C, H or O, n the number of C, H or O atoms in the k th species considered. The symbols Z C;F, Z H;F and Z O;O signify the mass fraction of C, H or O in the fuel or oxidizer streams, and W k is the molecular weight of the k th species. Mixture fraction is a conserved scalar with Z = 1 representing pure fuel and Z = 0 representing pure oxidizer. With this definition of Z, the stiochiometric mixture fraction Z st =0:055 [27]. as [20]: Under the flamelet assumption, Bilger [20] suggests that the scalar dissipation rate χ, defined @x k ; (11) should align with the reaction rate. In the two dimensional flame vortex interaction study, the species diffusivity D is defined as D μ=ρ Le CH4, where μ, thedynamic viscosity, ρ, the density, and Le CH4 the Lewis number for methane. Only the diffusivity of methane is considered in the simulation because the coherent counterrotating vortex pair originates from the fuel side and travels through the unstrained flame into the air side, thus, methane is the primary contributing species in the diffusion process. Results One Dimensional Laminar Flame Extinction Limits and Flame Structures The inverse of the strain rate a, is the characteristic residence time in the reaction zone of a diffusion flame stabilized on a Tsuji burner. By holding the wall fuel flux constant and incrementing 6

9 the strain rate, the maximum temperature decreases gradually until the flame is extinguished. The extinction limit occurs at the point where the vertical tangency on the upper branch of the S curve of maximum temperature versus Damköhler number [31, 32]. The computed extinction curves obtained with the three reduced kinetic schemes for methane air are shown in Figure 2. To ensure kinetic extinction, the wall fuel flux was adjusted so that the temperature gradient and hence the heat flux at the burner surface was essentially zero. The strain rates at extinction for the one, three, and four step reduced chemistries are a = 437, 536 and 342 s 1 respectively, with corresponding maximum temperatures of 1734, 1791 and 1926 K. The one step kinetic mechanism yields a much lower extinction temperature than the three and four step mechanisms, while the three step mechanism sustains the highest strain rate before flame extinction. The three step reduced mechanism results in the lowest overall peak temperature, however, at a = 100 s 1, the computed peak temperature is almost 500 K higher than the experimental results obtained by Dixon Lewis et al. [33]. This discrepancy, as suggested in [33], is probably caused by the lack ofa radiation correction to the reported thermocouple measurements. Several key features of the laminar methane air flame structure can be seen in Figure 3 with a =100s 1. Both three and four step reduced kinetic mechanisms successfully capture the knee in the O2 mole fraction close to the reaction zone, and also the bleeding of O2 molecules into the fuel side, as well as CH4 molecules leaking into the air side. Futher, the one step mechanism displays the slight outward bend for CH4 in the reaction zone, which is not seen in other literature. Except H2O and H2, whose maxima are much lower than the experiments, all other species mole fractions in our investigation appear to be consistently with the measurements reported by Tsuji and Yamaoka [34]. Although the observed extinction strain rates and maximum temperatures do not give a clear indication if flame extinction could be accurately predicted by successively increasing the complexity ofthechemistry involved, the resultant flame structure provides a means to characterize a laminar flame with various degrees of chemical reduction. This study also offers a guideline in selecting appropriate initial strain rates in the flame vortex interaction study. Table I provides a summary of the computed extinction characteristics for the three reduced kinetic schemes for methane air flame. 7

10 Strain rate at Scalar dissipation rate Peak temperature at Reduced Schemes extinction, a (s 1 ) at extinction, χ (s 1 ) extinction, T max (K) One step Three step Four step Table I. Strain rate, a, scalar dissipation rate, χ and peak temperature, T max at flame extinction for the one dimensional laminar flame extinction study with one, three and four step reduced kinetic schemes. Two Dimensional Flame Vortex Interaction Study The problem depicted in Figure 1 is solved with the time dependent code described above for one and three step cases. In order to fully resolve all characteristic length and time scales for this configuration, the domain is discretized into fixed, uniform grids, with typical grid sizes of for the one step cases and for three and four step cases, resulting in x's of 1: m and 1: m, and y's of 1: m and 1: m. Grid independence studies were carried out to ensure that the reaction zones are fully resolved and solutions are grid independent. The two dimensional unstrained methane air flame profiles are obtained by extending the converged one dimensional strained laminar flame profiles at low strain rate of 87 s 1 in the lateral y direction. The strain is removed and computations are allowed to evolve for 0.02 s. The resulting one, three and four step flame profiles have thicknesses of ffi =1: m, 0: m, and 0: m respectively, and corresponding peak temperatures of 1871 K, 1718 K and 1767 K. The flame thickness, ffi, is calculated base on 10% width of the fuel consumption step of the reaction rate profile in each case. Further, differences in the structure of the reaction rate profiles for the three reduced mechanisms should be noted. The global one step reduced kinetics carries a wider reaction zone than its counterparts. Since the rate limiting step in the three and four step reduced schemes is the fuel consumption step, once the strain is removed and computation evolved for 0.02 s, the thickness for the water gas shift, recombination and three body collision steps collapse into the thickness of the fuel consumption step. A pair of counter rotating vortices with a vortex stream 8

11 function, Ψ v : Ψ v = v " (x xv ) 2 2 # +(y y v ) exp 2r 2 v ; (12) where x v and y v are the coordinates of the vortex center, r v the vortex radius, and v the strength of the vortex, is then initialized on the fuel side and superimposed over the previously obtained flame profiles. To ensure minimal initial contact with the flame, the vortex pair is initialized such that there is a minimum separation of 2ffi between its leading edge and the flame front. Different combinations of sizes and strengths for the vortex pair are selected such that various regimes on a typical flame vortex interaction map are covered [1]. In the numerical experiments which have been carried out thus far, continuous burning is observed for all three reduced kinetic schemes, and flame extinction is observed for one and three step cases. Continuous Burning In the continuous burning case, r v =2: m, and l =2: m, where r v and l are the radii of the vortices and the distance between the vortex centers. The vortex Reynolds number, Re v v =ν is 962, where v is the strength of the vortex and ν is the cold mixture kinematic viscosity ofch4, which results in an initial peak vortex translational velocity of u max =15:9 m/s toward the unstrained flame, and a peak strain rate at the core of the vortex pair of a = 1720 s 1. During the early stages of the simulation, there is limited interaction between the flame and the vortex pair. However, it is evident that cold unreacted fuel and some hot products are being entrained by the vortex pair as it approaches the air side (Figure 4). At the time indicated, slight stretching of the flame zone begins to occur in all three cases. The stoichiometric mixture fraction line Z st = 0:055, also starts to bow out due to intense straining imposed by the vortex motion. As the vortex pair crosses the reaction zone into the air side at a later time (Figures 4c and d), the relatively slow moving vortex pair drags the flame front along with it as it crosses the reaction zone into the air side. In the continuous burning regime, reaction takes place on the surface of the cold fuel pocket in which the reaction zone acts as a partition between the fuel and oxidizer. In this simulation, although the strain rates on the periphery of the vortex pair exceed 1000 s 1, which is significantly higher than the steady extinction strain rates obtained from the laminar flame calculations for all cases, no extinction of the flame is observed. 9

12 Local Flame Extinction In the extinction case, r v =2: m, and l =1: m, with Re v v =ν =1763. The resultant initial peak translational velocity of the counterrotating vortex pair is u max =26:7 m/s. The peak strain rate for this case is a = 1419 s 1. This strain rate is located at the periphery of the it, slightly offset from its leading edge centerline. After the vortices have been introduced for ms, local extinction at the flame front due to the vortex motion is observed for the one step reduced kinetics case (Figure 5). However, the occurrence of localized extinction of the flame was observed earlier into the simulation at t = ms for the three step reduced kinetics case (Figure 6). The reaction zone at the tip of the vortex pair is locally quenched and the reaction rate drops to zero. At extinction, the temperatures at the leading edge of the vortex pair, i.e. on the Z = Z st = contour, where local extinction is observed are 1210 K and 1490 K for the one step and three step cases respectively, with maximum strain rates of 700 s 1 and 730 s 1 recorded in the vicinity where the reaction rate approaches zero. When compared with the laminar flame extinction results, the extinction temperatures in this two dimensional flame vortex study are well below the calculated laminar extinction temperatures. Further, for extinction to occur, the maximum recorded localized strain rates in this study are much higher than that obtained from the steady laminar calculations. This can be explained by the fact that the configurations between the Tsuji burner and the flame vortex interaction are vastly different. In the Tsuji burner configuration, the flame is imposed by a steady strain which acts on it normally, while as the counterrotating vortex pair approaches the initially planar flame, the strain acting on the flame is predominantly lateral and inherently transient in nature. At the onset of extinction, the drop in the peak temperatures at the apex of the vortex pair with respect to the initial peaks at vortex initialization are T max = 662 K and 229 K for the one and three step models respectively (Figure 7). The presence of such steep temperature gradients suggests that local extinction is the result of intense straining on the flame front in both reduced kinetic schemes, and not as a result of un mixedness between fuel and oxidizer. Discussion 10

13 The flame vortex interaction study for methane air flames provides a glimpse into the effect of successively more complex reduced kinetic mechanisms under the same computational environment in the events of continuous burning and conditions leading to local flame extinction. However, the precise mechanism as to how individual chemical species affect extinction is still under investigation, especially in the two dimensional flame coherent vortex interaction study. The one dimensional steady laminar flame study in a Tsuji burner configuration yields extinction strain rates and temperatures that does not show any trend as more complex reduced chemistry are integrated into the calculation. In low strain rate calculations, the mole fractions for respective species are generally in good agreement with the experimental results except for H2O and H2. The calculation captures features like theknee in the O2 profile for the three and four step chemistries and the leakage of O2 molecules into the fuel side, which agree with the experiments [34]. By comparing the one step species profile with that obtained from previous experiments, the leakage of CH4 into the air side demonstrate that the scheme does not accurate represent the chemistry involved. Although we cannot draw any conclusions as to how close the three and four step reduced kinetic schemes resembles actual chemistry from the simulation, the extinction strain rates do provide a means to select appropriate parameters for the vortex pair in the subsequent unsteady flame vortex interaction study. In the two dimensional flame vortex interaction study, there are no noticeable differences between the three methane air reduced kinetic schemes in mixture fraction and scalar dissipation rate for the continuous burning case. The species mass fractions profiles that are common to the three schemes are similar. Local quenching of the flame begins at the centerline leading edge of the vortex pair for the flame extinction case, and extinction in the three step case preceded the one step case by 0.32 ms. The flames in both schemes are quenched almost immediately upon contact with the vortex pair. Extinction is characterized by a sharp drop in the peak temperature at theapexofthevortex pair, i.e. Z st =0:055. This suggests that local flame extinction is cause by anadverse temperature gradient due to intense straining of the flame and not un mixedness of fuel and oxidizer. Unsteady extinction strain rates for both one and three step reduced kinetic schemes are significantly higher than the laminar flame results, while the extinction temperatures at the apex of the vortex are much lower. This is probably due to the transient and localized 11

14 property of this problem [35]. As suggested by Bilger [20] under the laminar flamelet concept, the reaction rate profile should align with the scalar dissipation rate profile at the flame front. For a one step reduced kinetic case, this alignment is evident from Figures 8a and 8b. However, the same is not observed for the three step reduced kinetic case (Figures 8c and 8d). One possible explanation may be attributed to differences in flame structures of the two schemes. In the three step case, H2 produced in the fuel consumption step (I 0 ) is readily consumed by O2 in the unidirectional recombination step to form H2O (III 0 ). Although there is significant leakage of O2 into the fuel side as seen in the one dimensional, low strain flame structure study (Figure 3a), the recombination step causes any O2 to vanish as H2 is produced from the fuel consumption step. In the one step reduced scheme, there is no such mechanism as in the three step case which prevents O2 from leaking into the fuel side. This also explains the three step flame thickness is much less than that of its one step counterpart, and thus, although steep gradients of mixture fraction and temperature are present at the trailing edge of the counterrotating vortex pair (as well as high scalar dissipation rate), no reaction can be sustained without the presence of oxidizer. Therefore, the reaction rate behind the vortex pair is essentially zero. This further supports our claim that localized extinction is caused by kinetic quenching, and not due to un mixedness of fuel and oxidizer. Recent numerical studies have found that when radiative heat loss is included in the flame vortex simulation of methane air flames, it takes a certain time before quenching of the flame can occur [36]. In our study, we observed that local extinction occurs soon after the vortex pair is in contact with the flame. This observation indicates that for strong vortices with high enough strain rates, local quenching can occur with virtually no radiative heatloss. The extinction dynamics in the flame vortex interaction study show that for the one step reduced mechanism, flame extinction is primarily caused by fluid strain effects, while the three step case is more intricate due to the contributions of each species to the flame structure. The three step extinction mechanism is still not fully understood and further studies are being performed. Summary and Conclusions 12

15 The flame structure and extinction characteristics in a Tsuji burner configuration for one-, three-, and four-step methane-air reduced kinetic mechanisms were studied. Although the extinction limits for the three schemes do not provide a clear trend as progressively more complicated reduced chemistry is integrated into the study, they serve as guidelines in the selection of vortex properties in the subsequent two dimensional unsteady flame vortex investigation. Continuous burning and localized extinction of both one and three step reduced cases are witnessed in the flame vortex study. Data shows that both one and three step flame extinction mechanisms are caused by intense strain of the flame front upon contact with the counterrotating vortex pair. The one step flame vortex extinction case is consistent with expected results, primarily explained through fluid strain effects, while in addition to strain effects, evidence suggests that chemical kinetics may play a significant role in the three step flame vortex extinction dynamics. Ongoing efforts are directed towards the investigation of the precise dynamics of local extinction for the three step case, and the construction of the four step flame vortex database. Acknowledgments The authors express their acknowledgment to the donors of The Petroleum Research Fund, administered by the American Chemical Society for partial support of this work through a type AC grant. We also acknowledge computer support from the San Diego Supercomputing Center. The authors express their appreciation to M. Read and Y. Khunatorn for technical assistance. References [1] Cuénot, B., and Poinsot, T., Twenty Fifth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, PA, 1994, pp [2] Li~nan, A., Acta Astron. 1: (1974). [3] Peters, N., and Williams, F. W., Combust. Flame 68: (1987). [4] Peters, N., and Kee, R. J., Combust. Flame 68:17-29 (1987). 13

16 [5] Seshadri, K., and Peters, N., Combust. Flame 73:23-44 (1988). [6] Seshadri, K., and Peters, N., Combust. Flame 81: (1990). [7] Bilger, R. W., Stνarner, S. H., and Kee., R. J., Combust. Flame 80: (1990). [8] Smooke, M. D., and Giovangigli, V., in Reduced Kinetic Mechanisms and Asymptotic Approximations for Methane Air Flames, (M. D. Smooke Ed.), Lecture Notes in Physics 384, Springer Verlag, 1991, pp [9] Chelliah, H. K., Seshadri, K., and Law, C. K., in Reduced Kinetic Mechanisms for Applications in Combustion Systems, (N. Peters and B. Rogg Eds.), Lecture Notes in Physics, Springer Verlag, 1993, pp [10] Chelliah, H. K., Trevi~no, C. and Williams, F. A., Reduced Kinetic Mechanisms and Asymptotic Approximations for Methane Air Flames, (M. D. Smooke Ed.), Lecture Notes in Physics 384, Springer Verlag, 1991, pp [11] Laverdant, A. M., and Candel, S. M., Combust. Sci. Technol. 60:79-96 (1988). [12] Thévenin, D., Rolon, J. C., Renard, P. H., Kendrick, D. W., Veynante, D., and Candel, S., Twenty Sixth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, PA, 1996, pp [13] Poinsot, T., Veynante, D., and Candel, S., J. Fluid Mech. 228: (1991). [14] Rutland, C. J. and Ferziger, J. H., Combust. Flame 84: (1991). [15] Rehm, R. G., Baum, H. R., Tang, H. C., and Lozier, D. C., Combust. Sci. Technol. 91: (1993). [16] Takahashi, F. and Katta, V. R., J. Propul. Power 11: (1995). [17] Thévenin, D., Renard, P. H., Rolon, J. C., and Candel, S., Twenty Seventh Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, PA, 1998, pp

17 [18] Katta, V. R., Carter, C. D., Fiechtner, G. J., Roquemore, W. M., Gord, J. R., and Rolon, J. C., Twenty Seventh Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, PA, 1998, pp [19] Maas, U. and Warnatz, J., Twenty-Second Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, PA, 1988, pp [20] Bilger, R. W. in Turbulent Reacting Flows, (P. A. Libby and F. A. Williams Eds.), Lecture Notes in Physics 44, Springer Verlag, 1980, pp [21] Lam, S. H. and Goussis, D. A. Twenty Second Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, PA, 1988, pp [22] Maas, U. and Pope, S. B., Combust. Flame 88: (1992). [23] Bédat, B., Egolfopoulos, F. N. and Poinsot, T., Combust. Flame 119:69-83 (1999). [24] Grcar, J. F., TWOPNT Program for Boundary Value Problems (Ver. 3.12), [25] Baum. M. and Poinsot, T. J., 2D Direct Simulation of Reacting Flows, COMBUSTION 2D (Rel. 1.0), [26] Mu, S. and Mahalingam, S., AIAA J., 34: (1996). [27] Bilger, R. W., Esler, M. B. and Stνarner, S. H., Reduced Kinetic Mechanisms and Asymptotic Approximations for Methane Air Flames, (M. D. Smooke Ed.), Lecture Notes in Physics 384, Springer Verlag, 1991, pp [28] Lele, S. K., J. Comput. Phys. 103:16-42 (1992). [29] Poinsot, T. J., and Lele, S. K., J. Comput. Phys. 101: (1992). [30] Bilger, R. W., Twenty Second Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, PA, 1988, pp [31] Fendell, F. E., J. Fluid Mech. 21: (1965). [32] Carrier, G. F., Fendell, F. E., and Marble, F., E., SIAM J. Appl. Math. 28(2): (1975). 15

18 [33] Dixon Lewis, G., David, T., Gaskell, P. H., Fukutani, S., Jinno, H., Miller, J. A., Kee, R. J., Smooke, M. D., Peters, N., Effelsberg, E., Warnatz, J., and Behrendt, F., Twentieth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, PA, 1984, pp [34] Tsuji, H., and Yamaoka, I., Thirteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, PA, 1970, pp [35] Haworth, D. C., Drake, M. C., Pope, S. B. and Blint, R. J., Twenty Second Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, PA, 1988, pp [36] Patnaik, G., and Kailasanath, K., Twenty Seventh Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, PA, 1998, pp

19 Figures 17

20 y Periodic top Fuel Air 4.00 cm Non-reflecting boundary Counterrotating vortex pair l r v Non-reflecting boundary x Initially unstrained planar diffusion flame with thickness, δ Periodic bottom 7.02 cm Figure 1. Domain description for two-dimensional time dependent flame-vortex interaction study. 18

21 step 4-step Tmax (K) step / (a x 10^-3) [s] Figure 2. Laminar methane air flame extinction curves for one, three and four step methane air reduced kinetic mechanisms. : one step reduced mechanism; : three step reduced mechanism; : four step reduced mechanism. 19

22 CH4 O Mole Fraction Distance (cm) Figure 3a. Laminar methane air flame structure for fuel (CH4) and oxidizer (O2) for one, three and four step reduced kinetic mechanisms, all with strain rate, a = 100 s 1. : one step reduced mechanism; : three step reduced mechanism; : four step reduced mechanism. 20

23 CO2 Mole Fraction CO Distance (cm) Figure 3b. Laminar methane air flame structure for product species H2O, H2 and H for one, three and four step reduced kinetic mechanisms, all with strain rate, a = 100 s 1. : one step reduced mechanism; : three step reduced mechanism; : four step reduced mechanism. 21

24 H2O Mole Fraction H H Distance (cm) Figure 3c. Laminar methane air flame structure for product species CO2 and CO for one, three and four step reduced kinetic mechanisms, all with strain rate, a = 100 s 1. : one step reduced mechanism; : three step reduced mechanism; : four step reduced mechanism. 22

25 0.030 (a) (b) (c) (d) Figure 4. Contour plots of reaction rate for a one step reduced kinetic mechanism, continuous burning flame vortex interaction case at t = (a) 0.50 ms ( _! max =0:03867 kg/m 3 s; _! min =0:00), (b) 1.00 ms ( _! max =0:03864 kg/m 3 s; _! min =0:00), (c) 1.50 ms ( _! max =0:03902 kg/m 3 s; _! min =0:00) and (d) 2.00 ms (_! max = 0:03952 kg/m 3 s; _! min = 0:00). Radius of vortices, r v = 2: m, distance between vortex centers, l =2: m, and Re v v =ν =

26 Figure 5. Contour plots of reaction rate for a one step reduced kinetic mechanism, extinction flame vortex interaction case at t = (a) 1.20 ms (_! max =0:04026 kg/m 3 s; _! min =0:00), (b) 1.40 ms (_! max = 0:04053 kg/m 3 s; _! min = 0:00), (c) 1.60 ms (_! max = 0:04111 kg/m 3 s; _! min = 0:00) and (d) 1.80 ms (_! max = 0:04081 kg/m 3 s; _! min = 0:00). Radius of vortices, r v = 2: m, distance between vortex centers, l =1: m, and Re v v =ν =1763. Localized extinction of the flame occurs at t = 1.46 ms. 24

27 Figure 6. Contour plots of reaction rate for the fuel consumption step of a three step reduced kinetic mechanism, extinction flame vortex interaction case at t = (a) 0.80 ms ( _! max =0:07656 kg/m 3 s; _! min = 0:00), (b) 1.00 ms (_! max = 0:07371 kg/m 3 s; _! min = 0:00), (c) 1.20 ms (_! max = 0:07178 kg/m 3 s; _! min =0:00) and (d) 1.40 ms ( _! max =0:07063 kg/m 3 s; _! min =0:00). Radius of vortices, r v =2: m, distance between vortex centers, l =1: m, and Re v v =ν =1763. Localized extinction of the flame occurs at t = 1.14 ms. 25

28 T (K) Figure 7a. Plots of centerline temperature profiles at the leading edge of the counter rotating vortex pair at various simulation times for one step reduced kinetic mechanisms, flame vortex extinction cases. Note the extinction temperature of 1210 K for the one step mechanism (t = 1.46 ms) on the rightmost curves on both plots where localized extinction is observed. Local extinction occurs at the leading edge and along the centerline of the counterrotating vortex pair. 26

29 T (K) Figure 7b. Plots of centerline temperature profiles at the leading edge of the counter rotating vortex pair at various simulation times for three step reduced kinetic mechanisms, flame vortex extinction cases. Note the extinction temperature of 1490 K for the three step mechanism (t = 1.14 ms) on the rightmost curves on both plots where localized extinction is observed. Local extinction occurs at the leading edge and along the centerline of the counterrotating vortex pair. 27

30 0.030 (a) (b) (c) (d) Figure 8. Contour plots of reaction rate for the fuel consumption step (left panels) and scalar dissipation rate (right panels) for a one step reduced kinetic mechanism flame vortex interaction case at extinction (t = 1.46 ms) (_! max = 0:04080 kg/m 3 s; _! min = 0:00; χ max = 417:93 s 1 ; χ min = 0:00 s 1 ), and a three step reduced kinetic mechanism flame vortex interaction case at extinction (t = 1.14 ms) (_! max =0:07230 kg/m 3 s; _! min =0:00; χ max = 323:17 s 1 ; χ min =0:00 s 1 )withz st = iso contour. 28

31 0.030 (a) (b) (c) (d) Figure 9. Contour plots of mixture fraction (left panels) and strain rate (right panels) for a one step reduced kinetic mechanism flame vortex interaction case at extinction (t = 1.46 ms) (Z max = 1:00; Z min = 0:00; a max = 3051:73 s 1 ; a min = 3051:73 s 1 ), and a three step reduced kinetic mechanism flame vortex interaction case at extinction (t = 1.14 ms) (Z max =0:97; Z min =0:00; a max = 3466:01 s 1 ; a min = 3466:01 s 1 ). Strain rate is defined as a = du=dy + dv=dx, and note the locations of maximum local strain rates occur slightly offset from the centerline of the counterrotating vortex pair. 29