Transported PDF modeling of high-Reynolds-number premixed turbulent flames

Abstract The transported PDF approach, closed at the joint composition–enthalpy level, is applied to model premixed turbulent flames at a wide range of Reynolds numbers. The initial aim of the study is to establish the impact of closure approximations for the scalar dissipation rate upon the relationship between turbulence fluctuations and predicted turbulent burning velocities. The cases considered feature stoichiometric methane–air flames with the chemical source term extracted from a detailed chemistry simulation of the corresponding unstrained laminar flame. The transported PDF approach is subsequently combined with a systematically reduced C/H/O mechanism featuring 142 reactions and 14 solved and 15 steady-state species and applied to piloted premixed stoichiometric methane–air flames investigated experimentally by Chen et al. [Combust. Flame 107 (1996) 223–226]. The cases considered here feature Re = 24 , 200 (flame F3) and 52,500 (flame F1) and Damkohler numbers approaching unity. The effects of variations in the time-scale ratio ( 2 ⩽ C ϕ ⩽ 8 ) and heat losses to the burner were investigated, along with the impact of an extended algebraic relationship for the scalar dissipation rate that accounts for small-scale properties. Comparisons with experimental data show that the modified Curl's model and the extended scalar dissipation-rate closure produce turbulent burning velocities in close agreement with measurements. The study further indicates that a closure at the joint scalar level combined with comprehensive chemistry has the potential to reproduce the detailed chemical structure of premixed turbulent flames. The importance of boundary conditions and comprehensive scalar statistics, including the scalar dissipation rate, is also emphasized by the study.

[1]  R. P. Lindstedt,et al.  Premixed turbulent burning velocities derived from mixing controlled reaction models with cold front quenching , 1991 .

[2]  S. Pope,et al.  Straining and scalar dissipation on material surfaces in turbulence: Implications for flamelets , 1990 .

[3]  C. Dopazo,et al.  A binomial sampling model for scalar turbulent mixing , 1990 .

[4]  S. Pope,et al.  Raman measurements and joint PDF modeling of a nonpremixed bluff-body-stabilized methane flame , 1994 .

[5]  Bassam B. Dally,et al.  Instantaneous and Mean Compositional Structure of Bluff-Body Stabilized Nonpremixed Flames , 1998 .

[6]  R. Lindstedt,et al.  Modeling of premixed turbulent flames with second moment methods , 1999 .

[7]  R. Lindstedt,et al.  Joint-scalar transported PDF modeling of soot formation and oxidation , 2005 .

[8]  R. Lindstedt,et al.  Absolute radical concentration measurements and modeling of low-pressure CH4/O2/NO flames , 1998 .

[9]  Stephen B. Pope,et al.  Fitting noisy data using cross-validated cubic smoothing splines , 1988 .

[10]  Monte Carlo PDF method for turbulent reacting flow in a jet-stirred reactor , 1992 .

[11]  P. Lindstedt.  Modeling of the chemical complexities of flames , 1998 .

[12]  Robert W. Bilger,et al.  Scalar gradient and related quantities in turbulent premixed flames , 1997 .

[13]  S. Pope.  PDF methods for turbulent reactive flows , 1985 .

[14]  J. B. Moss,et al.  Simultaneous Measurements of Concentration and Velocity in an Open Premixed Turbulent Flame , 1980 .

[15]  V. Sick,et al.  Quantitative laser-based measurements and detailed chemical kinetic modeling of nitric oxide concentrations in methane-air counterflow diffusion flames , 1998 .

[16]  R. Lindstedt,et al.  Joint scalar probability density function modeling of pollutant formation in piloted turbulent jet diffusion flames with comprehensive chemistry , 2000 .

[17]  J.-Y. Chen,et al.  Scalar Pdf Modeling of Turbulent Nonpremixed Methanol-Air Flames , 1993 .

[18]  Norbert Peters,et al.  The detailed flame structure of highly stretched turbulent premixed methane-air flames , 1996 .

[19]  Thierry Mantel,et al.  A new model of premixed wrinkled flame propagation based on a scalar dissipation equation , 1994 .

[20]  R. Cheng,et al.  The influence of burner geometry on premixed turbulent flame propagation , 1991 .

[21]  R. Lindstedt,et al.  Transported probability density function modeling of a bluff body stabilized turbulent flame , 2005 .

[22]  S. Pope,et al.  Monte Carlo solutions of a joint pdf equation for turbulent flows in general orthogonal coordinates , 1987 .

[23]  R. P. Lindstedt,et al.  Computations of steady-state and transient premixed turbulent flames using pdf methods , 1996 .

[24]  Derek Bradley,et al.  Turbulent burning velocities and flame straining in explosions , 1984, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[25]  T. Gatski,et al.  Modelling the pressure–strain correlation of turbulence: an invariant dynamical systems approach , 1991, Journal of Fluid Mechanics.

[26]  Joint scalar-velocity pdf modelling of finite rate chemistry in a scalar mixing layer , 1998 .

[27]  Philip H. Gaskell,et al.  Application of a reynolds stress, stretched flamelet, mathematical model to computations of turbulent burning velocities and comparison with experiments , 1994 .

[28]  P. Libby,et al.  Pre-mixed flames in stagnating turbulence , 2001 .

[29]  Stephen B. Pope,et al.  PDF modeling of a bluff-body stabilized turbulent flame , 2003 .

[30]  Robert W. Dibble,et al.  The structure of turbulent nonpremixed flames of methanol over a range of mixing rates , 1992 .

[31]  R. Borghi,et al.  Turbulent reactive flows , 1989 .

[32]  F. Williams,et al.  Turbulent Reacting Flows , 1981 .

[33]  Stephen B. Pope,et al.  Calculations of premixed turbulent flames by PDF methods , 1987 .

[34]  J. B. Moss,et al.  Turbulence Production in Premixed Turbulent Flames , 1981 .

[35]  D. Haworth,et al.  Probability density function approach for multidimensional turbulentflow calculations with application to in-cylinder flows in reciprocating engines , 1991 .

[36]  W. P. Jones,et al.  Closure of the Reynolds stress and scalar flux equations , 1988 .

[37]  César Dopazo,et al.  A binomial Langevin model for turbulent mixing , 1991 .

[38]  H. Pitsch,et al.  Large-eddy simulation of premixed turbulent combustion using a level-set approach , 2002 .

[39]  C. Dopazo.  Probability density function approach for a turbulent axisymmetric heated jet. Centerline evolution , 1975 .

[40]  Bassam B. Dally,et al.  The instantaneous spatial structure of the recirculation zone in bluff-body stabilized flames , 1998 .

[41]  K. Bray,et al.  Studies of the turbulent burning velocity , 1990, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[42]  Sanjay M. Correa,et al.  Comparison of a monte carlo pdf/finite-volume mean flow model with bluff-body raman data , 1992 .

[43]  Carl de Boor,et al.  A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[44]  Stephen B. Pope,et al.  PDF calculations of turbulent nonpremixed flames with local extinction , 2000 .

[45]  Stephen B. Pope,et al.  Probability density function calculations of local extinction and no production in piloted-jet turbulent methane/air flames , 2000 .

[46]  A. Masri,et al.  PROBABILITY DENSITY FUNCTION COMPUTATIONS OF A STRONGLY SWIRLING NONPREMIXED FLAME STABILIZED ON A NEW BURNER , 2000 .

[47]  R. Lindstedt,et al.  Finite Rate Chemistry Effects in Turbulent Reacting Flows , 2004 .

[48]  R. Lindstedt,et al.  Joint scalar transported probability density function modeling of turbulent methanol jet diffusion flames , 2002 .

[49]  S. Pope,et al.  A pdf modeling study of self‐similar turbulent free shear flows , 1987 .