Propagation Velocity of Premixed Turbulent Flames

Abstract The problem of propagation of turbulent premixed flame is analyzed using the field equation introduced recently by Kerstein, Ashurst and Williams (1987). The dynamic renormalization group method is applied to this equation and the formula for the turbulent flame velocity is derived in the lowest order in the e-expansion. The formula, which does not include adjustable parameters, agrees well with experimental (Abdel-Gayed et al., 1984) and numerical (Ashurst & Barr 1983) results on flame propagation in high-Reynolds number turbulent media. Ways to design transport and large-eddy (sub-grid) models for simulation of combustion processes, based on the ideas developed in the present paper, are discussed.

[1]  Steven A. Orszag,et al.  Computational test of the renormalization group theory of turbulence , 1988, J. Sci. Comput..

[2]  J. Sethian.  Curvature and the evolution of fronts , 1985 .

[3]  S. Orszag,et al.  Renormalization group analysis of turbulence. I. Basic theory , 1986, Physical review letters.

[4]  Ahmed F. Ghoniem,et al.  Effect of large scale structures on turbulent flame propagation , 1986 .

[5]  F. Williams,et al.  Theory of premixed-flame propagation in large-scale turbulence , 1979, Journal of Fluid Mechanics.

[6]  P. K. Barr,et al.  Stochastic Calculation of Laminar Wrinkled Flame Propagation via Vortex Dynamics , 1983 .

[7]  S. Orszag,et al.  Renormalization group analysis of turbulence. I. Basic theory , 1986 .

[8]  S. Orszag.  Analytical theories of turbulence , 1970, Journal of Fluid Mechanics.

[9]  A. Kerstein,et al.  Field equation for interface propagation in an unsteady homogeneous flow field. , 1988, Physical review. A, General physics.

[10]  Forman A. Williams,et al.  The Mathematics of Combustion , 1985, Frontiers in applied mathematics.

[11]  A. Kerstein.  Simple Derivation of Yakhot's Turbulent Premixed Flamespeed Formulad , 1988 .

[12]  Alan R. Kerstein,et al.  Pair-exchange model of turbulent premixed flame propagation , 1988 .

[13]  Paul C. Martin,et al.  Energy spectra of certain randomly-stirred fluids , 1979 .

[14]  J. A. Sethian,et al.  HYPERSURFACES MOVING WITH CURVATURE-DEPENDENT SPEED: HAMILTON-JACOBI EQUATIONS, CONSERVATION LAWS AND NUMERICAL ALGORITHMS , 1989 .

[15]  David R. Nelson,et al.  Large-distance and long-time properties of a randomly stirred fluid , 1977 .

[16]  A. Chorin.  Flame Advection and Propagation Algorithms , 1989 .

[17]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .