Validation of analytical expressions for turbulent burning velocity in stagnating and freely propagating turbulent premixed flames

Abstract

A general expression is derived for the turbulent burning velocity, ST, from the continuum form of the c¯ transport equation and shown to be valid in all turbulent premixed combustion regimes. It involves the inverse length scale, 1/Lw, for which new analytical relationships are proposed in the laminar flamelet and the distributed reaction regime. They are combined to give new predictive relationships for the ST in the two limiting regimes and extended to be applicable in the intermediate regime as well. They involve flamelet thickness, mean curvature, molecular and turbulent diffusivities at the leading edge without any tuning constants. The proposed relationships are shown to be consistent with measurements in literature at varying pressures, laminar flame speeds, turbulent intensities and mixture compositions. Convincing agreement is achieved for ST and 1/Lw for different turbulence and laminar flame properties of stagnating compressible flames and in parametric study with respect to turbulent intensity, laminar flamelet thickness and integral length scale for freely propagating incompressible flames. There is no gravity and the Lewis number is assumed unity for simplification.