APPLICATION OF A REYNOLDS STRESS, STRETCHED FLAMELET, MATHEMATICAL-MODEL TO COMPUTATIONS OF TURBULENT BURNING VELOCITIES AND COMPARISON WITH EXPERIMENTS

Equations are presented for a stretched laminar flamelet model of a one-dimensional turbulent, premixed flame. Reynolds stress modeling is employed and the computed laminar flame structures of other researchers, principally Dixon-Lewis, provide input data for the profiles of volumetric heat release rate against temperature. The probability density function (pdf) of stretch rate is based on the direct numerical simulations of Pope and co-workers and the pdf of temperature is an assumed beta function, employing first and second moments of temperature. Predictions of the ratio of turbulent to lamiar burning velocity are in good agreement with a comprehensive correlation of measured values over a wide range of wrinkling and stretch factors. Values also have been computed at the high levels of Reynolds number that can exist in the atmosphere. The predictions are in better agreement with experiment than those obtained from the k-epsilon model and the wave propagation model of Kolmogorov et al. Decay of flow field turbulence through the flow can reduce the burning velocity by about 10%. The importance of countergradient diffusion, arising from the pressure gradient, is clearly demonstrated. The turbulence generated in this way is reduced by an increase in product, K Le, of the Karlovitz stretch factor (K) and Lewis number (Le). All results are presented in dimensionless form and flame structures are reported over wide operational regimes. Maximum values of the second moment of temperature depend upon the ratio of flame stretch to wrinkling factor. The ratio of flame thickness to integral length scale increases with K Le, as a result of an increased degree of flame quenching. The principal limitations of the model probably reside in the closure procedures and the assumptions concerning the pdf of temperature.