A Simple Model for Evaluating Conditioned Velocities in Premixed Turbulent Flames

Abstract

A simple model is proposed to evaluate (a) the divergence of velocity vector conditioned on unburned mixture, and (b) the vector component normal to the mean flame brush in the flamelet regime of premixed turbulent combustion. The model involves a single constant and does not invoke an extra balance equation. To perform the first test of the model, six flames stabilized in impinging jets and experimentally investigated by 4 research groups were numerically simulated. In the computations, (a) approximations of the measured axial profiles of the mean combustion progress variable were invoked, (b) the well-known (Bray et al., 1998, and 2000) statistically steady and 1-dimensional Favre-averaged continuity and Euler equations were numerically integrated in order to approximate the measured axial profiles of the mean axial velocity, and, then, (c) the approximations were utilized in order to evaluate conditioned velocities and turbulent scalar flux using the proposed model supplemented with the BML approach and balance equation for the Favre-averaged combustion progress variable. The obtained agreement between the measured and computed axial profiles of the conditioned axial velocities or axial turbulent scalar flux was encouraging, thus, indicating that the proposed simple model is promising. Since the correlation between fluctuations of velocity and unity normal vectors, conditioned to flamelet surface, plays a key role in the model, the encouraging test results call for studying this correlation in future DNS. Moreover, further research into the difference in velocity conditioned on unburned mixture and velocity conditioned on the unburned side of flamelets is necessary for improving the model at the leading edge of a turbulent flame brush.