Effect of dilatation on scalar dissipation in turbulent premixed flames

The scalar dissipation rate signifies the local mixing rate and thus plays a vital role in the modeling of reaction rate in turbulent flames. The local mixing rate is influenced by the turbulence, the chemical, and the molecular diffusion processes which are strongly coupled in turbulent premixed flames. Thus, a model for the mean scalar dissipation rate, and hence the mean reaction rate, should include the contributions of these processes. Earlier models for the scalar dissipation rate include only a turbulence time scale. In this study, we derive exact transport equations for the instantaneous and the mean scalar dissipation rates. Using these equations, a simple algebraic model for the mean scalar dissipation rate is obtained. This model includes a chemical as well as a turbulence time scale and its prediction compares well with direct numerical simulation results. Reynolds-averaged Navier-Stokes calculations of a test flame using the model obtained here show that the contribution of dilatation to local turbulent mixing rate is important to predict the propagation phenomenon.