Scalar transport in self-similar, developing, premixed, turbulent flames

A statistically planar, one-dimensional, developing flame that propagates against a statistically stationary and uniform turbulent flow of an unburned mixture and does not affect the turbulence is theoretically studied invoking an assumption of the self-similarity of the mean flame structure. A generalized diffusion coefficient is introduced to account for the development of turbulent diffusivity, pressure-driven countergradient transport, and effects of chemical reactions on the transport term in the balance equation for the mean combustion progress variable. The pressure-driven transport and reactions counteract one another, thus, allowing us to use the gradient diffusion closure of the transport term even if turbulent scalar flux is countergradient. The derived expressions are used to extend the Flame Speed Closure model of premixed turbulent combustion and the extended model is applied to simulate recent experiments performed using the Leeds fan-stirred bomb. The model well predicts the speed, thickness and structure of statistically spherical flames that expand in the bomb after spark ignition.