Modelling of the correlation between velocity and reactive scalar gradients in turbulent premixed flames based on DNS data

The interaction between turbulence and reactive scalar fields is discussed for the wrinkled flamelets regime of turbulent premixed combustion. Emphasis is placed on the effects associated with the turbulent straining term. In the regime of turbulent combustion under consideration, which corresponds to Karlovitz and Damkohler numbers such that Ka < 1 and Da > 1, a clear and simple formulation is proposed to explain and to model the influence of the correlation between velocity and reactive scalar gradients. This formulation is based on the conservative variables budget across one-dimensional premixed laminar flamelets. The analysis firmly confirms the dependence on both the Damkohler number and the expansion factor, a feature already foreseen in recent studies. Nevertheless, in contrast with previous work, (i) the scaling arguments used in the present contribution are different from those used in other recent proposals, and (ii) the proposed closures are not only deduced from dimensional arguments but also from the consideration of conservative variable budgets across laminar flamelets. The resulting functional dependence on the expansion factor is found to be influenced by the underlying one-dimensional flamelet representation and two possible closures are put forward to take this dependence into account. (iii) The two closures do not exhibit a proportionality to the mean scalar dissipation rate (epsilon) over tilde (Y) as suggested in previous studies but to the square of this quantity. This results in the presence of a second contribution proportional to (epsilon) over tilde (2)(Y) in the modelled transport equation for the mean scalar dissipation rate, in addition to the modelled molecular dissipation term. (iv) Since previous Direct Numerical Simulation (DNS) studies have been essentially devoted to the influence of the Damkohler number, the present DNS validation step is focused on the effects of the expansion rate. To this purpose, the proposed models are validated against three available DNS databases obtained for turbulent premixed flames with different values of the density ratio between unburned and fully burned gases.