A consistent level set formulation for large-eddy simulation of premixed turbulent combustion

A consistent formulation of the G-equation approach for LES is developed. The unfiltered G equation is valid only at the instantaneous flame front location. Hence, in a filtering procedure applied to derive the appropriate LES equation, only the instantaneous unfiltered flame surface can be considered. A new filter kernel is provided, which averages along the flame surface. The filter kernel is used to derive the G equation for the filtered flame front location. This equation has two unclosed terms, involving a flame front conditional averaged flow velocity, and a filtered propagation term. A model for the conditional velocity is derived, expressing this quantity in terms of the Favre-filtered flow velocity, which is typically known from a flow solver. This model leads to the appearance of a density ratio in the propagation term of the G equation. LES of combustion in the thin reaction zones regime is discussed in the LES regime diagram. A new line is identified separating the thin reaction zones regime into two parts, where the broadened flame thickness is larger and smaller than the filter size, respectively. A model for the propagation term is provided. This leads to a term including the subfilter turbulent burning velocity and an additional term proportional to the resolved flame front curvature. For the former, an algebraic model is provided from an equation for the subfilter flame front wrinkling. The latter term depends on the inverse of the subfilter Damköhler number and disappears in the corrugated flamelets regime.