Towards the Development of an Evolution Equation for Flame Turbulence Interaction in Premixed Turbulent Combustion

Flame turbulence interaction is one of the leading order terms in the scalar dissipation (left (widetilde {varepsilon }_{c}right )) transport equation [35] and is thus an important phenomenon in premixed turbulent combustion. Swaminathan and Grout [36] and Chakraborty and Swaminathan [15, 16] have shown that the effect of strain rate on the transport of (widetilde {varepsilon }_{c}) is dominated by the interaction between the fluctuating scalar gradients and the fluctuating strain rate, denoted here by (overline {rho }widetilde {Delta }_{c}= overline {rho {alpha }nabla c^{prime prime }S_{ij}^{prime prime }nabla c^{prime prime }}) ; this represents the flame turbulence interaction. In order to obtain an accurate representation of this phenomenon, a new evolution equation for (widetilde {Delta }_{c}) has been proposed. This equation gives a detailed insight into flame turbulence interaction and provides an alternative approach to model the important physics represented by (widetilde {Delta }_{c}) . The (widetilde {Delta }_{c}) evolution equation is derived in detail and an order of magnitude analysis is carried out to determine the leading order terms in the (widetilde {Delta }_{c}) evolution equation. The leading order terms are then studied using a Direct Numerical Simulation (DNS) of premixed turbulent flames in the corrugated flamelet regime. It is found that the behaviour of (widetilde {Delta }_{c}) is determined by the competition between the source terms (pressure gradient and the reaction rate), diffusion/dissipation processes, turbulent strain rate and the dilatation rate. Closures for the leading order terms in (widetilde {Delta }_{c}) evolution equation have been proposed and compared with the DNS data.