On flame speed enhancement in turbulent premixed hydrogen-air flames during local flame-flame interaction

Given the need to develop zero-carbon combustors for power and aircraft engine applications, $S_d$ of a turbulent premixed flame, especially for H$_2$-air, is of immediate interest. The present study investigates 3D DNS cases of premixed H$_2$-air turbulent flames at varied pressures for different $Re_t$ and $Ka$ with detailed chemistry to theoretically model $S_d$ at negative curvatures. Prior studies at atmospheric pressure showed $\widetilde{S_d}$ to be enhanced significantly over $S_L$ at large negative $\kappa$ due to flame-flame interactions. 1D simulations of an imploding cylindrical H$_2$-air laminar premixed flame used to represent the local flame surfaces undergoing flame-flame interaction in a turbulent flame at the corresponding pressure conditions are performed to understand the interaction dynamics. These simulations emphasized the transient nature of the flame structure during flame-flame interactions and enabled analytical modeling of $\widetilde{S_d}$ at these regions of extreme negative $\kappa$ of the 3D DNS. The JPDF of $\widetilde{S_d}$ and $\kappa$ and the corresponding conditional averages from 3D DNS showed a negative correlation between $\widetilde{S_d}$ and $\kappa$. The model successfully predicts the variation of $\langle\widetilde{S_d}|_{\kappa}\rangle$ with $\kappa$ for the regions on the flame surface with $\kappa\delta_L \! \ll \! -1$ at all pressures, with good accuracy. This shows the aforementioned configuration to be fruitful in representing local flame-flame interaction in 3D turbulent flames. Moreover, at $\kappa=0$, on average $\widetilde{S_d}$ can deviate from $S_L$, manifested by the internal flame structure, controlled by turbulence transport in the large $Ka$ regime. Thus, the correlation of $\langle\widetilde{S_d}\rangle/S_L$ with $\langle|\widehat{\nabla c}|_{c_0}\rangle$ at $\kappa =0$ is explored.