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

Local flame displacement speed $S_d$ of a turbulent premixed flame is of fundamental and practical interest. For H${}_2$-air flames, the interest is further accentuated given the recent drive towards the development of zero-carbon combustors for both power and aircraft engine applications. The present study investigates several three-dimensional Direct Numerical Simulation (3D DNS) cases of premixed H${}_2$-air turbulent flames to theoretically model the $S_d$ at negative curvatures, building upon recent works. Two of the four DNS cases presented are simulated at atmospheric pressure and two at elevated pressure. The DNS cases at different turbulence Reynolds numbers ($R{e}_t$) and Karlovitz numbers ($Ka$) are generated using detailed chemistry. It has been shown in the previous studies that at atmospheric pressure, the density-weighted flame displacement speed $\widetilde{S_d}$ is enhanced significantly over its laminar value ($S_L$) at large negative curvature $\kappa$ due to flame-flame interactions. The current work justifiably employs an imploding cylindrical laminar flame configuration to represent the local flame surfaces undergoing flame-flame interaction in a 3D turbulent flame. Therefore, to acquire a deep understanding of the interacting flame dynamics at large negative curvatures, one-dimensional (1D) simulations of an inwardly propagating cylindrical H${}_2$-air laminar premixed flame, with detailed chemistry at the corresponding atmospheric and elevated pressure conditions are performed. In particular, the 1D simulations emphasized the transient nature of the flame structure during these interactions. Based on the insights from the 1D simulations, we utilize an analytical approach to model the $\widetilde{S_d}$ at these regions of extreme negative $\kappa$ of the 3D DNS. The analytical approach is formulated to include the effect of variable density, convection and the inner reaction zone motion. The joint probability density function (JPDF) of $\widetilde{S_d}$ and $\kappa$ and the corresponding conditional averages obtained from 3D DNS showed clear negative correlation between $\widetilde{S_d}$ and $\kappa$ at all pressures. The obtained model successfully predicts the variation of $〈\widetilde{S_d}{|}_{\kappa }〉$ with $\kappa$ for the regions on the flame surface with large negative curvature ($\kappa {\delta }_L\ll -1$) at atmospheric as well as at elevated pressure, with good accuracy. This showed that the 1D cylindrical, interacting flame model is a fruitful representation of a local flame-flame interaction that persists in a 3D turbulent flame, and is able to capture the intrinsically transient dynamics of the local flame-flame interaction. The 3D DNS cases further showed that even in the non-interacting state at $\kappa =0$, on average $\widetilde{S_d}$ can deviate from $S_L$. $\widetilde{S_d}$ at $\kappa =0$ is a manifestation of the internal flame structure, controlled by turbulence transport in the large $Ka$ regime. Therefore, the correlation of $〈\widetilde{S_d}〉/S_L$ with the the normalized gradient of the progress variable, $〈|\widehat{\nabla c}{|}_{c_0}〉$ at $\kappa =0$ is explored.