Bifractal nature of turbulent reaction waves at high Damköhler and Karlovitz numbers

Governing physical mechanisms of the influence of Kolmogorov turbulence on a reaction wave (e.g., a premixed flame) are often discussed by adopting (combustion) regime diagrams. While two limiting regimes associated with (i) a high Damköhler number Da, but a low Karlovitz number Ka, or (ii) a low Da, but a high Ka drew significant amount of attention, the third limiting regime associated with (iii) Da ≫ 1 and Ka ≫ 1 has yet been beyond the mainstream discussions in the literature. The present work aims at filling this knowledge gap by adapting the contemporary understanding of the fundamentals of the regimes (i) and (ii) in order to describe the basic features of the influence of intense turbulence on a reaction wave in the regime (iii). More specifically, in that regime, the entire turbulence spectrum is divided in two subranges: small-scale and large-scale eddies whose influence on the reaction wave is modeled similarly to the regimes (ii) and (i), respectively. Accordingly, the surface of the reaction wave is hypothesized to be a bifractal with two different fractal dimensions of Df = 8/3 and 7/3 at small and large scales, respectively. The boundary between the two ranges is found by equating the local eddy turn-over time to the laminar-wave time scale. Finally, a simple scaling of UT ∝ u′ is obtained for the turbulent consumption velocity at Da ≫ 1 and Ka ≫ 1. Here, u′ is the rms turbulent velocity.