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

Abstract

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 D f = 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 U T ∝ u ′ is obtained for the turbulent consumption velocity at Da ≫ 1 and Ka ≫ 1. Here, u ′ is the rms turbulent velocity.

Passive Front Propagation in Intense Turbulence: Early Transient and Late Statistically Stationary Stages of the Front Area Evolution

“…Indeed, third, the sole physical mechanism of smoothing small-scale wrinkles on the surface of an infinitely thin front consists of kinematic restoration due to the selfpropagation of the front [21,22]. This is the key difference between the present study and a recently developed bifractal model [32] of a highly turbulent reaction wave that has a mixing zone of a finite thickness. For such waves, the inner cut-off scale is controlled by molecular mixing [32].…”

“…This is the key difference between the present study and a recently developed bifractal model [32] of a highly turbulent reaction wave that has a mixing zone of a finite thickness. For such waves, the inner cut-off scale is controlled by molecular mixing [32]. For an infinitely thin front, the small inner cut-off scale in is identified as the Gibson scale corresponding to the front velocity u 0 .…”

“…A similar scenario was explored by Sreenevasan et al [20] when discussing turbulent mixing for Schmidt numbers far greater than unity, as portrayed in Figures 2a and 6 in the cited paper. Recently, such ideas were developed for a flame of a finite thickness [31,32]. In the present communication, the bifractal concept is applied to an infinitely thin front.…”

Smallest scale of wrinkles of a Huygens front in extremely strong turbulence

“…If a front thickness is comparable with or larger than the Kolmogorov length scale due to molecular transport processes, the smallest front wrinkles are expected to be controlled by molecular mixing. Nevertheless, even in such a case, a slowly propagating front can be bifractal [38] if Re T 1 and a timescale characterizing processes in the front, including molecular transport, is much smaller than the integral timescale of the turbulence (the Damköhler number Da 1) and is much larger than the Kolmogorov timescale (the Karlovitz number Ka 1). Moreover, under such conditions, the mean front speed scales as u , as discussed in detail elsewhere [38].…”