Bifractal nature of turbulent reaction waves at high Damköhler and Karlovitz numbers
Bifractal nature of turbulent reaction waves at high Damköhler and Karlovitz numbers
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高 Damköhler 和 Karlovitz 数下湍流反应波的双分形性质
DOI：
10.1063/5.0020384
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发表时间：
2020
影响因子：
4.6
通讯作者：
A. Lipatnikov
中科院分区：
文献类型：
--
作者：
V. Sabelnikov;A. Lipatnikov
柯尔莫哥洛夫湍流对反应波（如预混火焰）影响的控制物理机制通常采用（燃烧）状态图进行讨论。虽然(i)高Damkohler数Da，但低Karlovitz数Ka或（ii）低Da，但高Ka的两种极限状态引起了大量关注，但与（iii） Da和Ka 1相关的第三种极限状态尚未超出文献中的主流讨论。目前的工作旨在通过调整对（一）和（二）体系基本原理的当代理解来填补这一知识空白，以便描述（三）体系中强烈湍流对反应波影响的基本特征。更具体地说，在该状态下，整个湍流谱被分为两个子范围：小尺度和大尺度涡流，它们对反应波的影响分别与状态（ii）和(i)相似。据此，假设反应波的表面为分形，分形维数在小尺度和大尺度上分别为Df = 8/3和7/3。通过将局部涡旋翻转时间等同于层流波时间尺度，可以找到两个范围之间的边界。最后，对Da∶1和Ka∶1处的湍流消耗速度，得到了UT∶u′的简单标度。这里u '是湍流速度的均方根。
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 Damkohler 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.