A big database (23 cases characterized by Damkohler number less than unity) created recently in 3D Direct Numerical Simulation (DNS) of propagation of a statistically one-dimensional and planar, dynamically passive reaction wave in statistically stationary, homogeneous, isotropic turbulence is analyzed. On the one hand, the DNS data well support the classical Damkohler expression, i.e., square-root dependence of a ratio of turbulent and laminar consumption velocities on the turbulent Reynolds number. On the other hand, contrary to the common interpretation of the Damkohler theory and, in particular, to the concept of distributed burning, the DNS data show that the reaction is still localized to thin zones even at D$ as low as 0.01, with the aforementioned ratio of the consumption velocities being mainly controlled by the reaction-zone-surface area. To reconcile these apparently inconsistent numerical findings, an alternative regime of propagation of reaction waves in a highly turbulent medium is analyzed, i.e., propagation of an infinitely thin reaction sheet is theoretically studied, with molecular mixing of the reactant and product being allowed in wide layers. In this limiting case, an increase in the consumption velocity by turbulence is solely controlled by an increase in the reaction-sheet area. Based on physical reasoning and estimates, the area is hypothesized to be close to the mean area of an inert iso-scalar surface at the same turbulent Reynolds number. This hypothesis leads to the aforementioned square-root dependence. Thus, both the DNS data and the developed theory show that a widely accepted hypothesis on penetration of small-scale turbulent eddies into reaction zones is not necessary to obtain the classical Damkohler scaling for turbulent consumption velocity.

中文翻译：

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高湍流介质中的薄反应区

分析了最近在 3D 直接数值模拟 (DNS) 中创建的一个大型数据库（23 个案例的特点是 Damkohler 数小于 1），该数据库是统计一维和平面、动态被动反应波在统计平稳、均匀、各向同性湍流中的传播。一方面，DNS 数据很好地支持了经典的 Damkohler 表达式，即湍流和层流消耗速度之比对湍流雷诺数的平方根依赖性。另一方面，与 Damkohler 理论的普遍解释相反，特别是与分布式燃烧的概念相反，DNS 数据表明，即使 D$ 低至 0.01，反应仍然局限于薄区，其中上述消耗速度的比率主要由反应区表面积控制。为了调和这些明显不一致的数值发现，我们分析了反应波在高度湍流介质中传播的另一种方式，即理论上研究了无限薄反应片的传播，允许反应物和产物在宽层中进行分子混合. 在这种极限情况下，湍流消耗速度的增加仅由反应片面积的增加来控制。基于物理推理和估计，假设该面积接近于相同湍流雷诺数下的惰性等标量表面的平均面积。该假设导致上述平方根依赖性。因此，