The displacement speed that characterises the self-propagation of isosurfaces of a reaction progress variable is of key importance for turbulent premixed reacting flow. The evolution equation for the displacement speed was derived in a recent work of Yu and Lipatnikov (Phys Rev E 100:013107, 2019a) for the case where the flame is described by a transport equation for single reaction progress variable assuming simple transport and one-step chemistry. This equation represents interaction of a number of complex coupled mechanisms related to straining by the velocity field, surface curvature and the scalar gradient. The aim of the current work is to provide detailed physical explanations of the displacement speed equation and its various terms, and to provide a new perspective to understand the mechanisms responsible for observed variations in the displacement speed. The equation is then used to analyze the propagation of a statistically planar reaction wave in homogeneous isotropic constant-density turbulence using direct numerical simulations. Additional emphasis is put on retracting surface segments that have a negative displacement speed, a phenomenon that commonly occurs at high Karlovitz numbers.

中文翻译：

---

等密度反应标量场位移速度演化方程的评估

表征反应进程变量等值面自传播的位移速度对于湍流预混反应流至关重要。在 Yu 和 Lipatnikov (Phys Rev E 100:013107, 2019a) 的最近工作中推导出位移速度的演化方程，其中火焰由单个反应进程变量的传输方程描述，假设简单传输和单-步骤化学。该方程表示与速度场、表面曲率和标量梯度引起的应变相关的许多复杂耦合机制的相互作用。当前工作的目的是提供位移速度方程及其各种术语的详细物理解释，并提供一个新的视角来理解导致观察到的位移速度变化的机制。然后，该方程用于使用直接数值模拟分析均匀各向同性恒定密度湍流中统计平面反应波的传播。额外的重点放在收缩具有负位移速度的表面段上，这种现象通常发生在高卡洛维茨数下。