Assessment of an Evolution Equation for the Displacement Speed of a Constant-Density Reactive Scalar Field

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.

Automated summary

The evolution equation for the displacement speed, derived in a recent work, represents the interaction of complex mechanisms related to straining by the velocity field, surface curvature, and the scalar gradient. The study aims to provide detailed physical explanations and a new perspective on the mechanisms responsible for variations in the displacement speed. The analysis of statistically planar reaction wave propagation in turbulence shows the occurrence of negative displacement speed, particularly at high Karlovitz numbers.