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

Abstract

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.

Evolution equations for the decomposed components of displacement speed in a reactive scalar field

“…The analysis mainly consists of three parts. First, while previous numerical assessment of the S d -equation was limited to constant-density reaction waves (Yu et al 2020), the present work aims at investigating the effect of thermal expansion on the evolution of S d . For this purpose, results computed in cases B and C will be compared.…”

“…Following Yu et al (2020), (2.29) can be reorganized by grouping all sub-terms involving the velocity into a single term U in order to highlight the net contribution affected directly by the flow. By separating u contained in K from C s , the separated u terms can be cancelled with A 0 .…”

“…Then, using a DNS database obtained from constant-density turbulent reaction waves, we showed that all terms in the surface-averaged S d -equation could be numerically evaluated with satisfactory accuracy, with a reasonable match between the averaged left-hand and right-hand side terms being achieved. Further numerical investigation (Yu et al 2020) of the evolution equation for the surface-averaged S d (for brevity, we will write S d -equation in the following) provided insights into issues such as a retreating iso-surface element moving at a negative displacement speed and relation between rapidly propagating surface elements and curvature. By simply grouping all terms involving u, the direct effect of the flow velocity on the evolution of the surface-averaged S d was also explored.…”

“…Second, in a realistic turbulent combustion system, multiple phenomena can affect the self-propagation characteristics of a reaction wave. In order to isolate and study the effect of flow turbulence, our previous numerical assessment on the S d -equation (Yu et al 2020) was limited to DNS data obtained from a constant-density reaction wave that passively propagated through a background turbulent flow. A simple examination of the derived equation terms (Yu et al 2020) has identified multiple routes through which the flow dilatation can affect the evolution of S d .…”

“…In order to isolate and study the effect of flow turbulence, our previous numerical assessment on the S d -equation (Yu et al 2020) was limited to DNS data obtained from a constant-density reaction wave that passively propagated through a background turbulent flow. A simple examination of the derived equation terms (Yu et al 2020) has identified multiple routes through which the flow dilatation can affect the evolution of S d . However, it is still unknown whether or not such effects are significant enough to change the main trends observed in the constant-density case.…”