Assessment of an evolution equation for the averaged displacement speed of a reactive scalar field

Paper in proceeding, 2019

For turbulent premixed reacting flow modeled by a simplified transport equation for a reaction progress scalar field, an evolution equation for the displacement speed conditionally averaged on the reaction progress was derived in a recent work. In the current paper this equation is
used to analyze the basic problem of propagation of a planar reaction wave in homogeneous isotropic constant-density turbulence using a DNS approach. We examine both the transient process of the initial planar wave being disturbed by turbulence as well as the fully developed
wave after all statistics has evolved to a stationary state. The numerical results support the derived equation by showing good match between the left hand side term and the sum of all right hand side terms. The derived equation reveals three effects that cause temporal variation in averaged displacement speed: (i) T1, the isosurface-following rate of change in reaction surface density, (ii) T2, the isosurface-following rate of change due to diffusion, and (iii) T3, a stretch-rate-induced difference between averaged isosurface-following derivative and time derivative of the isosurface averaged value. For a fully developed wave the equation reduces to a constraint of zero sum of the three terms; this is realized by (i) the terms T1 and
T3 averaged over all reaction scalar zones stay positive and negative, respectively, and (ii) T2 stays largely positive except in the preheat zone for a highly disturbed reaction wave where it becomes slightly negative. Among the three terms, the diffusion contribution term T3 is found to be largely responsible for early transient variation in averaged displacement speed. For the transient evolution of highly turbulent reaction waves, it is also found that all three terms tend to flip their signs when moving from the preheat zone to the reaction zone.