Unsteady effects of strain rate and curvature on turbulent premixed flames in an inflow–outflow configuration

Abstract

Three-dimensional direct numerical simulation (DNS) studies of premixed turbulent flames have been carried out using an inflow–outflow configuration at moderate Reynolds number ( Re) and with single-step Arrhenius chemistry in the thin reaction zones regime. The compressible Navier–Stokes equations are solved together with a transport equation for a reaction progress variable ( c). Results are obtained for several quantities of interest, including the gradient magnitude of the progress variable (|∇ c|) and the displacement speed ( S d) of each progress variable isosurface. The probability density function (pdf) of displacement speed and the implications of the pdf shape are discussed in terms of the relative magnitude of reaction rate and molecular diffusion effects. The pdf of S d itself, as well as the pdfs of its different components S r, S n, and S t, in the present three-dimensional simulations is found to be consistent with previous results based on two-dimensional DNS with detailed chemistry. The validity of the assumption (ρS d ) s ≈ρ 0S L is assessed on averaging ρS d over the isosurfaces of c across the flame brush. The unsteady effects of tangential strain rate ( a T) and curvature ( κ m) on flame propagation are also considered. Curvature and displacement speed are found to be negatively correlated, while the conditional pdf of tangential strain rate and displacement speed at zero curvature locations also shows a negative correlation, again consistent with previous two-dimensional detailed-chemistry DNS.