Stochastic Calculation of Laminar Wrinkled Flame Propagation via Vortex Dynamics

Abstract

This paper explores the interaction between time dependent turbulent flow structure and an irreversible one-step decomposition reaction. A Lagrangian-calculated velocity field is combined with Eulerian scalar transport to describe premixed flame propagation in two dimensions. The time dependent flow structure is calculated by the discrete vortex dynamics method. The flow is two-dimensional and is confined to a unit square through the use of either periodic or non-equilibrium boundary conditions. The velocity field from the known vortex locations is used to describe the convection of a reacting scalar on a fixed Eulerian mesh. By variation of the numerical vortex parameters, the flow field length scale and root-mean-square (RMS) velocity can be changed. For this study, unit Lewis number with temperature-independent transport coefficients has been assumed. Some of the work also assumed a constant density flame model. In addition to calculating reacting scalar transport, calculations have also been done which replace the flame structure with a zero thickness front that moves into the unburned flow at a specified speed. These two constant density models predict the same variation of turbulent flame speed as a function of the flow length scale and RMS velocity. This agreement indicates that for the range of turbulence parameters studied, turbulence enhanced internal transport within the flame zone is not an important factor in increasing the flame speed above its normal flat flame value. Rather the increase is due to the increase in the flame area caused by the turbulence. The turbulent flame speed is determined from the overall rate of product formation. The calculated turbulent flame speed agrees with the wrinkled laminar flame model and experimental correlations in that at constant turbulent length scale the flame speed depends linearly on RMS intensity, and at constant RMS the flame speed increases with increasing Reynolds number.