Flame-generated Vorticity Production in Premixed Flame-vortex Interactions

INTRODUCTION Theoretical analysis, experimental observations, and numerical simulations have all indicated that flame-vortex interactions play an important role in the propagation and extinguishment of turbulent flames in microgravity [1]. Most studies of flame-vortex interactions ignore the effects of gravity and experiments are usually conducted in Earth gravity. Recently, Sinibaldi et al. [2] and Driscoll and coworkers [3] have reported the results of drop-tower experiments that show that for some vortex strengths, the reduction in gravity can significantly alter the structure of the flame produced by the flame-vortex interaction. These studies found that the flame is much more wrinkled in microgravity conditions, attributable to the lack of the stabilizing effect of buoyancy. In order to examine flame-generated vorticity (FGV), it is customary to look at the production and loss terms in the vorticity equation, that is, perform a vorticity budget. We will focus our attention on those terms that can increase or decrease the total vorticity in a region containing the flame. Terms that merely redistribute vorticity, such as convective terms, do not change the total vorticity and thus do not contribute to FGV. Only two terms in the vorticity equation can create vorticity where none was originally present before; these are the viscous term and the baroclinic torque term. The stretch term, cannot create new vorticity, but can amplify or attenuate the total vorticity. The baroclinic production term is perhaps the most interesting and has been studied in detail (see for example Refs. 4-7). It has been presumed that the misalignment of the density gradient and the pressure gradient is a major cause of FGV. The density gradient across the flame is very large, and so any small misalignment of the gradients will produce FGV. In flame-vortex interactions, the flame is highly curved and the gradients get misaligned. In order to extract the effect of gravity, it is customary to separate the pressure into a hydrostatic pressure and a dynamic pressure. The baroclinic torque can be then separated into two parts: one due to the dynamic pressure and the other due to the gravity-induced hydrostatic pressure. The role of the latter term will determine the effect of gravity. In this study, we use detailed time-dependent, multi-dimensional numerical simulations to investigate the relative importance of the processes leading to FGV in flame-vortex interactions in normal gravity and microgravity and to determine if the production of vorticity in flames in gravity is the same as that in zero gravity except for the contribution of the gravity term. The numerical simulations will be performed using the computational model developed at NRL, FLAME3D. FLAME3D is a parallel, multi-dimensional (either twoor three-dimensional) flame model based on FLIC2D [8], which has been used extensively to study the structure and stability of premixed hydrogen and methane flames.