Gravitationally unstable flames: Rayleigh-taylor stretching versus turbulent wrinkling

Abstract

In this paper, we provide support for the Rayleigh-Taylor-(RT)-based subgrid model used in full-star simulations of deflagrations in Type Ia supernovae explosions. We use the results of a parameter study of two-dimensional direct numerical simulations of an RT unstable model flame to distinguish between the two main types of subgrid models (RT or turbulence dominated) in the flamelet regime. First, we give scalings for the turbulent flame speed, the Reynolds number, the viscous scale, and the size of the burning region as the non-dimensional gravity (G) is varied. The flame speed is well predicted by an RT-based flame speed model. Next, the above scalings are used to calculate the Karlovitz number (Ka) and to discuss appropriate combustion regimes. No transition to thin reaction zones is seen at Ka = 1, although such a transition is expected by turbulence-dominated subgrid models. Finally, we confirm a basic physical premise of the RT subgrid model, namely, that the flame is fractal, and thus self-similar. By modeling the turbulent flame speed, we demonstrate that it is affected more by large-scale RT stretching than by small-scale turbulent wrinkling. In this way, the RT instability controls the flame directly from the large scales. Overall, these results support the RT subgrid model. © 2013. The American Astronomical Society. All rights reserved..