A model problem for the evolution of strain structure at the crossing of a flame front

Abstract

The local thermal effect of a flame front is simulated by a model for a mass density front by specifying a likely expansion rate. This model problem includes two independent parameters, namely the heat release parameter and a parameter akin to a Karlovitz number. The analysis is focused on the influence of the Karlovitz number on the evolution of strain properties at the crossing of the front. The latter are derived from an equation system for the velocity gradient tensor and the pressure Hessian tensor undergoing the forcing of the expansion rate. Strain eigenvalues, orientation of strain principal axes, and stretching in the direction of forcing are especially scrutinized. Furthermore, the model shows that, when approaching a flame front, the special alignments of strain are mostly caused by anisotropy of pressure Hessian resulting from forcing by expansion.