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. KeywordsVelocity gradient • Strain structure • Premixed flames • Variable mass density • Pressure Hessian 1 IntroductionMicromixing is the mere expression of the small-scale action of flow on scalar fields, more precisely, the outcome of the mechanical action exerted by the velocity gradient on the gradients of scalars. The straining part of the velocity gradient, at least in incompressible flows, tends to enhance scalar gradients through compression, thereby hastening local diffusive fluxes. Thus the level of micromixing tightly depends on strain main properties, namely intensity, direction, and lifetime.Mixing in non-solenoidal flows is a special case, for mass density variations may deeply affect the velocity gradient. Alteration of the intensity and/or orientation of strain, then, may influence the micromixing process. This is especially relevant in compressible flows [1,2] and in reacting flows with heat release such as flames [3][4][5][6][7][8][9]. More specifically, scalar dissipation -the key mechanism driving