Baroclinic distortion of laminar flames

Abstract

One of the most important divisions in studies of premixed gaseous combustion is that between the theoretically much favoured laminar flames, and the more com­monly observed case of turbulent burning. Laminar premixed flames clearly represent much simpler cases for theoretical and numerical study. Conversely experimental in­vestigations are much simpler in the case of turbulent combustion due to the inherent instability of laminar fluid flows. One mechanism which can effect the transition from laminar to turbulent com­bustion is baroclinicity (i. e. the non-alignment of pressure and density gradients). A laminar deflagration, or slow flame, may be thought of as a reaction front which prop­agates at a low Mach number and whose associated pressure field is therefore close to uniformity. On the other hand, very steep density gradients are associated with the rapid temperature increase due to the exothermic chemical reaction. (Note that a typical deflagration thickness is of the order of 1 mm, and densities may decrease by factors of between five and ten in going from unburnt to burnt gas.) Externally induced pressure disturbances, which are almost universally present in practical com­bustion systems, can introduce a baroclinic effect whenever a steep pressure gradient interacts with a flame front in such a way that the former is misaligned with the den­sity gradient associated with the latter. The differential acceleration of fluid elements can produce significant rotational motion and, if this field of vorticity is sufficiently strong, a laminar flame front may be broken up and the transition to turbulent burning may result. This scenario was clearly demonstrated in an experiment done by Markstein (1963) that involved the double passage of a large amplitude planar pressure signal across an expanding spherical flame bubble in a shock tube. The laminar flame front was com­pletely obliterated, and the evolution to fine grain turbulent combustion was revealed. In the current paper we report on numerical simulations of a number of similar experiments. Although we are here restricted to two space dimensions and cannot therefore investigate fully turbulent behaviour, these simulations do reveal qualita­tively similar behaviour to that found in the early stages of the Markstein experiment. It has been possible to repeat the simulations for a variety of different flames, so that the effects of the various processes (in particular the chemical reaction and the ther-moviscous diffusion) can be assessed. Attention is also given to the question of the grid dependency of the numerical solutions obtained.