Ga. Batley et al., BAROCLINIC DISTORTION OF LAMINAR FLAMES, Proceedings - Royal Society. Mathematical, physical and engineering sciences, 452(1945), 1996, pp. 199-221
One of the most important divisions in studies of premixed gaseous com
bustion is that between the theoretically much favoured laminar flames
, and the more commonly observed case of turbulent burning. Laminar pr
emixed flames clearly represent much simpler cases for theoretical and
numerical study. Conversely experimental investigations are much simp
ler in the case of turbulent combustion due to the inherent instabilit
y of laminar fluid flows. One mechanism which can effect the transitio
n 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 a
re associated with the rapid temperature increase due to the exothermi
c chemical reaction. (Note that a typical deflagration thickness is of
the order of 1 mm, and densities magi decrease by factors of between
five and ten in going from unburnt to burnt gas.) Externally induced p
ressure disturbances, which are almost universally present in practica
l combustion systems, can introduce a baroclinic effect whenever a ste
ep pressure gradient interacts with a flame front in such a way that t
he former is misaligned with the density gradient associated with the
latter. The differential acceleration of fluid elements can produce si
gnificant rotational motion and, if this field of vorticity is suffici
ently strong, a laminar flame front may be broken up and the transitio
n to turbulent burning may result. This scenario was clearly demonstra
ted in an experiment done by Markstein (1963) that involved the double
passage of a large amplitude planar pressure signal across an expandi
ng spherical flame bubble in a shock tube. The laminar flame front was
completely obliterated, and the evolution to fine grain turbulent com
bustion was revealed. In the current paper we report on numerical simu
lations of a number of similar experiments. Although we are here restr
icted to two space dimensions and cannot therefore investigate fully t
urbulent behaviour, these simulations do reveal qualitatively similar
behaviour to that found in the early stages of the Markstein experimen
t. It has been possible to repeat the simulations for a variety of dif
ferent flames, so that the effects of the various processes (in partic
ular the chemical reaction and the thermoviscous diffusion) can be ass
essed. Attention is also given to the question of the grid dependency
of the numerical solutions obtained.