Existence conditions and drift velocities of adiabatic flame-balls in weak gravity fields

Abstract

Combining activation energy asymptotics, suitable scalings and numerical methods, we study how flame-balls move under the action of the free convection that they themselves generate in the presence of a weak, uniform gravity field. Attention is focused on steady configurations (in a suitable reference frame), on an isolated flame-ball of size comparable to what is obtained in the absence of gravity, and on deficient reactants that are characterized by a low Lewis number. For the sake of simplicity, we consider an adiabatic combustion process, in the sense that the radiative exchanges are neglected. This work provides one with: (a) a description of the free-convection field around the flame-ball, along with an asymptotic estimate of the drift velocity; (b) a relationship between the flame-ball radius, strength of gravity and physico-chemical properties of the reactive premixture; (c) extinction conditions, caused by the net effect of heat extraction from the flame-ball to its surroundings by the free-convection field. Hints on generalizations currently under consideration are also given.