A theory for the free-convective burning of a condensed fuel particle

The highly buoyant combustion of a condensed spherical fuel particle is studied theoretically using boundary layer and flame sheet approximations. Self-similar solutions with the same Grashof scaling law are obtained for the bottom stagnation and the lateral regions. These solutions are used to generate the leading two terms of a series expansion solution for the flow. The solution provides an explicit expression for the mass burning rate along the droplet periphery up to the point of boundary layer separation. The predicted overall burning rates for Grashof numbers expected in buoyant droplet combustion are considerably larger than those predicted by spherical symmetry models. It is also shown that the d² law is not applicable to buoyant combustion. Instead, a variation of the form d(R²) dt ∼ R ^{3 4} is predicted. The upper spherical segment of the particle where wake flame combustion occurs is only treated qualitatively by comparison with pool burning liquids. The streamlines in the boundary layer and the induced inviscid flow are obtained and superimposed to provide an overall description of the gas flow field.