Flame-ball drift in the presence of a total diffusive heat flux

Abstract

For a one-component reaction model, the total diffusive heat flux (TDHF) is—∇( λT+pDQY ) where λ and pD are diffusive transport coefficients, T is the temperature, Y is the reactant mass-fraction, and Q is the heat of reaction. We show that a flame ball exposed to a weak TDHF will drift, and we derive an explicit formula for the drift speed. The key mathematical feature is that the flux generates a flametemperature perturbation that varies as cos φ , where φ is the polar angle measured from the axis parallel to the flux vector, and this is unacceptable as it leads to a simple boundary-value problem for a harmonic function (a temperature perturbation) that has no solution. Drift generates a like perturbation and the drift speed must be chosen so that the two cancel. If the TDHF is generated by a second flame ball whose far-temperature-field is suppressed by radiation, so that only ∇ Y contributes to the flux, the balls will drift apart with a separation distance that grows as the one-third power of time. Observations made during recent space shuttle flights are presented and are consistent with this prediction. We also formulate the problem of drift in a weak gravitational field and solve it in an approximate fashion.