Wind-Aided Firespread across Arrays of Discrete Fuel Elements. I. Theory

Abstract

The propagation for spread rate lrofwind-aided firespreadacross an array of very-small-diarne-ter, discrete fuel elements is sought, as a step toward the objective of predicting the advance in time of a firefront through either strewn debris in a heavily-blast-damaged scenario or through brush-and-grass-type wildlands. Here, the quasisteady rate (if one exists) is sought for conditions under which there is both (1) a wind whose mean speed U is constant and whose direction is constant, and (2) a horizontal bed with a macroscopically uniform fuel distribution m. More precisely, m is the mass of fuel (per unit planform area of the bed) consumed with firefront passage; here the fuel elements are thin. so that, for conditions under which fire propagates at all, the fuel consumed is identical with the fuel loading initially present. In accord with laboratory-scale experiments in a specially dedicated firetunnel, to be reported separately, analysis suggests thai I'r varies with (U/m)1/2 over a wide (but obviously finite) range of the parameters V and m. Also in accord with observations, the model adopted postulates a steadily translating firefront of finite streamwise expanse sandwiched between a thoroughly burned-out upwind expanse of the bed and a downwind expanse which is undergoing preheating from the ambient temperature to the onset-of-pyrolysis temperature. The analytic modeling further suggests the inference that fresh fuel is preheated to sustain the firespread by convection/diffusion. Only if the thin-fuel loading m approaches the rather large value of I'ery roughly 2 g/cm2 is radiative preheating likely to playa role comparable to that of convective/diffusive preheating.