ON POWER LAWS FOR DESCRIBING THE MASS FLUX IN THE NEAR-FIELD OF FIRES

A general, dimensionally homogeneous power law for describing the vert ical variation of the mass flux M within limited regions in the near f ield of fire-generated turbulent flames and plumes is derived. The der ivation assumes that M(z) is determined by the geometric size of the f ire-D, the buoyancy flux generated by the heat flux of the fire-B, and the total mass pur of fresh air required for stoichiometric combustio n of fuel-M(s), which implies that, in general, the variation of M dep ends on a dimensionless number N, which is approximately proportional to Q(2)/D-5, where Q is the heat flux of the fire. Simpler forms of th is general law are then derived for the asymptotic cases of small and large values of N and for geometrically similar fires whose hear outpu t Q is determined by D and M(s), which are shown to satisfy the condit ion N = constant. The required dimensionless specification of regions where such laws may be valid is also derived. Previously suggested pow er laws, some of which appear to be contradictory to each other, are t hen examined. Only two of them have been found to be incompatible with the derived power laws. The remainder are found to be of the simpler forms derived for small, large and constant values of N. copyright (C) 1997 Published by Elsevier Science Ltd.