A model is described for the overall structure of intense fire whirls, based on a spatially evolving vortex, with circulation enhancement driven by the axial acceleration of low-density gas in the core through the axial pressure gradient. The axial acceleration increases the entrainment rate into the core which, through mass conservation, increases the circulation if the angle between the tangential and radial velocity components remains fixed. The two-zone model employs general balance equations for regions inside and outside a cylinder of fixed radius, each inviscid, the inside region being presumed to have a constant density small compared with the (constant) value outside. In the outside region the tangential component of velocity is assumed to be large compared with the radial component, which, in turn, is assumed to be large compared with the axial component. The model predicts an exponential increase of the circulation with axial distance for sufficiently long whirls, which persists until the fuel in the core is completely consumed. Predictions of the model appear possibly to be consistent with the experimentally observed scaling of flame lengths of strong fire whirls.
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Williams, Forman A.
"A simplified model for the intermediate structure of strong fire whirls,"
Progress in Scale Modeling, an International Journal: Vol. 3:
1, Article 2.
Available at: https://uknowledge.uky.edu/psmij/vol3/iss1/2