The prediction of flame heights and flame shapes of small fire whirls

摘要

This paper adds vortex flows around Burke-Schumann diffusion flames to predict the flame heights and the flame shapes of small fire whirls. The resulting model matches the measurements of methanol flames in a previous laboratory experiment and the results of numerical calculations in this paper. Burgers Vortex is assumed inside the vortex core radius, while ideal flow is assumed outside the vortex core radius. The ideal flow is corrected for the viscosity changes inside and outside the flame. If the two vortices are combined, they can be approximated as a Sullivan Vortex. Both the experiments and the numerical calculations show that vortex flows stabilize the flame shape, allowing the flame height as defined in a regular diffusion flame to increase. In fact, regular diffusion flames chop off unburned fuel to form separate plumes. With vortex flow, the flame stretches as if the diffusion rate had been reduced. We adjust Roper's flame height equation to account for the vortex flow and find that the flame height depends on the volume fuel rate and the vortex core radius. If more flows than that required to stabilize the flame were supplied, the radial flows start reducing the flame diameter near the pan, which in turn is balanced by an increase in the volume fuel rate. In the experiment, a balance between the flame temperature, the volume fuel rate, and the flame shape explains why the flame height stops increasing with vortex flows after a fire whirl is generated. In the numerical calculations, we find that the temperature gradient above the port, which controls the fuel evaporation rate, increases with the vortex flows.