On flame height of circulation-controlled firewhirls with variable physical properties and in power-law vortices : a mass-diffusivity-ratio model correction

Abstract

This paper presents a theory on the flame height of circulation-controlled firewhirls, approximately combining variable physical properties, a power-law vortex model, and a mass-diffusivity-ratio model. The theoretical results show that the dimensionless flame height can be expressed as a multiplication of four dimensionless factors. The first factor is the stoichiometric-mixture-fraction-scaled Peclet number that was first identified by Chuah et al. (2011) in their theory based on the assumptions of Burgers vortex and constant physical properties. The second factor characterizes the axial flame-stretching effect found by Klimenko and Williams (2013) in their theory based on the assumptions of power-law strong vortex and constant physical properties. The third factor quantifies the effect of variable density, which was recently unveiled in Yu and Zhang's (2017) theory. The last factor describes the effect of distinct mass diffusivities of fuel and oxidizer, which has not been considered in the previous studies. Although integrating the first three factors in the theory would lead to an over-prediction to the flame height, accounting for the distinct mass diffusivities of fuel and oxidizer, leading to a mass-diffusivity-ratio model correction, results in the finding of a “reduction” mechanism for the flame height, which is comparable in order of magnitude with the other “enhancement” mechanisms obtained from considering either the power-law strong vortex or variable density.