Circulation-controlled firewhirls with differential diffusion

A flame-sheet theory for circulation-controlled firewhirls with differential diffusion is presented to investigate the effects of non-unity and unequal Lewis numbers on the flame shape and height of the firewhirls. Variable physical properties and a piecewise generalized power-law vortex model are implemented in the theory. For the fuel and oxidizer Lewis numbers being unequal but close to unity, the perturbation solutions of the Burke-Schumann-like transport equation for the Lewis-number-weighted coupling functions were obtained by using the Green's function method. The derived flame height expression not only confirms the previous discoveries, such as the Peclet number effect found by Chuah et al. (2011), the strong vortex effect by Klimenko and William (2013), and the variable density and mass diffusivity effects by Yu and Zhang (2017), but also demonstrates that the mass-diffusivity-ratio model correction newly proposed by Yu and Zhang (2017) is attributable to the leading-order non-unity Lewis number effect. The validity of the differential diffusion effects on the flame height was extended to arbitrary Lewis numbers and verified by means of the approximate far-field similarity solutions of the mixture fraction.