On the flame height of circulation-controlled firewhirls with variable density

Abstract

A theoretical analysis on the flame height of circulation-controlled firewhirls is presented with emphasis on studying the influence of variable density that was ignored in most previous studies. A circulation-controlled firewhirl is approximated as a non-premixed flame, with variable density and temperature-dependent diffusivities in a steady and axisymmetric Burgers vortex. A coupling-function-based formulation is established to describe the firewhirl by invoking the assumption of unity Lewis number. By virtue of a Howarth-Dorodnitsyn-like coordinate transformation, the transport equations for the coupling functions can be solved analytically to result in the well-known linear relation between the normalized flame height and the modified Peclet number. The variable density effect in enhancing the flame height is characterized by a dimensionless temperature factor multiplied to the linear relation. For the firewhirls supplied by a fuel in condensed phase, the boundary conditions at the fuel surface are specified by considering the physical mechanism of Stefan flow.