Effect of near-critical swirl on the Burke-Schumann reaction sheet

The influence of swirl on the shape of the Burke-Schumann reaction sheet in a straight cylindrical pipe is investigated by asymptotic and numerical means. Attention is confined to swirl levels that are near the critical value at which vortex breakdown occurs. A high Reynolds number, laminar, isothermal, low Mach number reacting flow is considered. An asymptotic analysis is developed to study the nonlinear interaction between near-critical swirl and mixture fraction distribution within the flow. It is first shown that leading-order perturbation of the velocity field from the columnar state, generated by the interaction of near-critical swirl and low viscosity, can be described by a nonlinear reduced-order model. This flow perturbation is computed, and then employed to determine the correction to the classical Burke-Schumann solution. Under lean conditions of reaction the reaction sheet becomes shorter and more compact as swirl is increased. For rich conditions of reaction, increasing swirl first causes the reaction-sheet length to decrease, and then increase after vortex breakdown has appeared. Numerical simulations of the flow and reaction-zone shape are substantiated by, and supplement, the asymptotic results.