An analytical and computational investigation of shock-induced vortical flows with applications to supersonic combustion

摘要

The motivation for study of shock-induced vortical flows is the problem of achieving rapid and efficient mixing of fuel and oxidizer in a SCRAMJET engine. In particular, the interaction of a shock wave with a jet of light gas generates vorticity which can be used to stir and mix the fluids. This investigation consists of two parts.ududThe first part is a characterization of the basic fluid mechanics of the interaction. The canonical problem is a shock wave passing over a circular light gas inhomogeneity located within a finite channel. The pressure gradient from the shock wave interacts with the density gradient at the edge of the inhomogeneity to deposit vorticity around the perimeter. As time goes on, the structure rolls up into a pair of counter-rotating vortices. This flow is simulated numerically by integrating the governing equations subject to specified initial conditions. From first principles, analytical models are developed to predict the circulation, spacing, and characteristic time for development as a function of initial conditions. From perturbation analysis, another model is developed to predict the vortex pair velocity as a function of the geometrical parameters vortex size/vortex spacing and vortex spacing/channel spacing. The agreement between models and computations is generally good. These models represent the first successful and comprehensive characterization of the fluid mechanics of the canonical flow.ududThe second part is an investigation of mixing efficiencies for various initial configurations. In the canonical flow, stabilization of the vortex pair eventually impairs the mixing. Various initial configurations are considered with the goal of improving the mixing. The mixing is quantified by an asymptotic stretching rate of a material element. Single jet shape perturbations yield little improvement in mixing, but multiple jet arrays do, especially through the phenomenon of entrainment. Another way to improve the mixing is to hit a vortex pair with a reflected shock. Finally, a mathematical correspondence is exhibited between the unsteady 2-D flows considered here and the corresponding 3-D steady flows that may be more typical of real combustor designs.