Vorticity production in shock diffraction

Abstract

The production of vorticity or circulation production in shock wave diffraction over sharp convex corners has been numerically simulated and quantified. The corner angle is varied from 5° to 180°. Total vorticity is represented by the circulation, which is evaluated by integrating the velocity along a path enclosing the perturbed region behind a diffracting shock wave. The increase of circulation in unit time, or the rate of circulation production, depends on the shock strength and wall angle if the effects of viscosity and heat conductivity are neglected. The rate of vorticity production is determined by using a solution-adaptive code, which solves the Euler equations. It is shown that the rate of vorticity production is independent of the computational mesh and numerical scheme by comparing solutions from two different codes. It is found that larger wall angles always enhance the vorticity production. The vorticity production increases sharply when the corner angle is varied from 15° to 45°. However, for corner angles over 90°, the rate of vorticity production hardly increases and reaches to a constant value. Strong shock waves produce vorticity faster in general, except when the slipstream originating from the shallow corner attaches to the downstream wall. It is found that the vorticity produced by the slipstream represents a large proportion of the total vorticity. The slipstream is therefore a more important source of vorticity than baroclinic effects in shock diffraction.