Dynamics of microscale shock/vortex interaction

Abstract

Molecular simulations in a dilute monatomic gas were carried out to characterize the mutual interactions of impinging planar shocks of up to Mach 3 with transverse microvortices having core sizes comparable to the thickness of the shock. Time dependent simulations were performed using the direct simulation Monte Carlo method and then analyzed by applying transport theory to the sampled molecular results. Several flow cases were computed for initially stationary, composite vortices. The results reveal the generic features of the interaction, the effect of vortex size, and the effects of shock strength. In all cases, the applied straining compression in the shock was of the same order as the time scale of the vortex rotation. Most of the features found in shock interaction with a macroscale vortex of the same type were also found at microscale. These include acoustic wave formation, shock diffraction and refraction, vortex deformation and displacement, and dilatational vorticity generation greater than baroclinic vorticity generation. However, the major characteristic that dominated at microscale was the viscous attenuation of the vortex. In contrast to the net vorticity production due to interaction that has been demonstrated at macroscale, the attenuation overwhelmed the vorticity generation mechanisms at microscale, within the parameter ranges studied. The data allowed for the direct computation of the dissipation rate of kinetic energy, which was found to be high inside the shock wave throughout the interaction and significantly higher than a local thermodynamic equilibrium rate computed using the Newtonian continuum constitutive law with Stokes’ hypothesis. The differences between the two rates were substantial for a Mach 3 shock; but at Mach 2 they were close enough to decompose the continuum rate expression to infer the contributions of the various forms of dissipation to the actual rate.