Shock generated vorticity in spark discharges

TL;DR

This study investigates how shock wave curvature and strength in spark discharges generate vortex ring vorticity, combining high-speed imaging, modeling, and experimental validation to understand the flow dynamics.

Contribution

It provides a quantitative analysis linking shock wave properties to vortex ring vorticity, validated by experimental measurements and modeling.

Findings

Vorticity peaks near maximum shock curvature.

Shock curvature and strength increase with electrical energy.

Model estimates of vorticity match experimental measurements.

Abstract

Spark discharges induce a complex flow field consisting of a shock wave at early times (~ 1 $\mu$ s), a pair of vortex rings, and a hot gas kernel. The vortex rings entrain ambient gas into the hot gas kernel and control its cooling and expansion. In this work, we investigate the shock wave's contribution in producing the vortex ring vorticity. We analyze high-speed (700 kHz) schlieren images of the shock wave for a range of electrical energies to measure the shock properties and estimate shock velocity and curvature. These measurements are combined with a model to calculate the vorticity generated. The measurements show that the highest vorticity is generated near the peak shock curvature location, and the shock curvature and strength increase with electrical energy deposited. A comparison of the vorticity estimated from the model to vorticity measurements from stereoscopic particle image velocimetry shows the results to be statistically equivalent. This suggests that the shock curvature and velocity contribute to the vortex rings induced by spark discharges.