Droplet Interaction with a Conical Shock

Abstract

This work presents an experimental investigation of the deformation and breakup of water drops behind conical shock waves. A conical shock is generated by firing a bullet at Mach 4.5 past a vertical column of drops with a mean initial diameter of 192 microns. The time-resolved drop position and maximum transverse dimension are characterized using backlit stereo videos taken at 500 kHz. A Reynolds-Averaged Navier Stokes (RANS) simulation of the bullet is used to estimate the gas density and velocity fields experienced by the drops. Classical correlations for breakup times derived from planar-shock/drop interactions are evaluated. Predicted drop breakup times are found to be in error by a factor of three or more, indicating that existing correlations are inadequate for predicting the response to the three-dimensional relaxation of the velocity and thermodynamic properties downstream of the conical shock. Next, the Taylor Analogy Breakup (TAB) model, which solves a transient equation for drop deformation, is evaluated. TAB predictions for drop diameter calculated using a dimensionless constant of C2=2, as compared to the accepted value of C2=2/3, are found to agree within the confidence bounds of the ensemble averaged experimental values for all drops studied. These results suggest the three-dimensional relaxation effects behind conical shock waves alter the drop response in comparison to a step change across a planar shock, and that future models describing the interaction between a drop and a non-planar shock wave should account for flow field variations.