A Numerical Study of Bubbles Captured by a Gaussian Vortex

Abstract

The capture mechanics of cavitation nuclei by a Gaussian Vortex is explored. The capture process is examined by both Direct Numerical Simulation of the Navier Stokes equations and a Particle Tracking model. We also investigate the parameters that effect the capture and bubble growth process, and finally we compare the results of the two approaches. The DNS results show that the shape of the bubbles can be significantly distorted as they are captured by a vortex. This distortion can lead to the creation of lift forces that shorten the capture time of the bubbles. The capture times computed with the two methods varied over less than an order of magnitude for most cases, and this suggests that one might derive and average capture time. The exact results of the particle tracking models can vary widely depending on the selected values of the lift and drag coefficients and nominal Weber number of the captured nucleus. For model scale flows, the Weber number may vary from 1 to 100. Thus, it is possible that a particle-tracking model should have variable lift and drag coefficients that better take into account the estimated instantaneous bubble deformation. The drag coefficient by Haberman and Morton (1953) yielded a trajectory that was closer to the DNS trajectory than when using the drag coefficient given by Clift et al.(1978). It was determined that the lift coefficients given by Dandy and Dwyer (1990) and Auton et al. (1988) yielded capture times that were much bigger than the DNS results and that lift coefficient between the those given by Saffman (1965) and Dandy and Dwyer (1990) would give results that are closer to the DNS results.