The influence of non-spherical deformations on the peak pressures reached during the collapse of a bubble

In this work we study the influence of non-spherical deformations on the maximal gas pressures reached during the collapse of a cavitating bubble. We use a compressible Navier-Stokes solver [1] to obtain the peak pressures reached for different prolate and oblate spheroidal bubbles with the same initial volume. It is shown that small initial deformations can dramatically reduce the maximum pressures with respect to the case of a spherical bubble, this reduction increasing as the ratio between the ambient pressure and the minimum bubble pressure reached at the instant of maximum volume increases. An energy analysis shows that the kinetic energy at the instant of minimum volume acts as a penalization term on the theoretical peak pressures reached during the collapse. This quantity is shown to be directly related to the generation of vorticity at the interface. The importance of the various mechanisms of vorticity production on the peak pressures is discussed using the numerical results.

[1] Fuster D. and Popinet S., An all-Mach method for the simulation of bubble dynamics problems in the presence of surface tension, J. Comput. Phys., 2018