Euler-Lagrange Simulations of Bubble Cloud Dynamics Near a Wall

Abstract

We present in this paper a two-way coupled Eulerian-Lagrangian model to study the dynamics of microbubble clouds exposed to incoming pressure waves and the resulting pressure loads on a nearby rigid wall. The model simulates the two-phase medium as a continuum and solves the N-S equations using Eulerian grids with a time and space varying density. The microbubbles are modeled as interacting spherical bubbles, which follow a modified Rayleigh-Plesset-Keller-Herring equation and are tracked in a Lagrangian fashion. A two-way coupling between the Euler and Lagrange components is realized through the local mixture density associated with the bubbles volume change and motion. Using this numerical framework, simulations involving a large number of bubbles were conducted under driving pressures of different frequencies. The results show that the frequency of the driving pressure is critical in determining the overall dynamics: either a collective strongly coupled cluster behavior or non-synchronized weaker multiple bubble oscillations. The former creates extremely high pressures with peak values orders of magnitudes higher than that of the excitation pressures. This occurs when the driving frequency matches the natural frequency of the bubble cloud. The initial distance between the bubble cloud and the wall is also critical on the resulting pressure loads. A bubble cloud collapsing very close to the wall exhibits a cascading collapse with the bubbles farthest from the wall collapsing first and the nearest ones collapsing last, thus the energy accumulates and then results in very violent pressure peaks at the wall. Farther from the wall, the bubble cloud collapses quasi spherically with the cloud center collapsing last.