Euler-Lagrange Simulations of Bubble Cloud Dynamics Near a Wall

We present in this paper a two-way coupled Eulerian-Lagrangian model to study the dynamics of clouds of microbubbles subjected to pressure variations and the resulting pressures on a nearby rigid wall. The model simulates the two-phase medium as a continuum and solves the Navier-Stokes equations using Eulerian grids with a time and space varying density. The microbubbles are modeled as interacting singularities representing moving and oscillating spherical bubbles, following 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 determined by the bubbles' volume change and motion. Using this numerical framework, simulations involving a large number of bubbles were conducted under driving pressures at 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 nonsynchronized weaker multiple bubble oscillations. The former creates extremely high pressures with peak values orders of magnitudes higher than that of the excitation pressure. This occurs when the driving frequency matches the natural frequency of the bubble cloud. The initial distance between the bubble cloud and the wall also affects significantly the resulting pressures. 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 this results in very high pressure peaks at the wall. At farther cloud distances from the wall, the bubble cloud collapses quasi-spherically with the cloud center collapsing last.