A penalization method for the simulation of bubbly flows

This work is devoted to the development of a penalization method for the simulation of bubbly flows. Spherical bubbles are considered as moving penalized obstacles interacting with the fluid and a numerical method for ensuring the shear free condition at the liquid-bubble interface is proposed. Three test-cases (curved channel, inclined channel and 3D translating bubble) are used to validate the accuracy of the discretization ensuring the slip condition at the interface. Numerical simulations of a rising bubble in a quiescent liquid are performed for moderate Reynolds numbers. Considering bubble terminal velocities, initial accelerations and wake decay, the effect of the penalization viscosity used to ensure a uniform velocity in the penalized object is discussed. Finally, simulations of bubble swarms have been carried out in a fully periodic box with a large range of void fractions from 1% to 15%. The statistics provided by the simulations characterizing the bubble-induced agitation are found in remarkable agreement with the experiments.