Numerical simulation of gas -liquid bubbly flows.

Abstract

The properties of gas-liquid bubbly flows are investigated by direct numerical simulation. Using a parallelized version of a front-tracking/finite-difference method, three-dimensional simulations of up to 216 bubbles are performed at Reynolds number of about 20. The effects of inertia, viscosity, surface tension, and interface deformation are all accounted for. Homogeneous flows are analyzed first to examine the interaction of the bubbles in the absence of walls. They are approximated by a periodic cell model, where each cell contains between 1 and 216 bubbles of the same size. Simulations are performed for both spherical and ellipsoidal bubbles. The effect of the number of bubbles in the periodic cell is investigated. A good estimate of the average rise velocity can be obtained with 12 bubbles but larger simulations are needed to determine the fluctuation velocities of the bubbles and the liquid. The void fraction ranges from 2% to 24%, corresponding to dilute and dense suspensions, respectively. As the void fraction increases, it is found that the average rise velocity decreases, but the fluctuation velocities increase. The dispersion process can be described by a diffusion model, with strongly anisotropic diffusion coefficients. The kinetic energy spectrum follows a power law at high wavenumbers, with a slope of -3.6 for spherical and ellipsoidal bubbles and for all void fractions. An analysis of the microstructure reveals a preference for pairs of spherical bubbles to align themselves horizontally and for pairs of ellipsoidal bubbles to align themselves vertically. A consequence for the ellipsoidal bubbles is the development of an instability, where the bubbles form a vertical stream and accelerate. For the spherical bubbles, the formation of horizontal layers is observed at high void fraction. Finally, vertical wall-bounded channel flows are analyzed to examine the effect of walls and of a mean pressure gradient on the lateral migration of the bubbles. A peak of bubble concentration is observed at the walls in the case of an upflow.