Two-way coupling in shear layers with dilute bubble concentrations

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Abstract
Direct numerical simulations are used to analyze the evolution of a temporally growing two-dimensional shear layer seeded with dilute concentrations of bubbles under gravity. The bubble concentrations are dilute enough so that bubble–bubble interactions can be neglected, but are large enough for cumulative effects of bubbles to influence the flow. The evolution of the bubble field is determined by tracking many individual bubbles, and the flow field is advanced by using the Navier–Stokes equations with a coupling term representing the effect of the bubbles on the flow. The results are interpreted in terms of the vorticity, density, and pressure fields relative to the one-way coupled or passive case. For the coupled case, a reduction in the magnitude of the vorticity and pressure gradients near the vortex center is observed. In addition to modification of the flow, it is observed that the accumulation of bubbles is smaller and the location of the equilibrium points are shifted farther from the vortex center as a result of the coupling. It is explored how these changes are modified by different Froude numbers and bubble sizes. The differences between passive and coupled cases usually increase due to larger accumulations as larger bubbles are considered. However, for certain Froude numbers an optimum coupling is observed at intermediate bubble sizes due to the absence of equilibrium points for large bubbles.