Direct numerical simulations of bubbly flows

Abstract

Direct numerical simulations (DNS) of multi-fluid and multiphase flows have progressed enormously over the last decade or two. It is, in particular, now possible to simulate the evolution of hundreds of bubbles in laminar and turbulent flows for a long enough time so that meaningful statistical quantities can be collected. For bubbly flow in vertical channels DNS have provided considerable new insight into the structure of the flow and how it can be modeled. The flow structure depends sensitively on the sign of the lift force on the bubbles. For nearly spherical bubbles in both upflow and downflow the lateral migration of bubbles results in a core region where the weight of the mixture exactly balances the imposed pressure gradient. For upflow bubbles accumulate at the wall but for downflow the region next to the wall is free of bubbles. The results lead to a very simple model of the void fraction distribution and, for downflow the velocity and the flow rate can be predicted relatively accurately. Deformable bubbles result in a very different flow structure, with no bubbles accumulating at the wall. Simulations of the transient motion show that it takes a long time for the flow to reach a steady state and that the evolution is complex, with bubbles moving in and out of the wall-layer. The availability of DNS results calls for more intense efforts to use the data for developing closure terms for models of the average and large-scale flows, as well as the development of efficient and accurate methods for more complex flows, such as those undergoing topology changes and involving additional physical effects like surfactants and heat and mass transfer.