Modelling bubbly flows

Abstract

Modelling formulations for the transport dynamics of bubbles, drops and particles as disperse elements within turbulently flowing liquid and gas as fluid continua remain contentious and essentially unresolved issues. Broadly, three schools may be distinguished, as follows.First, exclusively Eulerian approaches where Reynolds averaged equations are couched in terms of phase-discriminated quantities. The resulting description conveys a statistically smeared picture of interpenetrating continua coupled by undetermined interphase exchanges for which various force law closures have been advocated semi-empirically. Second, mixed Eulerian-Lagrangian approaches where Reynolds averaged equations are used to represent the continuous phase flow and turbulence in which the motions of individual discrete elements are then simulated using a Lagrangian force law model. Most commonly the fluctuating flows are described as a Gaussian construct on the intensity and scale measures, an approximation which eliminates important features of discrete phase engagement and entrapment within transiently coherent eddies. Third, exclusively Lagrangian approaches where both the continuous and discrete phases are simulated as individual trajectory reaksations prior to recovery of the transport statistics by ensemble averaging.Whilst this last approach incorporates important eddy structural effects on transport, it still relies on independent formulation of the Lagrangian force law whose status remains uncertain for other than a few asymptotic idealisations. Our paper concentrates on the recent history of these developments.