On the dynamics of instabilities in two-fluid models for bubbly flows

Abstract

In this paper we look at instabilities in bubbly gas-liquid flows and investigate the emergence and characteristics of phase heterogeneities. We apply a shared-pressure two-fluid model to low bubble loadings and demonstrate the existence of persistent gas fraction instabilities of a characteristic size larger than the applied computational grid. In particular, we investigate the influence of a virtual mass effect on the stability of the two-fluid model and we demonstrate a change in the emergence and the dynamics of the phase heterogeneities. The change is accounted to a difference in the degree of hyperbolicity due to the inclusion of the virtual mass force. Furthermore, the results indicate that an initial instability, concluded as numerical in its character, evolves into a state with a physical character of the heterogeneities. We discuss implications of the existence and dynamics of the heterogeneities and the importance of the numerical behavior for interpretation of the results. In particular, we argue that underlying characteristics of the model cannot and should not be concealed with additional sub-models (such as momentum exchange terms) but must be acknowledged in the analysis of results from the two-fluid model for bubbly flows.