Analysis of the turbulence statistics and anisotropy in homogeneous shear bubbly flow using a turbulent viscosity model

A first-order turbulence model based on a turbulent viscosity formulation is derived from a second-order turbulence closure developed for bubbly flows. The interpretation of the second-order turbulence closure in terms of the turbulent viscosity model leads to an analytical analysis of homogeneous bubbly flows. Based on this analysis, a kepsilon turbulence model is then developed and applied to two homogeneous bubbly flows (uniform and with a constant shear). The simulations show that this ke turbulence model that involves a supplementary scale related to the bubble effects succeeds in the representation of the interfacial effects on the turbulence structure in the two homogeneous bubbly flows.