Euler-Euler Closure for Bubbly Flows with Full Reynolds Stress Model and Anisotropic Bubble-induced Turbulence

In the present work, Euler-Euler modeling of bubbly flows is combined with a full Reynolds stress model for the turbulence in the liquid carrier phase. Reynolds stress models have only rarely been explored in this context, although effects requiring this level of description are frequently encountered in industrial applications towards which the Euler-Euler approach is geared. In particular, source terms describing the additional bubble-induced contribution to the liquid phase turbulence with proper account for its anisotropy have not firmly been established yet. A formulation based on the direction of bubble motion relative to the liquid is given here. Two well-known variants of Reynolds stress models due to Launder, Reece and Rodi and Speziale, Sarkar and Gatski are compared. Closure relations for the bubble forces are applied that have been shown previously to work well over a range of conditions. The model is validated by comparison with a set of pipe flow data that contains variations of liquid and gas flow rates as well as different pipe diameters. An important criterion for the selection of the data was to provide measurements of individual components of the Reynolds stress tensor.