First and Second Order Turbulence Closures Applied to Homogeneous Turbulent Bubbly Flows

First and second turbulence models for turbulent bubbly flows are implemented in the CFD code. In the second order turbulence closure, the Reynolds stress tensor of the continuous phase is split into two parts: a turbulent part produced by the gradient of the mean velocity and a pseudo-turbulent part induced by the bubbles displacements; each part is predetermined by a transport equation. The turbulent viscosity issued from this modeling takes into account the excess of the agitation and the supplementary eddies stretching due to the bubbles displacements. First order turbulence closure based on this turbulent viscosity is deduced and a three-equation turbulence model (k, ks, epsilon) is developed. We present the most prominent steps of the modeling and of its implementation in the CFD code then we comment the application of the model in the two homogeneous turbulent flows (uniform and uniformly sheared bubbly flows).