For most bubbly flow applications the flow field is turbulent. In that case, use a turbulence model and solve for the averaged velocity field. The Bubbly Flow, Turbulent Flow interfaces include the turbulence models described in Theory for the Turbulent Flow Interfaces, but the material properties of the liquid phase are used. In addition to the options of the single-phase flow model, in The Bubbly Flow, k-ε Interface, The Bubbly Flow, Realizable k-ε Interface, The Bubbly Flow, k-ω Interface, The Bubbly Flow, SST Interface, The Bubbly Flow, Low Re k-ε Interface and The Bubbly Flow, v2-f Interface it is also possible to account for bubble-induced turbulence — that is, extra production of turbulence due to relative motion between the gas bubbles and the liquid. The transport equation for the turbulent kinetic energy, k, includes a source term Sk which accounts for bubble-induced turbulence and is given by

The transport equation for the turbulent energy’s dissipation rate, ε, includes the following source term:

The following source term is added to the transport equation for the specific dissipation rate, ω:

Suitable values for the model parameters Ck, Cε, and αω are not as well established as the parameters for single-phase flow. In the literature, values within the ranges 0.01 < Ck < 1, 1 < Cε < 1.92 have been suggested (Ref. 1), and αω can be defined as αω = Cε − 1.

In the v2-f turbulence model, the ζ-equation also gets a contribution,

where lw is the wall distance variable and its gradient gives the wall-normal direction. Such modeling assumes that the bubble-induced turbulence kinetic energy is pumped into the component of k aligned with uslip.

Using a turbulence model that solves for the turbulent kinetic energy, k, together with a gas concentration that is not assumed to be low, the stress tensor contains an extra contribution, and the momentum equations becomes