A two-equation multidimensional model of turbulent bubbly flows

A new model of turbulence in bubbly flows was developed based on the two-phase extension of single-phase k-3 model. Phase indicator function approach together with ensemble averaging was applied to the single-phase equations of fluid motion to receive a two-fluid model. An exact equation of turbulent kinetic energy for the two-phase system was derived. This equation contained single-phase and unknown interfacial terms. A closure was proposed for the turbulent interfacial terms. The proposed closure was based on the assumption of high density ratio typical for the most of bubbly flows. The interfacial turbulence terms account for an additional turbulence in liquid created by the bubble wakes. The modeled form of liquid dissipation rate balance contained two distinct turbulence dissipation time scales: one for the single-phase shear induced turbulence and the other for the bubble induced turbulence. The proposed turbulence model contains unknown empirical constants. To estimate the values of these constants, the model was implemented in CFX4.2 commercial CFD solver. Comparing numerical prediction to experiment, constant values were estimated by trial and error method. To verify universality of found constants, model's predictions were compared to other experiments. The comparison showed, that the model constants have certain generality. In particular, experimentally observed phenomenon of bubble induced liquid turbulence reduction was predicted and elucidated. Model was also able to qualitatively predict bubble size effect on the liquid turbulence. However, it was found that for some downward flows eddy diffusivity assumption is not valid.;A new logarithmic wall law was derived for bubbly flows. The derivation of the law was based on the assumption of additional turbulent viscosity associated with bubble wakes in the boundary layer. The new wall law contained empirical constant accounting for non-linearity of bubble and shear induced turbulence interaction. The value of this constant was deduced from experimental data. An improved wall friction prediction was achieved with the new wall law over conventional single-phase wall law. The improvement was especially noticeable for the low liquid flow rates when bubble induced turbulence plays a significant role. The model was also able to predict bubble size effect on the wall shear stress.