A two-equation turbulence model of turbulent bubbly flows

Abstract

A two-fluid model of turbulent, adiabatic bubbly flow was implemented in the computational fluid dynamics (CFD) CFX4.2 program and validated. Turbulence in the dispersed (bubble) phase was neglected. Liquid turbulence was modeled through a two-phase extension of the single-phase standard k– ε model. Conservation equations of turbulent scales contain single-phase and interfacial terms. A closure for the interfacial turbulence terms was proposed based on the assumption of low-bubble inertia and neglecting surface tension. The interfacial turbulence terms account for additional pseudoturbulence in liquid created by bubble-induced mixing. The proposed turbulence model contained the single empirical constant in the modeled dissipation rate balance. The model was implemented in the CFX4.2 commercial CFD solver. Comparing numerical predictions to the experimental data the value of the model constant was estimated. Model predictions were compared to other bubbly flows to prove the universality of the model constant. The comparison showed that the constant has a certain generality. A new, two-phase logarithmic wall law was also implemented and validated. The derivation of the new law was based on an assumption of the additional eddy diffusivity due to the bubble-induced stirring in the boundary layer. An improved wall friction prediction was achieved with the new wall law over conventional single-phase law. The improvement was especially noticeable for the low-liquid flow rates when bubble-induced pseudoturbulence plays a significant role. The ability of the model to account for bubble size effect was also studied.