Improvement of the two-fluid momentum equation using a modified Reynolds stress model for horizontal turbulent bubbly flows

- Numerical simulations are performed for horizontal turbulent bubbly flows.
- Three different ways to formulate the momentum diffusion terms are tested.
- Proper forms of the momentum diffusion terms are suggested.

Two-fluid equations are widely used for practical applications involving multi-phase flows in chemical reactor, nuclear reactor, desalination systems, boilers, and internal combustion engines. The popular two-fluid equation for a gas-liquid two-phase flow is based on the assumption of interpenetrating continua. According to the experimental data of fully-developed turbulent bubbly flows in a horizontal pipe, the bubble phase velocity is close to or slightly smaller than the liquid phase velocity. The velocity profile is nearly symmetric along the vertical centerline of the horizontal pipe, or tends to be slightly skewed toward the bottom region of the pipe. However, numerical simulations using the momentum equation based on interpenetrating continua showed that, in contrast, the bubble phase was faster than the liquid phase. In addition, the velocity profile was predicted to be skewed toward the upper region of the pipe. These simulation results are not consistent with experimental observations. In the meantime, there are particle averaged momentum equations in which the continuous and disperse phase equations are developed from the equations of motions of fluid and particle, respectively. We considered two different particle averaged momentum equations. The form of one particle averaged momentum equation is similar to that of the momentum equation based on interpenetrating continua, except for the laminar viscosity term. Thus, for a turbulent bubbly flow, this particle averaged equation showed similar results as observed in the momentum equation based on interpenetrating continua. The other particle averaged equation differs from the momentum equation based on interpenetrating continua in both laminar and turbulent viscosity terms. This particle averaged equation showed good agreement with experimental observations.