Turbulent bubbly flows are encountered widely in various industrial applications such as nuclear reactor cooling, bubble column reactors, cavitation on ship propellers, and several others. The efficient design of these systems requires the accurate CFD prediction of multiphase flow turbulence. Though the applications involving turbulent bubbly flows are widely encountered, little attention is paid towards developing accurate turbulence CFD models for prediction of these flows. Most works (Ranade, 1997; Behzadi et al., 2004; Lahey, 2005) adopt ad-hoc turbulence models by extending the standard k-ε
model by adding a source term for turbulence production due to the presence of the bubbles, without considering the exact form of the turbulent transport equations. Moreover, second order turbulence closure models are rare and not adopted in many works despite the high degree of anisotropy involved in turbulent bubbly flows (Lance and Bataille, 1991). Keeping in mind these weaknesses, in the present study we propose a multiphase Reynolds-stress model for turbulent bubbly flows derived by Reynolds averaging (RA) the two-fluid model (Drew, 1983) following the procedure described in Fox (2014). The RA of the two-fluid model results in many unclosed terms due to the presence of non-linear terms in the two-fluid equations. The unclosed term resulting due to the RA of convection term or in other words Reynolds stress is accounted by deriving an exact form of transport equation for Reynolds stress from the two-fluid model. The values of all the unclosed terms involved in the momentum and the Reynolds stress transport equations are computed by means of fully resolved mesoscale simulations (Zhang, 2002), and the dependency of the unclosed terms on the loading of the bubbles is investigated. The computational domain for mesoscale direct simulations considered in the present study is a three-dimensional column with square cross-section. Periodic boundary conditions are applied to the sides of the column to create a homogenous turbulent flow to isolate and study the gradient independent unclosed terms which account for the exchange of turbulent quantities between the phases
. The momentum and turbulence energy budgets computed from the mesoscale simulations are reported. Modeling strategies involved in modeling of the unclosed terms based on the budget are also discussed.
Behzadi, A., Issa, R.I., Rusche, H., 2004. Modelling of dispersed bubble and droplet flow at high phase fractions. Chem. Eng. Sci. 59, 759–770.
Drew, 1983. Mathematical modelling of two-phase flow. Annu. Rev. Fluid Mech. 15, 261–291.
Fox, R.O., 2014. On multiphase turbulence models for collisional fluid–particle flows. J. Fluid Mech. 742, 368–424.
M. Lance and J. Bataille (1991). Turbulence in the liquid phase of a uniform bubbly air–water flow. J. Fluid Mech., 222, pp 95-118 doi:10.1017/S0022112091001015
Lahey Jr., R.T., 2005. The simulation of multidimensional multiphase flows. Nucl. Eng. Des. 235, 1043–1060.
Ranade, V., 1997. Modelling of turbulent flow in a bubble column reactor. Chem. Eng. Res. Des. 75, 14–23.
Zhang, Duan Z., and W. Brian VanderHeyden. "The effects of mesoscale structures on the macroscopic momentum equations for two-phase flows." Intl J. Multiphase Flow 28.5 (2002): 805-822.