Modeling Turbulent Flows with Free-Surface in Unbaffled Agitated Vessels

In the present study, numerical simulations of turbulent flow with free-surface vortex in unbaffled vessels agitated by a paddle impeller and a Rushton turbine, which were investigated experimentally by Nagata (John Wiley & Sons:  New York, 1974) and Ciofalo et al. (Chem. Eng. Sci.1996, 51, 3557−3573), respectively, have been carried out. A homogeneous multiphase flow model coupled with a volume-of-fluid (VOF) method for interface capturing has been applied to determine the shapes of the gas−liquid interface and to compute the turbulent flow fields in unbaffled vessels. Turbulence is modeled using the k−/k− based shear-stress transport model (Menter, F. R. AIAA J.1994, 32, 1598−1605) and a second-moment differential Reynolds-stress transport model. Calculations are carried out using the ANSYS CFX-5.7 CFD code (ANSYS:  Canonsburg, PA, 2004). Validation of the predictions is effected against the measured free-surface profiles (Nagata, 1974; Ciofalo et al., 1996), and the mean velocity distributions (Nagata, 1974). The predicted liquid surface profiles using the VOF method in conjunction with both turbulence models are generally in good agreement with measurements. As for the mean velocity components, the Reynolds-stress transport model predictions are superior than those obtained using the shear-stress transport model.