Numerical modelling of gas–liquid flow in stirred tanks

Abstract

A numerical modelling method is presented for gas–liquid flow in mechanically stirred tanks. In this method, the tank is represented by a mesh which explicitly includes the impeller geometry, with impeller motion treated by the multiple frames of reference or sliding mesh methods. Gas–liquid flow is modelled using an ensemble-averaged form of the Eulerian two-fluid equations. This leads to an interfacial force term containing a turbulent dispersion force term, for which a closure expression is applied following the method proposed by Bel F’dhila and Simonin (Proceedings of the Sixth Workshop on Two-Phase Flow Prediction, Erlangen, Germany, pp. 264–273). An important consideration is the increase in drag coefficient on bubbles due to interaction between bubbles and turbulence. By analysing literature data, a new correlation is proposed to account for this increase in drag. Bubble size is also predicted through a bubble number density equation, which accounts for break-up and coalescence phenomena. However, the rapid coalescence near impeller blades is modelled through an algebraic equation, as a function of gas volume fraction, allowing prediction of gas cavities. The modelling method has been applied to a baffled tank stirred by a Rushton turbine, and simulation results are compared with the experimental measurements of Barigou and Greaves (Chem. Eng. Sci. 47(8) (1992) 2009; Trans. I. Chem. E. 74 (1996) 397) for bubble size and gas volume fraction. In comparison with this data, reasonable agreement is obtained over a range of operating conditions, and a significant improvement is demonstrated using the proposed correlation for drag in turbulent flow. The modelling method has also been applied to a tank stirred by a Lightnin A315 impeller. Again, improved results are obtained using the proposed correlation for drag in turbulent flow, and predicted gas holdup is in good agreement with experimental data.