Numerical Simulation of Dynamic Flow Behaviour in a Bubble Column: Comparison of the Bubble-Induced Turbulence Models in the k-ε Model

Numerical simulations of the gas-liquid bubbly flow in a bubble column were conducted with the commercial CFD package CFX-4.4 to investigate the performance of three models (Pfleger and Becker, 2001; Sato and Sekoguchi, 1975; Troshko and Hassan, 2001) to account for the bubble-induced turbulence in the k-ε model. Furthermore, the effect of two different interfacial closure models was investigated. All the predicted results were compared with experimental data. All three approaches could produce good solutions for the time-averaged velocity. The models of Troshko and Hassan (2001) and Pfleger and Becker (2001) resolve more details of the bubbly flow than the model of Sato and Sekoguchi (1975) does. In the top part of the column, the models of Troshko and Hassan and Pfleger and Becker under-predicts the liquid phase vertical velocity. Based on the comparison of the results for two columns of different aspect ratio (H/D = 3 and H/D = 6), it was found that the model of Pfleger and Becker (2001) performs better than the model of Troshko and Hassan (2001), while the model of Sato and Sekoguchi (1975) performs the worst. Furthermore, it was found that the interfacial closure model proposed by Tomiyama et al (2002) performs better for the tall column. NOMENCLATURE Ck model constant CD drag coefficient CL lift coefficient CVM virtual mass coefficient Cε model constant Cε2 model constant Cε1 model constant Cμ model constant Cμ ,BIT model constant d diameter D column depth E bubble aspect ratio Eo Eötvös number g acceleration of gravity H column height k turbulent kinetic energy M r interface force vector p pressure t time U r velocity vector W column width α phase volume fraction ε turbulence dissipation rate μ dynamic viscosity ρ density σk model constant σε model constant τ strain-stress tensor Subscripts k phase indices rms root of mean square B bubble BIT bubble-induced turbulence D drag force G gas L liquid, lift force Lam Laminar Tur turbulent VM virtual mass force INTRODUCTION Bubble column reactors are widely used in chemical, petrochemical and biochemical processes. The ability to predict fluid flow dynamics is of paramount importance in designing and developing bubble column reactors. Experimental investigation and numerical simulations are widely used to carry out predictions and analyse gas-liquid fluid flow process. Two approaches are mostly used to simulate the flow in bubble columns: the Euler-Euler (E-E) and EulerLagrange (E-L) approach. The E-L method is more suited for fundamental investigations of the bubbly flow while the E-E method is preferred in high gas hold-up and churn turbulent flows (Pan, Dudukovic and Chang, 1999). For both approaches, despite considerable efforts, accurate modelling of the two-phase turbulent Reynolds stress and interfacial forces remains an open question even for simple dispersed bubbly flow. In most work on gas-liquid two-phase flow, turbulence in the liquid phase is assumed as the sum of the shear and bubble-induced turbulence field and turbulence modelling is mostly done using a similar approach as for singlephase flow. Both k-ε and sub-grid scale (SGS) models are widely used in the simulation of the gas-liquid two-phase flow in the literature. Through a study of both the k-ε and sub-grid scale (SGS) models used in the simulation of