On the force competition in bubble columns: A numerical study

Abstract

Computational Fluid Dynamics (CFD) is nowadays fully accepted in engineering practice as a potential tool for the prediction of flows, conversion rates and process efficiency. The Euler/Lagrange is one of the available approaches for describing dispersed multiphase systems, for example in bubble columns. Hence, the flow field within the bubble column is computed using large eddy simulations (LES) considering full coupling with the bubble phase through momentum source terms as well as sub-grid-scale (SGS) turbulence modification by modelling bubble induced turbulence (BIT). Despite the required point-particle approximation, necessary for computing large-scale technical and industrial systems, bubble dynamics was included in the numerical modelling, through shape (eccentricity) and trajectory oscillations. The performance of the proposed bubble dynamics model is analysed in detail and it is shown that without a bubble dynamics model the bubble fluctuating velocities cannot be predicted correctly. In order to predict the bubble motion accurately it is necessary to account for all relevant acting forces in the calculations, namely, gravity/buoyancy, drag, transverse lift, added (virtual) mass, fluid inertia (part of the pressure term), Basset (history term) force and possibly modifications of these forces due to the presence of walls. Based on the state-of-the-art, instantaneous resistance coefficients for all these forces were elaborated and extended for allowing consideration of the bubble dynamic behaviour and deformation through the eccentricity. The proposed resistance coefficients do not consider any swarm effects and are therefore only applicable to bubbly systems with volume fractions of less than 5%. For the beginning clean systems with mobile bubbles are considered only which are moving in low-viscous systems such as a water-air two phase flows with small bubble Morton numbers. Most important, a lift force coefficient which is valid for such low viscous systems is applied based on recent studies. Consequently, a comprehensive and complete model is introduced for describing bubble motion in a point-particle approximation including bubble dynamics (eccentricity) and therefore using composite formulations especially for drag and transverse lift, and in addition accounting for added mass with bubble deformation and wall effects as well as the Basset force. For the regime of deformable bubbles, the resulting instantaneous resistance coefficients are extracted from bubble column simulations and compared with the mean resistance coefficients. Moreover, the local importance of all considered forces on the motion of bubbles within the bubble column was evaluated in detail in terms of bubble size, column height, radial position and Stokes number without and with bubble dynamics model. The importance of these forces and the correspondent effects on the velocity and volume fraction profiles are explored for a laboratory-scale bubble column. The influence of the bubble dynamics model and the considered interfacial forces on the predicted hydrodynamics of the laboratory bubble column is analysed for validation considering two cases with different bubble size distributions with sizes smaller than about 5 mm. Furthermore, the effect of Basset term on particle dispersion is highlighted in a turbulent pipe flow test case.