A bubble coalescence model was developed on the basis of the Lagrangian approach, where bubbles are followed through the turbulent flow field along their trajectories. The collision process was described using a stochastic inter‐particle collision model. Coalescence occurred if the contact time became larger than the film drainage time. The film drainage time was determined by a simple formulation according to classical approaches, whereas the contact time resulted directly from the collision model. The performance of the model was analyzed for bubble rise in a prescribed homogeneous isotropic turbulence field. Moreover, numerical calculations by the coupled Euler/Lagrange approach were performed and compared with measurements in a bubble driven loop facility. The comparison showed reasonably good agreement for liquid and bubble velocities.

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This paper describes an extension and validation of the Euler/Lagrange approach for three-dimensional time-dependent calculations of the flow in a bubble column. The fluid phase was calculated based on the Euler approach solving the unsteady Reynolds-averaged Navier-Stokes equations in a time-dependent way. The conservation equations were closed using the standard k-ε turbulence model. The coupling between the phases is considered through the momentum source terms and source terms in the k- and ε-equations. The usage of the Consistent term for the k-equation and taking into account an additional dissipation due to the presence of small bubbles yielded a reasonable agreement of the predicted turbulent kinetic energy level with measurements. Bubble motion was calculated by solving the equations of motion taking into account drag force, pressure, added mass force, transverse lift force, buoyancy and gravity. Numerical calculations are presented providing information on the sensitivity of the results on several boundary conditions, such as disturbed aeration. The computational results are validated based on available measurements in a laboratory-scale bubble column.

Abstract. This paper presents a mathematical model based on EulerlLagrange approach for time-dependent calculations of two-(gas-liquid) and three-(gasliquid-solid) phase flows in a bubble column. The fluid phase flow was calculated based on the Euler approach by solving the three-dimensional Reynolds-averaged conservation equations in a time dependent way. The set of equations was closed using the standard k-e turbulence model. Two-way coupling was accounted for by adding dispersed phase source terms in all conservation equations of the continuous phase and additionally considering wake-induced turbulence. Bubble motion was calculated by solving the equation of motion taking into account drag force, pressure, added mass force, transverse lift force, buoyancy and gravity. The tracking of solid particles was based on considering drag force, pressure, added mass force, Saffman force, Magnus force and gravity. The introduction of the effective density in the continuous phase conservation equations permitted to perform the calculations up to relatively high volume fractions of the dispersed phase. The interaction between bubbles and particles was considered by adding simple correction terms to the drag coefficient of both bubbles and particles. Alternatively, the interaction was described by collisions between bubbles and particles using a stochastic collision model. The comparison of the predicted results with experimental data from the literature showed reasonable good agreement for the cases of two-phase and three-phase flows.

MehrphasenströmungenModellbildung und numerische Berechnung von Gas/Flüssig-Systemen P r o f. D r. -I n g . M . S o m m e r f e l d * D r. E . B o u r l o u t s k i