To account for the interaction between bubbles in a swarm

cell models were applied to simulating numerically the bubble motion in a swarm of deformable gas bubbles with a Reynolds number of 50.Simulations were based on the full Navier-Stokes equation of liquid flow in a spherical cell.The stream function and vorticity of the axi-symmetrical flow field were solved in a boundary-fitted orthogonal reference frame.Numerical results suggested significant effects of gas holdup on the drag coefficient and deformation of bubbles in a swarm

but the drag coefficient predicted by the model was much higher than that from theoretical equations based on spherical bubbles in creeping flow.The cell model with zero shear stress as the outer cell boundary condition seemed to behave better than that with zero vorticity condition.It is suggested that the cell model is a potentially reliable approach to resolve the bubble behavior in a dense swarm.