Simulation models for unsteady dispersed multiphase flows

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The early-time evolution of two-dimensional flows induced by rising small bubbles, which are released at short intervals on the bottom of an open vessel, has been examined by using a new numerical method. In the present method, the variation of the relative liquid velocity along bubble trajectories is approximately represented to be piecewise linear, and the short-time motion of discrete bubbles is described in terms of the exact solution to the full Basset-Boussinesq-Oseen (B-B-O) equation for constant fluid acceleration. Bubbly fluid is then assumed to be a continuum, the mass desity and the viscosity of which fluctuate in space and time via intermittent existence of moving bubbles, and the velocity and pressure of the bubbly fluid is obtained from numerical integration of the Navier-Stokes and continuity equations. The numerical method to be proposed in this study has the following significant advantages : The use of the exact solution to the B-B-O equation reduces both computer mem … More ory and CPU time necessary to numerically analyze the motion of a large number of bubbles. The use of the full B-B-O equation makes it possible to take into account the historical effects on bubble behavior, which are represented by the so-called Basset term and often neglected without any consensus for the difficulty in its numerical treatment. We applied this method to numerical simulations of the transient bubbly flow in a two-dimensional vessel of a square cross-section under the effect of the gravity. The validity of this method has been confirmed by comparing the numerical results with the experimental ones. In this application, we have shown that the whole flow becomes highly asymmertric and plume exhibits unstable meandering, when relatively small bubbles are released with their arrangement being symmetric with respect to the vessel centerline. In addition, it is observed that the flow recovers its symmetry and the plume is stabilized if we introduce relatively large bubbles into the unstable above flow by adding the large ones to the symmetric arrangement of the small ones. Less