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turbulence model was used for simulating the effect of turbulence on the flow field. Predictions were compared with experimental data for the axial variation of the solids concentration for model validation. Results of the radial variation of the phase velocities are also presented.
doi:10.1016/0894-1777(91)90032-M 
Copyright © 1991 Published by Elsevier Inc.
Modeling the mechanical interaction between the velocity fields in three-phase flow
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Nikolay Ivanov Kolev
, a, Akio Tomiyamab and Tadashi Sakaguchib
Received 24 September 1990;
Abstract
The predictions of IVA3 computer code models describing the mechanical interactions between the velocity fields in liquid-gas, liquid-solid, and liquid-solid-gas bubble flows are systematically compared with Sakaguchi's experimental data for upward pipe flows. For better understanding of the physics of the experiments, a simple model, describing especially the conditions observed in the experiments, was derived by simplifying the theory on which the IVA3 code relies. The model describes an adiabatic, steady-state, three-phase, three-component flow with thermal equilibrium, mechanical nonequilibrium between the velocity fields, and the condition for critical flow.
Ishii and Chawla's correlations for calculation of drag forces for bubbles or solid particles in liquid are checked against the experimental data obtained by Sakaguchi et al The model developed by Kolev for computation of the drag forces when solid particles are free in the flow and the volume fraction of the space among the particles if they were closely packed is larger than the liquid volume fraction was checked against data obtained by Sakaguchi et al for three-phase bubble flow. The agreement obtained between the IVA3 predictions and the data for two- and three-phase flow shows the ability of the Ishii-Chawla correlation and the method proposed by Kolev to predict successfully the drag forces for two- and three-phase flows and the correctness of the mathematical modeling technique incorporated in the IVA3 computer code, the so-called partial resolution of local velocity coupling.
Keywords: multiphase flows; numerical methods; modeling; drag; turbulent flow
