Numerical simulation model of gas–liquid–solid flows with gas–liquid free surface and solid-particle flows

Gas–liquid–solid flow is an important phenomenon in large-scale industrial processes. The difficulties in numerical simulations of these processes lie in the problems of high calculation cost for a large-scale system, the simultaneous occurrence of dispersed and sedimented particle flows, and the coexistence of solid particles and a gas–liquid free surface. In this study, a numerical simulation model of gas–liquid–solid flows was developed based on the continuum description. The volume-of-fluid (VOF) method and granular flow model were coupled in the proposed model. As a result, the proposed model is applicable to gas–liquid–solid flows where a gas–liquid free surface and solid-particle flows coexist. In addition, the use of the granular flow model enabled simultaneous simulations of dispersed and sedimented particle flows. Based on the continuum description, the proposed model has the advantage of low calculation cost compared to the DEM-VOF method. Numerical simulations were conducted to verify the model for the submerged granular collapse, floated granular collapse, water entry, and oscillation on a free surface. The results of the numerical simulations using the proposed model were compared with the simulation results using the DEM-VOF method, experimental results or theoretical relationships. These comparisons indicate that the proposed model is reasonably applicable to the gas–liquid–solid flows. In addition, the limitations of the model were evident in the granular flow along a gas–liquid surface under the influence of capillary effects. Therefore, if the solid particles are small such that the capillary effect is not negligible, the capillary effect should be considered for more accurate numerical simulations.