A Numerical Method for Bubbly Flow Simulation Based on a Multi-Fluid Model

A numerical method based on an $N+1$-fluid model is proposed for the prediction of a three-dimensional unsteady turbulent bubbly flow with nonuniform bubble sizes. Among the $N+1$ fluids, one fluid corresponds to the liquid phase and the N fluids to bubbles. The model can therefore take account of N different bubble sizes. Since the fluid density of each bubble group can differ from that of other groups, the method is also applicable to multi-component flows such as a gas-liquid-solid flow and a liquid-solid flow with various particles. The increase in the number of fluids to be solved does not require any lengthy complicated programming because the calculation of N field equations for the gas phase is easily conducted using a single DO-loop. To demonstrate the potential of the proposed method, unsteady bubble plumes in a water-filled vessel were simulated using the $N+1$-fluid and two-fluid models. As a result, it was confirmed that the $N+1$-fluid model gave better predictions than the two-fluid model for bubble plumes with nonuniform bubble sizes.