| Summary: | 碩士 === 國立臺灣大學 === 應用力學研究所 === 102 === This study presents a two-way coupled Eulerian-Lagrangian model to simulate the solid-liquid two-phase flow system with suspension of fine particles. The numerical model solves the momentum equations of carrier flow phase on the Eulerian grid. Particle motion is governed by Newton’s second law and is solved with the particle-in-cell(PIC) method. We develop a three-dimensional particle transport algorithm, in which particle information is stored in the Eulerian grid. The particle motion is split into three directions of the Cartesian coordinate system, and particle movement at each computational time step is restricted to be within one cell in each direction. The algorithm significantly simplifies the calculation of particle motion and the resulting volume flux. To include the finite-size effect of particles, we develop a two-phase projection method that takes mixture incompressibility into account. The method modified both the source term and solver of Poisson-type pressure equation in the fractional-step incompressible flow calculation. Compared to existing models that only consider incompressibility of the carrier flow phase for dilute suspensions, the present model captures the volumetric effect of solid particles. In addition, in order to have a complete physical consideration, the present model takes the added mass into account.
The model is then applied to study the RT instability induced by fine suspended particles. We analyze the thickness of mixing layer and examine the effect of particle size and concentration. Comparison between the present two-phase model and traditional solid-liquid model demonstrates that the influence of pressure coupling becomes important as the concentration increases. To assess the magnitude of the pressure-coupling effect induced by particles only, special cases that only account for particle flux are simulated. The results show that the pressure field induced by the volumetric effect of particles can be of the same order of magnitude of the single-phase pressure field, which demonstrates the importance of the volumetric effect of settling particles.
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