محدودیت های بسته بندی ذرات در شبیه سازی سیستم ذرات مایع

A procedure is described for limiting the void fraction in fluid particle systems, computed by means of numerical multiphase flow simulation codes, to values which do not fall below those realisable in practice. It is based on a computation of the particle–particle contact forces which come into play only when computed void fractions fall to values below those corresponding to random packing of the particles. The general method is illustrated with reference to the process of sedimentation using a specific fluid-dynamic formulation of the equations of change for fluidization. Without the particle contact force algorithm, the particles compact to the physically meaningless void-fraction of 0.17; with the algorithm the random packing value of 0.4 is achieved.

A serious problem that arises in the application of numerical multiphase-flow codes to the two- and three-dimensional simulation of fluid–particle interaction systems concerns the lower void fraction limit. This corresponds to the situation of the particles coming into contact with one another, giving rise to contact forces which return the void fraction to the value corresponding to that in a randomly packed bed (typically, 0.4 for spherical particles of a uniform size). Formulations in terms of a continuum description of the particle phase pay no heed to this phenomenon unless possessed of a specific mechanism which comes into play as this limit is approached. Without such a term, void fractions may fall unrealistically, resulting in physically meaningless solutions. The problem becomes particularly acute for the simulation of gas-fluidized beds of moderately sized particles (above about 100 μm in diameter), which tend to give rise to almost completely void gas bubbles rising through a particle phase which remains at a void fraction very close to the packing limit. G(ε) is typically assumed to be a power or exponential function of void fraction. Many forms for G(ε), representing orders of magnitude differences, have been proposed in the literature ( Massoudi, Rajagopal, Ekmann & Mathur, 1992). The problem with this approach is that, to be effective, G(ε) must increase enormously over a narrow range of void fraction at the approach to the packing condition. In contrast to the notion of such a term being necessary for system stability ( Gidaspow, 1986), its inclusion in the equations may well lead to numerical instability. A close reading of reported applications (see for example Gidaspow, 1994), supports these misgivings

A numerical approach has been described for the estimation of particle pressure in regions of a fluid particle system that prevents the void fraction from falling below the fixed-bed value for randomly packed spheres during the course of a CFD simulation. The proposed mechanism effectively simulates the particle–particle contact forces that come into play in practice limiting the compaction of the solids. The approach is similar to the one adopted for the adjustment of fluid pressure in the K-FIX simulation code of Rivard and Torrey (1977).