University of Toronto
Toronto, Ontario, Canada
Computational methods for predicting the motion of pure and dusty gases using the Euler and Navier-Stokes equations have advanced considerably over the past thirty years. However, immense difficulties in obtaining practical solutions to interesting and industrial problems must still be overcome. For example, do credible predictions exist for the formation and movement of sand dunes from atmospheric winds, the erosion and settling of sediment in river flows with meandering channels, the explosive impregnation of metal surfaces by ceramic powder to increase surface-wear resistance, the falling flow of undulating sand from the neck of a simple time clock, the upward percolating flow of gas through porous beds of jostling particles in some combustion chambers, the motion of volcanic ash and man-made pollutants in the atmosphere, and the mixing and solidification of stirred materials in molds? These immense computational difficulties stem from a variety of separate and inter-related sources, some of which involve the inadequate modelling of physical processes and others involve inadequate computational schemes and insufficient speed and storage of modern computers. In more detail, some computational difficulties include the following:
-- inadequate grid schemes and related resolution of viscous two- and three-dimensional flow fields around many moving particles of different shapes and sizes,
-- omission of some relevant source and other terms from Euler's equations for flows with embedded finite-sized particles moving under the influence of drag with mass and heat transfer,
-- inadequate turbulence models to properly include the effects of turbulence in the flow field near and far away from moving particles
-- inability to include realistic effects of the interactions of densely packed, finite-volume, particles with each other when the particle phase is treated simply as a continuum,
-- inadequate models of intergranular friction between colliding particles and between particles and wall surfaces,
-- inadequate treatment of particle-particle collisions with resulting transfers of linear and angular momentum and energy, and
-- restricted central processor times of modern computers to compute three-dimensional, realistically sized, flow fields with adequate fine-grid resolution.
Current computational limitations and difficulties of predicting dusty-gas flows are discussed with examples taken from past publications and reports. The specific intent of the discussion is to help classify various methods of solving dusty-gas flows and thereby illustrate the current state-of-the-art. This approach should help to illustrate future trends in solving dusty-gas flow problems and their related two-phase flow problems.