A Mathematical Model of Aluminum Depth Filtration with Ceramic Foam Filters: Part I. Validation for Short-Term Filtration

This work presents a mathematical model to compute the efficiency of depth filtration of molten aluminum using ceramic foam filters. In the model, the porous structure of foam filters was represented by a unit cell that takes into account the convergentdivergent nature of the flow field. The steady, two-dimensional, and fully developed flow field within the unit cell was obtained from the numerical solution of the continuity and Navier-Stokes equations. The assessment of the proper assumptions for the model was carried out by comparing the computed velocity field with that experimentally determined for a physical model of the unit cell with scale 10:1 and containing an aqueous solution of CaCl2. The measurements were done using the particle image velocimetry (PIV) technique. The efficiency and the coefficient of initial filtration for foam filters were obtained from the determination of the particle limiting trajectory, resulting from a force balance on a spherical inclusion. This balance included the buoyancy and the viscous drag forces. The last force took into consideration the wall effect on the particle motion. The values of the computed initial filtration coefficient show an excellent agreement with the corresponding measured ones reported for laboratory and plant tests for short-term filtration. This comparison involves several combinations of particle sizes and downward fluid superficial velocities. This model is further extended to study long-term filtration in the second part of the article.