A mathematical model of aluminum depth filtration with ceramic foam filters: Part I. Validation for short-term filtration

Abstract

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 convergent-divergent 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 CaCl 2 . 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 shortterm 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.

Non‐Isothermal Simulations of Aluminum Depth Filtration

“…[2,3] 2) The fluid flow remains laminar during the depth filtration of liquid aluminum, since Re pore % 28 and Re strut % 5.…”

“…This mechanism is known in the literature as the depth filtration. [1][2][3][4] A clear understanding of the filtration process is essential in order to assess the importance of the filter geometry and the process conditions for the desired deposition of particles. However, the effective physical processes cannot be readily identified by the conventional measurement methods, owing to the complex filter geometry and the harsh conditions (e.g., high temperature), encountered during the casting process.…”

“…[2] On the other hand, Tian et al [7] numerically solved the mass balance equations for investigating the transient effects during aluminum filtration. Acosta and Castillejos [3,4] simulated the aluminum depth filtration using the FVM. Considering the same process, Riviere et al [8] applied a 2D single relaxation time (SRT) lattice Boltzmann method (LBM) in order to solve the fluid flow.…”

“…[10,11,14,15] The trajectories of inclusions are most often determined by numerically solving the equation of motion for the particles. [3,4,[8][9][10][11][12][13][14][15] In the present work, both fluid flow and heat transfer during the aluminum depth filtration are considered. In particular, the influence of local temperature variation on the fluid flow and the particle deposition due to temperature-dependent density and viscosity of the melt is investigated.…”

“…[14,15] In addition, the filtration efficiency is most often observed to be an exponential function of the depth inside the filter. [1,3] Employing the filtration coefficient, obtained from the numerical simulation for a representative section of the filter, the filtration efficiency can be extrapolated for the larger filter depths, encountered in the filtration experiments.…”