2D transient filtration model for aluminum

A two-dimensional, transient mathematical model representing the behavior of a deep-bed filter was developed. The flow and mass fraction equations are solved using CFX™ commercial code. The rate equation representing the inclusion deposition and re-entrainment is incorporated into a model as a source term of the mass fraction equation. The resistance of the bed is calculated using the pressure drop calculated by the Ergun equation. The model takes into account all the major physical processes occurring during filtration. For each time step, the model calculates the inclusion concentrations remaining in the liquid and deposited on the filter media. It updates the bed porosity and bed particle size as the inclusions deposit. The model can use either an average inclusion size or a discrete inclusion size distribution. It is also possible to assign different densities to different inclusion sizes if an inclusion distribution is used.