Experimental and Mathematical Study of Incompressible Fluid Flow through Ceramic Foam Filters

Abstract: Ceramic Foam Filters (CFFs) are widely used to filter solid particles and inclusions from molten metal in metal production, particularly in the aluminum industry. In general, the molten metal is poured on the top of a ceramic foam filter until it reaches a certain height, also known as metal head or gravity head. This is done to build the required pressure to prime the filter media and to initiate filtration. To predict the required metal head, it is necessary to obtain the Darcy and non-Darcy permeability coefficients of the filter. The coefficients vary upon filter type. Here, it is common to classify CFFs based on grades or pore per inches (PPI). These CFFs range from10 to100 PPI and their properties vary in everything from cell and window size to strut size. The 80-100 PPI CFFs are generally not practical for use by industry, since the priming of the filters by a gravitational force requires an excessive metal head. However, recently a new method has been developed to prime such filters by using electromagnetic Lorentz forces. This allows the filters to be primed at a low metal head.To continue the research work, it was deemed necessary to measure the pressure gradients of single and stack of commercial alumina ceramic foam filters and to obtain the permeability characteristics. Therefore, efforts have been made to validate the previously obtained results, to improve the permeametry experimental setup, and to obtain Darcy and non-Darcy permeability coefficients of single 30, 50, and 80 PPI filters and stacks of filters. Furthermore, the experimentally obtained pressure gradients were analyzed and compered to the mathematically and analytically estimated pressure gradients.The studies showed that, in permeametry experiments, the sample sealing procedure plays an important role for an accurate estimation of the permeability constants. An inadequate sealing or an un-sealed sample results in an underestimation of the pressure drop, which causes a considerable error in the obtained Darcy and non-Darcy permeability coefficients. Meanwhile, the results from the single filter experiments showed that the permeability values of the similar PPI filters are not identical. However, the stacks of three identical filters gave substantially the same measured pressure drop values and roughly the same Darcy and non-Darcy coefficients as for the single filters.The permeability coefficients of the filters are believed to be best defined and calculated by using the Forchheimer equation. The well-known and widely used Ergun and Dietrich equations cannot correctly predict the pressure drop unless a correction factor is introduced. The accuracy of the mathematically estimated pressure drop, using COMSOL Multiphysics® 5.1, found to be dependent on the drag term used in the Brinkman-Forchheimer equation.  Unacceptable error, as high as 84 to 89 percent for the 30, 50 and 80 PPI single filters, compared to the experimentally obtained pressure gradient values were observed when the literature defined Brinkman-Forchheimer drag term was used. However, when the same second order drag term (containing the non-Darcy coefficient) as defined in the Forchheimer equation was used, the predicted pressure gradient profiles satisfactorily agreed with the experiment data with as little as 0.3 to 5.5 percent deviations for the 30, 50 and 80 PPI single filters.