To analyze a flow through an Aluminium porous body, is it necessary to consider any relationship between the porosity and its permeability?
It depends on the pore size and structure of your metalic foam. I think the approaches made in geophysics should help you:
Pape et al.: Permeability Prediction Based on Fractal Pore Space Geometry, Geophysics 64 (5), 1447-1460, DOI 10.1190/1.1444649
Hi Tuhin,
I'm not an expert in metallic foams, but I would expect the permeability to scale almost linearly with the porosity in that kind of systems. I would also expect the permeability to be proportional to the square of the pore size. These are quite general guidelines for such highly porous materials with low tortuosity (see for instance the Kozeny-Carman model). The effect of porosity might be more complex when it comes to porous materials with lower porosity and higher tortuosity, such as porous rocks (see for instance the Archie's law).
This book chapter might be relevant to you:
http://cdn.intechweb.org/pdfs/19418.pdf
Jean-Michel Hugo, Emmanuel Brun and Frédéric Topin (2011). Metal Foam Effective Transport Properties, Evaporation, Condensation and Heat transfer, Dr. Amimul Ahsan (Ed.), ISBN: 978-953-307-583-9, InTech, Available from: http://www.intechopen.com/books/evaporation-condensation-and-heat-transfer/metal-foam- effective-transport-properties
Cheers,
Romain
Permeability generally depends on porosity in foams because the cell size generally depends on porosity ... It is indeed very common that the higher the porosity, the higher the cell size: this is the usual case for foams. But once you succeed in preparing foams for which the porosity and the cell size can be independently controlled, this is not what you observe, see Fig. 3 of the attached paper. In fact, the permeability doesn't depend on the porosity, but only on the cell size. As a rule of thumb, a power law describes the behaviour very well, but whether the foam is cellular or reticulated, the value of the exponent is not the same.
Alain
See my teaching support materials for permeability within the resin transfer moulding page at https://www.fose1.plymouth.ac.uk/sme/MATS347/MATS347C6%20RTM.htm#k
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