Pore-scale level numerical simulation of flow in a solid foam: an Immersed Boundary Method (IBM) based approach

There has been an increasing trend on the use of novel materials to improve the process efficiency in a cost effective way and to minimize the total weight/volume of equipment. Open cell solid foams, consisting of cellular structures made of metal or ceramics is one such material which is extensively used over the past few decades to form porous media. Due to its large surface area to volume ratio with minimal pressure drop, it is widely applied in heat transfer devices like heat exchangers, thermal energy absorbers, vaporizers, heat shielding devices etc.. Moreover, it is also gaining popularity in several other applications like high temperature filters, pneumatic silencers, catalytic reactors etc. In chemical process industries solid foams are popular as catalyst support which improves gas-liquid contacting to enhance heat and/or mass transfer rates with minimal pressure drop as compared to other packing material. Also high velocity difference between the flowing phase and stationary support increase the transport rate, which can be achieved by using solid foam. To design and optimize such processes it is necessary to understand the hydrodynamic behaviour of fluid flow through such material. Due to the random and complex geometrical shapes, most of the work on solid foams is experimental, and a limited number of numerical and analytical studies are available in literature. To study the flow at pore-scale level, we have developed an Immersed Boundary Method (IBM) based simulation technique. A second order accurate implicit Immersed Boundary Method (IBM) inspired by Deen et al. (2012, Chem. Eng. Sci. 81, pp. 329-344) is implemented to resolve such structure on a non-boundary fitted computational-grid. A single representative unit cell (RUC) of the solid foam in a periodic computational domain is considered and the geometry of the RUC is approximated based on structural packing of a tetrakaidecahedron (Kelvin?s unit cell) with cylindrical strut morphology [Fig. 1]. A total of twelve foam structures of different porosity varying from 0.638 to 0.962 are considered. The flow Reynolds number based on superficial velocity and equivalent spherical diameter is varied from creeping flow regime to as high as 500. The current simulation results can also be extended for foams of different pore densities. An empirical correlation for the friction factor is proposed as a function of porosity and Reynolds number.