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

S. Das, J.A.M. Kuipers, N. G. Deen*

Multiphase Reactors Group (SMR),

Dept. Chemical Engineering and Chemistry (ST),

Den Dolech 2, 5612 AZ, P.O. Box 513,

5600 MB Eindhoven, The Netherlands.

Abstract:

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.

Figure 1: (a) A single
tetrakaidecahedron unit cell and its important geometric dimensions. (b)
Snapshot of direct numerical simulation in periodic computational domain: the
velocity contours at the mid-plane and Immersed Boundary (IB). The
representative unit cell (RUC) of solid foam is approximated by structural
packing of tetrakaidecahedron and in periodic Cartesian computational domain it
is resolved by IB method. By changing the ratio of ligament length (l_s)
to ligament diameter (d_s) foam of different porosity can be formed. 
The length of the periodic box (L_p) relates the pore density of the
solid foam. Second order accurate implicit IB method is implemented where no
calibration of ligament diameter is required.

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.

Keywords: Open cell solid Foam, porous medium,
fully resolved simulation, Immersed Boundary Method (IBM), tetrakaidecahedron,
Kelvin?s unit cell.

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* Corresponding author

Email: N.G.Deen@tue.nl

Tel.: +31-40-2473681