# Pore-Scale Level Numerical Simulation of Flow in a Solid Foam: An Immersed Boundary Method (IBM) Based Approach

GLS_Saurish_Das.docx

12.0pt;margin-left:0in;line-height:200%">**Pore-scale level numerical
simulation of flow in a solid foam: an Immersed Boundary Method (IBM) based
approach**

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

normal">Multiphase Reactors Group (SMR),

normal">Dept. Chemical Engineering and Chemistry (ST),

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

5600 MB Eindhoven, The Netherlands.

12.0pt;margin-left:0in;text-align:justify;line-height:200%">Abstract:

12.0pt;margin-left:0in;text-align:justify;line-height:200%">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.

12.0pt;margin-left:0in;text-align:justify;line-height:200%">

justify;line-height:normal;text-autospace:none">**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.Â

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.

12.0pt;margin-left:0in;text-align:justify;line-height:200%">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.Â 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.

12.0pt;margin-left:0in;text-align:justify;line-height:200%">**Keywords**: Open cell solid Foam, porous medium,

fully resolved simulation, Immersed Boundary Method (IBM), tetrakaidecahedron,

Kelvin?s unit cell.

normal">__________________________________

justify;line-height:normal">* Corresponding author

justify;line-height:normal">Email: N.G.Deen@tue.nl

justify;line-height:normal">Tel.: +31-40-2473681Â Â Â