An efficient Immersed Boundary Method based on penalized direct forcing for simulating flows through arbitrary porous media

MSc graduation project of Vincent van Dijk
Location: Lab. for Aero & Hydrodynamics
Supervisors: W.-P. Breugem & R. Delfos
Defense:  July 1 2011

Project description:

Porous media are characterized by an open solid structure with interconnected pores through which a fluid may flow. Examples of porous media are pebble bed nuclear reactors, packed beds in the chemical industry and river beds composed of granular material. Until recently, it was neither possible to measure nor to simulate the flow within the pores of such beds because of their complex geometry.

The aim of this project is the development of an efficient Immersed Boundary Method (IBM) for simulating flow through the pores of an arbitrary porous medium. The IBM is integrated in a finite-volume method in which the full Navier-Stokes equations are solved for the fluid phase. The essence of the IBM is that the solid particles are immersed in a three-dimensional Cartesian grid. Instead of imposing the no-slip/no-penetration conditions at the surface of the solid particles, forces are imposed on the fluid to enforce zero flow within the particles. The proposed IBM is based on penalized direct forcing in which the prediction velocity in the employed pressure-correction scheme is set to zero inside the solid phase.

In this project the accuracy of the IBM will be determined for a few simple geometries. Next, the IBM will be applied to several realistic packed beds of different granular material. The geometries of the packed beds will be obtained from a high-resolution micro CT scanner at the Faculty of Civil Engineering. From the simulations the so-called permeability of the packed beds will be determined. To validate the simulations, experiments will be conducted in the Laboratory for Aero & Hydrodynamics to experimentally determine the permeability of the packed beds.

After extensive validation of the IBM, the method may be applied to study heat transfer in a pebble bed nuclear reactor or the interaction between flow above and within a granular river bed.

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