|M.Sc Student||Rosenzweig Ravid|
|Subject||The Macroscopic Velocity Profile Near Permeable Interfaces:|
PIV Measurements, Numerical Simulations, and an
Analytical Solution of the Laminar
|Department||Department of Agricultural Engineering||Supervisor||Professor Emeritus Abraham Shaviv|
A solution to the problem of laminar flow above a porous surface is essential when investigating phenomena such as erosion, re-suspension, and mass transfer between a saturated porous medium and a free flow above it. Previous studies proposed theoretical, experimental, and numerical insight but failed to provide a general useful tool that predicts the macroscopic flow in combined open and porous domains.
In this thesis, we present a modification of the Brinkman equation, named the MBE, which was derived by averaging the momentum equations over a representative elementary volume (REV). The MBE provides a prediction of the macroscopic velocity profile within and above the porous media provided a steady, laminar, and unidirectional flow.
The applicability of the MBE was tested on simple geometries, simulating porous media. The MBE was first tested by comparing its solution with the averaged numerical solution of the micro-scale velocity, obtained by solving the Stokes equation for 37 2D grooved sets. The results show that the MBE accurately predicts the macroscopic velocity profile when the REV size is equal to the product of the square root of the permeability and an exponential function of the porosity.
Next, the flow inside and above an array of Sierpinski sets was used to simulate the flow through a 3D porous medium. The micro-scale velocity field within a laboratory physical model was measured using a Particle Image Velocimeter (PIV) and compared with a numerical solution of the 3D Navier-Stokes equations. The computed and measured velocity fields were averaged and compared with the MBE solution. A good agreement between the three velocity profiles was found for low Reynolds numbers.