HR: 1330h
AN: H42F-1147    [PDF]
TI: Free Flows at the Interface of Grooved Geometries
AU: * Shavit, U
EM: aguri@tx.technion.ac.il
AF: Technion, Civil and Environment Engineering, Technion, Haifa, 32000 Israel
AU: Rosenzweig, R
EM: rravid@techunix.technion.ac.il
AF: Technion, Civil and Environment Engineering, Technion, Haifa, 32000 Israel
AU: Shmuel, A
EM: vwshmuel@agri.gov.il
AF: Volcani Center, Institute of Soil, Water and Environmental Sciences, Volcani Center, Bet Dagan, 50250 Israel
AB: A solution to the problem of shallow laminar water flow above a permeable surface composed of deep grooves is presented. Previous studies proposed theoretical, experimental, and numerical insight with no single general solution to the problem. Many studies have used the Brinkman equation, while others showed that it does not represent the actual interface flow conditions. Here we show that the interface macroscopic velocity can be accurately modeled by introducing a modification to the Brinkman equation. A moving average approach was proved to be successful when choosing the correct representative elementary volume and comparing the macroscopic solution with the average microscopic flow. As the size of the representative elementary volume was found to be equal to the product of the square root of the permeability and an exponential function of the porosity, a general solution is now available for any brush configuration. Given the properties of the porous media (porosity and permeability), the flow height and its driving force, a complete macroscopic solution of the interface flow is obtained. The presentation will begin with a theoretical background and the mathematical formulation of the modified Brinkman equation (MBE). Then, a comparison between the macroscopic velocity profile obtained by the MBE and the result of the microscopic numerical solutions will be presented. The comparison was obtained for laminar flows through a variety of 37 groove geometries. Measurement results of the micro-scale velocity field using Particle Image Velocimeter (PIV) inside and above a fractal Cantor-Taylor brush configuration will be shown. The results obtained for the Cantor-Taylor brush configuration and for the other 36 groove geometries show that the modified Brinkman equation (MBE) accurately describes the macroscopic velocity profile given that the flow regime is laminar.
DE: 1815 Erosion and sedimentation
DE: 1829 Groundwater hydrology
DE: 1860 Runoff and streamflow
DE: 5104 Fracture and flow
DE: 5114 Permeability and porosity
SC: Hydrology [H]
MN: 2003 Fall Meeting