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Theoretical, Numerical and Experimental Study of the Laminar Macroscopic Velocity Profile near Permeable Interfaces. Uri Shavit Civil and Environmental Engineering, Technion, Haifa, Israel. Kyiv, May 8 th , 2004. The laminar flow field at the vicinity of permeable surfaces. Rainfall events
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Theoretical, Numerical and Experimental Study of the Laminar Macroscopic Velocity Profile near Permeable Interfaces Uri Shavit Civil and Environmental Engineering, Technion, Haifa, Israel Kyiv, May 8th, 2004
The laminar flow field at the vicinity of permeable surfaces • Rainfall events • Fractures • Wetlands • Industrial processes
The Beavers and Joseph study And the Brinkman Eq. z Beavers and Joseph The Brinkman Eq. (1947) (Beavers and Joseph ,1967)
The Cantor-Taylor Brush The Taylor Brush z x y (Vignes-Adler et al., 1987) (G.I. Taylor, 1971) (Shavit et al., 2002, WRR)
Spatial averaging for the parallel grooves configuration v=w=0
Hrev The result of the spatial averaging q – Local porosity n – The structure porosity (n = 5/9)
A numerical solution of the microscale field Z (cm) Y (cm)
The Modified Brinkman Equation (MBE) The Cantor-Taylor brush
The Modified Brinkman Equation (MBE) (Shavit et al., 2004)
MBE’s analytical solution Where: And C1, C2, C3, C4 are constants.
Sierpinski Carpet 30 x 5 = 150 sets 150 wide columns 1200 narrow columns L = 108 cm, B = 20.4 cm n = 0.79
PIV Nd:YAG Lasers Camera Optics Laser sheet
Z = -5 mm h = 10 mm Q = 150 cc/s PIV Results
The RMS Velocity Profile (Q = 150 cm3 s-1)
CFD (Fluent) Contours of u(x,y)
CFD (Fluent) Contours of u(x,y) Flow direction Z = -2 mm
Numerical Solution of the Laminar Flow versus the MBE
Turbulent Numerical Solution versus PIV (Q = 150 cm3 s-1)
Acknowledgments: • Ravid Rosenzweig • Shmuel Assouline • Mordechai Amir • Amir Polak • The Israel Science Foundation • Grand Water Research Institute • Technion support • Joseph & Edith Fischer Career • Development Chair