Theoretical, Numerical and Experimental Study of the Laminar Macroscopic Velocity Profile near Permeable Interfaces Uri Shavit Civil and Environmental.

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Presentation transcript:

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 Fractures Wetlands Industrial processes

The Beavers and Joseph study And the Brinkman Eq. z Beavers and Joseph ( Beavers and Joseph,1967) The Brinkman Eq. (1947)

The Taylor Brush The Cantor-Taylor Brush (G.I. Taylor, 1971) (Vignes-Adler et al., 1987) (Shavit et al., 2002, WRR) z x y

Spatially averaged N-S equation (x-comp)

v=w=0 Spatial averaging for the parallel grooves configuration

Hrev The result of the spatial averaging – Local porosity n – The structure porosity (n = 5/9)

The Modified Brinkman Equation (MBE)

The MBE solution as a function of H rev Z (cm)

A numerical solution of the microscale field Y (cm) Z (cm)

The Modified Brinkman Equation (MBE) The Cantor-Taylor brush

The Modified Brinkman Equation (MBE) (Shavit et al., 2004)

MBEs analytical solution And C1, C2, C3, C4 are constants. Where:

Experimental

30 x 5 = 150 sets 150 wide columns 1200 narrow columns Sierpinski Carpet n = 0.79 L = 108 cm, B = 20.4 cm

Nd:YAG Lasers PIV Camera Optics Laser sheet

Flow Direction

Z = -5 mm h = 10 mm Q = 150 cc/s PIV Results

The Velocity Vertical Profile (Q = 150 cm 3 s -1 )

The RMS Velocity Profile (Q = 150 cm 3 s -1 )

Numerical

CFD (Fluent)Contours of u(x,y)

CFD (Fluent) Z = -2 mm Flow direction Contours of u(x,y)

Numerical Solution of the Laminar Flow versus the MBE

Turbulent Numerical Solution versus PIV (Q = 150 cm 3 s -1 )

Ravid Rosenzweig Shmuel Assouline Mordechai Amir Amir Polak Acknowledgments: The Israel Science Foundation Grand Water Research Institute Technion support Joseph & Edith Fischer Career Development Chair