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Uri Shavit Civil and Environmental Engineering, Technion, Haifa, Israel

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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Uri Shavit Civil and Environmental Engineering, Technion, Haifa, Israel

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  1. 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

  2. The laminar flow field at the vicinity of permeable surfaces • Rainfall events • Fractures • Wetlands • Industrial processes

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

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

  5. Spatially averaged N-S equation (x-comp)

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

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

  8. The Modified Brinkman Equation (MBE)

  9. The MBE solution as a function of Hrev Z (cm)

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

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

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

  13. MBE’s analytical solution Where: And C1, C2, C3, C4 are constants.

  14. Experimental

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

  16. PIV Nd:YAG Lasers Camera Optics Laser sheet

  17. Flow Direction

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

  19. The Velocity Vertical Profile (Q = 150 cm3 s-1)

  20. The RMS Velocity Profile (Q = 150 cm3 s-1)

  21. Numerical

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

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

  24. Numerical Solution of the Laminar Flow versus the MBE

  25. Turbulent Numerical Solution versus PIV (Q = 150 cm3 s-1)

  26. 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

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