American Journal of Fluid Dynamics
pISSN: 21684707 eISSN: 21684715
2012; 2(5): 7888
doi: 10.5923/j.ajfd.20120205.02
Nagia E. Elghanduri
School of Engineering, University of Aberdeen, UK, Fraser Noble Building, King’s College AB24 3UE
Correspondence to: Nagia E. Elghanduri , School of Engineering, University of Aberdeen, UK, Fraser Noble Building, King’s College AB24 3UE.
Email: 
Copyright © 2012 Scientific & Academic Publishing. All Rights Reserved.
Abstact The main objective of this study is to improve our knowledge about the velocity profile and turbulence within and over a permeable bed. The study was using computation fluid dynamics (CFD) methodology to simulate the studied cases. It includes a detail analysis for twodimensional fully developed turbulent flow over and through a permeable bed. Five different cases were simulated numerically. The analysis is set for the three flow zones (free stream, porous, and interface). The detailed two dimensional flow simulations were subsequently validated using previously published results, then it was specially averaged to overcome the heterogeneity of flow. The focus in this study is on the effect of porosity and free stream thickness on longitudinal and vertical velocities in different flow zones. On the basis of this study results, it is shown that the flow velocity within the porous zone increases with bed porosity, and decreases with increasing the water depth. It is also confirmed that the turbulence parameters (turbulent kinetic energy, turbulent dissipation rate, and turbulent kinetic energy production) penetrate practically throughout the whole porous layer to reach maximum values at the interface then decreases smoothly to minimum at the water surface.
Keywords: Permeable Bed, Porous Layer, Free Stream, Penetration Layer
Cite this paper: Nagia E. Elghanduri , "CFD Analysis for Turbulent Flow within and over a Permeable Bed", American Journal of Fluid Dynamics, Vol. 2 No. 5, 2012, pp. 7888. doi: 10.5923/j.ajfd.20120205.02.
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Figure 1. Columns of the arranged rods bundle and symbols for geometry 

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Figure 2. Comparison Between Previously Published and Present Study for Normalized Turbulent Kinetic Energy Profile Above and Within Porous Medium(Left), and Normalized Velocity Distribution at The Free Stream(Right) for The Simulated Cases 
Figure 3. The Longitudinal velocity distribution (m/s): Contours (Left) and the profile along the central line between tworod columns (Right), for spar30 Case (Top) and dens30 Case (Bottom). Grey Areas on The Right Indicate The Position of The Rods 

Figure 4. The velocity vectors between two adjacent rods for spar30 (left), and dens30 (right) cases; rods are numbered topdown. Vectors are colourcoded based on U_{x} 
Figure 5. The Velocity vectors between two adjacent rods for top rod (left), and second rod (Right) at dens30 ; vectors are colourcoded based on lateral velocity 
Figure 6. Velocity vectors (m/s) in the free space between The rods; spar30 (Left), and dens30 (Right) cases; rods are numbered topdown. vectors are colourcoded based on lateral velocity 
Figure 7. Normalized longitudinal velocity within the porous zone Porosity effect on normalized longitudinal velocity for flow within porous zone; (a) for spars cases, and (b) dense cases 
Figure 8. Free stream thickness effect on the longitudinal velocity within the porous zone; (a) for spars cases, and (b) dense cases 
Figure 9. Effect of bed porosity on the longitudinal velocity in the free stream zone 
Figure 10. The bednormal velocity distribution (m/s); contours (left) and the profile along the central line between two rod columns (right), for spar30 case (top) and dens30 case (bottom).Grey areas on the right indicate the position of the rods 
Figure 11. The Vertical Velocity Contours Around a Top Rods; dens30 (UP) and spar30 (Bottom) Cases 

Figure 12. Penetration thickness, versus (C_{d}αd)^{1} 
Figure 13. The turbulent kinetic energy distribution (m^{2}/s^{2}): contours (left) and the profile along the central line between two rod columns (right), for spar30 case (top) and dens30 case (bottom). Grey zones on the right indicate the positions of rods 
Figure 14. Normalized spatially averaged turbulent kinetic energy distribution with normalized bed height at both free stream zone (Top), and porous zone. Bed normalized coordinate is (z/h_{f}) 
Figure 15. Normalized turbulent kinetic energy production distribution at both free stream zone (top), and porous zone (bottom) for different studied cases 
Figure 16. Porosity effect on the turbulent dissipation rate in both free stream (Top) and porous (Bottom) regions 
[1]  Iehisa Nezu, H. Nakagawa, “Turbulence in open channel flows, International Association for Hydraulic Research”, 3^{rd} ed., A. A . Balkema, Netherlands, 1993 . 
[2]  Xingwei Chen, YeeMeng Chiew, “Velocity distribution of turbulent openchannel flow with bed suction, Journal of Hydraulic Engineering, Feb. pp. 140148, 2004. 
[3]  Alstair Maclean, “Open channel velocity profiles over a zone of rapid infiltration”, Journal of Hydraulic Research, vol. 29, No. 1, pp. 1527. 1991. 
[4]  Vladimir Nikora, Derek Goring, Ian McEwan, George Griffiths, “Stability averaged openchannel flow over rough bed”, Journal of Hydraulic Engineering, Feb., pp. 123133, 2001. 
[5]  Heidi Nepf, Marco Ghisalberti, “Flow transport in channels with submerged vegetation, Acta Geophysica, vol. 56, No. 3, pp. 753777, 2008. 
[6]  Constantino Manes, Dubravaka . Pokrajac, and Ian McEwan (2007), “Doubleaveraged openchannel flows with small relative submergence”, Journal of Hydraulic Engineering, August, pp. 896904. 
[7]  Hossein Afzalimehr, and Vijay Singh, ”Influence of Modeling on The Estimation of Velocity And Shear Velocity in CobbleBed Channels”, Journal of Hydrologic Engineering, Oct., pp.11261135, 2009. 
[8]  Dimitris Sofialidis, Panayotis Prinos, “Numerical study of momentum exchange in compound open channel flow”, Journal of Hydraulic Engineering, Feb, pp. 152165, 1999. 
[9]  Brian White, Heidi Nepf, “Shear instability and coherent structures in shallow flow adjacent to a porous layer”, Journal of Fluid Mechanics, vol. 593, pp. 132, 2007 . 
[10]  Nancy Steinberger, Midhat Hondzo, “Diffusional mass transfer at sedimentwater interface”, Journal of Environmental Engineering, Feb., pp. 192 – 200, 1999 
[11]  Suga, K., and S. Nishiguchi, “Computation of turbulent flows over porous/fluid interfaces”, Fluid Dynamics Research, vol. 31, pp. 115, 2009. 
[12]  Marco Ghisalbrti, “Obstructed shear flows: Similarities across systems and scales”, Journal of Fluid Mechanics, vol. 641, pp. 5161, 2009. 
[13]  Heidi Nepf, Marco Ghisalberti, Brian White, and E. Murphy, “Retention and dispersion associated with submerged aquatic canopies”, Water Resource Research, vol. 43, W04422, pp.110; DOI:10.1029/2006WR005362, 2007. 
[14]  Ahmad Sana, AbdulRazzaq Ghumman, Hitoshi Tanaka, “Modelling of a roughwall boundary layer using twoequation turbulence models”, Journal of Hydraulic Engineering, Jan., No.1, pp. 6065, 2009. 
[15]  Panayotis Prinos, “Bed suction effect on structure of turbulent open channel flow”, Journal of Hydraulic Engineering, May, PP. 404412, 1995. 
[16]  H.C. Chan, M. Leu, C. Lai, M., and Yafi Jia, “Turbulent flow over a channel with fluid – saturated porous bed”, Journal of Hydraulic Engineering, June, pp. 610 – 617, 2007. 
[17]  Hink Versteeg, Weeratunge Malasekera, “An introduction to computational fluid dynamics, the finite volume method”, 1^{st} ed., Pearson Education Limited, UK, 1995. 
[18]  Panayotis Prinos, Dimitrios Sofialdis, and Evangelos. Keramaris, “Turbulent flow over and within a porous bed”, Journal of Hydraulic Engineering, Sep., pp. 720 – 733, 2003. 
[19]  ANSYS FLUENT, (2009), Documentation, Fluent user’s guide. 
[20]  Dubravka Pokrajac, Constantino Manes, and Ian McEwan, “ Peculiar mean velocity profile within a porous bed of open channel”, Physics of Fluids, vol. 19, no.9, 09810915, 2007 
[21]  Marco Ghisalberti, and Heidi Nepf, “Shallow flows over a permeable medium: The hydrodynamics of submerged aquatic canopies”, Transport Porous Med., 78 pp. 309  326. DOI 10.1007/s1124200809305x, 2009. 
[22]  Heidi Nepf, Enrique Vivoni, “Flow structure in depthlimited vegetated flow”, Journal of Geophysical Research, vol. 105, pp. 547557, 2000. 
[23]  Brian White, Hiedi Nepf, “Shear instability and coherent structures in shallow flow adjacent to a porous layer”, Journal of Fluid Mechanics, vol. 593, pp. 132, 2007. 
[24]  Dimitris Souliotis, Panayotis Prinos, “Macroscopic turbulence models and their application in turbulent vegetated flows”, Journal of Hydraulic Engineering, March, pp. 315332, 2011. 