Abstract
We present a laboratory experimental investigation of the interaction between the turbulent flow in an open channel and the turbulent flow within its very permeable bed. The bed was composed of uniform-size spheres packed in a cubic pattern. Fluid velocities were measured by Particle Image Velocimetry (PIV), which allowed us to investigate the spatial distribution of the time-averaged flow properties in the zone where they are strongly affected by the geometry of the rough bed. We investigate the effect of bed porosity on these flow properties by comparing the results of two experimental configurations: one with an impermeable bed composed of a single layer of spheres and another with a permeable bed composed of five layers. For the latter case, PIV measurements of velocities were also carried out inside two pores adjacent to the bed surface. This data provides an insight into the mechanisms of momentum transfer between the turbulent open channel flow and the turbulent flow within its very permeable bed.
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Beavers G.S., Joseph D.D.: Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30(1), 197–207 (1967). doi:10.1017/S0022112067001375
Breugem W.P., Boersma B.J., Uittenbogaard R.E.: The influence of wall permeability on turbulent channel flow. J. Fluid Mech. 562, 35–72 (2006)
Choi C.Y., Waller P.M.: Momentum transport mechanism for water flow over porous media. J. Environ. Eng. 123(8), 792–799 (1997). doi:10.1061/(ASCE)0733-9372(1997)123:8(792)
Darby S.E.: Refined hydraulic geometry data for British gravel-bed rivers. ASCE J. Hydr. Eng. 131(1), 60–64 (2005). doi:10.1061/(ASCE)0733-9429(2005)131:1(60)
Finnigan J.J.: Turbulence in plant canopies. Annu. Rev. Fluid Mech. 32, 519–571 (2000). doi:10.1146/annurev.fluid.32.1.519
James D.F., Davis A.M.: Flow at the interface of a model fibrous porous medium. J. Fluid Mech. 426, 47–72 (2001). doi:10.1017/S0022112000002160
Larson R.E., Higdon J.J.: Microscopic flow near the surface of two-dimensional porous media. Part 1(Axial flow. J. Fluid Mech. 166), 449–472 (1986). doi:10.1017/S0022112086000228
Manes, C.: Turbulent open channel flows over and within rough and permeable beds. Ph.D. thesis, University of Aberdeen (2006)
Manes C., Pokrajac D., McEwan I.: Double-averaged open-channel flows with small relative submergence. ASCE J. Hydr. Eng. 133(8), 896–904 (2007). doi:10.1061/(ASCE)0733-9429(2007)133:8(896)
Manes C., Pokrajac D., McEwan I., Nikora V., Campbell L.J.: Application of UVP within porous beds. J Hydr. Eng., ASCE 132(9), 983–986 (2006)
Nikora V., Goring D., McEwan I., Griffiths G.: Spatially-averaged open-channel flow over rough bed. J. Hydr. Eng., ASCE 127(2), 123–133 (2001)
Nikora V., McEwan I., McLeanS.Coleman Pokrajac D., Walters R.: Double averaging concept for rough-bed open-channel and overland flows: Theoretical background. J. Hydrol. Eng. 133(8), 873–883 (2007). doi:10.1061/(ASCE)0733-9429(2007)133:8(873)
Ochoa-Tapia A.J., Whitaker S.: Momentum transfer at the boundary between a porous medium and a homogeneous fluid. I: Theoretical development. Int. J. Heat Mass Transf. 38(14), 2635–2646 (1995a). doi:10.1016/0017-9310(94)00346-W
Ochoa-Tapia A.J., Whitaker S.: Momentum transfer at the boundary between a porous medium and a homogeneous fluid II: Comparison with experiment. Int. J. Heat Mass Transf. 38(14), 2647–2655 (1995b). doi:10.1016/0017-9310(94)00347-X
Pokrajac D., Manes C., McEwan I.: Peculiar mean velocity profiles within a porous bed of an open channel. Phys. Fluids 19(9), 098109:1–98109-4 (2007)
Raffel M., Willert CE., Kompenhans J.: Particle Image Velocimetry, A Practical Guide. Springer-Verlag, Berlin Hedelberg (1998)
Raupach M.R., Antonia R.A., Rajagopalan S.: Rough-wall turbulent boundary layers. ASME Appl. Mech. Rev. 44(1), 1–25 (1991)
Ruff J.F., Gelhar L.W.: Turbulent shear flow in porous boundary. J. Eng. Mech. Div. 98(EM4), 975–991 (1972)
Sahraoui M., Kaviany M.: Slip and no-slip velocity boundary conditions at the interface of porous, plain media. Int. J. Heat Mass Transf. 35, 927–943 (1992). doi:10.1016/0017-9310(92)90258-T
Shavit U., Bar-Yosef G., Rosenzweig R.: Modified Brinkman equation for a free flow problem at the interface of porous surfaces: The Cantor-Taylor brush configuration case. Water Resour. Res. 38(12), 1320–1334 (2002). doi:10.1029/2001WR001142
Shimizu Y., Tsujimoto T., Nakagawa H.: Experiment and macroscopic modelling of flow in highly permeable porous medium under free-surface flow. J. Hydrosci. Hydraul. Eng. 8(1), 69–78 (1990)
Vafai K., Thiyagaraja R.: Analysis of flow and heat transfer at the interface region of a porous medium. Int. J. Heat Mass Transf. 30, 1391–1405 (1987). doi:10.1016/0017-9310(87)90171-2
Vollmer S., Franciscodelos Santos R., Daebel H., Kuhn G.: Micro-scale exchange processes between surface and subsurface water. J. Hydrol. (Amst.) 269, 3–10 (2002). doi:10.1016/S0022-1694(02)00190-7
Westerweel J.: Efficient detection of spurious vectors in particle image velocimetry data sets. Exp. Fluids 16, 236–247 (1994). doi:10.1007/BF00206543
Zagni A., Smith K.: Channel flow over permeable beds of graded spheres. J. Hydraul. Div., ASCE 102(2), 207–222 (1976)
Zippe H.J., Graf W.H.: Turbulent boundary layer flow over permeable and non-permeable rough surface. J. Hydraul. Res. 21(1), 300–316 (1983)
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Pokrajac, D., Manes, C. Velocity Measurements of a Free-Surface Turbulent Flow Penetrating a Porous Medium Composed of Uniform-Size Spheres. Transp Porous Med 78, 367–383 (2009). https://doi.org/10.1007/s11242-009-9339-8
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DOI: https://doi.org/10.1007/s11242-009-9339-8