Experimental Investigation on Nonlinear Analysis of Unsteady Flow Through Coarse Porous Media

Document Type : Research Paper

Authors

1 Ph.D. Student of Civil Eng., Khajeh Nasireddin Toosi University of Tech., Tehran

2 Assist. Prof., Dept. of Civil and Environmental Eng., Khajeh Nasireddin Toosi University of Tech., Tehran

3 Assoc. Prof., Dept. of Civil Eng., Amir Kabir University of Tech., Tehran

4 Faculty Member of Civil Eng., Bu-Ali Sina University, Hamedan

Abstract

An experimental investigation of water flowing through coarse porous media in an open channel with free surface was conducted to better understand the mechanism of energy loss and changes with flow velocity. In this research, experimentally, investigate water flowing through coarse porous media in nonlinear unsteady state .To cast light on the analytical characteristics of unsteady-turbulent flow within coastal rockfill structures, an extensive research program has been carried out using the open channel flow principles. Crushed coarse aggregates with pre-determined gradations were carefully packed in a 600 mm wide flume through which, variation of pheartic surface as a result of the tail-water variation – to resume unsteady flow conditions – were optically recorded by means of a set of piezometers installed along the flume’s side-wall. Discharge rates were measured by a calibrated v-notch and the tail-water surface variations were precisely timed by means of delicate electrical equipments specially designed and manufactured for these experiments. Observations on the flow behaviors were then analyzed using SPSS software in order to drive mathematical relationships between measured parameters. Findings indicate that: a) The so-called Forchheimer equation can be successfully employed for analyses of nonlinear- steady as well as nonlinear-unsteady regimes in coarse granular porous media. b) Although a third term defining effects of unsteadiness may be included in the above mentioned equation, it is of little engineering importance. c) The nature of hydraulic gradient (i) variations versus Reynolds number (Re) – which were plotted for all sets of observations – confirms existence of turbulent conditions in all experiments. d) Our unique experimentation set-up adequately resembles the actual prototype conditions.

Keywords


1- Burcharth, H.F., and Andersen, O.H. (1995). “On the one-dimensional steady and unsteady porous media flow equation.” J. of Coastal Engineering, 24, 233-257.
2- Sheidegger, A.E. (1974). Physics of flow through porous media, University of Toronto Press, Toronto.
3- Venkataraman, P., and Rao, P.R.M. (1998). “Darcian, transitional and turbulent flow through porous media.” J. of Hydra. Eng.,  124(8), 840-846.
4- Ahmed, N., and Sunada, D.K. (1969). “Nonlinear flow in porous media.” J. of Hydra. Divi., 95(6), 1847-1857.
5- Ahmed, N., and Sunada, D.K. (1971). “Closure on nonlinear flow in porous media.” J. of Hydra. Divi., 8, 1233-1234.
6- Curtic, R.P., and Lawson, J.D. (1967). “Flow over and through rockfill banks.” J. of Hydra. Divi., 5, 1-21.
7- George, G.H., and Hansen, D. (1992). “Conversion between quadratic and power law for non- Darcy flow.” J. of Hydra. Engineering, 118(5), 792-797.
8- Bazargan, J. (2002), “Design and analysis of rockfill intakes.” Ph.D. Thesis, Dept. of Civil and Environmental Engineering, Amir kabir University, Tehran, Iran. (In Persian)
9- Straughan, B. (2010), “Structure of the dependence of Darcy and Forchheimer coefficients on porosity.” International J. of Engineering Science, 48(11), 1610-1621.
10- Li, B., Garga, V., and Davies, M. (1998), “Relationships for Non-Darcy flow in rockfill.” J. of Hydraulic Engineering, 124(2), 206-212.
11- Afzali, S.H., Abedini, J.M., and Monajemi, P. (2009). “Identification of network physical properties in simulation of flow through porous media using network model.” J. of Water and Wastewater, 68, 48-56.
(In Persian)
12- Moutsopoulos, K.N., and Tsihrintzis, V.A. (2005). “Approximate analytical solutions of the Forchheimer equation.” J. of Hydrology, 309, 93-103.
13- Moutsopoulos, K.N., Papaspyros, I.N.E., and Tsihrintzis, V.A. (2009). “Experimental investigation of inertial flow processes in porous media.” J. of Hydrology, 374, 242-254.
14- Fourar, M., Radilla, G., Lenormand, R., and Moyne, Ch. (2004). “On the non-linear behavior of a laminar single-phase flow through two and three-dimensional porous media.” J. of Advances in Water Resources, 27, 669-677.
15- Cheng, N.Sh., Hao, Zh., and Tan, S.K. (2008). “Comparison of quadratic and power law for nonlinear flow through porous media.” J. of Experimental Thermal and Fluid Science, 32, 1538-1547.
16- Poluobarinova-Kochina, Y.P. (1952). Theory of groundwater movement, English Tranlation by DeWiest, R.M.J. Princeton University Press, Princeton, New Jersey.
17- Hall, K.R., Smith, G.M., and Turcket, D.J. (1994). “Development of a non-linear porous media flow relationship for oscillatory unsteady flow.” J. of Coastal Research, 10(1), 158-169.
18- Majid Hassanizadeh, S. (1978). “High velocity flow in porous media.” J. of Transport in Porous Media, 2, 521-537.
19- Hall, k., Smith, G.M., and Turcke, D.J. (1994). “Development of a non-linear porous media flow relationship for oscillatory unsteady flow.” J. of Coastal Research, 10(1) 158-169.
20- Wang, X.A., and Liu, Zh.F. (2004). “The Forchheimer equation in two-dimensional percolation porous media.” J. of Physica, 337, 384-388.
21- Shokri, M. (2004), “Investigating parameters affecting nonlinear unsteady flow in porous media.” M.Sc. Thesis, Dept. of Civil and Environmental Engineering, Amirkabir University of Technology, Tehran, Iran. (In Persian)