An Analytical Solution for 1-D Non-Darcy Flow Through Slanting Coarse Deposits

Transport in Porous Media

Volumn 104, Issue 3, 2014, Pages 565-579

  Sedghi Asl, Mohammad ^a   Farhoudi, Javad ^b   Rahimi, Hassan ^b   Hartmann, Sven ^c  

^a YASOUJ UNIVERSITY   (Iran)

^b UNIVERSITY OF TEHRAN   (Iran)

^c UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Analytical solution; Coarse porous media; Fully developed turbulent flow; Non Darcy flow; Slanting valley fills

Indexed keywords

OPEN CHANNEL FLOW; TURBULENT FLOW;

ANALYTICAL RESULTS; CRUSHED MATERIALS; FLOW PROFILE; NON-DARCY FLOW; NORMAL DEPTHS; POROUS MEDIUM; VALLEY FILLS; WATER SURFACE PROFILE;

POROUS MATERIALS;

ANALYTICAL METHOD; FLOW MODELING; ONE-DIMENSIONAL MODELING; OPEN CHANNEL FLOW; PERMEABILITY; POROUS MEDIUM; TURBULENT FLOW;

EID: 84907594555     PISSN: 01693913     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11242-014-0350-3     Document Type: Article

References (44)

1. Bari, M. R.: The Hydraulics of Buried Streams. MSc Thesis, Department of Civil Engineering, Technical University of Nova Scotia, Halifax, NS, Canada (1997).
2. Bari, R., Hansen, D.: Application of gradually-varied flow algorithms to simulate buried streams. J. Hydraul. Res. 40(6), 673-683 (2002).
3. Barr, D. W.: Turbulent flow through porous media. Ground Water 39(5), 646-650 (2001).
4. Basak, P.: Non-Darcy flow and its implications to seepage problems. J. Irrig. Drain. Eng. 103(4), 459-473 (1977).
5. Basak, P.: Steady non-Darcian seepage through embankments. J. Irrig. Drain. Eng. 102(4), 435-443 (1976).
6. Bear, J.: Dynamics of Fluids in Porous Media. Elsevier Science, New York (1972).
7. Bordier, C., Zimmer, D.: Drainage equations and non-Darcian modeling in coarse porous media or geosynthetic materials. J. Hydrol. 228, 174-187 (2000).
8. Brutsaert, W.: The unit response of groundwater outflow from a hillslope. Water Resour. Res. 30(10), 2759-2763 (1994).
9. Campbell, D. B.: Some observations relevant to the performance of flow through rock drains. In: 13th Annual B. C. Mine Reclamation Symposium, 7-9 June, BiTech, Vancouver, B. C., pp. 119-128 (1989).
10. Childs, E.: Drainage of groundwater resting on a sloping bed. Water Resour. Res. 7(5), 1256-1263 (1971).
11. Chow, V. T.: Open Channel Hydraulics. McGraw-Hill Book Co., New York (1959).
12. Dupuit, J.: E'tude the'orique et pratique sur le movement des eaux dans les canaux de'couverts et a' travers les terrains perme'ables, 2nd edn. Dunod, Paris (1863).
13. Eck, B. J., Barrett, M. E., Charbeneau, R. J.: Forchheimer flow in gently sloping layers: Application to drainage of porous asphalt. Water Resour. Res. 48, W01530 (2012). doi: 10. 1029/2011WR010837.
14. Findikakis, A. N., Tu, S.-W.: Flood Routing through Rock Dumps in Natural Channels. In: Proc. of Conf. on Hydr. and Hydrol. in Small Comput. Age, ASCE, Lake Buena Vista, Florida, pp. 1213-1218 (1985).
15. Freeze, R. A., Cherry, J. A.: Ground Water. Prentice-Hall, Englewood Cliffs (1979).
16. Greenly, B. T., Joy, D. M.: One-dimensional finite-element model for high flow velocities in porous media. J. Geotech. Eng. 122(10), 789-796 (1996).
17. Harr, M. E.: Groundwater and Seepage. McGraw-Hill, New York (1962).
18. Henderson, F. M.: Open Channel Flow. Macmillan Book Co., New York (1966).
19. Hosseini, S. M., Joy, D. M.: Development of an unsteady model for flow through coarse heterogeneous porous. Int. J. River Basin Manag. 5(4), 253-265 (2007).
20. Kolditz, O.: Non-linear flow in fractured rock. Int. J. Numer. Methods Heat Fluid Flow 11(6), 547-575 (2001).
21. Kovacs, G.: Developments in Water Science, Volume 10: Seepage Hydraulics. Elsevier, Amsterdam (1977).
22. Mathias, S., Butler, A., Zhan, H.: Approximate solutions for Forchheimer flow to a well. J. Hydraul. Eng. 134(9), 1318-1325 (2008).
23. McCorquodale, J. A., Hannoura, A., Nasser, M. S.: Hydraulic conductivity of rockfill. J. Hydraul. Res. 16(2), 123-137 (1978).
24. Mijic, A., Mathias, S. A., LaForce, T. C.: Multiple well systems with non-Darcy flow. Ground Water 51(4), 588-596 (2013).
25. Moutsopoulos, K. N., Papaspyros, J. N. E., Tsihrintzis, V. A.: Experimental investigation of inertial flow processes in porous media. J. Hydrol. 374, 242-254 (2009).
26. Moutsopoulos, K. N., Tsihrintzis, V. A.: Approximate analytical solutions of the Forchheimer equation. J. Hydrol. 309(1-4), 93-103 (2005).
27. Moutsopoulos, K. N.: Exact and approximate analytical solutions for unsteady fully developed turbulent flow in porous media and fractures for time dependent boundary conditions. J. Hydrol. 369(1-2), 78-89 (2009).
28. Moutsopoulos, K. N.: One-dimensional unsteady inertial flow in phreatic aquifers, induced by a sudden change of the boundary head. Transp. Porous Media 70(1), 97-125 (2007).
29. Panfilov, M., Fourar, M.: Physical splitting of non-linear effects in high-velocity stable flow through porous media. Adv. Water Resour. 331, 41-48 (2006).
30. Pavlosky, N. N.: Collected Works. Akad. Nauk USSR, Leningrad (1956).
31. Reddy, L. N.: Seepage in Soils: Principles and Applications. Wiley, New York (2003).
32. Ritcey, G. M.: Tailings Management: Problems and Solutions in the Mining Industry. Elsevier Science, New York (1989).
33. Sedghi-Asl, M., Rahimi, H., Farhoudi, J., Hoorfar, A., Hartmann, S.: 1-D fully-developed turbulent flow through coarse porous medium. J. Hydrol. Eng. ASCE (2014a). doi: 10. 1061/(ASCE)HE. 1943-5584. 0000937.
34. Sedghi-Asl, M., Rahimi, H., Salehi, R.: Non-Darcy flow of water through a packed column test. Transp. Porous Media 101(2), 215-227 (2014b).
35. Sedghi-Asl, M., Rahimi, H.: Adoption of Manning's equation to 1D non-Darcy flow problems. J. Hydraul. Res. 49(6), 814-817 (2011).
36. Sen, Z.: Nonlinear flow toward wells. J. Hydraul. Eng. 115(2), 193-209 (1989).
37. Sidiropoulou, M. G., Moutsopoulos, K. N., Tsihrintzis, V. A.: Determination of Forchheimer equation coefficients a and b. Hydrol. Process. 21(4), 534-554 (2007).
38. Sophocleous, M.: Interactions between groundwater and surface water: the state of the science. Hydrogeol. J. 10(1), 52-67 (2002).
39. Sophocleous, M. A.: Stream-flood wave propagation through the Great Bend alluvial aquifer, Kansas: field measurements and numerical simulations. J. Hydrol. 124, 207-228 (1991).
40. Verhoest, N., Troch, P.: Some analytical solutions of the linearized Boussinesq equation with recharge for a sloping aquifer. Water Resour. Res. 36(3), 793-800 (2000).
41. Wen, Z., Huang, G., Zhan, H., Li, J.: Two-region non-Darcian flow toward a well in a confined aquifer. Adv. Water Resour. 31(5), 818-827 (2008b).
42. Wen, Z., Huang, G., Zhan, H.: An analytical solution for non-Darcian flow in a confined aquifer using the power law function. Adv. Water Resour. 31, 44-55 (2008a).
43. Yamada, H., Nakamura, F., Watanabe, Y., Murakami, M., Nogami, T.: Measuring hydraulic permeability in a streambed using the packer test. Hydrol. Process. 19, 2507-2524 (2005).
44. Zeng, Z., Grigg, R. A.: criterion for non-Darcy flow in porous media. Transp. Porous Media 63, 57-69 (2006).