Macroscopic turbulence modeling for incompressible flow through undeformable porous media

Darcy, 1856 Forchheimer, 1901, Wasserbewegung durch boden, Z. Ver. Deutsch. Ing., 45, 1782 Brinkman, 1947, A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles, Appl. Sci. Res. A, 1, 27, 10.1007/BF02120313 Ward, 1964, Turbulent flow in porous media, J. Hydraul. Div. ASCE, 90, 1 Whitaker, 1969, Advances in theory of fluid motion in porous media, Ind. Eng. Chem., 61, 14, 10.1021/ie50720a004 Bear, 1972 Vafai, 1981, Boundary and inertia effects on flow and heat transfer in porous media, Int. J. Heat Mass Transfer, 24, 195, 10.1016/0017-9310(81)90027-2 K. Lee, J.R. Howell, Forced convective and radiative transfer within a highly porous layer exposed to a turbulent external flow field, in: Proceedings of the 1987 ASME–JSME Thermal Engineering Joint Conference, Honolulu, Hawai, vol. 2, 22–27 March 1987, pp. 377–386 Wang, 1995, Boundary-layer flow and turbulence near porous obstacles, Boundary Layer Meteorology, 74, 73, 10.1007/BF00715711 Antohe, 1997, A general two-equation macroscopic turbulence model for incompressible flow in porous media, Int. J. Heat Mass Transfer, 40, 3013, 10.1016/S0017-9310(96)00370-5 Masuoka, 1996, Turbulence model for flow through porous media, Int. J. Heat Mass Transfer, 39, 2803, 10.1016/0017-9310(95)00353-3 Kuwahara, 1998, Numerical modeling of turbulent flow in porous media using a spatially periodic array, J. Porous Media, 1, 47, 10.1615/JPorMedia.v1.i1.40 F. Kuwahara, A. Nakayama, Numerical modeling of non-Darcy convective flow in a porous medium, in: Proceedings of the 11th International Heat Transfer Conference, Kyongyu, Korea, vol. 4, 23–28 August 1998, pp. 411–416 Takatsu, 1998, Turbulent phenomena in flow through porous media, J. Porous Media, 3, 243 Nakayama, 1999, A macroscopic turbulence model for flow in a porous medium, ASME J. Fluids Eng., 121, 427, 10.1115/1.2822227 V.S. Travkin, K. Hu, I. Catton, Turbulent kinetic energy and dissipation rate equation models for momentum transport in porous media, in: Proceedings of the Third ASME/JSME Joint Fluids Engineering Conference (on CD-ROM), Paper FEDSM99-7275, San Francisco, California, 18–23 July 1999 Gray, 1977, On the theorems for local volume averaging of multiphase system, Int. J. Multiphase Flow, 3, 333, 10.1016/0301-9322(77)90013-1 Slattery, 1967, Flow of viscoelastic fluids through porous media, AIChEJ, 13, 1066, 10.1002/aic.690130606 Hsu, 1990, Thermal dispersion in a porous medium, Int. J. Heat Mass Transfer, 33, 1587, 10.1016/0017-9310(90)90015-M Pedras, 2000, On the definition of turbulent kinetic energy for flow in porous media, Int. Commun. Heat Mass Transfer, 27, 211, 10.1016/S0735-1933(00)00102-0 M.H.J. Pedras, M.J.S. de Lemos, On volume and time averaging of transport equations for turbulent flow in porous media, in: Proceedings of the Third ASME/JSME Joint Fluids Engineering Conference (on CD-ROM), Paper FEDSM99-7273, San Francisco, CA, 18–23 July 1999 Hinze, 1959 Tennekes, 1972 Abe, 1992, An improved k–ε model for prediction of turbulent flows with separation and reattachment, Trans. JSME Ser. B, 58, 3003, 10.1299/kikaib.58.3003 Patankar, 1980 F.D. Rocamora Jr., M.J.S. de Lemos, Numerical solution of turbulent flow in porous media using a spatially periodic aArray and the k–ε model, in: Proceedings of the ENCIT-98 – 7th. Braz. Cong. Eng. Th. Sci., Rio de Janeiro, RJ, Brazil, vol. 2, 3–6 November 1998, pp. 1265–1271 M.H.J. Pedras, M.J.S. de Lemos, Numerical solution of turbulent flow in porous media using a spatially periodic cell and the low Reynolds k–ϵ model, to be presented at CONEM2000 – National Mechanical Engineering Congress, Natal, Rio Grande do Norte, Brazil, 7–11 August 2000 (in Portuguese) F.D. Rocamora Jr., M.J.S. de Lemos, Simulation of turbulent heat transfer in porous media using a spatially periodic cell and the k–ε model, in: Proceedings of the 15th Braz. Congr. Mech. Eng. (on CD-ROM), ISBN: 85-85769-03-3, Águas de Lindóia, São Paulo, Brazil, 22–26 November 1999 F.D. Rocamora Jr., M.J.S. de Lemos, Prediction of velocity and temperature profiles for hybrid porous medium-clean fluid domains, to be presented at CONEM2000 – National Mechanical Engineering Congress, Natal, Rio Grande do Norte, Brazil, 7–11 August 2000 F.D. Rocamora Jr., M.J.S. de Lemos, Laminar recirculating flow and heat transfer in hybrid porous medium-clear fluid computational domains, to be presented at 34th ASME – National Heat Transfer Conference, Paper NHTC2000-12317, Pittsburgh, PA, 20–22 August 2000