Turbulence models proposed for flow through permeable structures depend on the order of application of time and volume average operators. Two developed methodologies, following the two orders of integration, lead to different governing equations for the statistical quantities. The flow turbulence kinetic energy resulting in each case is different. This paper reviews recently published mathematical models developed for such flows. The concept of double decomposition is discussed and models are classified in terms of the order of application of time and volume averaging operators, among other peculiarities. A total of four major classes of models are identified and a general discussion on their main characteristics is carried out. Proposed equations for turbulence kinetic energy following time-space and space-time integration sequences are derived and similar terms are compared. Treatment of the drag coefficient and closure of the interfacial surface integrals are discussed.
Issue Section:
Technical Papers
1.
Darcy, H., 1856, Les Fontaines Publiques de la Vile de Dijon, Victor Dalmond, Paris.
2.
Forchheimer
, P.
, 1901
, “Wasserbewegung durch Boden
,” Z. Ver. Deutsch. Ing.
45
, pp. 1782
–1788
.3.
Brinkman
, H. C.
, 1947
, “A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles
,” Appl. Sci. Res.
, 1
, pp. 27
–34
.4.
Ward
, J. C.
, 1964
, “Turbulent flow in porous media
,” J. Hydraul. Div., Am. Soc. Civ. Eng.
, 90
(HY5), pp. 1
–12
.5.
Whitaker
, S.
, 1969
, “Advances in theory of fluid motion in porous media
,” Ind. Eng. Chem.
, 61
, pp. 14
–28
.6.
Bear, J., 1972, Dynamics of Fluids in Porous Media, American Elsevier, New York.
7.
Vafai
, K.
, and Tien
, C. L.
, 1981
, “Boundary and inertia effects on flow and heat transfer in porous media
,” Int. J. Heat Mass Transf.
, 24
, pp. 195
–203
.8.
Lee, K., Howell, and J. R., 1987, “Forced convective and radiative transfer within a highly porous layer exposed to a turbulent external flow field,” Proc. of the 1987 ASME-JSME Thermal Eng. Joint Conf., Vol. 2, pp. 377–386.
9.
Wang
, H.
, and Takle
, E. S.
, 1995
, “Boundary-layer flow and turbulence near porous obstacles
,” Boundary-Layer Meteorol.
, 74
, pp. 73
–88
.10.
Antohe
, B. V.
, and Lage
, J. L.
, 1997
, “A general two-equation macroscopic turbulence model for incompressible flow in porous media
,” Int. J. Heat Mass Transf.
, 40
, pp. 3013
–3024
.11.
Getachew
, D.
, Minkowycz
, W. J.
, and Lage
, J. L.
, 2000
, “A modified form of the k-ε model for turbulent flow of an incompressible fluid in porous media
,” Int. J. Heat Mass Transf.
, 43
, pp. 2909
–2915
.12.
Masuoka
, T.
, and Takatsu
, Y.
, 1996
, “Turbulence model for flow through porous media
,” Int. J. Heat Mass Transf.
, 39
, pp. 2803
–2809
.13.
Kuwahara
, F.
, Kameyama
, Y.
, Yamashita
, S.
, and Nakayama
, A.
, 1998
, “Numerical modeling of turbulent flow in porous media using a spatially periodic array
,” J. Porous Media
, 1
, pp. 47
–55
.14.
Kuwahara, F., and Nakayama, A., 1998, “Numerical modeling of non-Darcy convective flow in a porous medium,” Proc. 11th Int. Heat Transf. Conf., Kyongyu, Korea, August 23–28.
15.
Takatsu
, Y.
, and Masuoka
, T.
, 1998
, “Turbulent phenomena in flow through porous media
,” J. Porous Media
, 3
, pp. 243
–251
.16.
Nakayama
, A.
, and Kuwahara
, F.
, 1999
, “A macroscopic turbulence model for flow in a porous medium
,” ASME J. Fluids Eng.
, 121
, pp. 427
–433
.17.
Travkin, V. S., and Catton, I., 1992, “Models of turbulent thermal diffusivity and transfer coefficients for a regular packed bed of spheres,” Proc. 28th National Heat Transfer Conference, San Diego, C-4, ASME-HTD-193, pp. 15–23.
18.
Travkin, V. S., Catton, I., and Gratton, L., 1993, “Single-phase turbulent transport in prescribed non-isotropic and stochastic porous media,” Heat Transfer in Porous Media, ASME-HTD-240, pp. 43–48.
19.
Gratton, L., Travkin, V. S., and Catton, I., 1994, “Numerical solution of turbulent heat and mass transfer in a stratified geostatistical porous layer for high permeability media,” ASME Proceedings HTD-Vol. 41, pp. 1–14.
20.
Travkin
, V. S.
, and Catton
, I.
, 1995
, “A two temperature model for turbulent flow and heat transfer in a porous layer
,” ASME J. Fluids Eng.
, 117, pp.
181
–188
.21.
Travkin
, V. S.
, and Catton
, I.
, 1998
, “Porous media transport descriptions–non-local, linear, and non-linear against effective thermal/fluid properties
,” Adv. Colloid Interface Sci.
, 76–77
, pp. 389
–443
.22.
Travkin, V. S., Hu, K., and Catton, I., 1999, “Turbulent kinetic energy and dissipation rate equation models for momentum transport in porous media,” Proc. 3rd ASME/JSME Joint Fluids Engineering Conference (on CD-ROM), Paper FEDSM99-7275, San Francisco, California, 18–23 July.
23.
Lage, J. L., 1998, “The fundamental theory of flow through permeable media from Darcy to turbulence,” in Transport Phenomena in Porous Media, D. B. Ingham and I. Pop, eds., Elsevier Science, ISBN: 0-08-042843-6, 446 pp.
24.
Pedras, M. H. J., and de Lemos, M. J. S., 1998, “Results for macroscopic turbulence modeling for porous media,” Proc. of ENCIT98-7th Braz. Cong. Eng. Th. Sci., Vol. 2, pp. 1272–1277, Rio de Janeiro, Brazil, Nov. 3–6 (in Portuguese).
25.
Pedras, M. H. J., and de Lemos, M. J. S., 1999, “On volume and time averaging of transport equations for turbulent flow in porous media,” Proc. of 3rd ASME/JSME Joint Fluids Engineering Conference (on CD-ROM), ASME-FED-248, Paper FEDSM99-7273, ISBN 0-7918-1961-2, San Francisco, California, July 18–23.
26.
Pedras, M. H. J., and de Lemos, M. J. S., 1999, “Macroscopic turbulence modeling for saturated porous media,” Proc. of COBEM99-15th Braz. Congr. Mech. Eng. (on CD-ROM), ISBN: 85-85769-03-3, A´guas de Lindo´ia, Sa˜o Paulo, Brazil, November 22–26 (in Portuguese).
27.
Pedras
, M. H. J.
, and de Lemos
, M. J. S.
, 2000
, “On the definition of turbulent kinetic energy for flow in porous media
,” Int. Commun. Heat Mass Transfer
, 27
, No. 2
, pp. 211
–220
.28.
Pedras, M. H. J., and de Lemos, M. J. S., 2000, “Numerical solution of turbulent flow in porous media using a spatially periodic cell and the low Reynolds k-ε model,” Proc. of CONEM2000–National Mechanical Engineering Congress (on CD-ROM), Natal, Rio Grande do Norte, Brazil, August 7–11 (in Portuguese).
29.
Rocamora, Jr., F. D., and de Lemos, M. J. S., 1998, “Numerical solution of turbulent flow in porous media using a spatially periodic array and the k-ε model,” Proc. ENCIT-98–7th Braz. Cong. Eng. Th. Sci., Vol. 2, pp. 1265–1271, Rio de Janeiro, RJ, Brazil, November 3–6.
30.
de Lemos, M. J. S., and Pedras, M. H. J., 2000, “Modeling turbulence phenomena in incompressible flow through saturated porous media,” Proc. of 34th ASME-National Heat Transfer Conference (on CD-ROM), ASME-HTD-1463CD, Paper NHTC2000-12120, ISBN:0-7918-1997-3, Pittsburgh, Pennsylvania, August 20–22.
31.
Rocamora, Jr., F. D., and de Lemos, M. J. S., 1999, “Simulation of turbulent heat transfer in porous media using a spatially periodic cell and the k-ε model,” Proc. of COBEM99–15th Braz. Congr. Mech. Eng. (on CD-ROM), ISBN: 85-85769-03-3, A´guas de Lindo´ia, Sa˜o Paulo, Brazil, November 22–26.
32.
Rocamora
, Jr., F. D.
, and de Lemos
, M. J. S.
, 2000
, “Analysis of convective heat transfer for turbulent flow in saturated porous media
,” Int. Commun. Heat Mass Transfer
, 27
, No. 6
, pp. 825
–834
.33.
de Lemos, M. J. S., and Pedras, M. H. J., 2000, “Simulation of turbulent flow through hybrid porous medium-clear fluid domains,” Proc. of IMECE2000–ASME–Intern. Mech. Eng. Congr., ASME-HTD-366-5, pp. 113–122, ISBN:0-7918-1908-6, Orlando, Florida.
34.
Rocamora, Jr., F. D., and de Lemos, M. J. S., 2000, “Prediction of velocity and temperature profiles for hybrid porous medium-clean fluid domains,” Proc. of CONEM2000–National Mechanical Engineering Congress (on CD-ROM), Natal, Rio Grande do Norte, Brazil, August 7–11.
35.
Rocamora, Jr., F. D., and de Lemos, M. J. S., 2000, “Laminar recirculating flow and heat transfer in hybrid porous medium-clear fluid computational domains,” Proc. of 34th ASME-National Heat Transfer Conference (on CD-ROM), ASME-HTD-I463CD, Paper NHTC2000-12317, ISBN:0-7918-1997-3, Pittsburgh, Pennsylvania, August 20–22.
36.
Rocamora, Jr., F. D., and de Lemos, M. J. S., 2000, “Heat transfer in suddenly expanded flow in a channel with porous inserts,” Proc. of IMECE2000–ASME–Intern. Mech. Eng. Congr., ASME-HTD-366-5, pp. 191–195, ISBN:0-7918-1908-6, Orlando, Florida, November 5–10.
37.
Rocamora, F. D., and de Lemos, M. J. S., 2001, “
Turbulence Modeling for non-isothermal flow in undeformable porous media”, Proc. of NHTCOI, 35th Nat. Heat Transfer Conf. ASME-HTD-IY9SCD, Paper NHTC 2001-20178 ISBN: 0791835278, Anaheim, California, June 10–12.
38.
de Lemos, M. J. S., 2001, “Modeling turbulent flow in saturated rigid porous media,” Proc. of NHTC’01, 35th National Heat Transfer Conference, T15-04 Panel on Porous Media, Anaheim, CA, June 10–12.
39.
de Lemos, M. J. S., and Pedras, M. H. J., 2001, “Alternative transport equations for turbulent kinetic energy for flow in porous media,” Proc. of NHTC’01, 35th National Heat Transfer Conference, ASME-HTD-I495CD, Paper NHTC2001-20177, ISBN: 0-7918-3527-8, Anaheim, California, June 10–12.
40.
Pedras
, M. H. J.
, and de Lemos
, M. J. S.
, 2001
, “Macroscopic Turbulence Modeling for Incompressible Flow Through Undeformable Porous Media
,” Intern. J. Heat and Mass Transfer
44
, No. 6
, pp. 1081
–1093
.41.
Pedras
, M. H. J.
, and de Lemos
, M. J. S.
, 2001
, “Simulation of turbulent flow in porous media using a spatially periodic array and a low Re two-equation closure
,” Numer. Heat Transfer, Part A
, 39
, No. 1
, pp. 35
–59
.42.
Hinze, J. O., 1959, Turbulence, McGraw-Hill, New York.
43.
Warsi, Z. U. A., 1998, Fluid Dynamics–Theoretical and Computational Approaches, 2nd ed., CRC Press, Boca Raton.
44.
Pedras, M. H. J., and de Lemos, M. J. S., 2001, “Soluc¸a˜o Nume´rica do Escoamento Turbulento num Meio Poroso Formado por Hastes Elı´pticas—Aplicac¸a˜o do modelo k-ε para baixo e alto Reynolds,” Proc. of COBEM01–16th Braz. Congr. Mech. Eng. (on CD-ROM), Uberla^ndia, MG, Brazil, November 26–30.
45.
Hsu
, C. T.
, and Cheng
, P.
, 1990
, “Thermal dispersion in a porous medium
,” Int. J. Heat Mass Transf.
, 33
, pp. 1587
–1597
.46.
Chan, E. C., Lien, F.-S., and Yavonovich, M. M., 2000, “Numerical Study of Forced Flow in a Back-Step Channel Through Porous Layer,” Proc. of 34th ASME-National Heat Transfer Conference (on CD-ROM), ASME-HTD-1463CD, Paper NHTC2000-12118, ISBN:0-7918-1997-3, Pittsburgh, Pennsylvania, August 20–22.
47.
Pedras, M. H. J., and de Lemos, M. J. S., 2001, “Adjustment of a macroscopic turbulence model for a porous medium formed by an infinite array of elliptic rods,” 2nd International Conference on Computational Heat and Mass Transfer, Rio de Janeiro, Brazil, Oct. 22–26.
48.
Bird, R. B., Stewart, W. E., and Lightfoot, E. N., 1960, Transport Phenomena, Wiley, New York.
49.
Fox, R. W., and McDonald, A. T., 1998, Introduction to Fluids Mechanics, Wiley, New York, 5th ed., p. 156.
Copyright © 2001
by ASME
You do not currently have access to this content.
