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Understanding and Modelling Turbulence Over and Inside Porous Media

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Abstract

To understand turbulence over porous media, a series of PIV measurements were carried out in porous-walled channel flows. The porous walls were made of three types of foamed ceramics which had the same porosity but different permeability. For turbulence inside porous media, LES studies of fully developed flows in three different model porous media were performed. Referring to these databases, a multi-scale k − ε four equation eddy viscosity model for turbulence around and/or inside porous media was developed. Through the comparison to the experimental results, the proposed model was validated with satisfactory accuracy.

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References

  1. Aidun, C.K., Clausen, J.R.: Lattice Boltzmann method for complex flows. Annu. Rev. Fluid Mech. 42, 439–472 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Alazmi, B., Vafai, K.: Analysis of fluid flow and heat transfer interfacial conditions between a porous medium and a fluid layer. Int. J. Heat Mass Tran. 44, 1735–1749 (2001)

    Article  MATH  Google Scholar 

  3. Amano, R.S., Arakawa, H., Suga, K.: Turbulent heat transfer in a two-pass cooling channel by several wall turbulence models. Int. J. Heat Mass Tran. 77, 406–418 (2014)

    Article  Google Scholar 

  4. Amiri, A., Vafai, K.: Analysis of dispersion effects and non-thermal equilibrium, non Darcian, variable porosity incompressible flow through porous media. Int. J. Heat Mass Tran. 37, 939–954 (1994)

    Article  Google Scholar 

  5. Antohe, B.V., Lage, J.L.: A general two-equation macroscopic turbulence model for incompressible flow in porous media. Int. J. Heat Mass Tran. 40, 3013–3024 (1997)

    Article  MATH  Google Scholar 

  6. Arakawa, H., Suga, K.: Numerical analysis of a 3D turbulent serpentine channel flow over permeable walls. In: Proceedings of the 10th Int. ERCOFTAC Symp. Engineering Turbulence Modelling and Measurements. S2.3. ERCOFTAC, Marbella, Spain (2014)

  7. Beavers, G.S., Joseph, D.D.: Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30, 197–207 (1967)

    Article  Google Scholar 

  8. 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)

    Article  MathSciNet  MATH  Google Scholar 

  9. Chandesris, M., D’Hueppe, A., Mathieu, B., Jamet, D., Goyeau, B.: Direct numerical simulation of turbulent heat transfer in a fluid-porous domain. Phys. Fluids 25(125), 110 (2013)

    Google Scholar 

  10. Chun, B., Ladd, A.J.: Interpolated boundary condition for lattice Boltzmann simulations of flows in narrow gaps. Phys. Rev. E 75(066), 705 (2007)

    MathSciNet  Google Scholar 

  11. van Der Merwe, D.F., Gauvin, W.H.: Velocity and turbulence measurements of air flow through a packed bed. AIChE J. 17(3), 519–528 (1971)

    Article  Google Scholar 

  12. d’Humiéres, D., Ginzburg, I., Krafczyk, M., Lallemand, P., Luo, L.S.: Multiple-relaxation-time lattice Boltzmann models in three dimensions. Phil. Trans. R. Soc. A 360, 437–451 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  13. Drouin, M., Grégoire, O., Simonin, O.: A consistent methodology for the derivation and calibration of a macroscopic turbulence model for flows in porous media. Int. J. Heat Mass Tran. 63(0), 401–413 (2013)

    Article  Google Scholar 

  14. Dybbs, A., Edwards, R.V.: A new look at porous media fluid mechanics-Darcy to turbulent. In: Bear, J., Corapcioglu, M.Y. (eds.) Fundamentals of Transport Phenomena in Porous Media, NATO ASI Series, vol. 82, pp 199–256. Springer, Netherlands (1984)

    Chapter  Google Scholar 

  15. Getachew, D., Minkowycz, W.J., Lage, J.L.: A modified form of the k − ε model for turbulent flows of an incompressible fluid in porous media. Int. J. Heat Mass Tran. 43, 2909–2915 (2000)

    Article  MATH  Google Scholar 

  16. Guo, B., Yu, A., Wright, B., Zulli, P.: Simulation of turbulent flow in a packed bed. Chem. Eng. Technol. 29, 596–603 (2006)

    Article  Google Scholar 

  17. Hall, M.J., Hiatt, J.P.: Measurements of pore scale flows within and exiting ceramic foams. Exp. Fluids 20(6), 433–440 (1996)

    Article  Google Scholar 

  18. Hsu, C.T.: A closure model for transient heat conduction in porous media. J. Heat Tran. 121(3), 733–739 (1999)

    Article  Google Scholar 

  19. Hsu, C.T., Cheng, P., Wong, K.W.: A lumped-parameter model for stagnant thermal conductivity of spatially periodic porous media. J. Heat Tran. 117, 264–269 (1995)

    Article  Google Scholar 

  20. Hutter, C., Zenklusen, A., Kuhn, S., Von Rohr, P.R.: Large eddy simulation of flow through a streamwise-periodic structure. Chem. Eng. Sci. 66(3), 519–529 (2011)

    Article  Google Scholar 

  21. Jolls, K.R., Hanratty, T.J.: Transition to turbulence for flow through a dumped bed of spheres. Chem. Eng. Sci. 21(12), 1185–1190 (1966)

    Article  Google Scholar 

  22. Kaviany, M.: Principles of heat transfer in porous media, 2nd edn. Springer, New York (1995)

    Book  MATH  Google Scholar 

  23. Kim, J., Moin, P., Moser, R.: Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166 (1987)

    Article  MATH  Google Scholar 

  24. Kong, F.Y., Schetz, J.A.: Turbulent boundary layer over porous surfaces with different surface geometries. Technical Report 82-0030. AIAA (1982)

  25. Kuwahara, F., Shirota, M., Nakayama, A.: A numerical study of interfacial convective heat transfer coefficient in two-energy equation model for convection in porous media. Int. J. Heat Mass Tran. 44(6), 1153–1159 (2001)

    Article  MATH  Google Scholar 

  26. Kuwahara, F., Yamane, T., Nakayama, A.: Large eddy simulation of turbulent flow in porous media. Int. Commum. Heat Mass Tran. 33, 411–418 (2006)

    Article  Google Scholar 

  27. Kuwata, Y., Suga, K.: Modelling turbulence around and inside porous media based on the second moment closure. Int. J. Heat Fluid Flow 43, 35–51 (2013)

    Article  Google Scholar 

  28. Kuwata, Y., Suga, K.: A study on the volume averaged turbulence transport equations by performing LES of square rod array flows. Trans. Japan Soc. Mech. Engrs. (B) 79, 1752–1763 (2013). (in Japanese)

    Article  Google Scholar 

  29. Kuwata, Y., Suga, K.: Large eddy simulations of pore-scale turbulent flows in porous media by the lattice boltzmann method. Int. J. Heat Fluid Flow 55 (2015). doi:10.1016/j.ijheatfluidflow.2015.05.015

  30. Kuwata, Y., Suga, K.: Progress in the extension of a second-moment closure for turbulent environmental flows. Int. J. Heat Fluid Flow 51, 268–284 (2015)

    Article  Google Scholar 

  31. Kuwata, Y., Suga, K.: Turbulent heat transfer modelling in porous media with a multi-scale second moment closure. Spec. Top. Rev. Porous Med. 6 (2015). doi:10.1615/.2015012377

  32. Kuwata, Y., Suga, K., Sakurai, Y.: Development and application of a multi-scale k−ε model for turbulent porous medium flows. Int. J. Heat Fluid Flow 49, 135–150 (2014)

    Article  Google Scholar 

  33. Latifi, M.A., Midoux, N., Storck, A., Gence, J.N.: The use of micro-electrodes in the study of the flow regimes in a packed bed reactor with single phase liquid flow. Chem. Eng. Sci. 44(11), 2501–2508 (1989)

    Article  Google Scholar 

  34. Launder, B.E., Sharma, B.I.: Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc. Lett. Heat Mass Tran. 1, 131–138 (1974)

    Google Scholar 

  35. Lee, K.B., Howell, J.R.: Forced convective and radiative transfer within a highly porous layer exposeed to a turbulent external flow field. In: Proceedings 2nd ASME/JSME Therm. Engrg. Joint Conf., vol. 2, pp 377–386 (1987)

  36. De Lemos, M.J.S.: Turbulence in porous media. Elsevier, UK (2006)

    Google Scholar 

  37. Lien, F.S., Eugene, Y., Wilson, D.: Numerical modelling of the turbulent flow developing within and over a 3-D building array, part II: A mathematical foundation for a distributed drag force approach. Bound. Layer Meteorol. 114, 245–285 (2005)

    Article  Google Scholar 

  38. Lien, F.S., Leschziner, M.A.: A general non-orthogonal finite-volume algorithm for turbulent flow at all speeds incorporating second-moment turbulence-transport closure, Part1: Numerical implementation. Comp. Meth. Appl. Mech. Engng. 114, 123–148 (1994a)

    Article  MathSciNet  Google Scholar 

  39. Lien, F.S., Leschziner, M.A.: Upstream monotonic interpolation for scalar transport with application in complex turbulent flows. Int. J. Num. Meth. Fluids 19, 527–548 (1994b)

    Article  MATH  Google Scholar 

  40. Lovera, F., Kennedy, J.F.: Friction factors for flat bed flows in sand channels. J. Hydr. Div., ASCE 95, 1227–1234 (1969)

    Google Scholar 

  41. Masuoka, T., Takatsu, Y.: Turbulence model for flow through porous media. Int. J. Heat Mass Tran. 39, 2803–2809 (1996)

    Article  MATH  Google Scholar 

  42. Mickley, H.S., Smith, K.A., Korchak, E.I.: Fluid flow in packed beds. Chem. Eng. Sci. 20(3), 237–246 (1965)

    Article  Google Scholar 

  43. Nakayama, A., Kuwahara, F.: A macroscopic turbulence model for flow in a porous medium. J. Fluids Eng. 121, 427–433 (1999)

    Article  Google Scholar 

  44. Nakayama, A., Kuwahara, F.: A general macroscopic turbulence model for flows in packed beds, channels, pipes, and rod bundles. J. Fluids Eng. 130(101), 205–1–7 (2008)

    Google Scholar 

  45. Nakayama, A., Kuwahara, F., Sugiyama, M., Xu, G.: A two-energy equation model for conduction and convection in porous media. Int. J. Heat Mass Tran. 44(22), 4375–4379 (2001)

    Article  MATH  Google Scholar 

  46. Nicoud, F., Ducros, F.: Subgrid-scale stress modelling based on the square of the velocity gradient tensor. Flow Turbul. Combust. 62, 183–200 (1999)

    Article  MATH  Google Scholar 

  47. Nield, D.A., Bejan, A.: Convection in porous media, 3rd edn. Springer, Berlin (2006)

    MATH  Google Scholar 

  48. Nikora, V.I., McEwan, I.K., McLean, S.R., Coleman, S.E., Pokarajac, D., Walters, R.: Double-averaging concept for rough-bed open channel and overland flows: Theoretical background. J. Hydraul. Eng. 133, 873–883 (2007)

    Article  Google Scholar 

  49. Ochoa-Tapia, A.J., Whitaker, S.: Momentum transfer at the boundary between a porous medium and a homogeneous fluid. I.: Theoretical development, II: Comparison with experiment. Int. J. Heat Mass Tran. 38, 2635–2655 (1995)

    Article  MATH  Google Scholar 

  50. Patankar, S.V.: Numerical heat transfer and fluid flow. Hemisphere/ McGraw Hill, Washington (1980)

    MATH  Google Scholar 

  51. Pedras, M.H.J, De Lemos, M.J.S.: On the definition of turbulent kinetic energy for flow in porous media. Int. Commum. Heat Mass Tran. 27, 211–220 (2000)

    Article  Google Scholar 

  52. Pedras, M.H.J, De Lemos, M.J.S.: Macroscopic turbulence modeling for incompressible flow through undeformable porous media. Int. J. Heat Mass Tran. 44, 1081–1093 (2001)

    Article  MATH  Google Scholar 

  53. Pedras, M.H.J, De Lemos, M.J.S.: On the mathematical description and simulation of turbulent flow in a porous medium formed by an array of elliptic rods. J. Fluids Eng. 123(4), 941–947 (2001)

    Article  Google Scholar 

  54. Pedras, M.H.J, De Lemos, M.J.S.: Simulation of turbulent flow in porous media using a spatially periodic array and a low Re two equation closure. Numer. Heat Tran. Part A 39, 35–59 (2001)

    Article  Google Scholar 

  55. Pinson, F., Grégoire, O., Simonin, O.: k − ε Macro-scale modeling of turbulence based on a two scale analysis in porous media. Int. J. Heat Fluid Flow 27, 955–966 (2006)

    Article  Google Scholar 

  56. 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)

    Article  Google Scholar 

  57. Quintard, M., Whitaker, S.: One- and two-equation models for transient diffusion processes in two-phase systems. Adv. Heat Tran. 23, 369–367 (1993)

    Article  Google Scholar 

  58. Quintard, M., Whitaker, S.: Local thermal equilibrium for transient heat conduction: theory and comparison with numerical experiments. Int. J. Heat Mass Tran. 38(15), 2779–2796 (1995)

    Article  MATH  Google Scholar 

  59. Raupach, M.R.: Conditional statistics of Reynolds stress in rough-wall and smooth-wall turbulent boundary layers. J. Fluid Mech. 21, 363–382 (1981)

    Article  MATH  Google Scholar 

  60. Raupach, M.R., Shaw, R.H.: Averaging procedures for flow within vegetation canopies. Bound. Layer Meteorol. 22, 79–90 (1982)

    Article  Google Scholar 

  61. Rhie, C.M., Chow, W.L.: Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA J. 21, 1525–1532 (1983)

    Article  MATH  Google Scholar 

  62. Rode, S., Midoux, N., Latifi, M.A., Storck, A., Saatdjian, E.: Hydrodynamics of liquid flow in packed beds: an experimental study using electrochemical shear rate sensors. Chem. Eng. Sci. 49(6), 889–900 (1994)

    Article  Google Scholar 

  63. Ruff, J.F., Gelhar, L.W.: Turbulent shear flow in porous boundary. J. Eng. Mech. Div., ASCE 98, 975–991 (1972)

    Google Scholar 

  64. Saito, M.B, de Lemos, M.J.: A correlation for interfacial heat transfer coefficient for turbulent flow over an array of square rods. J. Heat Tran. 128(5), 444–452 (2006)

    Article  Google Scholar 

  65. Saito, M.B, De Lemos, M.J.S.: A macroscopic two-energy equation model for turbulent flow and heat transfer in highly porous media. Int. J. Heat Mass Tran. 53, 2424–2433 (2010)

    Article  MATH  Google Scholar 

  66. Sakurai, Y., Kuwata, Y., Suga, K.: Lattice Boltzmann LES of conjugate turbulent heat transfer in square rod arrays. In: Proceedings 10th International ERCOFTAC Symp. Engineering Turbulence Modelling and Measurements. S20.4. ERCOFTAC, Marbella, Spain (2014)

  67. 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, 69–78 (1990)

    Google Scholar 

  68. Suga, K.: Lattice Boltzmann methods for complex micro flows: Applicability and limitations for practical applications. Fluid Dyn. Res. 45(034), 501 (2013)

    MathSciNet  MATH  Google Scholar 

  69. Suga, K., Kuwata, Y.: On the budget terms of the double averaged turbulent stress transport equations in porous media. Procedia Eng. 79, 3–8 (2014)

    Article  Google Scholar 

  70. Suga, K., Kuwata, Y., Takashima, K., Chikasue, R.: A D3Q27 multiple-relaxation-time lattice Boltzmann method for turbulent flows. Comput. Math. Appl. 69, 518–529 (2015)

    Article  MathSciNet  Google Scholar 

  71. Suga, K., Matsumura, Y., Ashitaka, Y., Tominaga, S., Kaneda, M.: Effects of wall permeability on turbulence. Int. J. Heat Fluid Flow 31, 974–984 (2010)

    Article  Google Scholar 

  72. Suga, K., Mori, M., Kaneda, M.: Vortex structure of turbulence over permeable walls. Int. J. Heat Fluid Flow 32, 586–595 (2011)

    Article  Google Scholar 

  73. Suga, K., Nishimura, W., Yamamoto, T., Kaneda, M.: Measurements of serpentine channel flow characteristics for a proton exchange membrane fuel cell. Int. J. Hydrog. Energy 39(11), 5942–5954 (2014)

    Article  Google Scholar 

  74. Suga, K., Nishio, Y.: Three dimensional microscopic flow simulation across the interface of a porous wall and clear fluid by the lattice Boltzmann method. Open Tran. Phenom. J. 1, 35–44 (2009)

    Article  Google Scholar 

  75. Suga, K., Tanaka, T., Nishio, Y., Murata, M.: A boundary reconstruction scheme for lattice Boltzmann flow simulation in porous media. Prog. Comput. Fluid Dyn. 9, 201–207 (2009)

    Article  Google Scholar 

  76. Suga, K., Tominaga, S., Mori, M., Kaneda, M.: Turbulence characteristics in flows over solid and porous square ribs mounted on porous walls. Flow Turb. Combust. 91, 19–40 (2013)

    Article  Google Scholar 

  77. Takeda, K., Lockwood, F.C.: Gas flow calculation with a turbulence model in a packed bed. Tetsu-to-Hagane 82, 486–491 (1996)

    Google Scholar 

  78. Teruel, F.E.: Rizwan-uddin: A new turbulence model for porous media flows. Part I: Constructive equations and model closure. Int. J. Heat Mass Tran. 52, 4264–4272 (2009)

    Article  MATH  Google Scholar 

  79. Vafai, K., Bejan, A., Minkowycz, W.J., Khanafer, K.: Chapter 12: A critical synthesis of pertinent models for turbulent transport through porous media. In: Handbook of Numerical Heat Transfer. 2nd edn, pp 389–416. Wiley, Hoboken (2006)

  80. Vollmer, S., Francisco de los Santos, R., Daebel, H., Kuhn, G.: Micro-scale exchange processes between surface and subsurface water. J. Hydrol. 269, 3–10 (2002)

    Article  Google Scholar 

  81. Whitaker, S.: Flow in porous media I: A theoretical derivation of Darcy’s law. Transp. Porous Med. 1, 3–25 (1986)

    Article  Google Scholar 

  82. Whitaker, S.: The Forchheimer equation: A theoretical development. Transp. Porous Med. 25, 27–61 (1996)

    Article  Google Scholar 

  83. Willmarth, W.W., Lu, S.S.: Structure of the Reynolds stress near the wall. J. Fluid Mech. 55, 65–92 (1972)

    Article  Google Scholar 

  84. Yang, C., Nakayama, A.: A synthesis of tortuosity and dispersion in effective thermal conductivity of porous media. Int. J. Heat Mass Tran. 53, 3222–3230 (2010)

    Article  MATH  Google Scholar 

  85. Zagni, A.F.E., Smith, K.V.H.: Channel flow over permeable beds of graded spheres. J. Hydraul. Div. 102, 207–222 (1976)

    Google Scholar 

  86. Zenklusen, A., Kenjereš, S., von Rohr, P.R.: Vortex shedding in a highly porous structure. Chem. Eng. Sci. 106, 253–263 (2014)

    Article  Google Scholar 

  87. Zhu, W., van Hout, R., Katz, J.: PIV measurements in the atmospheric boundary layer within and above a mature corn canopy. Part II: Quadrant-hole analysis. J. Atom. Sci. 64, 2825–2838 (2007)

    Article  Google Scholar 

  88. Zippe, H.J., Graf, W.H.: Turbulent boundary-layer flow over permeable and non-permeable rough surfaces. J. Hydraul. Res. 21, 51–65 (1983)

    Article  Google Scholar 

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  1. Department of Mechanical Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka, 599-8531, Japan

    Kazuhiko Suga

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Suga, K. Understanding and Modelling Turbulence Over and Inside Porous Media. Flow Turbulence Combust 96, 717–756 (2016). https://doi.org/10.1007/s10494-015-9673-6

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