Hostname: page-component-6b989bf9dc-llglr Total loading time: 0 Render date: 2024-04-14T20:49:52.830Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical investigation of the possibility of macroscopic turbulence in porous media: a direct numerical simulation study

Published online by Cambridge University Press:  02 February 2015

Y. Jin ,
M.-F. Uth ,
A. V. Kuznetsov  and
H. Herwig
Y. Jin
Affiliation:
Institute of Thermo-Fluid Dynamics, Hamburg University of Technology, Hamburg, D-21073, Germany
M.-F. Uth
Affiliation:
Institute of Thermo-Fluid Dynamics, Hamburg University of Technology, Hamburg, D-21073, Germany
A. V. Kuznetsov
Affiliation:
Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695-7910, USA
H. Herwig*
Affiliation:
Institute of Thermo-Fluid Dynamics, Hamburg University of Technology, Hamburg, D-21073, Germany
*
†Email address for correspondence: h.herwig@tuhh.de
Get access Rights & Permissions [Opens in a new window]

Abstract

When a turbulent flow in a porous medium is determined numerically, the crucial question is whether turbulence models should account only for turbulent structures restricted in size to the pore scale or whether the size of turbulent structures could exceed the pore scale. The latter would mean the existence of macroscopic turbulence in porous media, when turbulent eddies exceed the pore size. In order to determine the real size of turbulent structures in a porous medium, we simulated the turbulent flow by direct numerical simulation (DNS) calculations, thus avoiding turbulence modelling of any kind. With this study, which for the first time uses DNS calculations, we provide benchmark data for turbulent flow in porous media. Since perfect DNS calculations require the resolution of scales down to the Kolmogorov scale, often only approximate DNS solutions can be obtained, especially for high Reynolds numbers. This is accounted for by using and comparing two different DNS approaches, a finite volume method (FVM) with grid refinement towards the wall and a lattice Boltzmann method (LBM) with equal grid distribution. The solid matrix was simulated by a large number of rectangular bars arranged periodically. The number of bars in the solution domain with periodic boundary conditions was reduced systematically until a minimum size was found that does not suppress any large-scale turbulent structures. Two-point correlations, integral length scales and energy spectra were determined in order to answer the question of whether or not macroscopic turbulence can be found in porous media.

JFM classification

Low-Reynolds-number flows: Porous media Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent convection
Type
Papers
Information
Journal of Fluid Mechanics , Volume 766 , 10 March 2015 , pp. 76 - 103
Check for updates
Copyright
© 2015 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Afgan, I., Kahil, Y., Benhamadouche, S. & Sagaut, P. 2011 Large eddy simulation of the flow around single and two side-by-side cylinders at subcritical Reynolds numbers. Phys. Fluids 23, 075101.Google Scholar
Aidun, C. K. & Clausen, J. R. 2009 Lattice-Boltzmann method for complex flows. Annu. Rev. Fluid Mech. 41, 439–472.Google Scholar
Antohe, B. V. & Lage, J. L. 1997 A general two-equation macroscopic turbulence model for incompressible flow in porous media. Intl J. Heat Mass Transfer 40, 3013–3024.Google Scholar
Balakumar, B. J. & Adrian, R. J. 2007 Large- and very-large-scale motions in channel and boundary-layer flows. Phil. Trans. R. Soc. Lond. A 365, 665–681.Google ScholarPubMed
Bhatnagar, P. L., Gross, E. P. & Krook, M. 1954 A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94, 511–525.Google Scholar
Dullien, F. A. L. 1992 Porous Media: Fluid Transport and Pore Structure, 2nd edn. Academic Press.Google Scholar
Guala, M., Hommema, S. E. & Adrian, R. J. 2006 Large-scale and very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 554, 521–542.Google Scholar
Herwig, H. 2002 Strömungsmechanik. Springer.Google Scholar
Jimenez, J. 1998 The largest scales of turbulent wall flows. In Center for Turbulence Research, Annual Research Briefs, pp. 137–154. Stanford University.Google Scholar
Jin, Y. & Herwig, H. 2013 From single obstacles to wall roughness: some fundamental investigations based on DNS results for turbulent channel flow. Z. Angew. Math. Phys. 64, 1337–1352.CrossRefGoogle Scholar
Jin, Y. & Herwig, H. 2014 Turbulent flow in channels with shark skin surfaces: entropy generation and its physical significance. Intl J. Heat Mass Transfer 70, 10–22.CrossRefGoogle Scholar
Jin, Y., Uth, M.-F. & Herwig, H. 2015 Structure of a turbulent flow through plane channels with smooth and rough walls: an analysis based on high resolution DNS results. Comput. Fluids 107 (31), 77–88.CrossRefGoogle Scholar
Kazerooni, R. B. & Hannani, S. K. 2009 Simulation of turbulent flow through porous media employing a v2f model. Sci. Iran. Trans. B 16, 159–167.Google Scholar
Kis, P.2011 Analyse turbulenter gemischter Konvektion auf der Basis von DNS-Daten. PhD dissertation, TU Hamburg-Harburg, Verlag Dr Hut, München, ISBN 978-3-8439-0104-8.Google Scholar
Kolmogorov, A. N. 1941 Dissipation of energy in locally isotropic turbulence. Dokl. Akad. Nauk SSSR 32, 19–21.Google Scholar
Kundu, P., Kumar, V. & Mishra, I. M. 2014 Numerical modeling of turbulent flow through isotropic porous media. Intl J. Heat Mass Transfer 75, 40–57.CrossRefGoogle Scholar
Kuwahara, F., Kameyama, Y., Yamashita, S. & Nakayama, A. 1998 Numerical modeling of turbulent flow in porous media using a spatially periodic array. J. Porous Media 1, 47–55.Google Scholar
Lage, J. L., de Lemos, M. J. S. & Nield, D. A. 2002 Modeling turbulence in porous media. In Transport Phenomena in Porous Media II (ed. Ingham, D. B. & Pop, I.), pp. 198–230. Elsevier.Google Scholar
Lee, K. B. & Howell, J. R. 1991 Theoretical and experimental heat and mass transfer in highly porous media. Intl J. Heat Mass Transfer 34, 2123–2132.Google Scholar
de Lemos, M. J. S. 2004 Turbulent heat and mass transfer in porous media. In Emerging Technologies and Techniques in Porous Media (ed. Ingham, D. B., Bejan, A., Mamut, E. & Pop, I.), pp. 157–168. Kluwer Academic.CrossRefGoogle Scholar
de Lemos, M. J. S. 2005 The double-decomposition concept for turbulent transport in porous media. In Transport Phenomena in Porous Media III (ed. Ingham, D. B. & Pop, I.), pp. 1–33. Elsevier.Google Scholar
de Lemos, M. J. S. 2012 Turbulence in Porous Media, Modeling and Applications, 2nd edn. Elsevier.Google Scholar
de Lemos, M. J. S. & Braga, E. J. 2003 Modeling of turbulent natural convection in porous media. Intl Commun. Heat Mass Transfer 30, 615–624.Google Scholar
de Lemos, M. J. S. & Mesquita, M. S. 2003 Turbulent mass transport in saturated rigid porous media. Heat Mass Transfer 30, 105–113.Google Scholar
de Lemos, M. J. S. & Pedras, M. H. J. 2000 On the definitions of turbulent kinetic energy for flow in porous media. Intl Commun. Heat Mass Transfer 27, 211–220.Google Scholar
de Lemos, M. J. S. & Pedras, M. H. J. 2001 Recent mathematical models for turbulent flow in saturated rigid porous media. Trans. ASME J. Fluids Engng 123, 935–940.Google Scholar
de Lemos, M. J. S. & Rocamora, F. D. 2002 Turbulent transport modeling for heat flow in rigid porous media. In Heat Transfer 2002, Proceedings of the 12th Intl Heat Transfer Conference, vol. 2, pp. 791–796. Elsevier.Google Scholar
de Lemos, M. J. S. & Tofaneli, L. A. 2004 Modelling of double-diffusive turbulent natural convection in porous media. Intl J. Heat Mass Transfer 47, 4233–4241.CrossRefGoogle Scholar
Ma, X., Karamanos, G. S. & Karniadakis, G. E. 2000 Dynamics and low-dimensionality of a turbulent near wake. J. Fluid Mech. 410, 29–65.Google Scholar
Moin, P. & Mahesh, K. 1998 Direct numerical simulation: a tool in turbulence research. Annu. Rev. Fluid Mech. 30, 538–539.Google Scholar
Nakayama, A. & Kuwahara, F. 1999 A macroscopic turbulence model for flow in a porous medium. Trans. ASME J. Fluids Engng 121, 427–433.CrossRefGoogle Scholar
Nield, D. A. 1991 The limitations of the Brinkman–Forchheimer equation in modeling flow in a saturated porous medium and at an interface. Intl J. Heat Fluid Flow 12, 269–272.CrossRefGoogle Scholar
Nield, D. A. 2001 Alternative models of turbulence in a porous medium, and related matters. Trans. ASME J. Fluids Engng 123, 928–931.CrossRefGoogle Scholar
Nield, D. A. & Bejan, A. 1992 Convection in Porous Media, 1st edn. p. 8. Springer.Google Scholar
Nield, D. A. & Bejan, A. 2013 Convection in Porous Media, 4th edn. Springer.CrossRefGoogle Scholar
Parnaudeau, P., Carlier, J., Heitz, D. & Lamballais, E. 2008 Experimental and numerical studies of the flow over a circular cylinder at Reynolds number 3900. Phys. Fluids 20, 085101.CrossRefGoogle Scholar
Pedras, M. H. J. & de Lemos, M. J. S. 2000 On the definition of turbulent kinetic energy for flow in porous media. Intl Commun. Heat Mass Transfer 27, 211–220.CrossRefGoogle Scholar
Pedras, M. H. J. & de Lemos, M. J. S. 2001a Macroscopic turbulence modeling for incompressible flow through undeformable porous media. Intl J. Heat Mass Transfer 44, 1081–1093.CrossRefGoogle Scholar
Pedras, M. H. J. & de Lemos, M. J. S. 2001b Simulation of turbulent flow in porous media using a spatially periodic array and low $\mathit{Re}$ two-equation closure. Numer. Heat Transfer A 39, 35–59.Google Scholar
Pedras, M. H. J. & de Lemos, M. J. S. 2001c On the mathematical description and simulation of turbulent flow in a porous medium formed by an array of elliptical rods. Trans. ASME J. Fluids Engng 123, 941–947.CrossRefGoogle Scholar
Pedras, M. H. J. & de Lemos, M. J. S. 2003 Computation of turbulent flow in porous media using a low Reynolds number $k{-}{\it\varepsilon}$ model and an infinite array of transversely displaced elliptic rods. Numer. Heat Transfer A 43, 585–602.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.Google Scholar
Prescott, P. J. & Incropera, F. P. 1995 The effect of turbulence on solidification of a binary metal alloy with electromagnetic stirring. Trans. ASME J. Heat Transfer 117, 716–724.Google Scholar
Rocamora, F. D. & de Lemos, M. J. S. 2000 Analysis of convective heat transfer for turbulent flow in saturated porous media. Intl Commun. Heat Mass Transfer 27, 825–834.Google Scholar
Silva, R. A. & de Lemos, M. J. S. 2003 Turbulent flow in a channel occupied by a porous layer considering the stress jump at the interface. Intl J. Heat Mass Transfer 46, 5113–5136.Google Scholar
Succi, S. 2001 The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. Oxford University Press.CrossRefGoogle Scholar
Vafai, K., Minkowycz, W. J., Bejan, A. & Khanafer, K. 2006 Synthesis of models for turbulent transport through porous media. In Handbook of Numerical Heat Transfer (ed. Minkowycz, W. J. & Sparrow, E. M.), chap. 12, Wiley.Google Scholar
Wibel, W. & Ehrhard, P.2006 Experiments on liquid pressure-drop in rectangular microchannels, subject to non-unity aspect ratio and finite roughness. In Proceedings of Fourth International Conference on Nanochannels, Microchannels and Minichannels, Limerick, Ireland.Google Scholar
Wibel, W. & Ehrhard, P. 2009 Experiments on the laminar/turbulent transition of liquid flows in rectangular microchannels. Heat Transfer Engng 30, 70–77.CrossRefGoogle Scholar