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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: [email protected]
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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
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Copyright
© 2015 Cambridge University Press 

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