Hostname: page-component-77c89778f8-gvh9x Total loading time: 0 Render date: 2024-07-18T15:47:44.410Z Has data issue: false hasContentIssue false
  • English
  • Français

Symmetry breaking of turbulent flow in porous media composed of periodically arranged solid obstacles

Published online by Cambridge University Press:  19 October 2021

Vishal Srikanth ,
Ching-Wei Huang ,
Timothy S. Su  and
Andrey V. Kuznetsov Open the ORCID record for Andrey V. Kuznetsov [Opens in a new window]
Vishal Srikanth
Affiliation:
Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695, USA
Ching-Wei Huang
Affiliation:
Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695, USA
Timothy S. Su
Affiliation:
Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695, USA
Andrey V. Kuznetsov*
Affiliation:
Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695, USA
*
† Email address for correspondence: avkuznet@ncsu.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

The focus of this paper is a numerical simulation study of the flow dynamics in a periodic porous medium to analyse the physics of a symmetry-breaking phenomenon, which causes a deviation in the direction of the macroscale flow from that of the applied pressure gradient. The phenomenon is prominent in the range of porosity from 0.43 to 0.72 for circular solid obstacles. It is the result of the flow instabilities formed when the surface forces on the solid obstacles compete with the inertial force of the fluid flow in the turbulent regime. We report the origin and mechanism of the symmetry-breaking phenomenon in periodic porous media. Large-eddy simulation (LES) is used to simulate turbulent flow in a homogeneous porous medium consisting of a periodic, square lattice arrangement of cylindrical solid obstacles. Direct numerical simulation is used to simulate the transient stages during symmetry breakdown and also to validate the LES method. Quantitative and qualitative observations are made from the following approaches: (1) macroscale momentum budget and (2) two- and three-dimensional flow visualization. The phenomenon draws its roots from the amplification of a flow instability that emerges from the vortex shedding process. The symmetry-breaking phenomenon is a pitchfork bifurcation that can exhibit multiple modes depending on the local vortex shedding process. The phenomenon is observed to be sensitive to the porosity, solid obstacle shape and Reynolds number. It is a source of macroscale turbulence anisotropy in porous media for symmetric solid-obstacle geometries. In the macroscale, the principal axis of the Reynolds stress tensor is not aligned with any of the geometric axes of symmetry, nor with the direction of flow. Thus, symmetry breaking in porous media involves unresolved flow physics that should be taken into consideration while modelling flow inhomogeneity in the macroscale.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Vortex Flows: Vortex dynamics Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 929 , 25 December 2021 , A2
Check for updates
Copyright
© The Author(s), 2021. Published by 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

Abba, A., Cercignani, C. & Valdettaro, L. 2003 Analysis of subgrid scale models. Comput. Math. Appl. 46 (4), 521–535.CrossRefGoogle Scholar
Abed, N. & Afgan, I. 2017 A CFD study of flow quantities and heat transfer by changing a vertical to diameter ratio and horizontal to diameter ratio in inline tube banks using URANS turbulence models. Intl Commun. Heat Mass Transfer 89, 18–30.CrossRefGoogle Scholar
Addad, Y., Gaitonde, U., Laurence, D. & Rolfo, S. 2008 Optimal unstructured meshing for large eddy simulations. In Quality and Reliability of Large-Eddy Simulations (ed. J. Meyers, B.J. Geurts & P. Sagaut), Ercoftac Series, vol. 12, pp. 93–103. Springer.CrossRefGoogle Scholar
Agnaou, M., Lasseux, D. & Ahmadi, A. 2016 From steady to unsteady laminar flow in model porous structures: an investigation of the first Hopf bifurcation. Comput. Fluids 136, 67–82.CrossRefGoogle Scholar
ANSYS Inc. 2016 Ansys® Academic Research Fluent, Release 16.0, Help System, Fluent Theory Guide.Google Scholar
Boghosian, M.E. & Cassel, K.W. 2016 On the origins of vortex shedding in two-dimensional incompressible flows. J. Theor. Comput. Fluid Dyn. 30, 511–527.CrossRefGoogle ScholarPubMed
Celik, I.B., Cehreli, Z.N. & Yavuz, I. 2005 Index of resolution quality for large eddy simulations. Trans. ASME I: J. Fluids Engng 127 (5), 949–958.Google Scholar
Chapman, D.R. 1979 Computational aerodynamics development and outlook. AIAA J 17 (12), 1293–1313.CrossRefGoogle Scholar
Choi, H. & Moin, P. 2012 Grid-point requirements for large eddy simulation: Chapman's estimates revisited. Phys. Fluids 24 (1), 011702.CrossRefGoogle Scholar
Chu, X., Weigand, B. & Vaikuntanathan, V. 2018 Flow turbulence topology in regular porous media: from macroscopic to microscopic scale with direct numerical simulation. Phys. Fluids 30 (6), 065102.CrossRefGoogle Scholar
Chu, X., Yang, G., Pandey, S. & Weigand, B. 2019 Direct numerical simulation of convective heat transfer in porous media. Intl J. Heat Mass Transfer 133, 11–20.CrossRefGoogle Scholar
Durgin, W.W. & Karlsson, S.K.F. 1971 On the phenomenon of vortex street breakdown. J. Fluid Mech. 48 (3), 507–527.CrossRefGoogle Scholar
Eitel-Amor, G., Órlú, R., Schlatter, P. & Flores, O. 2015 Hairpin vortices in turbulent boundary layers. Phys. Fluids 27 (2), 025108.CrossRefGoogle Scholar
He, X., Apte, S.V., Finn, J.R. & Wood, B.D. 2019 Characteristics of turbulence in a face-centred cubic porous unit cell. J. Fluid Mech. 873, 608–645.CrossRefGoogle Scholar
He, X., Apte, S., Schneider, K. & Kadoch, B. 2018 Angular multiscale statistics of turbulence in a porous bed. Phys. Rev. Fluids 3 (8), 084501.CrossRefGoogle Scholar
Iacovides, H., Launder, B., Laurence, D. & West, A. 2013 Alternative Strategies for Modelling Flow over In-line Tube Banks, Proceedings of the 8th International Symposium on Turbulence and Shear Flow Phenomena (TSFP-8), Poitiers, France.Google Scholar
Iacovides, H., Launder, B. & West, A. 2014 A comparison and assessment of approaches for modelling flow over in-line tube banks. Intl J. Heat Fluid Flow 49, 69–79.CrossRefGoogle Scholar
Jiang, P.X., Fan, M.H., Si, G.S. & Ren, Z.P. 2001 Thermal-hydraulic performance of small scale micro-channel and porous-media heat-exchangers. Intl J. Heat Mass Transfer 44 (5), 1039–1051.CrossRefGoogle Scholar
Jin, Y. & Kuznetsov, A.V. 2017 Turbulence modeling for flows in wall bounded porous media: an analysis based on direct numerical simulations. Phys. Fluids 29 (4), 045102.CrossRefGoogle Scholar
Jin, C., Potts, I., Swailes, D.C. & Reeks, M.W. 2016 An LES study of turbulent flow over in-line tube-banks and comparison with experimental measurements. http://arxiv.org/abs/1605.08458Google Scholar
Jin, Y., Uth, M.F., Kuznetsov, A.V. & Herwig, H. 2015 Numerical investigation of the possibility of macroscopic turbulence in porous media: a direct numerical simulation study. J. Fluid Mech. 766, 76–103.CrossRefGoogle Scholar
Jouybari, N.F. & Lundström, T.S. 2019 A subgrid-scale model for turbulent flow in porous media. Transp. Porous Med. 129 (3), 619–632.CrossRefGoogle Scholar
Khayamyan, S., Lundström, T.S., Gren, P., Lycksam, H. & Hellström, J.G.I. 2017 Transitional and turbulent flow in a bed of spheres as measured with stereoscopic particle image velocimetry. Transp. Porous Med. 117 (1), 45–67.CrossRefGoogle Scholar
Kim, W.W. & Menon, S. 1997 Application of the localized dynamic subgrid-scale model to turbulent wall-bounded flows. In 35th Aerospace Sciences Meeting and Exhibit. AIAA Paper 1997-210.CrossRefGoogle Scholar
Krajnovic, S. & Davidson, L. 2000 Flow around a three-dimensional bluff body. In 9th International Symposium on Flow Visualisation. Paper no. 177. Heriot–Watt University.CrossRefGoogle 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. & Nakayama, A. 1998 Numerical modelling of non-Darcy convective flow in a porous medium. In Proceedings of the 11th International Heat Transfer Conference, IHTC-11, pp. 411–416. Kyongju, Korea.CrossRefGoogle Scholar
Kuwahara, F., Yamane, T. & Nakayama, A. 2006 Large eddy simulation of turbulent flow in porous media. Intl Commun. Heat Mass Transfer 33 (4), 411–418.CrossRefGoogle Scholar
Kuwata, Y. & Suga, K. 2015 Large eddy simulations of pore-scale turbulent flows in porous media by the lattice Boltzmann method. Intl J. Heat Fluid Flow 55, 143–157.CrossRefGoogle Scholar
Kuwata, Y., Suga, K. & Sakurai, Y. 2014 Development and application of a multi-scale k–ε model for turbulent porous medium flows. Intl J. Heat Fluid Flow 49, 135–150.CrossRefGoogle Scholar
Lage, J.L., de Lemos, M.J.S. & Nield, D.A. 2007 Modeling turbulence in porous media. In Transport Phenomena in Porous Media II (ed. D.B. Ingham, & I. Pop), pp. 198–230. Pergamon.CrossRefGoogle Scholar
Laizet, S. & Lamballais, E. 2009 High-order compact schemes for incompressible flows: a simple and efficient method with quasi-spectral accuracy. J. Comput. Phys. 228 (16), 5989–6015.CrossRefGoogle Scholar
Lasseux, D., Valdés-Parada, F.J. & Bellet, F. 2019 Macroscopic model for unsteady flow in porous media. J. Fluid Mech. 862, 283–311.CrossRefGoogle Scholar
Lee, J.H. & Sung, H.J. 2008 Effects of an adverse pressure gradient on a turbulent boundary layer. Intl J. Heat Fluid Flow 29 (3), 568–578.CrossRefGoogle Scholar
de Lemos, M. 2012 Turbulence in Porous Media. Turbulence in Porous Media. Elsevier Ltd.Google Scholar
Leonard, B.P. 1991 The ULTIMATE conservative difference scheme applied to unsteady one-dimensional advection. Comput. Meth. Appl. Mech. Engng 88 (1), 17–74.CrossRefGoogle Scholar
Li, Q., Pan, M., Zhou, Q. & Dong, Y. 2020 Turbulent drag modification in open channel flow over an anisotropic porous wall. Phys. Fluids 32 (1), 015117.CrossRefGoogle Scholar
Linsong, J., Hongsheng, L., Dan, W., Jiansheng, W. & Maozhao, X. 2018 Pore-scale simulation of vortex characteristics in randomly packed beds using LES/RANS models. Chem. Engng Sci. 177, 431–444.CrossRefGoogle Scholar
Moser, R.D. & Moin, P. 1987 The effects of curvature in wall bounded turbulent flows. J. Fluid Mech. 175, 479–510.CrossRefGoogle Scholar
Mujeebu, M.A., Mohamad, A.A. & Abdullah, M.Z. 2014 Applications of porous media combustion technology. In The Role of Colloidal Systems in Environmental Protection (ed. M. Fanun), pp. 615–633. Elsevier.CrossRefGoogle Scholar
Nguyen, T., Muyshondt, R., Hassan, Y.A. & Anand, N.K. 2019 Experimental investigation of cross flow mixing in a randomly packed bed and streamwise vortex characteristics using particle image velocimetry and proper orthogonal decomposition analysis. Phys. Fluids 31 (2), 25101.CrossRefGoogle Scholar
Nield, D.A. 2002 Alternative models of turbulence in a porous medium, and related matters. J. Fluids Engng 123 (4), 928–931.CrossRefGoogle Scholar
Nield, D.A. & Bejan, A. 2017 Convection in Porous Media, 5th edn. Springer International Publishing.CrossRefGoogle Scholar
Patil, V.A. & Liburdy, J.A. 2015 Scale estimation for turbulent flows in porous media. Chem. Engng Sci. 123, 231–235.CrossRefGoogle Scholar
Pedras, M.H.J. & de Lemos, M.J.S. 2001 Macroscopic turbulence modeling for incompressible flow through undeformable porous media. Intl J. Heat Mass Transfer 44 (6), 1081–1093.CrossRefGoogle Scholar
Pedras, M.H.J. & de Lemos, M.J.S. 2003 Computation of turbulent flow in porous media using a low-reynolds k-ε model and an infinite array of transversally displaced elliptic rods. Numer. Heat Transfer; A: Appl. 43 (6), 585–602.CrossRefGoogle Scholar
Pinson, F., Grégoire, O. & Simonin, O. 2006 k–ε macro-scale modeling of turbulence based on a two scale analysis in porous media. Intl J. Heat Fluid Flow 27 (5), 955–966.CrossRefGoogle Scholar
Pope, S.B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Pope, S.B. 2004 Ten questions concerning the large-eddy simulation of turbulent flows. New J. Phys. 6, 35.CrossRefGoogle Scholar
Rodi, W. 1997 Comparison of LES and RANS calculations of the flow around bluff bodies. J. Wind Engng Ind. Aerodyn. 69–71, 55–75.CrossRefGoogle Scholar
Seguin, D., Montillet, A. & Comiti, J. 1998 a Experimental characterisation of flow regimes in various porous media-I: limit of laminar flow regime. Chem. Engng Sci. 53 (21), 3751–3761.CrossRefGoogle Scholar
Seguin, D., Montillet, A., Comiti, J. & Huet, F. 1998 b Experimental characterization of flow regimes in various porous media—II: transition to turbulent regime. Chem. Engng Sci. 53 (22), 3897–3909.CrossRefGoogle Scholar
Slattery, J.C. 1967 Flow of viscoelastic fluids through porous media. AIChE J. 13 (6), 1066–1071.CrossRefGoogle Scholar
Suga, K. 2016 Understanding and modelling turbulence over and inside porous media. Flow Turbul. Combust. 96 (3), 717–756.CrossRefGoogle Scholar
Suga, K., Chikasue, R. & Kuwata, Y. 2017 Modelling turbulent and dispersion heat fluxes in turbulent porous medium flows using the resolved LES data. Intl J. Heat Fluid Flow 68, 225–236.CrossRefGoogle Scholar
Sujudi, D. & Haimes, R. 1995 Identification of swirling flow in 3-D vector fields. In 12th Computational Fluid Dynamics Conference, pp. 792–799. AIAA Paper 1995-1715.Google Scholar
Tanarro, Á, Vinuesa, R. & Schlatter, P. 2020 Effect of adverse pressure gradients on turbulent wing boundary layers. J. Fluid Mech. 883, A8.CrossRefGoogle Scholar
Uth, M.F., Jin, Y., Kuznetsov, A.V. & Herwig, H. 2016 A direct numerical simulation study on the possibility of macroscopic turbulence in porous media: effects of different solid matrix geometries, solid boundaries, and two porosity scales. Phys. Fluids 28 (6), 065101.CrossRefGoogle Scholar
Vafai, K. 2015 Handbook of Porous Media. Handbook of Porous Media, 3rd edn. CRC Press.CrossRefGoogle Scholar
Vafai, K., Bejan, A., Minkowycz, W.J. & Khanafer, K. 2009 A Critical Synthesis of Pertinent Models for Turbulent Transport through Porous Media. Handbook of Numerical Heat Transfer, 2nd edn, pp. 389–416. John Wiley & Sons, Inc.CrossRefGoogle Scholar
Vafai, K. & Kim, S.J. 1995 On the limitations of the Brinkman-Forchheimer-extended Darcy equation. Intl J. Heat Fluid Flow 16 (1), 11–15.CrossRefGoogle Scholar
Von Kármán, T. 1911 Über den Mechanismus des Widerstandes, den ein bewegter Körper in einer Flüssigkeit erfährt. Nachrichten von der Gesellschaft der Wissenschaften zu Gättingen, Mathematisch-Physikalische Klasse, 1912, 509–517.Google Scholar
West, A., Launder, B.E. & Iacovides, H. 2014 On the computational modelling of flow and heat transfer in in-line tube banks. Adv. Heat Transfer 46, 1–46.CrossRefGoogle Scholar
Wood, B.D., He, X. & Apte, S.V. 2020 Modeling turbulent flows in porous media. Annu. Rev. Fluid Mech. 52 (1), 171–203.CrossRefGoogle Scholar
Yang, T. & Wang, L. 2000 Microscale flow bifurcation and its macroscale implications in periodic porous media. Comput. Mech. 26 (6), 520–527.CrossRefGoogle Scholar
Zenklusen, A., Kenjereš, S. & von Rohr, R. 2014 Vortex shedding in a highly porous structure. Chem. Engng Sci. 106, 253–263.CrossRefGoogle Scholar
Zhang, L. 2008 DNS Study of Flow Over Periodic and Random Distribution of Cylinders and Spheres. PhD Thesis, University of Illinois Urbana-Champaign.Google Scholar

Srikanth et al. Supplementary Movie 1

Time series of instantaneous flow streamlines projected on the xy- plane overlaid on static pressure contours at the plane z = 0, showing the transient stages of symmetry-breaking from Rep = 300 to 489 for a porosity φ = 0.5.

Download Srikanth et al. Supplementary Movie 1(Video)
Video 44.4 MB

Srikanth et al. Supplementary Movie 2

Time series of 3D coherent turbulent structures visualized using the Q- criterion overlaid on instantaneous flow streamlines and static pressure contours at the plane z = 0, showing the transient stages of symmetry-breaking from Rep = 300 to 489 for a porosity φ = 0.5.

Download Srikanth et al. Supplementary Movie 2(Video)
Video 44.5 MB