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Role of spanwise rollers by Kelvin–Helmholtz instability in turbulence over a permeable porous wall

Yusuke Kuwata*

  • Department of Mechanical Engineering, Osaka Prefecture University, 1-1 Sakai, Osaka 599-8531, Japan

  • *kuwata@me.osakafu-u.ac.jp
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Phys. Rev. Fluids 7, 084606 – Published 22 August, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.084606

Abstract

Direct numerical simulations of porous-walled channel flows with computational domain size constraints were performed to clarify the role of spanwise rollers associated with the Kelvin–Helmholtz instability on turbulent flows over a porous wall. The constraints of the domain size, which effectively hindered the development of the spanwise roller sustaining the near-wall turbulent motions, were imposed to isolate the effects of the near-wall turbulent motions and spanwise rollers. For each domain case, we considered thick and thin porous walls to isolate the effects of surface roughness and vertical permeability. It is found that the surface roughness plays a principal role in the modification of near-wall turbulent motions, including streaks and longitudinal vortices, whereas vertical permeability is essential for the development of spanwise rollers with streamwise alternating low- and high-speed regions. The spanwise roller contributes to an increase in the skin friction coefficient at the porous wall, and considerably increases the turbulence intensities deep inside the porous wall. The discussion in the logarithmic region based on the extended Jackson model reveals that the von Kármán constant is increased in the presence of the spanwise rollers, which is considered to reflect an increase in the characteristic vortex size owing to the spanwise rollers. The increase in the mixing length due to the role of the spanwise roller can be reasonably predicted by the classical mixing-length model with an increased von Kármán constant.

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References (90)

  1. H. Darcy, Les fontaines publiques de la ville de dijon, Dalmont, Paris (1856).
  2. W. P. Breugem, B. J. Boersma, and R. E. Uittenbogaard, The influence of wall permeability on turbulent channel flow, J. Fluid Mech. 562, 35 (2006).
  3. K. Suga, Y. Matsumura, Y. Ashitaka, S. Tominaga, and M. Kaneda, Effects of wall permeability on turbulence, Int. J. Heat Fluid Flow 31, 974 (2010).
  4. K. Suga, M. Mori, and M. Kaneda, Vortex structure of turbulence over permeable walls, Int. J. Heat Fluid Flow 32, 586 (2011).
  5. C. Manes, D. Poggi, and L. Ridol, Turbulent boundary layers over permeable walls: Scaling and near-wall structure, J. Fluid Mech. 687, 141 (2011).
  6. Y. Kuwata and K. Suga, Lattice Boltzmann direct numerical simulation of interface turbulence over porous and rough walls, Int. J. Heat Fluid Flow 61, 145 (2016).
  7. Y. Kuwata and K. Suga, Direct numerical simulation of turbulence over anisotropic porous media, J. Fluid Mech. 831, 41 (2017).
  8. Y. Kuwata and K. Suga, Extensive investigation of the influence of wall permeability on turbulence, Int. J. Heat Fluid Flow 80, 108465 (2019).
  9. G. Gómez-de-Segura, A. Sharma, and R. García-Mayoral, Turbulent drag reduction using anisotropic permeable substrates, Flow Turbul. Combust. 100, 995 (2018).
  10. M. E Rosti, L. Brandt, and A. Pinelli, Turbulent channel flow over an anisotropic porous wall-drag increase and reduction, J. Fluid Mech. 842, 381 (2018).
  11. M. R. Raupach, P. A. Coppin, and B. J. Legg, Experiments on scalar dispersion within a model plant canopy part I: The turbulence structure, Boundary-Layer Meteorol. 35, 21 (1986).
  12. M. R. Raupach, J. J. Finnigan, and Y. Brunet, Coherent eddies and turbulence in vegetation canopies: The mixing-layer analogy, Boundary-Layer Meteorol. 78, 351 (1996).
  13. J. Finnigan, Turbulence in plant canopies, Annu. Rev. Fluid Mech. 32, 519 (2000).
  14. B. L. White and H. M. Nepf, Shear instability and coherent structures in shallow flow adjacent to a porous layer, J. Fluid Mech. 593, 1 (2007).
  15. J. Jimenez, M. Uhlmann, A. Pinelli, and G. Kawahara, Turbulent shear flow over active and passive porous surfaces, J. Fluid Mech. 442, 89 (2001).
  16. G. Gómez-de-Segura and R. García-Mayoral, Turbulent drag reduction by anisotropic permeable substrates—analysis and direct numerical simulations, J. Fluid Mech. 875, 124 (2019).
  17. Y. Kuwata and K. Suga, Transport mechanism of interface turbulence over porous and rough walls, Flow Turbul. Combust. 97, 1071 (2016).
  18. X. Chu, W. Wang, G. Yang, A. Terzis, R. Helmig, and B. Weigand, Transport of turbulence across permeable interface in a turbulent channel flow: Interface-resolved direct numerical simulation, Transp. Porous Media 136, 165 (2021).
  19. K. Suga, Y. Okazaki, U. Ho, and Y. Kuwata, Anisotropic wall permeability effects on turbulent channel flows, J. Fluid Mech. 855, 983 (2018).
  20. A. B. Shvidchenko and G. Pender, Macroturbulent structure of open-channel flow over gravel beds, Water Resour. Res. 37, 709 (2001).
  21. A. G. Roy, T. Buffin-Belanger, H. Lamarre, and A. D. Kirkbride, Size, shape and dynamics of large-scale turbulent flow structures in a gravel-bed river, J. Fluid Mech. 500, 1 (2004).
  22. H. M. Nepf and E. R. Vivoni, Flow structure in depth-limited, vegetated flow, J. Geophys. Res. Oceans 105, 28547 (2000).
  23. C. Manes, D. Pokrajac, I. McEwan, and V. Nikora, Turbulence structure of open channel flows over permeable and impermeable beds: A comparative study, Phys. Fluids 21, 125109 (2009).
  24. D. Pokrajac and C. Manes, Velocity measurements of a free-surface turbulent flow penetrating a porous medium composed of uniform-size spheres, Transp. Porous Media 78, 367 (2009).
  25. P. Lammers, K. N. Beronov, R. Volkert, G. Brenner, and F. Durst, Lattice BGK direct numerical simulation of fully developed turbulence in incompressible plane channel flow, Comput. Fluids 35, 1137 (2006).
  26. K. Suga, Y. Kuwata, K. Takashima, and R. Chikasue, A D3Q27 multiple-relaxation-time lattice Boltzmann method for turbulent flows, Comput. Math. Appl. 69, 518 (2015).
  27. M. Gehrke, C. F. Janßen, and T. Rung, Scrutinizing lattice Boltzmann methods for direct numerical simulations of turbulent channel flows, Comput. Fluids 156, 247 (2017).
  28. C. K. Aidun and J. R. Clausen, Lattice-Boltzmann method for complex flows, Annu. Rev. Fluid Mech. 42, 439 (2010).
  29. X. Wang and T. Aoki, High performance computation by multi-node GPU cluster-Tsubame2.0 on the air flow in an urban city using lattice Boltzmann method, Int. J. Aero. Lightweight Struct. (IJALS) 2, 77 (2012).
  30. N. Onodera, T. Aoki, T. Shimokawabe, and H. Kobayashi, Large-scale LES wind simulation using lattice Boltzmann method for a 10km× 10 km area in metropolitan Tokyo, Tsubame ESJ 9, 2 (2013).
  31. M. Hasert, J. Bernsdorf, and S. Roller, Lattice Boltzmann simulation of non-Darcy flow in porous media, Proc. Comput. Sci. 4, 1048 (2011).
  32. M. Krafczyk, K. Kucher, Y. Wang, and M. Geier, DNS/LES studies of turbulent flows based on the cumulant lattice Boltzmann approach, in High Performance Computing in Science and Engineering 14 (Springer, Berlin, 2015), pp. 519–531.
  33. G. Tóth and I. M. Jánosi, Vorticity generation by rough walls in 2D decaying turbulence, J. Stat. Phys. 161, 1508 (2015).
  34. Y. Jin, M. F. Uth, and H. Herwig, Structure of a turbulent flow through plane channels with smooth and rough walls: An analysis based on high resolution DNS results, Comput. Fluids 107, 77 (2015).
  35. Y. Kuwata and Y. Kawaguchi, Direct numerical simulation of turbulence over systematically varied irregular rough surfaces, J. Fluid Mech. 862, 781 (2019).
  36. P. Eichler, V. Fuka, and R. Fučík, Cumulant lattice Boltzmann simulations of turbulent flow above rough surfaces, Comput. Math. Appl. 92, 37 (2021).
  37. L.-P. Wang, O. Ayala, H. Gao, C. Andersen, and K. L. Mathews, Study of forced turbulence and its modulation by finite-size solid particles using the lattice Boltzmann approach, Comput. Math. Appl. 67, 363 (2014).
  38. A. Eshghinejadfard, A. Abdelsamie, S. A. Hosseini, and D. Thevenin, Immersed boundary lattice Boltzmann simulation of turbulent channel flows in the presence of spherical particles, Int. J. Multiphase Flow 96, 161 (2017).
  39. G. Wang, D. Wan, C. Peng, K. Liu, and L.-P. Wang, LBM study of aggregation of monosized spherical particles in homogeneous isotropic turbulence, Chem. Eng. Sci. 201, 201 (2019).
  40. Y. Kuwata and R. Nagura, Direct numerical simulation on the effects of surface slope and skewness on rough-wall turbulence, Phys. Fluids 32, 105113 (2020).
  41. Y. Kuwata, T. Sugiyama, and Y. Kawaguchi, On the scaling of turbulence over an irregular rough surface in a transitionally rough regime, J. Therm. Sci. Tech. 15, JTST0015 (2020).
  42. Y. Kuwata, K. Tsuda, and K. Suga, Direct numerical simulation of turbulent conjugate heat transfer in a porous-walled duct flow, J. Fluid Mech. 904, A9 (2020).
  43. W. Thomson, LXIII, On the division of space with minimum partitional area, London, Edinburgh, Dublin Philos. Mag. J. Sci. 24, 503 (1887).
  44. M. Chandesris, A. D'Hueppe, B. Mathieu, D. Jamet, and B. Goyeau, Direct numerical simulation of turbulent heat transfer in a fluid-porous domain, Phys. Fluids 25, 125110 (2013).
  45. J. Jiménez and P. Moin, The minimal flow unit in near-wall turbulence, J. Fluid Mech. 225, 213 (1991).
  46. A. Busse and N. D. Sandham, Parametric forcing approach to rough-wall turbulent channel flow, J. Fluid Mech. 712, 169 (2012).
  47. Y. Kuwata and Y. Kawaguchi, Direct numerical simulation of turbulence over resolved and modelled rough walls with irregularly distributed roughness, Int. J. Heat Fluid Flow 77, 1 (2019).
  48. J. T. Richardson, Y. Peng, and D. Remue, Properties of ceramic foam catalyst supports: Pressure drop, Appl. Catal. A 204, 19 (2000).
  49. W. Xu, H. Zhang, Z. Yang, and J. Zhang, Numerical investigation on the flow characteristics and permeability of three-dimensional reticulated foam materials, Chem. Eng. J. 140, 562 (2008).
  50. Z. Nie, Y. Lin, and Q. Tong, Modeling structures of open cell foams, Comput. Mater. Sci. 131, 160 (2017).
  51. A. Inayat, H. Freund, T. Zeiser, and W. Schwieger, Determining the specific surface area of ceramic foams: The tetrakaidecahedra model revisited, Chem. Eng. Sci. 66, 1179 (2011).
  52. F. Lucci, A. Della Torre, J. von Rickenbach, G. Montenegro, D. Poulikakos, and P. D. Eggenschwiler, Performance of randomized kelvin cell structures as catalytic substrates: Mass-transfer based analysis, Chem. Eng. Sci. 112, 143 (2014).
  53. A. Bhattacharya, V. V. Calmidi, and R. L. Mahajan, Thermophysical properties of high porosity metal foams, Int. J. Heat Mass Transfer 45, 1017 (2002).
  54. Y. Kuwata and K. Suga, Imbalance-correction grid-refinement method for lattice Boltzmann flow simulations, J. Comput. Phys. 311, 348 (2016).
  55. Y. Kuwata, Direct numerical simulation of turbulent heat transfer on the Reynolds analogy over irregular rough surfaces, Int. J. Heat Fluid Flow 92, 108859 (2021).
  56. M. E. Rosti, L. Cortelezzi, and M. Quadrio, Direct numerical simulation of turbulent channel flow over porous walls, J. Fluid Mech. 784, 396 (2015).
  57. W.-P. Breugem and B.-J. Boersma, Direct numerical simulations of turbulent flow over a permeable wall using a direct and a continuum approach, Phys. Fluids 17, 025103 (2005).
  58. D. Poggi, A. Porporato, L. Ridolfi, J. D. Albertson, and G. G. Katul, The effect of vegetation density on canopy sub-layer turbulence, Boundary-Layer Meteorol. 111, 565 (2004).
  59. S. Toh and T. Itano, Interaction between a large-scale structure and near-wall structures in channel flow, J. Fluid Mech. 524, 249 (2005).
  60. O. Flores and J. Jiménez, Hierarchy of minimal flow units in the logarithmic layer, Phys. Fluids 22, 071704 (2010).
  61. M. MacDonald, D. Chung, N. Hutchins, L. Chan, A. Ooi, and R. García-Mayoral, The minimal-span channel for rough-wall turbulent flows, J. Fluid Mech. 816, 5 (2017).
  62. H. Abe, R. A. Antonia, and S. Toh, Large-scale structures in a turbulent channel flow with a minimal streamwise flow unit, J. Fluid Mech. 850, 733 (2018).
  63. A. W. Vreman and J. G. M. Kuerten, Statistics of spatial derivatives of velocity and pressure in turbulent channel flow, Phys. Fluids 26, 085103 (2014).
  64. D. Chung, L. Chan, M. MacDonald, N. Hutchins, and A. Ooi, A fast direct numerical simulation method for characterising hydraulic roughness, J. Fluid Mech. 773, 418 (2015).
  65. M. MacDonald, N. Hutchins, and D. Chung, Roughness effects in turbulent forced convection, J. Fluid Mech. 861, 138 (2019).
  66. P. M. Ligrani and R. J. Moffat, Structure of transitionally rough and fully rough turbulent boundary layers, J. Fluid Mech. 162, 69 (1986).
  67. P.-Å. Krogstadt and R. A. Antonia, Surface roughness effects in turbulent boundary layers, Exp. Fluids 27, 450 (1999).
  68. K. A. Flack, M. P. Schultz, and T. A. Shapiro, Experimental support for Townsend's Reynolds number similarity hypothesis on rough walls, Phys. Fluids 17, 035102 (2005).
  69. A. Busse, M. Lützner, and N. D. Sandham, Direct numerical simulation of turbulent flow over a rough surface based on a surface scan, Comput. Fluids 116, 129 (2015).
  70. P. Forooghi, A. Stroh, P. Schlatter, and B. Frohnapfel, Direct numerical simulation of flow over dissimilar, randomly distributed roughness elements: A systematic study on the effect of surface morphology on turbulence, Phys. Rev. Fluids 3, 044605 (2018).
  71. Y. Brunet, J. J. Finnigan, and M. R. Raupach, A wind tunnel study of air flow in waving wheat: Single-point velocity statistics, Boundary-Layer Meteorol. 70, 95 (1994).
  72. M. R. Raupach, Simplified expressions for vegetation roughness length and zero-plane displacement as functions of canopy height and area index, Boundary-Layer Meteorol. 71, 211 (1994).
  73. I. Nezu and M. Sanjou, Turbulence structure and coherent motion in vegetated canopy open-channel flows, J. Hydro-Environ. Res. 2, 62 (2008).
  74. H. M. Nepf, Flow and transport in regions with aquatic vegetation, Annu. Rev. Fluid Mech. 44, 123 (2012).
  75. P. S. Jackson, On the displacement height in the logarithmic velocity profile, J. Fluid Mech. 111, 15 (1981).
  76. S. Leonardi, P. Orlandi, R. J. Smalley, L. Djenidi, and R. A. Antonia, Direct numerical simulations of turbulent channel flow with transverse square bars on one wall, J. Fluid Mech. 491, 229 (2003).
  77. S. Leonardi and I. P. Castro, Channel flow over large cube roughness: A direct numerical simulation study, J. Fluid Mech. 651, 519 (2010).
  78. D. Pokrajac, J. J. Finnigan, C. Manes, I. McEwan, and V. Nikora, On the definition of the shear velocity in rough bed open channel flows, in River Flow, Vol. 1 (Taylor & Francis, 2006), pp. 89–98.
  79. S. Whitaker, Flow in porous media I: A theoretical derivation of Darcy's law, Transp. Porous Media 1, 3 (1986).
  80. S. Whitaker, The Forchheimer equation: A theoretical development, Transp. Porous Media 25, 27 (1996).
  81. A. A. Townsend, The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, UK, 1980).
  82. G. J. Kunkel and I. Marusic, Study of the near-wall-turbulent region of the high-Reynolds-number boundary layer using an atmospheric flow, J. Fluid Mech. 548, 375 (2006).
  83. J. Jiménez, Turbulent flows over rough walls, Annu. Rev. Fluid Mech. 36, 173 (2004).
  84. J. Jiménez and R. D. Moser, What are we learning from simulating wall turbulence? Philos. Trans. R. Soc. A 365, 715 (2007).
  85. M. Lee and R. D. Moser, Direct numerical simulation of turbulent channel flow up to Reτ≈5200, J. Fluid Mech. 774, 395 (2015).
  86. G. G. Katul, L. Mahrt, D. Poggi, and C. Sanz, One- and two-equation models for canopy turbulence, Boundary-Layer Meteorol. 113, 81 (2004).
  87. I. P. Castro, Rough-wall boundary layers: Mean flow universality, J. Fluid Mech. 585, 469 (2007).
  88. L. Chan, M. MacDonald, D. Chung, N. Hutchins, and A. Ooi, A systematic investigation of roughness height and wavelength in turbulent pipe flow in the transitionally rough regime, J. Fluid Mech. 771, 743 (2015).
  89. P. Forooghi, A. Stroh, F. Magagnato, S. Jakirlić, and B. Frohnapfel, Toward a universal roughness correlation, J. Fluids Eng. 139, 121201 (2017).
  90. M. Thakkar, A. Busse, and N. D. Sandham, Surface correlations of hydrodynamic drag for transitionally rough engineering surfaces, J. Turbul. 18, 138 (2017).

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Phys. Rev. Fluids 7, 084606– Published 22 August, 2022
  • Received 10 February 2022
  • Accepted 29 July 2022
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