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Direct numerical simulation of turbulent conjugate heat transfer in a porous-walled duct flow

Published online by Cambridge University Press:  06 October 2020

Y. Kuwata Open the ORCID record for Y. Kuwata [Opens in a new window] ,
K. Tsuda  and
K. Suga Open the ORCID record for K. Suga [Opens in a new window]
Y. Kuwata*
Affiliation:
Department of Mechanical Engineering, Osaka Prefecture University, Sakai, Osaka599-8531, Japan
K. Tsuda
Affiliation:
Department of Mechanical Engineering, Osaka Prefecture University, Sakai, Osaka599-8531, Japan
K. Suga
Affiliation:
Department of Mechanical Engineering, Osaka Prefecture University, Sakai, Osaka599-8531, Japan
*
†Email address for correspondence: [email protected]
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Abstract

In this study, the effects of permeable porous walls on momentum and heat transfer in a rectangular duct were studied by means of direct numerical simulation of the turbulent conjugate heat transfer. For this purpose, airflow through a rectangular duct, partially filled with a porous medium consisting of aluminium square bars, was simulated at a bulk mean Reynolds number of 3500, where the geometry of the duct used was identical to that employed in the experimental study of Suga et al. (J. Fluid Mech., vol. 884, 2020, A7). It was found that the large-scale perturbations arising from the Kelvin–Helmholtz type of instability developed over the porous medium wall, and the turbulence intensity, particularly in the porous wall-normal component, was enhanced significantly. The secondary flow was enhanced by a factor of three compared to that in a smooth-walled square duct flow, and could be characterized by a strong upward flow along the lateral walls and downward flow in the symmetry plane. The convection by the secondary flow considerably contributed to the momentum and heat transfer in the top half of the clear flow region, whereas the enhanced turbulence over the porous wall largely affected the momentum and heat transfer just above the porous medium wall, as seen in the case of a porous-walled channel flow. It should be noted that in the porous medium region, the mean temperature at the surface of the porous medium is non-uniform, with the solid- and fluid-phase temperatures reaching the equilibrium state. This could be correctly reproduced only with the conjugate heat transfer. It was found that the mean velocity dispersion as well as the turbulent velocity fluctuation contributed significantly to the energy transfer below the porous wall, which demonstrated the importance of the dispersion heat flux for heat transfer modelling of porous medium flows. Furthermore, it was observed that the secondary flow penetrated the porous medium region resulting in large-scale mean flow currents, which enhanced heat transfer inside the porous medium region.

JFM classification

Convection: Convection in porous media Low-Reynolds-number flows: Porous media Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 904 , 10 December 2020 , A9
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Adrian, R. J. & Marusic, I. 2012 Coherent structures in flow over hydraulic engineering surfaces. J. Hydraul Res. 50 (5), 451–464.CrossRefGoogle Scholar
Breugem, W. P., Boersma, B. J. & Uittenbogaard, R. E. 2006 The influence of wall permeability on turbulent channel flow. J. Fluid Mech. 562, 35–72.CrossRefGoogle Scholar
Chukwudozie, C. & Tyagi, M. 2013 Pore scale inertial flow simulations in 3-D smooth and rough sphere packs using lattice Boltzmann method. AIChE J. 59 (12), 4858–4870.CrossRefGoogle Scholar
Darcy, H. 1856 Les fontaines publiques de la ville de dijon. Dalmont, Paris 647.Google Scholar
Fattahi, E., Waluga, C., Wohlmuth, B., Rüde, U., Manhart, M. & Helmig, R. 2016 Lattice Boltzmann methods in porous media simulations: from laminar to turbulent flow. Comput. Fluids 140, 247–259.CrossRefGoogle Scholar
Finnigan, J. 2000 Turbulence in plant canopies. Annu. Rev. Fluid Mech. 32, 519–571.CrossRefGoogle Scholar
Gavrilakis, S. 1992 Numerical simulation of low-Reynolds-number turbulent flow through a straight square duct. J. Fluid Mech. 244, 101–129.CrossRefGoogle Scholar
Huser, A. & Biringen, S. 1993 Direct numerical simulation of turbulent flow in a square duct. J. Fluid Mech. 257, 65–95.CrossRefGoogle Scholar
Iwamoto, K., Suzuki, Y. & Kasagi, N. 2002 Database of fully developed channel flow-thtlab internal report no. ILR-0201, Rapport technique, THTLAB, Department of Mechanical Engineering, The University of Tokyo.Google Scholar
Jimenez, J., Uhlmann, M., Pinelli, A. & Kawahara, G. 2001 Turbulent shear flow over active and passive porous surfaces. J. Fluid Mech. 442, 89–117.CrossRefGoogle Scholar
Kawamura, H., Abe, H. & Shingai, K. 2000 DNS of turbulence and heat transport in a channel flow with different Reynolds and Prandtl numbers and boundary conditions. In Proceedings of the 3rd Symposium on Turbulence, Heat and Mass Transfer.Google Scholar
Kimura, S. & Bejan, A. 1983 The heatline visualization of convective heat transfer. Trans. ASME: J. Heat Transfer 105 (4), 916–919.CrossRefGoogle Scholar
Kong, F. Y. & Schetz, J. A. 1982 Turbulent boundary layer over porous surfaces with different surface geometries. AIAA Paper, pp. 82–0030.Google Scholar
Kuwahara, F., Nakayama, A. & Koyama, H. 1996 A numerical study of thermal dispersion in porous media. Trans. ASME: J. Heat Transfer 118 (3), 756–761.CrossRefGoogle Scholar
Kuwata, Y. & Kawaguchi, Y. 2018 a Direct numerical simulation of turbulence over systematically varied irregular rough surfaces. J. Fluid Mech. 862, 781–815.CrossRefGoogle Scholar
Kuwata, Y. & Kawaguchi, Y. 2018 b Statistical discussions on skin frictional drag of turbulence over randomly distributed semi-spheres. Intl J. Adv. Engng Sci. Appl. Mater. 10 (4), 263–272.CrossRefGoogle Scholar
Kuwata, Y. & Kawaguchi, Y. 2019 Direct numerical simulation of turbulence over resolved and modeled rough walls with irregularly distributed roughness. Intl J. Heat Fluid Flow 77, 1–18.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. 2016 a Lattice Boltzmann direct numerical simulation of interface turbulence over porous and rough walls. Intl J. Heat Fluid Flow 61, 145–157.CrossRefGoogle Scholar
Kuwata, Y. & Suga, K. 2016 b Transport mechanism of interface turbulence over porous and rough walls. Flow Turbul. Combust. 97 (4), 1071–1093.CrossRefGoogle Scholar
Kuwata, Y. & Suga, K. 2017 Direct numerical simulation of turbulence over anisotropic porous media. J. Fluid Mech. 831, 41–71.CrossRefGoogle Scholar
Kuwata, Y. & Suga, K. 2019 Extensive investigation of the influence of wall permeability on turbulence. Intl J. Heat Fluid Flow 80, 108465.CrossRefGoogle Scholar
Latt, J. & Chopard, B. 2006 Lattice Boltzmann method with regularized pre-collision distribution functions. Maths Comput. Simul. 72 (2–6), 165–168.CrossRefGoogle Scholar
Lenz, S., Schoenherr, M., Geier, M., Krafczyk, M., Pasquali, A., Christen, A. & Giometto, M. 2019 Towards real-time simulation of turbulent air flow over a resolved urban canopy using the cumulant lattice Boltzmann method on a GPGPU. J. Wind Engng Ind. Aerodyn. 189, 151–162.CrossRefGoogle Scholar
Madabhushi, R. K. & Vanka, S. P. 1991 Large eddy simulation of turbulence-driven secondary flow in a square duct. Phys. Fluids A 3 (11), 2734–2745.CrossRefGoogle Scholar
Manes, C., Poggi, D. & Ridol, L. 2011 Turbulent boundary layers over permeable walls: scaling and near-wall structure. J. Fluid Mech. 687, 141–170.CrossRefGoogle Scholar
Manes, C., Pokrajac, D., McEwan, I. & Nikora, V. 2009 Turbulence structure of open channel flows over permeable and impermeable beds: a comparative study. Phys. Fluids 21 (12), 125109.CrossRefGoogle Scholar
Nakayama, A. & Kuwahara, F. 1999 A macroscopic turbulence model for flow in a porous medium. Trans. ASME: J. Fluids Engng 121, 427–433.Google Scholar
Nishiyama, Y., Kuwata, Y. & Suga, K. 2020 Direct numerical simulation of turbulent heat transfer over fully resolved anisotropic porous structures. Intl J. Heat Fluid Flow 81, 108515.CrossRefGoogle Scholar
Onodera, N., Aoki, T., Shimokawabe, T. & Kobayashi, H. 2013 Large-scale LES wind simulation using lattice Boltzmann method for a $10\ \textrm {km}\times 10\ \textrm {km}$ area in metropolitan Tokyo. Tsubame ESJ 9, 2–8.Google Scholar
Pinelli, A., Uhlmann, M., Sekimoto, A. & Kawahara, G. 2010 Reynolds number dependence of mean flow structure in square duct turbulence. J. Fluid Mech. 644, 107–122.CrossRefGoogle Scholar
Prandtl, L. 1926 Uber die ausgebildete Turbulenz. In Proceedings 2nd International Congress Applied Mechanics, Zurich, pp. 62–75.Google Scholar
Raupach, M. R, Finnigan, J. J. & Brunet, Y. 1996 Coherent eddies and turbulence in vegetation canopies: the mixing-layer analogy. In Boundary-Layer Meteorology 25th Anniversary Volume, 1970–1995 (ed. Garratt, J. R. & Taylor, P. A.), pp. 351–382. Springer.CrossRefGoogle Scholar
Rosti, M. E., Brandt, L. & Pinelli, A. 2018 Turbulent channel flow over an anisotropic porous wall–drag increase and reduction. J. Fluid Mech. 842, 381–394.CrossRefGoogle Scholar
Rosti, M. E., Cortelezzi, L. & Quadrio, M. 2015 Direct numerical simulation of turbulent channel flow over porous walls. J. Fluid Mech. 784, 396–442.CrossRefGoogle Scholar
Saito, M. B. & de Lemos, M. J. S 2005 Interfacial heat transfer coefficient for non-equilibrium convective transport in porous media. Intl Commun. Heat Mass Transfer 32 (5), 666–676.CrossRefGoogle Scholar
Samanta, A., Vinuesa, R., Lashgari, I., Schlatter, P. & Brandt, L. 2015 Enhanced secondary motion of the turbulent flow through a porous square duct. J. Fluid Mech. 784, 681–693.CrossRefGoogle Scholar
Sekimoto, A., Kawahara, G., Sekiyama, K., Uhlmann, M. & Pinelli, A. 2011 Turbulence-and buoyancy-driven secondary flow in a horizontal square duct heated from below. Phys. Fluids 23 (7), 075103.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
Suga, K., Kuwata, Y., Takashima, K. & Chikasue, R. 2015 A D3Q27 multiple-relaxation-time lattice Boltzmann method for turbulent flows. Comput. Maths Applics. 69, 518–529.CrossRefGoogle Scholar
Suga, K., Matsumura, Y., Ashitaka, Y., Tominaga, S. & Kaneda, M. 2010 Effects of wall permeability on turbulence. Intl J. Heat Fluid Flow 31, 974–984.CrossRefGoogle Scholar
Suga, K., Mori, M. & Kaneda, M. 2011 Vortex structure of turbulence over permeable walls. Intl J. Heat Fluid Flow 32, 586–595.CrossRefGoogle Scholar
Suga, K., Nishimura, W., Yamamoto, T. & Kaneda, M. 2014 Measurements of serpentine channel flow characteristics for a proton exchange membrane fuel cell. Intl J. Hydrogen Energy 39 (11), 5942–5954.CrossRefGoogle Scholar
Suga, K., Okazaki, Y., H O, U. & Kuwata, Y. 2018 Anisotropic wall permeability effects on turbulent channel flows. J. Fluid Mech. 855, 983–1016.CrossRefGoogle Scholar
Suga, K., Okazaki, Y. & Kuwata, Y. 2020 Characteristics of turbulent square duct flows over porous media. J. Fluid Mech. 884.CrossRefGoogle Scholar
Vázquez, M. S. & Métais, O. 2002 Large-eddy simulation of the turbulent flow through a heated square duct. J. Fluid Mech. 453, 201–238.CrossRefGoogle Scholar
Vinuesa, R., Noorani, A., Lozano-Durán, A., Khoury, G. K. E., Schlatter, P., Fischer, P. F. & Nagib, H. M. 2014 Aspect ratio effects in turbulent duct flows studied through direct numerical simulation. J. Turbul. 15 (10), 677–706.CrossRefGoogle Scholar
Wang, J., Wang, M. & Li, Z. 2007 A lattice Boltzmann algorithm for fluid–solid conjugate heat transfer. Intl J. Therm. Sci. 46 (3), 228–234.CrossRefGoogle Scholar
Whitaker, S. 1986 Flow in porous media I: a theoretical derivation of Darcy's law. Transp. Porous Med. 1, 3–25.CrossRefGoogle Scholar
Whitaker, S. 1996 The Forchheimer equation: a theoretical development. Transp. Porous Med. 25, 27–61.CrossRefGoogle Scholar
White, B. L. & Nepf, H. M. 2007 Shear instability and coherent structures in shallow flow adjacent to a porous layer. J. Fluid Mech. 593, 1–32.CrossRefGoogle Scholar
Yoshida, H. & Nagaoka, M. 2010 Multiple-relaxation-time lattice Boltzmann model for the convection and anisotropic diffusion equation. J. Comput. Phys. 229 (20), 7774–7795.CrossRefGoogle Scholar
Zagni, A. F. E. & Smith, K. V. H. 1976 Channel flow over permeable beds of graded spheres. J. Hydraul. Div. ASCE 102 (2), 207–222.Google Scholar
Zhang, H., Trias, F. X., Gorobets, A., Tan, Y. & Oliva, A. 2015 Direct numerical simulation of a fully developed turbulent square duct flow up to Re$\tau$= 1200. Intl J. Heat Fluid Flow 54, 258–267.CrossRefGoogle Scholar