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Influence of Prandtl number in turbulent Rayleigh-Bénard convection over rough surfaces

Mukesh Sharma, Krishan Chand, and Arnab Kr. De*

  • Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Assam, 781039 India

  • *Author to whom correspondence should be addressed: akd@iitg.ac.in
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Phys. Rev. Fluids 7, 104609 – Published 26 October, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.104609

Abstract

The present study numerically investigates the effect of the Prandtl number (0.1≤Pr≤100) on the flow structures and heat transport mechanism in a two-dimensional rectangular rough cell of aspect ratio 2, for more than 2 decades of the Rayleigh number (107≤Ra≤5×109). Large-scale diffuse structures transform into finer ones with increase in either Ra or Pr. The height of roughness elements relative to the thermal boundary layer (TBL) thickness establishes the level of perturbations introduced into the system. A stronger thermal forcing or larger Pr facilitates a thinner TBL, which triggers a quicker response from the elements in the emission of plumes. In comparison to the smooth case, heat transport is enhanced significantly with the introduction of roughness. The near invariance of the Nusselt number Nu with Pr in smooth cells is overcome in the rough cell, where a monotonically increasing heat flux is obtained. A greater presence of plumes in the domain is identified by an augmented volume fraction and thermal dissipation from plumes. The flow intensity measured in terms of the global Reynolds number Re shows significant improvement for 108≤Ra≤5×109 and 5≤Pr≤100 in comparison to the smooth case.

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References (43)

  1. E. Bodenschatz, W. Pesch, and G. Ahlers, Recent developments in Rayleigh-Bénard convection, Annu. Rev. Fluid Mech. 32, 709 (2000).
  2. F. Chilla and J. Schumacher, New perspectives in turbulent Rayleigh-Bénard convection, Eur. Phys. J. E: Soft Matter Biol. Phys. 35, 58 (2012).
  3. G. Ahlers, S. Grossmann, and D. Lohse, Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection, Rev. Mod. Phys. 81, 503 (2009).
  4. S. Grossmann and D. Lohse, Scaling in thermal convection: a unifing theory, J. Fluid Mech. 407, 27 (2000).
  5. S. Grossmann and D. Lohse, Thermal Convection for Large Prandtl Numbers, Phys. Rev. Lett. 86, 3316 (2001).
  6. G. Silano, K. R. Sreenivasan, and R. Verzicco, Numerical simulations of Rayleigh-Bénard convection for Prandtl numbers between 10−1 and 104 and Rayleigh numbers between 105 and 109, J. Fluid Mech. 662, 409 (2010).
  7. R. Verzicco and R. Camussi, Prandtl number effects in convective turbulence, J. Fluid Mech. 383, 55 (1999).
  8. A. V. Malevsky, Patterns of convective turbulence: An effect of Prandtl number, Phys. Earth Planet. Inter. 88, 31 (1995).
  9. V. Yakhot, Probability Distributions in High-Rayleigh Number Bénard Convection, Phys. Rev. Lett. 63, 1965 (1989).
  10. T. H. Solomon and J. P. Gollub, Sheared Boundary Layers in Turbulent Rayleigh-Bénard Convection, Phys. Rev. Lett. 64, 2382 (1990).
  11. T. H. Solomon and J. P. Gollub, Thermal boundary layers and heat flux in turbulent convection: The role of recirculating flows, Phys. Rev. A 43, 6683 (1991).
  12. A. M. Obukhov, On the influence of Archimedean forces on the structure of the temperature field in a turbulent flow, Dokl. Akad. Nauk. SSR 125, 1246 (1959).
  13. R. Bolgiano, Turbulent spectra in a stably stratified atmosphere, J. Geophys. Res. 64, 2226 (1959).
  14. A. Brandenburg, Energy Spectra in a Model for Convective Turbulence, Phys. Rev. Lett. 69, 605 (1992).
  15. M. Lesieur, Turbulence in Fluids (Martinus Nijhoff, Dordrecht, 1987).
  16. Y. X. Huang and Q. Zhou, Counter-gradient heat transport in two-dimensional turbulent Rayleigh-Bénard convection, J. Fluid Mech. 737, R3 (2013).
  17. Y.-H. Yang, X. Zhu, B.-F. Wang, Y.-L. Liu, and Q. Zhou, Experimental investigation of turbulent Rayleigh-Bénard convection of water in a cylindrical cell: The Prandtl number effects for Pr > 1, Phys. Fluids 32, 015101 (2020).
  18. E. P. van der Poel, R. J. A. M. Stevens, and D. Lohse, Comparison between two-and three-dimensional Rayleigh-Bénard convection, J. Fluid Mech. 736, 177 (2013).
  19. A. Pandey, M. K. Verma, A. G. Chatterjee, and B. Dutta, Similarities between 2D and 3D convection for large Prandtl number, Pramana - J. Phys. 87, 13 (2016).
  20. X.-M. Li, J.-D. He, Y. Tian, P. Hao, and S.-D. Huang, Effects of Prandtl number in quasi-two-dimensional Rayleigh-Bénard convection, J. Fluid Mech. 915, A60 (2021).
  21. Y. Zhang, C. Sun, Y. Bao, and Q. Zhou, How surface roughness reduces heat transport for small roughness heights in turbulent Rayleigh-Bénard convection, J. Fluid Mech. 836, R2 (2018).
  22. S. Toppaladoddi, S. Succi, and J. S. Wettlaufer, Roughness as a Route to the Ultimate Regime of Thermal Convection, Phys. Rev. Lett. 118, 074503 (2017).
  23. X. Zhu, R. J. A. M. Stevens, R. Verzicco, and D. Lohse, Roughness Facilitated Local 1/2 Scaling Does Not Imply the Onset of the Ultimate Regime of Thermal Convection, Phys. Rev. Lett. 119, 154501 (2017).
  24. X. Zhu, R. J. A. M. Stevens, O. Shishkina, R. Verzicco, and D. Lohse, Nu∼Ra1/2 scaling enabled by multiscale wall roughness in Rayleigh-Bénard turbulence, J. Fluid Mech. 869, R4 (2019).
  25. S. Toppaladoddi, A. J. Wells, C. R. Doering, and J. S. Wettlaufer, Thermal convection over fractal surfaces, J. Fluid Mech. 907, A12 (2021).
  26. R. H. Kraichnan, Turbulent thermal convection at arbitrary Prandtl number, Phys. Fluids 5, 1374 (1962).
  27. E. A. Speigel, Convection in stars I. Basic Boussinesq convection, Annu. Rev. Astron. Astrophys. 9, 323 (1971).
  28. K. Chand, M. Sharma, and A. K. De, Significance of near-wall dynamics in enhancement of heat flux for roughness aided turbulent Rayleigh-Bénard convection, Phys. Fluids 33, 065114 (2021).
  29. Y. Zhang, Q. Zhou, and C. Sun, Statistics of kinetic and thermal energy dissipation rates in two-dimensional turbulent Rayleigh-Bénard convection, J. Fluid Mech. 814, 165 (2017).
  30. D.-L. Dong, B.-F. Wang, Y.-H. Dong, Y.-X. Huang, N. Jiang, Y.-L. Liu, Z.-M. Lu, X. Qiu, Z.-Q. Tang, and Q. Zhou, Influence of spatial arrangements of roughness elements on turbulent Rayleigh-Bénard convection, Phys. Fluids 32, 045114 (2020).
  31. Y. C. Xie and K. Q. Xia, Turbulent thermal convection over rough plates with varying roughness geometries, J. Fluid Mech. 825, 573 (2017).
  32. J. L. Yang, Y. Z. Zhang, T. C. Jin, Y. H. Dong, B. F. Wang, and Q. Zhou, The Pr-dependence of the critical roughness height in two-dimensional turbulent Rayleigh-Bénard convection, J. Fluid Mech. 911, A52 (2021).
  33. A. K. De, A diffuse interface immersed boundary method for complex moving boundary problems, J. Comput. Phys. 366, 226 (2018).
  34. S. Peter and A. K. De, Wake instability modes for forced transverse oscillation of a sphere, Ocean Eng. 115, 48 (2016).
  35. A. K. De, V. Eswaran, and P. K. Mishra, Dynamics of plumes in turbulent Rayleigh-Bénard convection, Eur. J. Mech. B Fluids 72, 164 (2018).
  36. A. K. De and S. Sarkar, Three-dimensional wake dynamics behind a tapered cylinder with large taper ratio, Phys. Fluids 32, 063604 (2020).
  37. K. Chand, A. K. De, and P. K. Mishra, Enhanced heat flux and flow structures in turbulent Rayleigh-Bénard convection with rough boundaries, Phys. Rev. Fluids 6, 124605 (2021).
  38. A. K. De and S. Sarkar, Dependence of wake structure on pitching frequency behind a thin panel at Re=1000, J. Fluid Mech. 924, A33 (2021).
  39. A. K. De and S. Sarkar, Spatial wake transition past a thin pitching plate, Phys. Rev. E 104, 025106 (2021).
  40. Y. B. Du and P. Tong, Enhanced Heat Transport in Turbulent Convection over a Rough Surface, Phys. Rev. Lett. 81, 987 (1998).
  41. Y. B. Du and P. Tong, Turbulent thermal convection in a cell with ordered rough boundaries, J. Fluid Mech. 407, 57 (2000).
  42. M. S. Emran and J. Schumacher, Conditional statistics of thermal dissipation rate in turbulent Rayleigh-Bénard convection, Eur. Phys. J. E: Soft Matter Biol. Phys. 35, 108 (2012).
  43. A. K. De, A diffuse interface immersed boundary method for convective heat and fluid flow, Int. J. Heat Mass Transfer 92, 957 (2016).

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Phys. Rev. Fluids 7, 104609– Published 26 October, 2022
  • Received 14 June 2022
  • Accepted 4 October 2022
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