Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-05-28T05:42:15.827Z Has data issue: false hasContentIssue false

Wall-sheared thermal convection: heat transfer enhancement and turbulence relaminarization

Published online by Cambridge University Press:  29 March 2023

Ao Xu
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, PR China Institute of Extreme Mechanics, Northwestern Polytechnical University, Xi'an 710072, PR China
Ben-Rui Xu
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, PR China
Heng-Dong Xi*
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, PR China Institute of Extreme Mechanics, Northwestern Polytechnical University, Xi'an 710072, PR China
*
Email address for correspondence: hengdongxi@nwpu.edu.cn

Abstract

We studied the flow organization and heat transfer properties in two-dimensional and three-dimensional Rayleigh–Bénard cells that are imposed with different types of wall shear. The external wall shear is added with the motivation of manipulating flow mode to control heat transfer efficiency. We imposed three types of wall shear that may facilitate the single-roll, the horizontally stacked double-roll, and the vertically stacked double-roll flow modes, respectively. Direct numerical simulations are performed for fixed Rayleigh number $Ra = 10^{8}$ and fixed Prandtl number $Pr = 5.3$, while the wall-shear Reynolds number ($Re_{w}$) is in the range $60 \leqslant Re_{w} \leqslant 6000$. Generally, we found enhanced heat transfer efficiency and global flow strength with the increase of $Re_{w}$. However, even with the same magnitude of global flow strength, the heat transfer efficiency varies significantly when the cells are under different types of wall shear. An interesting finding is that by increasing the wall-shear strength, the thermal turbulence is relaminarized, and more surprisingly, the heat transfer efficiency in the laminar state is higher than that in the turbulent state. We found that the enhanced heat transfer efficiency at the laminar regime is due to the formation of more stable and stronger convection channels. We propose that the origin of thermal turbulence laminarization is the reduced amount of thermal plumes. Because plumes are mainly responsible for turbulent kinetic energy production, when the detached plumes are swept away by the wall shear, the reduced number of plumes leads to weaker turbulent kinetic energy production. We also quantify the efficiency of facilitating heat transport via external shearing, and find that for larger $Re_{w}$, the enhanced heat transfer efficiency comes at a price of a larger expenditure of mechanical energy.

Type
JFM Papers
Copyright
© The Author(s), 2023. 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

Ahlers, G., Grossmann, S. & Lohse, D. 2009 Heat transfer and large scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81 (2), 503507.CrossRefGoogle Scholar
Batchelor, G.K. 1959 Small-scale variation of convected quantities like temperature in turbulent fluid. Part 1. General discussion and the case of small conductivity. J. Fluid Mech. 5 (1), 113133.CrossRefGoogle Scholar
Bhattacharya, S., Pandey, A., Kumar, A. & Verma, M.K. 2018 Complexity of viscous dissipation in turbulent thermal convection. Phys. Fluids 30 (3), 031702.CrossRefGoogle Scholar
Blass, A., Tabak, P., Verzicco, R., Stevens, R.J.A.M. & Lohse, D. 2021 The effect of Prandtl number on turbulent sheared thermal convection. J. Fluid Mech. 910, A37.CrossRefGoogle Scholar
Blass, A., Zhu, X.-J., Verzicco, R., Lohse, D. & Stevens, R.J.A.M. 2020 Flow organization and heat transfer in turbulent wall sheared thermal convection. J. Fluid Mech. 897, A22.CrossRefGoogle ScholarPubMed
Chandra, M. & Verma, M.K. 2011 Dynamics and symmetries of flow reversals in turbulent convection. Phys. Rev. E 83 (6), 067303.CrossRefGoogle ScholarPubMed
Chandra, M. & Verma, M.K. 2013 Flow reversals in turbulent convection via vortex reconnections. Phys. Rev. Lett. 110 (11), 114503.CrossRefGoogle ScholarPubMed
Chen, X., Huang, S.-D., Xia, K.-Q. & Xi, H.-D. 2019 Emergence of substructures inside the large-scale circulation induces transition in flow reversals in turbulent thermal convection. J. Fluid Mech. 877, R1.CrossRefGoogle Scholar
Chillà, F., Rastello, M., Chaumat, S. & Castaing, B. 2004 Long relaxation times and tilt sensitivity in Rayleigh–Bénard turbulence. Eur. Phys. J. B 40 (2), 223227.CrossRefGoogle Scholar
Chillà, F. & Schumacher, J. 2012 New perspectives in turbulent Rayleigh–Bénard convection. Eur. Phys. J. E 35 (58), 125.CrossRefGoogle ScholarPubMed
Chong, K.L., Wagner, S., Kaczorowski, M., Shishkina, O. & Xia, K.-Q. 2018 Effect of Prandtl number on heat transport enhancement in Rayleigh–Bénard convection under geometrical confinement. Phys. Rev. Fluids 3 (1), 013501.CrossRefGoogle Scholar
Chong, K.L., Yang, Y.-T., Huang, S.-D., Zhong, J.-Q., Stevens, R.J.A.M., Verzicco, R., Lohse, D. & Xia, K.-Q. 2017 Confined Rayleigh–Bénard, rotating Rayleigh–Bénard, and double diffusive convection: a unifying view on turbulent transport enhancement through coherent structure manipulation. Phys. Rev. Lett. 119 (6), 064501.CrossRefGoogle ScholarPubMed
Ciliberto, S., Cioni, S. & Laroche, C. 1996 Large-scale flow properties of turbulent thermal convection. Phys. Rev. E 54 (6), R5901.CrossRefGoogle ScholarPubMed
Ciliberto, S. & Laroche, C. 1999 Random roughness of boundary increases the turbulent convection scaling exponent. Phys. Rev. Lett. 82 (20), 3998.CrossRefGoogle Scholar
Deville, M.O., Fischer, P.F. & Mund, E.H. 2002 High-Order Methods for Incompressible Fluid Flow, vol. 9. Cambridge University Press.CrossRefGoogle Scholar
Fischer, P.F. 1997 An overlapping Schwarz method for spectral element solution of the incompressible Navier–Stokes equations. J. Comput. Phys. 133 (1), 84101.CrossRefGoogle Scholar
Fischer, P.F., Kruse, G.W. & Loth, F. 2002 Spectral element methods for transitional flows in complex geometries. J. Sci. Comput. 17 (1), 8198.CrossRefGoogle Scholar
Gasteuil, Y., Shew, W.L., Gibert, M., Chillà, F., Castaing, B. & Pinton, J.-F. 2007 Lagrangian temperature, velocity, and local heat flux measurement in Rayleigh–Bénard convection. Phys. Rev. Lett. 99 (23), 234302.CrossRefGoogle ScholarPubMed
Guzman, D.N., Xie, Y.-B., Chen, S.-Y., Rivas, D.F., Sun, C., Lohse, D. & Ahlers, G. 2016 Heat-flux enhancement by vapour-bubble nucleation in Rayleigh–Bénard turbulence. J. Fluid Mech. 787, 331366.CrossRefGoogle Scholar
Gvozdić, B., Alméras, E., Mathai, V., Zhu, X.-J., van Gils, D.P.M., Verzicco, R., Huisman, S.G., Sun, C. & Lohse, D. 2018 Experimental investigation of heat transport in homogeneous bubbly flow. J. Fluid Mech. 845, 226244.CrossRefGoogle Scholar
Heslot, F., Castaing, B. & Libchaber, A. 1987 Transitions to turbulence in helium gas. Phys. Rev. A 36 (12), 5870.CrossRefGoogle ScholarPubMed
Huang, S.-D., Kaczorowski, M., Ni, R. & Xia, K.-Q. 2013 Confinement-induced heat-transport enhancement in turbulent thermal convection. Phys. Rev. Lett. 111 (10), 104501.CrossRefGoogle ScholarPubMed
Huang, S.-D. & Xia, K.-Q. 2016 Effects of geometric confinement in quasi-2-D turbulent Rayleigh–Bénard convection. J. Fluid Mech. 794, 639654.CrossRefGoogle Scholar
Huang, Y.-X. & Zhou, Q. 2013 Counter-gradient heat transport in two-dimensional turbulent Rayleigh–Bénard convection. J. Fluid Mech. 737, R3.CrossRefGoogle Scholar
Hunt, J.C.R 1991 Industrial and environmental fluid mechanics. Annu. Rev. Fluid Mech. 23 (1), 142.CrossRefGoogle Scholar
Jiang, H.-C., Zhu, X.-J., Mathai, V., Verzicco, R., Lohse, D. & Sun, C. 2018 Controlling heat transport and flow structures in thermal turbulence using ratchet surfaces. Phys. Rev. Lett. 120 (4), 044501.CrossRefGoogle ScholarPubMed
Jin, T.-C., Wu, J.-Z., Zhang, Y.-Z., Liu, Y.-L. & Zhou, Q. 2022 Shear-induced modulation on thermal convection over rough plates. J. Fluid Mech. 936, A28.CrossRefGoogle Scholar
Kooij, G.L., Botchev, M.A., Frederix, E.M.A., Geurts, B.J., Horn, S., Lohse, D., van der Poel, E.P., Shishkina, O., Stevens, R.J.A.M. & Verzicco, R. 2018 Comparison of computational codes for direct numerical simulations of turbulent Rayleigh–Bénard convection. Comput. Fluids 166, 18.CrossRefGoogle Scholar
Kraichnan, R.H. 1962 Turbulent thermal convection at arbitrary Prandtl number. Phys. Fluids 5 (11), 13741389.CrossRefGoogle Scholar
Kühnen, J., Song, B.-F., Scarselli, D., Budanur, N.B., Riedl, M., Willis, A.P., Avila, M. & Hof, B. 2018 Destabilizing turbulence in pipe flow. Nat. Phys. 14 (4), 386390.CrossRefGoogle Scholar
Lakkaraju, R., Stevens, R.J.A.M., Oresta, P., Verzicco, R., Lohse, D. & Prosperetti, A. 2013 Heat transport in bubbling turbulent convection. Proc. Natl Acad. Sci. USA 110 (23), 92379242.CrossRefGoogle ScholarPubMed
Liu, S. & Huisman, S.G. 2020 Heat transfer enhancement in Rayleigh–Bénard convection using a single passive barrier. Phys. Rev. Fluids 5 (12), 123502.CrossRefGoogle Scholar
Lohse, D. & Xia, K.-Q. 2010 Small-scale properties of turbulent Rayleigh–Bénard convection. Annu. Rev. Fluid Mech. 42, 335364.CrossRefGoogle Scholar
Patera, A.T. 1984 A spectral element method for fluid dynamics: laminar flow in a channel expansion. J. Comput. Phys. 54 (3), 468488.CrossRefGoogle Scholar
Petschel, K., Wilczek, M., Breuer, M., Friedrich, R. & Hansen, U. 2011 Statistical analysis of global wind dynamics in vigorous Rayleigh–Bénard convection. Phys. Rev. E 84 (2), 026309.CrossRefGoogle Scholar
van der Poel, E.P., Ostilla-Mónico, R., Verzicco, R. & Lohse, D. 2014 Effect of velocity boundary conditions on the heat transfer and flow topology in two-dimensional Rayleigh–Bénard convection. Phys. Rev. E 90 (1), 013017.CrossRefGoogle ScholarPubMed
van der Poel, E.P., Stevens, R.J.A.M. & Lohse, D. 2011 Connecting flow structures and heat flux in turbulent Rayleigh–Bénard convection. Phys. Rev. E 84 (4), 045303.CrossRefGoogle ScholarPubMed
van der Poel, E.P., Stevens, R.J.A.M., Sugiyama, K. & Lohse, D. 2012 Flow states in two-dimensional Rayleigh–Bénard convection as a function of aspect-ratio and Rayleigh number. Phys. Fluids 24 (8), 085104.CrossRefGoogle Scholar
van der Poel, E.P., Verzicco, R., Grossmann, S. & Lohse, D. 2015 Plume emission statistics in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 772, 515.CrossRefGoogle Scholar
Pope, S.-B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Roche, P.-E., Castaing, B., Chabaud, B. & Hébral, B. 2002 Prandtl and Rayleigh numbers dependences in Rayleigh–Bénard convection. Europhys. Lett. 58 (5), 693.CrossRefGoogle Scholar
Rusaouën, E., Liot, O., Castaing, B., Salort, J. & Chillà, F. 2018 Thermal transfer in Rayleigh–Bénard cell with smooth or rough boundaries. J. Fluid Mech. 837, 443460.CrossRefGoogle Scholar
Scagliarini, A., Einarsson, H., Gylfason, Á. & Toschi, F. 2015 Law of the wall in an unstably stratified turbulent channel flow. J. Fluid Mech. 781, R5.CrossRefGoogle Scholar
Scagliarini, A., Gylfason, Á. & Toschi, F. 2014 Heat-flux scaling in turbulent Rayleigh–Bénard convection with an imposed longitudinal wind. Phys. Rev. E 89 (4), 043012.CrossRefGoogle ScholarPubMed
Scarselli, D., Kühnen, J. & Hof, B. 2019 Relaminarising pipe flow by wall movement. J. Fluid Mech. 867, 934948.CrossRefGoogle Scholar
Shankar, P.N. & Deshpande, M.D. 2000 Fluid mechanics in the driven cavity. Annu. Rev. Fluid Mech. 32 (1), 93136.CrossRefGoogle Scholar
Shraiman, B.I. & Siggia, E.D. 1990 Heat transport in high-Rayleigh-number convection. Phys. Rev. A 42 (6), 3650.CrossRefGoogle ScholarPubMed
Silano, G., Sreenivasan, K.R. & Verzicco, R. 2010 Numerical simulations of Rayleigh–Bénard convection for Prandtl numbers between $10^{-1}$ and $10^{4}$ and Rayleigh numbers between $10^{5}$ and $10^{9}$. J. Fluid Mech. 662, 409446.CrossRefGoogle Scholar
Solomon, T.H. & Gollub, J.P. 1990 Sheared boundary layers in turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 64 (20), 2382.CrossRefGoogle ScholarPubMed
Stevens, R.J.A.M., Clercx, H.J.H. & Lohse, D. 2013 Heat transport and flow structure in rotating Rayleigh–Bénard convection. Eur. J. Mech. (B/Fluids) 40, 4149.CrossRefGoogle Scholar
Stevens, R.J.A.M., Zhong, J.-Q., Clercx, H.J.H., Ahlers, G. & Lohse, D. 2009 Transitions between turbulent states in rotating Rayleigh–Bénard convection. Phys. Rev. Lett. 103 (2), 024503.CrossRefGoogle ScholarPubMed
Sun, C., Xi, H.-D. & Xia, K.-Q. 2005 Azimuthal symmetry, flow dynamics, and heat transport in turbulent thermal convection in a cylinder with an aspect ratio of 0.5. Phys. Rev. Lett. 95 (7), 074502.CrossRefGoogle Scholar
Wagner, S. & Shishkina, O. 2015 Heat flux enhancement by regular surface roughness in turbulent thermal convection. J. Fluid Mech. 763, 109135.CrossRefGoogle Scholar
Wang, B.-F., Zhou, Q. & Sun, C. 2020 Vibration-induced boundary-layer destabilization achieves massive heat-transport enhancement. Sci. Adv. 6 (21), eaaz8239.CrossRefGoogle ScholarPubMed
Wang, Q., Xia, S.-N., Wang, B.-F., Sun, D.-J., Zhou, Q. & Wan, Z.-H. 2018 Flow reversals in two-dimensional thermal convection in tilted cells. J. Fluid Mech. 849, 355372.CrossRefGoogle Scholar
Wang, Z.-Q., Mathai, V. & Sun, C. 2019 Self-sustained biphasic catalytic particle turbulence. Nat. Commun. 10 (1), 17.Google ScholarPubMed
Weiss, S. & Ahlers, G. 2011 Turbulent Rayleigh–Bénard convection in a cylindrical container with aspect ratio $\gamma =0.50$ and Prandtl number $Pr=4.38$. J. Fluid Mech. 676, 540.CrossRefGoogle Scholar
Xi, H.-D., Lam, S. & Xia, K.-Q. 2004 From laminar plumes to organized flows: the onset of large-scale circulation in turbulent thermal convection. J. Fluid Mech. 503, 4756.CrossRefGoogle Scholar
Xi, H.-D. & Xia, K.-Q. 2008 Flow mode transitions in turbulent thermal convection. Phys. Fluids 20 (5), 055104.CrossRefGoogle Scholar
Xi, H.-D., Zhang, Y.-B., Hao, J.-T. & Xia, K.-Q. 2016 Higher-order flow modes in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 805, 3151.CrossRefGoogle Scholar
Xia, K.-Q. 2013 Current trends and future directions in turbulent thermal convection. Theor. Appl. Mech. Lett. 3 (5), 052001.CrossRefGoogle Scholar
Xia, K.-Q. & Lui, S.-L. 1997 Turbulent thermal convection with an obstructed sidewall. Phys. Rev. Lett. 79 (25), 5006.CrossRefGoogle Scholar
Xia, K.-Q., Sun, C. & Zhou, S.-Q. 2003 Particle image velocimetry measurement of the velocity field in turbulent thermal convection. Phys. Rev. E 68 (6), 066303.CrossRefGoogle ScholarPubMed
Xu, A., Chen, X., Wang, F. & Xi, H.-D. 2020 Correlation of internal flow structure with heat transfer efficiency in turbulent Rayleigh–Bénard convection. Phys. Fluids 32 (10), 105112.CrossRefGoogle Scholar
Xu, A., Chen, X. & Xi, H.-D. 2021 Tristable flow states and reversal of the large-scale circulation in two-dimensional circular convection cells. J. Fluid Mech. 910, A33.CrossRefGoogle Scholar
Xu, A. & Li, B.-T. 2023 Multi-GPU thermal lattice Boltzmann simulations using OpenACC and MPI. Intl J. Heat Mass Transfer 201, 123649.CrossRefGoogle Scholar
Xu, A., Shi, L. & Xi, H.-D. 2019 Lattice Boltzmann simulations of three-dimensional thermal convective flows at high Rayleigh number. Intl J. Heat Mass Transfer 140, 359370.CrossRefGoogle Scholar
Xu, A., Shi, L. & Zhao, T.S. 2017 Accelerated lattice Boltzmann simulation using GPU and OpenACC with data management. Intl J. Heat Mass Transfer 109, 577588.CrossRefGoogle Scholar
Yang, R., Chong, K.L., Wang, Q., Verzicco, R., Shishkina, O. & Lohse, D. 2020 a Periodically modulated thermal convection. Phys. Rev. Lett. 125 (15), 154502.CrossRefGoogle ScholarPubMed
Yang, W.-W., Zhang, Y.-Z., Wang, B.-F., Dong, Y.-H. & Zhou, Q. 2022 Dynamic coupling between carrier and dispersed phases in Rayleigh–Bénard convection laden with inertial isothermal particles. J. Fluid Mech. 930, A24.CrossRefGoogle Scholar
Yang, Y.-T., Verzicco, R., Lohse, D. & Stevens, R.J.A.M. 2020 b What rotation rate maximizes heat transport in rotating Rayleigh–Bénard convection with Prandtl number larger than one? Phys. Rev. Fluids 5 (5), 053501.CrossRefGoogle Scholar
Zhang, L., Dong, J. & Xia, K.-Q. 2022 Exploring the plume and shear effects in turbulent Rayleigh–Bénard convection with effective horizontal buoyancy under streamwise and spanwise geometrical confinements. J. Fluid Mech. 940, A37.CrossRefGoogle Scholar
Zhang, Y., Zhou, Q. & Sun, C. 2017 Statistics of kinetic and thermal energy dissipation rates in two-dimensional turbulent Rayleigh–Bénard convection. J. Fluid Mech. 814, 165184.CrossRefGoogle Scholar
Zhong, J.-Q., Stevens, R.J.A.M., Clercx, H.J.H., Verzicco, R., Lohse, D. & Ahlers, G. 2009 Prandtl-, Rayleigh-, and Rossby-number dependence of heat transport in turbulent rotating Rayleigh–Bénard convection. Phys. Rev. Lett. 102 (4), 044502.CrossRefGoogle ScholarPubMed
Zhu, X.-J., Stevens, R.J.A.M., Shishkina, O., Verzicco, R. & Lohse, D. 2019 Scaling enabled by multiscale wall roughness in Rayleigh–Bénard turbulence. J. Fluid Mech. 869, R4.CrossRefGoogle Scholar

Xu et al. Supplementary Movie 1

Temperature and flow fields under the wall shear

Download Xu et al. Supplementary Movie 1(Video)
Video 9.9 MB

Xu et al. Supplementary Movie 2

Turbulence relaminarization process

Download Xu et al. Supplementary Movie 2(Video)
Video 8.5 MB