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Prandtl number dependence of flow topology in quasi-two-dimensional turbulent Rayleigh–Bénard convection

Published online by Cambridge University Press:  22 August 2024

Ze-Hao Wang ,
Xin Chen Open the ORCID record for Xin Chen [Opens in a new window] ,
Ao Xu Open the ORCID record for Ao Xu [Opens in a new window]  and
Heng-Dong Xi Open the ORCID record for Heng-Dong Xi [Opens in a new window]
Ze-Hao Wang
Affiliation:
School of Aeronautics and Institute of Extreme Mechanics, Northwestern Polytechnical University, Xi'an 710072, PR China
Xin Chen*
Affiliation:
School of Aeronautics and Institute of Extreme Mechanics, Northwestern Polytechnical University, Xi'an 710072, PR China Shanghai Institute of Applied Mathematics and Mechanics and Shanghai Key Laboratory of Mechanics in Energy Engineering, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, PR China
Ao Xu
Affiliation:
School of Aeronautics and Institute of Extreme Mechanics, Northwestern Polytechnical University, Xi'an 710072, PR China National Key Laboratory of Aircraft Configuration Design, Northwestern Polytechnical University, Xi'an 710072, PR China
Heng-Dong Xi*
Affiliation:
School of Aeronautics and Institute of Extreme Mechanics, Northwestern Polytechnical University, Xi'an 710072, PR China National Key Laboratory of Aircraft Configuration Design, Northwestern Polytechnical University, Xi'an 710072, PR China
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

To date, a comprehensive understanding of the influence of the Prandtl number ($Pr$) on flow topology in turbulent Rayleigh–Bénard convection (RBC) remains elusive. In this study, we present an experimental investigation into the evolution of flow topology in quasi-two-dimensional turbulent RBC with $7.0 \leq Pr \leq 244.2$ and $2.03\times 10^{8} \leq Ra \leq 2.81\times 10^{9}$. Particle image velocimetry (PIV) measurements reveal the flow transitions from multiple-roll state to single-roll state with increasing $Ra$, and the transition is hindered with increasing $Pr$, i.e. the transitional Rayleigh number $Ra_t$ increases with $Pr$. We mapped out a phase diagram on the flow topology change on $Ra$ and $Pr$, and identified the scaling of $Ra_t$ on $Pr$: $Ra_t \sim Pr^{0.93}$ in the low $Pr$ range, and $Ra_t \sim Pr^{3.3}$ in the high $Pr$ range. The scaling in the low $Pr$ range is consistent with the model of balance of energy dissipation time and plume travel time that we proposed in our previous study, while the scaling in the high $Pr$ range implies a new governing mechanism. For the first time, the scaling of $Re$ on $Ra$ and $Pr$ is acquired through full-field PIV velocity measurement, $Re \sim Ra^{0.63}\,Pr^{-0.87}$. We also propose that increasing horizontal velocity promotes the formation of the large-scale circulation (LSC), especially for the high $Pr$ case. Our proposal was verified by achieving LSC through introducing horizontal driving force $Ra_H$ by tilting the convection cell with a small angle.

JFM classification

Turbulent Flows: Turbulent convection
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 991 , 25 July 2024 , A14
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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References

Ahlers, G., Brown, E. & Nikolaenko, A. 2006 The search for slow transients, and the effect of imperfect vertical alignment, in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 557, 347–367.CrossRefGoogle Scholar
Ahlers, G., Grossmann, S. & Lohse, D. 2009 Heat transfer and large scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81 (2), 503–537.CrossRefGoogle Scholar
Brown, E. & Ahlers, G. 2006 Rotations and cessations of the large-scale circulation in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 568, 351–386.CrossRefGoogle Scholar
Brown, E. & Ahlers, G. 2009 The origin of oscillations of the large-scale circulation of turbulent Rayleigh–Bénard convection. J. Fluid Mech. 638, 383–400.CrossRefGoogle Scholar
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
Chen, X., Wang, D.-P. & Xi, H.-D. 2020 Reduced flow reversals in turbulent convection in the absence of corner vortices. J. Fluid Mech. 891, R5.CrossRefGoogle Scholar
Chen, X., Xu, A., Xia, K.-Q. & Xi, H.-D. 2023 The effect of the cell tilting on the temperature oscillation in turbulent Rayleigh–Bénard convection. Phys. Fluids 35 (8), 085141.Google Scholar
Chilla, F. & Schumacher, J. 2012 New perspectives in turbulent Rayleigh–Bénard convection. Eur. Phys. J. E 35 (7), 58.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
Cioni, S., Ciliberto, S. & Sommeria, J. 1996 Experimental study of high-Rayleigh-number convection in mercury and water. Dyn. Atmos. Oceans 24 (1–4), 117–127.CrossRefGoogle Scholar
Cioni, S., Ciliberto, S. & Sommeria, J. 1997 Strongly turbulent Rayleigh–Bénard convection in mercury: comparison with results at moderate Prandtl number. J. Fluid Mech. 335, 111–140.CrossRefGoogle Scholar
Grossmann, S. & Lohse, D. 2000 Scaling in thermal convection: a unifying theory. J. Fluid Mech. 407, 27–56.CrossRefGoogle Scholar
Guo, S.-X., Zhou, S.-Q., Cen, X.-R., Qu, L., Lu, Y.-Z., Sun, L. & Shang, X.-D. 2014 The effect of cell tilting on turbulent thermal convection in a rectangular cell. J. Fluid Mech. 762, 273–287.CrossRefGoogle Scholar
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
Hughes, G.O. & Griffiths, R.W. 2008 Horizontal convection. Annu. Rev. Fluid Mech. 40, 185–208.CrossRefGoogle Scholar
Jiang, L., Sun, C. & Calzavarini, E. 2019 Robustness of heat transfer in confined inclined convection at high Prandtl number. Phys. Rev. E 99 (1), 013108.CrossRefGoogle ScholarPubMed
Krishnamurti, R. & Howard, L.N. 1981 Large-scale flow generation in turbulent convection. Proc. Natl Acad. Sci. USA 78 (4), 1981–1985.CrossRefGoogle ScholarPubMed
Lam, S., Shang, X.-D., Zhou, S.-Q. & Xia, K.-Q. 2002 Prandtl number dependence of the viscous boundary layer and the Reynolds numbers in Rayleigh–Bénard convection. Phys. Rev. E 65 (6), 066306.CrossRefGoogle ScholarPubMed
Li, X.-M., He, J.-D., Tian, Y., Hao, P. & Huang, S.-D. 2021 Effects of Prandtl number in quasi-two-dimensional Rayleigh–Bénard convection. J. Fluid Mech. 915, A60.CrossRefGoogle Scholar
Li, Y.-Z., Chen, X., Xu, A. & Xi, H.-D. 2022 Counter-flow orbiting of the vortex centre in turbulent thermal convection. J. Fluid Mech. 935, A19.CrossRefGoogle Scholar
Lohse, D. & Xia, K.-Q. 2010 Small-scale properties of turbulent Rayleigh–Bénard convection. Annu. Rev. Fluid Mech. 42 (1), 335–364.CrossRefGoogle Scholar
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
Qiu, X.-L. & Tong, P. 2001 Large-scale velocity structures in turbulent thermal convection. Phys. Rev. E 64 (3), 036304.CrossRefGoogle ScholarPubMed
Ren, L., Tao, X., Zhang, L., Ni, M.-J., Xia, K.-Q. & Xie, Y.-C. 2022 Flow states and heat transport in liquid metal convection. J. Fluid Mech. 951, R1.CrossRefGoogle Scholar
Shishkina, O. & Horn, S. 2016 Thermal convection in inclined cylindrical containers. J. Fluid Mech. 790, R3.CrossRefGoogle Scholar
Sugiyama, K., Ni, R., Stevens, R.J., Chan, T.-S., Zhou, S.-Q., Xi, H.-D., Sun, C., Grossmann, S., Xia, K.-Q. & Lohse, D. 2010 Flow reversals in thermally driven turbulence. Phys. Rev. Lett. 105 (3), 034503.CrossRefGoogle ScholarPubMed
Tropea, C., Yarin, A.L. & Foss, J.F. 2007 Springer Handbook of Experimental Fluid Mechanics, vol. 1. Springer.CrossRefGoogle Scholar
Vogt, T., Horn, S., Grannan, A.M. & Aurnou, J.M. 2018 Jump rope vortex in liquid metal convection. Proc. Natl Acad. Sci. USA 115 (50), 12674–12679.CrossRefGoogle ScholarPubMed
Wagner, S. & Shishkina, O. 2013 Aspect-ratio dependency of Rayleigh–Bénard convection in box-shaped containers. Phys. Fluids 25 (8), 085110.CrossRefGoogle Scholar
Wang, Q., Verzicco, R., Lohse, D. & Shishkina, O. 2020 Multiple states in turbulent large-aspect-ratio thermal convection: what determines the number of convection rolls? Phys. Rev. Lett. 125 (7), 074501.CrossRefGoogle ScholarPubMed
Wei, P. 2021 The persistence of large-scale circulation in Rayleigh–Bénard convection. J. Fluid Mech. 924, A28.CrossRefGoogle Scholar
Weiss, S. & Ahlers, G. 2011 Turbulent Rayleigh–Bénard convection in a cylindrical container with aspect ratio $\varGamma = 0.50$ and Prandtl number $Pr = 4.38$. J. Fluid Mech. 676, 5–40.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, 47–56.CrossRefGoogle Scholar
Xi, H.-D. & Xia, K.-Q. 2007 Cessations and reversals of the large-scale circulation in turbulent thermal convection. Phys. Rev. E 75, 066307.CrossRefGoogle ScholarPubMed
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, 31–51.CrossRefGoogle Scholar
Xi, H.-D., Zhou, Q. & Xia, K.-Q. 2006 Azimuthal motion of the mean wind in turbulent thermal convection. Phys. Rev. E 73, 056312.CrossRefGoogle ScholarPubMed
Xi, H.-D., Zhou, S.-Q., Zhou, Q., Chan, T.-S. & Xia, K.-Q. 2009 Origin of the temperature oscillation in turbulent thermal convection. Phys. Rev. Lett. 102 (4), 044503.CrossRefGoogle ScholarPubMed
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., Lam, S. & Zhou, S.-Q. 2002 Heat-flux measurement in high-Prandtl-number turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 88 (6), 064501.CrossRefGoogle ScholarPubMed
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, 066303.CrossRefGoogle ScholarPubMed
Zhang, J., Childress, S. & Libchaber, A. 1997 Non-Boussinesq effect: thermal convection with broken symmetry. Phys. Fluids 9 (4), 1034–1042.CrossRefGoogle Scholar
Zhang, L., Ding, G.-Y. & Xia, K.-Q. 2021 On the effective horizontal buoyancy in turbulent thermal convection generated by cell tilting. J. Fluid Mech. 914, A15.CrossRefGoogle Scholar
Zhu, X.-J., Mathai, V., Stevens, R.J.A.M., Verzicco, R. & Lohse, D. 2018 Transition to the ultimate regime in two-dimensional Rayleigh–Bénard convection. Phys. Rev. lett. 120 (14), 144502.CrossRefGoogle Scholar
Zwirner, L. & Shishkina, O. 2018 Confined inclined thermal convection in low-Prandtl-number fluids. J. Fluid Mech. 850, 984–1008.CrossRefGoogle Scholar