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Heat transport and flow structure in thermal convection with two liquid layers

Published online by Cambridge University Press:  27 December 2023

Mu Wang Open the ORCID record for Mu Wang [Opens in a new window] ,
Xin-Yu Chen ,
Wei Wang  and
Ping Wei Open the ORCID record for Ping Wei [Opens in a new window]
Mu Wang
Affiliation:
School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, PR China
Xin-Yu Chen
Affiliation:
School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, PR China
Wei Wang
Affiliation:
School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, PR China
Ping Wei*
Affiliation:
School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, PR China Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems, Shanghai 201804, PR China
*
†Email address for correspondence: ping.wei@tongji.edu.cn
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Abstract

We report an experimental investigation of the heat transport and flow field in a rectangular Rayleigh–Bénard convection (RBC) cell with two immiscible fluids: silicone oil and glycerol. The global heat transport of the system is divided into three ranges corresponding to the different flow structures formed in the glycerol layer. In range I, the glycerol layer is dominated by conduction, and no plume is formed over the interface. In range II, cellular rolls are formed in the glycerol layer and the horizontal motion of rolls causes an oscillation of temperature in the interface. In range III, the cellular pattern is time-independent, and the interface forms a group of wavelets with wave numbers consistent with the mode of the cellular pattern. In lower-thin glycerol, the Nusselt (Nu) grows from conduction to convection through an oscillating subcritical bifurcation at critical Rayleigh number $Ra_c$. The value of $Ra_c$ in the present work is smaller than the theoretical prediction of both-rigid boundaries and greater than the prediction of one-rigid and one-free boundaries. In the upper-thick silicone oil layer, $Nu$ increases with increasing $Ra$, but it is smaller than that of traditional RBC. For the silicone oil layer in two-layer RBC, the hot plumes emitting over the liquid–liquid interface showed different shape and different velocity from cold plumes emitting from the top rigid plate. This implies that the velocity boundary condition strongly influences the flow structure in turbulent convection.

JFM classification

Convection: Convection in cavities Convection: Marangoni convection
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 978 , 10 January 2024 , A4
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

Ahlers, G., Bodenschatz, E. & He, X. 2014 Logarithmic temperature profiles of turbulent Rayleigh–Bénard convection in the classical and ultimate state for a Prandtl number of 0.8. J. Fluid Mech. 758, 436–467.CrossRefGoogle Scholar
Ahlers, G., Grossmann, S. & Lohse, D. 2009 Heat transfer and large scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81, 503–538.CrossRefGoogle Scholar
Bodenschatz, E., Pesch, W. & Ahlers, G. 2000 Recent developments in Rayleigh–Bénard convection. Annu. Rev. Fluid Mech. 32, 709–778.CrossRefGoogle Scholar
Busse, F.H. 1981 On the aspect ratios of two-layer mantle convection. Phys. Earth Planet. Inter. 24 (4), 320–324.CrossRefGoogle Scholar
Busse, F.H. & Petry, M. 2009 Homologous onset of double layer convection. Phys. Rev. E 80, 046316.CrossRefGoogle ScholarPubMed
Casper, J.M. 1977 Physical chemistry of surfaces (3rd ed.), Arthur W. Adamson, Wiley-Interscience, New York, 1976. J. Polym. Sci., Polym. Lett. Ed. 15 (10), 632–633.CrossRefGoogle Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.Google Scholar
Chillà, F. & Schumacher, J. 2012 New perspectives in turbulent Rayleigh–Bénard convection. Eur. Phys. J. E 35, 58.CrossRefGoogle ScholarPubMed
Clever, R.M. & Busse, F.H. 1974 Transition to time-dependent convection. J. Fluid Mech. 65, 625.CrossRefGoogle Scholar
Croquette, V. 1989 Convective pattern dynamics at low Prandtl number: part I. Contemp. Phys. 30 (2), 113–133.CrossRefGoogle Scholar
Daubert, T.E. & Danner, R.P. 1989 Physical and Thermodynamic Properties of Pure Chemicals. Hemisphere Publishing Corporation.Google Scholar
Degen, M.M., Colovas, P.W. & Andereck, C.D. 1998 Time-dependent patterns in the two-layer Rayleigh–Bénard system. Phys. Rev. E 57, 6647–6659.CrossRefGoogle Scholar
Diwakar, S.V., Tiwari, S., Das, S.K. & Sundararajan, T. 2014 Stability and resonant wave interactions of confined two-layer Rayleigh–Bénard systems. J. Fluid Mech. 754, 415–455.CrossRefGoogle Scholar
Hébert, F., Hufschmid, R., Scheel, J. & Ahlers, G. 2010 Onset of Rayleigh–Bénard convection in cylindrical containers. Phys. Rev. E 81, 046318.CrossRefGoogle ScholarPubMed
Huang, H.l., Xu, W., Wang, Y., Wang, X.-P., He, X.-Z. & Tong, P. 2022 Fluctuation-induced slip of thermal boundary layers at a stable liquid–liquid interface. J. Fluid Mech. 951, A10.CrossRefGoogle Scholar
Huang, S.-D. & Xia, K.-Q. 2016 Effects of geometric confinement in quasi-2D turbulent Rayleigh–Bénard convection. J. Fluid Mech. 794, 639–654.CrossRefGoogle Scholar
Johnson, D. & Narayanan, R. 1997 Geometric effects on convective coupling and interfacial structures in bilayer convection. Phys. Rev. E 56, 5462–5472.CrossRefGoogle Scholar
Johnson, D. & Narayanan, R. 1999 A tutorial on the Rayleigh–Marangoni–Bénard problem with multiple layers and side wall effects. Chaos 9 (1), 124–140.CrossRefGoogle ScholarPubMed
Juel, A., Burgess, J.M., McCormick, W.D, Swift, J.B. & Swinney, H.L. 2000 Surface tension-driven convection patterns in two liquid layers. Physica D 143 (1), 169–186.CrossRefGoogle Scholar
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
Liu, H.-R., Chong, K.L., Wang, Q., Ng, C.S., Verzicco, R. & Lohse, D. 2021 Two-layer thermally driven turbulence: mechanisms for interface breakup. J. Fluid Mech. 913, A9.CrossRefGoogle Scholar
Liu, H.-R., Chong, K.L., Yang, R., Verzicco, R. & Lohse, D. 2022 Heat transfer in turbulent Rayleigh–Bénard convection through two immiscible fluid layers. J. Fluid Mech. 938, A31.CrossRefGoogle Scholar
Lohse, D. & Xia, K.-Q. 2010 Small-scale properties of turbulent Rayleigh–Bénard convection. Annu. Rev. Fluid Mech. 42, 335–364.CrossRefGoogle Scholar
Lyubimov, D.V., Lyubimova, T.P., Alexander, J.I.D. & Lobov, N.I. 1998 On the Boussinesq approximation for fluid systems with deformable interfaces. Adv. Space Res. 22 (8), 1159–1168, proceedings of the G0.1 Symposium of COSPAR Scientific Commission G.CrossRefGoogle Scholar
Lyubimov, D.V., Lyubimova, T.P., Lobov, N.I. & Alexander, J.I.D. 2018 Rayleigh–Bénard–Marangoni convection in a weakly non-Boussinesq fluid layer with a deformable surface. Phys. Fluids 30 (2), 024103.CrossRefGoogle Scholar
Nataf, H.C., Moreno, S. & Cardin, Ph. 1988 What is responsible for thermal coupling in layered convection? J. Phys. (Paris) 49, 1707–1714.CrossRefGoogle Scholar
Neelin, J.D., Latif, M & Jin, F 1994 Dynamics of coupled ocean-atmosphere models: the tropical problem. Annu. Rev. Fluid Mech. 26 (1), 617–659.CrossRefGoogle Scholar
Olson, P., Silver, P.G. & Carlson, R.W. 1990 The large-scale structure of convection in the Earth's mantle. Nature 344 (6263), 209–215.CrossRefGoogle Scholar
Prakash, A. & Koster, J.N. 1994 Convection in multiple layers of immiscible liquids in a shallow cavity - I. Steady natural convection. Intl J. Multiphase Flow 20, 383–396.CrossRefGoogle Scholar
Rasenat, S., Busse, F.H. & Rehberg, I. 1989 A theoretical and experimental study of double-layer convection. J. Fluid Mech. 199, 519–540.CrossRefGoogle Scholar
Regnier, V.C., Dauby, P.C. & Lebon, G. 2000 Linear and nonlinear Rayleigh–Bénard–Marangoni instability with surface deformations. Phys. Fluids 12 (11), 2787–2799.CrossRefGoogle Scholar
Renardy, Y. & Renardy, M. 1985 Perturbation analysis of steady and oscillatory onset in a Bénard problem with two similar liquids. Phys. Fluids 28 (9), 2699–2708.CrossRefGoogle Scholar
Richter, F.M. & Johnson, C.E. 1974 Stability of a chemically layered mantle. J. Geophys. Res. 79 (11), 1635–1639.CrossRefGoogle Scholar
Scanlon, J.W. & Segel, L.A. 1967 Finite amplitude cellular convection induced by surface tension. J. Fluid Mech. 30 (1), 149–162.CrossRefGoogle Scholar
Schatz, M.F., VanHook, S.J., McCormick, W.D., Swift, J.B. & Swinney, H.L. 1995 Onset of surface-tension-driven Bénard convection. Phys. Rev. Lett. 75, 1938–1941.CrossRefGoogle ScholarPubMed
Schatz, M.F., VanHook, S.J., McCormick, W.D., Swift, J.B. & Swinney, H.L. 1999 Time-independent square patterns in surface-tension-driven Bénard convection. Phys. Fluids 11 (9), 2577–2582.CrossRefGoogle Scholar
Scheel, J.D., Kim, E. & White, K.R. 2012 Thermal and viscous boundary layers in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 711, 281–305.CrossRefGoogle Scholar
Shishkina, O., Horn, S., Wagner, S. & Ching, E.S.C. 2015 Thermal boundary layer equation for turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 114, 114302.CrossRefGoogle ScholarPubMed
Tackley, P.J. 2000 Mantle convection and plate tectonics: toward an integrated physical and chemical theory. Science 288 (5473), 2002–2007.CrossRefGoogle ScholarPubMed
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
Xia, K.-Q., Lam, S. & Zhou, S.Q. 2002 Heat-flux measurement in high-Prandtl-number turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 88, 064501.CrossRefGoogle ScholarPubMed
Xie, Y.-C. & Xia, K.-Q. 2013 Dynamics and flow coupling in two-layer turbulent thermal convection. J. Fluid Mech. 728, R1.CrossRefGoogle Scholar
Yoshida, M. & Hamano, Y. 2016 Numerical studies on the dynamics of two-layer Rayleigh–Bénard convection with an infinite Prandtl number and large viscosity contrasts. Phys. Fluids 28 (11), 116601.CrossRefGoogle Scholar
Supplementary material: File

Wang et al. supplementary movie 1

The shadowgraph result above the bottom plate for run E1
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Supplementary material: File

Wang et al. supplementary movie 2

The shadowgraph result below the top plate for run E1
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File 9.3 MB
Supplementary material: File

Wang et al. supplementary movie 3

The shadowgraph result above the bottom plate for run E2
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File 8.1 MB
Supplementary material: File

Wang et al. supplementary movie 4

The shadowgraph result below the top plate for run E2
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File 10 MB
Supplementary material: File

Wang et al. supplementary movie 5

The shadowgraph result above the bottom plate for run E3
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File 7.6 MB
Supplementary material: File

Wang et al. supplementary movie 6

The shadowgraph result below the top plate for run E3
Download Wang et al. supplementary movie 6(File)
File 5.8 MB