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Flow structures of turbulent Rayleigh–Bénard convection in annular cells with aspect ratio one and larger

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Abstract

We present an experimental study of flow structures in turbulent Rayleigh–Bénard convection in annular cells of aspect ratios \(\varGamma =1\), 2 and 4, and radius ratio \(\backsimeq \) 0.5. The convecting fluid is water with Prandtl number \(Pr= 4.3\) and 5.3. Rayleigh number Ra ranges \(4.8 \times 10^{7} \le Ra \le 4.5 \times 10^{10}\). The dipole state (two-roll flow structure) for \(\varGamma = 1\) and the quadrupole state (four-roll flow structure) for \(\varGamma = 2\) and 4 are found by multi-temperature-probe measurement. Nusselt number Nu is described by a power-law scaling \(Nu=0.11Ra^{0.31}\), which is insensitive to the change of flow structures. However, the Reynolds number Re is influenced by increasing aspect ratios, where Re is found to scale with Ra and \(\varGamma \) as \(Re\sim Ra^{0.46}\varGamma ^{-0.52}\). The normalized amplitudes of two flow structures as a function of Ra exist difference. Based on relative weights of the first four modes using the Fourier analysis, we find that the first mode dominates in \(\varGamma =1\) cell, but the second mode contains the most energy in \(\varGamma =2\) and 4 cells. With increasing \(\varGamma \), the flow structures exhibit different characteristics.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grants 11988102, 11825204, 92052201, 91852202), the Program of Shanghai Academic Research Leader (Grant 19XD1421400), and Science and Technology Innovation Plan Of Shanghai Science and Technology Commission (STCSM) (Project 19JC1412802).

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  1. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai, 200072, China

    Xu Zhu & Quan Zhou

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Correspondence to Quan Zhou.

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Zhu, X., Zhou, Q. Flow structures of turbulent Rayleigh–Bénard convection in annular cells with aspect ratio one and larger. Acta Mech. Sin. 37, 1291–1298 (2021). https://doi.org/10.1007/s10409-021-01104-z

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