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

Zhu, Xiangwei; Zhou, Quan

doi:10.1007/s10409-021-01104-z

“…Recent RBC experiments by Zhu & Zhou (2021) for 1 Γ 4, 4.8 × 10 7 Ra 4.5 × 10 10 and 4.3 Pr 5.3 found that Re ∼ Γ −0.52 , the exponent of Γ being close to that in (B1). The prefactor in (B1) is also very close to the prefactor 1.1 in the expression for Re based on the oscillation frequency of the LSF, obtained by Lam et al (2002).…”

Section: Discussionsupporting

confidence: 55%

“…Since it is known that , as shown in the inset in figure 11 we plot the variation of with and find the value that collapses the normalised onto a horizontal line. Then the Reynolds number based on the LSF velocities () and scales as Recent RBC experiments by Zhu & Zhou (2021) for , and found that , the exponent of being close to that in (B1). The prefactor in (B1) is also very close to the prefactor 1.1 in the expression for based on the oscillation frequency of the LSF, obtained by Lam et al.…”

Section: Figure 11mentioning

confidence: 76%

Effect of shear on local boundary layers in turbulent convection

Shevkar

¹

,

Mohanan

²

,

Puthenveettil

³

2023

J. Fluid Mech.

2

0

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In Rayleigh Bénard convection, for a range of Prandtl numbers $4.69 \leqslant Pr \leqslant 5.88$ and Rayleigh numbers $5.52\times 10^5 \leqslant Ra \leqslant 1.21\times 10^9$ , we study the effect of shear by the inherent large-scale flow (LSF) on the local boundary layers on the hot plate. The velocity distribution in a horizontal plane within the boundary layers at each $Ra$ , at any instant, is (A) unimodal with a peak at approximately the natural convection boundary layer velocities $V_{bl}$ ; (B) bimodal with the first peak between $V_{bl}$ and $V_{L}$ , the shear velocities created by the LSF close to the plate; or (C) unimodal with the peak at approximately $V_{L}$ . Type A distributions occur more at lower $Ra$ , while type C occur more at higher $Ra$ , with type B occurring more at intermediate $Ra$ . We show that the second peak of the bimodal type B distributions, and the peak of the unimodal type C distributions, scale as $V_{L}$ scales with $Ra$ . We then show that the areas of such regions that have velocities of the order of $V_{L}$ increase exponentially with increase in $Ra$ and then saturate. The velocities in the remaining regions, which contribute to the first peak of the bimodal type B distributions and the single peak of type A distributions, are also affected by the shear. We show that the Reynolds number based on these velocities scale as $Re_{bs}$ , the Reynolds number based on the boundary layer velocities forced externally by the shear due to the LSF, which we obtained as a perturbation solution of the scaling relations derived from integral boundary layer equations. For $Pr=1$ and aspect ratio $\varGamma =1$ , $Re_{bs} \sim Ra^{0.375}$ for small shear, similar to the observed flux scaling in a possible ultimate regime. The velocity at the edge of the natural convection boundary layers was found to increase with $Ra$ as $Ra^{0.35}$ ; since $V_{bl}\sim Ra^{1/3}$ , this suggests a possible shear domination of the boundary layers at high $Ra$ . The effect of shear, however, decreases with increase in $Pr$ and with increase in $\varGamma$ , and becomes negligible for $Pr\geqslant 100$ at $\varGamma =1$ or for $\varGamma \geqslant 20$ at $Pr=1$ , causing $Re_{bs}\sim Ra_w^{1/3}$ .

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“…In recent years, the planar particle image velocimetry (PIV) technique has been applied to study the viscous BL properties of the RBC system in the mean large-scale circulation (LSC) plane (Xia, Sun & Zhou 2003;Sun, Xia & Tong 2005;Sun, Cheung & Xia 2008;Wei & Xia 2013). In a cylindrical convection cell, the LSC presents complicated flow dynamics including meandering (Cioni, Ciliberto & Sommeria 1997;Funfschilling & Ahlers 2004;Ahlers, Brown & Nikolaenko 2006;Xi, Zhou & Xia 2006;Xi & Xia 2008;Zhu & Zhou 2021), torsional (Funfschilling, Brown & Ahlers 2008) and sloshing (Xi et al 2009;Zhou et al 2009;Vogt et al 2018). For such a three-dimensional (3-D) configuration, given the potential effects of the complex motions of the LSC, the velocity components in the mean LSC plane alone may not be sufficient to fully characterise the instantaneous BL properties.…”

Section: Introductionmentioning

confidence: 99%

“…2010; Wei & Xia 2013). In a cylindrical convection cell, the LSC presents complicated flow dynamics including meandering (Cioni, Ciliberto & Sommeria 1997; Funfschilling & Ahlers 2004; Ahlers, Brown & Nikolaenko 2006; Xi, Zhou & Xia 2006; Xi & Xia 2008; Zhu & Zhou 2021), torsional (Funfschilling, Brown & Ahlers 2008) and sloshing (Xi et al. 2009; Zhou et al.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional properties of the viscous boundary layer in turbulent Rayleigh–Bénard convection

Xu

¹

,

Zhang

²

,

Xia

³

2022

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We report an experimental study of the viscous boundary layer (BL) properties of turbulent Rayleigh–Bénard convection in a cylindrical cell. The velocity profile with all three components was measured from the centre of the bottom plate by an integrated home-made particle image velocimetry system. The Rayleigh number $Ra$ varied in the range $1.82 \times 10^8 \le Ra \le 5.26 \times 10^9$ and the Prandtl number $Pr$ was fixed at $Pr = 4.34$ . The probability density function of the wall-shear stress indicates that using the velocity component in the mean large-scale circulation (LSC) plane alone may not be sufficient to characterise the viscous BL. Based on a dynamic wall-shear frame, we propose a method to reconstruct the measured full velocity profile which eliminates the effects of complex dynamics of the LSC. Various BL properties including the eddy viscosity are then obtained and analysed. It is found that, in the dynamic wall-shear frame, the eddy viscosity profiles along the centre line of the convection cell at different $Ra$ all collapse on a single master curve described by $\nu _t^d / \nu = 0.81 (z / \delta _u^d) ^{3.10 \pm 0.05}$ . The Rayleigh number dependencies of several BL quantities are also determined in the dynamic frame, including the BL thickness $\delta _u^d$ ( ${\sim } Ra^{-0.21}$ ), the Reynolds number $Re^d$ ( ${\sim }Ra^{-0.46}$ ) and the shear Reynolds number $Re_s^d$ ( ${\sim } Ra^{0.24}$ ). Within the experimental uncertainty, these scaling exponents are the same as those obtained in the static laboratory frame. Finally, with the measured full velocity profile, we obtain the energy dissipation rate at the centre of the bottom plate $\varepsilon _{w}$ , which is found to follow $\langle \varepsilon _{w} \rangle _t \sim Ra^{1.25}$ .

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“…However, most of the existing experiments, numerical simulations and theoretical analyses are carried out in 3-D domains with a finite aspect ratio Γ , which is defined as the ratio between the horizontal scale and vertical scale of the convection domain (with a typical value of about one). Extending the convection domain to large aspect ratio (Γ > 1) significantly changes the flow structure but has only a minor effect on heat transport (Funfschilling et al 2005;Pandey, Scheel & Schumacher 2018;Stevens et al 2018;Zhu & Zhou 2021).…”

Section: Introductionmentioning

confidence: 99%

Heat transfer in a quasi-one-dimensional Rayleigh–Bénard convection cell

Zhang,

Xia

2023

J. Fluid Mech.

5

0

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We report an experimental and numerical study on Rayleigh–Bénard convection in a slender rectangular geometry with the aspect ratio $\varGamma$ varying from 0.05 to 0.3 and a Rayleigh number range of $10^5\leqslant Ra\leqslant 3\times 10^9$ . The Prandtl number is fixed at $Pr=4.38$ . It is found that the onset of convection is postponed when the convection domain approaches the quasi-one-dimensional limit. The onset Rayleigh number shows a $Ra_c=328\varGamma ^{-4.18}$ scaling for the experiment and a $Ra_c=810\varGamma ^{-3.95}$ scaling for the simulation, both consistent with a theoretical prediction of $Ra_c\sim \varGamma ^{-4}$ . Moreover, the effective Nusselt–Rayleigh scaling exponent $\beta =\partial (\log Nu)/\partial (\log Ra)$ near the onset of convection also shows a rapid increase with decreasing $\varGamma$ . Power-law fits to the experimental and numerical data yield $\beta =0.290\varGamma ^{-0.90}$ and $\beta =0.564\varGamma ^{-0.92}$ , respectively. Near onset, the flow shows a stretched cell structure. In this regime, the velocity and temperature variations in a horizontal cross-section are found to be almost invariant with height in the core region of a slender domain. As the Rayleigh number increases, the system evolves from the viscous dominant regime to a plume-controlled one, a feature of which is enhancement in the heat transport efficiency. Upon further increase of $Ra$ , the flow comes back to the classical boundary-layer-controlled regime, in which the quasi-one-dimensional geometry has no apparent effect on the global heat transfer.

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

Cited by 21 publications

References 61 publications

Effect of shear on local boundary layers in turbulent convection

Effect of shear on local boundary layers in turbulent convection

Three-dimensional properties of the viscous boundary layer in turbulent Rayleigh–Bénard convection

Heat transfer in a quasi-one-dimensional Rayleigh–Bénard convection cell

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