Aspect Ratio Dependence of Heat Transfer in a Cylindrical Rayleigh-Bénard Cell

Ahlers, Guenter; Bodenschatz, Eberhard; Hartmann, R.A.; He, Xiaozhou; Lohse, Detlef; Reiter, Philipp; Stevens, Richard J. A. M.; Verzicco, Roberto; Wedi, Marcel; Weiss, Stephan; Zhang, Xuan; Zwirner, Lukas; Shishkina, Olga

doi:10.1103/physrevlett.128.084501

Cited by 32 publications

(43 citation statements)

References 72 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Due to rotational symmetry, most experiments and many numerical investigations have been conducted in upright cylinders, hence the aspect ratio Γ = D/H between cylinder diameter D = 2R and height H is a parameter quantifying the geometrical constraints. The height H is a good length scale in RBC only for sufficiently large Γ because only then is Nu independent of Γ (Ahlers et al 2022;Zwirner et al 2021). Nevertheless, most experiments are conducted in cylinders of Γ close to 1 in order to maximize H, and in this way Ra.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Experimental evidence for the boundary zonal flow in rotating Rayleigh–Bénard convection

et al. 2022

Self Cite

View full text Add to dashboard Cite

We report on the presence of the boundary zonal flow in rotating Rayleigh–Bénard convection evidenced by two-dimensional particle image velocimetry. Experiments were conducted in a cylindrical cell of aspect ratio $\varGamma =D/H=1$ between its diameter ( $D$ ) and height ( $H$ ). As the working fluid, we used various mixtures of water and glycerol, leading to Prandtl numbers in the range $6.6 \lesssim \textit {Pr} \lesssim 76$ . The horizontal velocity components were measured at a horizontal cross-section at half height. The Rayleigh numbers were in the range $10^8 \leq \textit {Ra} \leq 3\times 10^9$ . The effect of rotation is quantified by the Ekman number, which was in the range $1.5\times 10^{-5}\leq \textit {Ek} \leq 1.2\times 10^{-3}$ in our experiment. With our results we show the first direct measurements of the boundary zonal flow (BZF) that develops near the sidewall and was discovered recently in numerical simulations as well as in sparse and localized temperature measurements. We analyse the thickness $\delta _0$ of the BZF as well as its maximal velocity as a function of Pr, Ra and Ek, and compare these results with previous results from direct numerical simulations.

show abstract

Section: Introductionmentioning

confidence: 99%

“…The height is a good length scale in RBC only for sufficiently large because only then is independent of (Ahlers et al. 2022; Zwirner et al. 2021).…”

Section: Introductionmentioning

confidence: 99%

Experimental evidence for the boundary zonal flow in rotating Rayleigh–Bénard convection

et al. 2022

Self Cite

View full text Add to dashboard Cite

show abstract

“…Finally, the system becomes too confined to initiate convection Ra c (Γ −1 ) > Ra (e.g. Chandrasekhar 1961;Catton & Edwards 1970;Chong & Xia 2016;Ahlers et al 2022). Similar to the rotation-controlled regime in rotating RBC, vertically coherent structures form within the plume-controlled regime in confined RBC (Chong et al 2015;Hartmann et al 2021).…”

Section: Introductionmentioning

confidence: 99%

Multiple heat transport maxima in confined-rotating Rayleigh–Bénard convection

et al. 2022

Self Cite

View full text Add to dashboard Cite

Moderate rotation and moderate horizontal confinement similarly enhance the heat transport in Rayleigh–Bénard convection (RBC). Here, we systematically investigate how these two types of flow stabilization together affect the heat transport. We conduct direct numerical simulations of confined-rotating RBC in a cylindrical set-up at Prandtl number $\textit {Pr}=4.38$ , and various Rayleigh numbers $2\times 10^{8}\leqslant {\textit {Ra}}\leqslant 7\times 10^{9}$ . Within the parameter space of rotation (given as inverse Rossby number $0\leqslant {\textit {Ro}}^{-1}\leqslant 40$ ) and confinement (given as height-to-diameter aspect ratio $2\leqslant \varGamma ^{-1}\leqslant 32$ ), we observe three heat transport maxima. At lower $ {\textit {Ra}}$ , the combination of rotation and confinement can achieve larger heat transport than either rotation or confinement individually, whereas at higher $ {\textit {Ra}}$ , confinement alone is most effective in enhancing the heat transport. Further, we identify two effects enhancing the heat transport: (i) the ratio of kinetic and thermal boundary layer thicknesses controlling the efficiency of Ekman pumping, and (ii) the formation of a stable domain-spanning flow for an efficient vertical transport of the heat through the bulk. Their interfering efficiencies generate the multiple heat transport maxima.

show abstract

“…For details about the aspect-ratio effects on the ultimate-state transition, please see the review by Ahlers et al. (2022) and references therein.…”

Section: Introductionmentioning

confidence: 99%

“…For a slender sample with an aspect ratio of 1/10, it is found in DNS that the classical scaling Nu ∼ Ra 1/3 can hold up to Ra = 10 15 (Iyer et al 2020). For details about the aspect-ratio effects on the ultimate-state transition, please see the review by Ahlers et al (2022) and references therein.…”

Section: Introductionmentioning

confidence: 99%

Heat transport and temperature boundary-layer profiles in closed turbulent Rayleigh–Bénard convection with slippery conducting surfaces

et al. 2022

Self Cite

View full text Add to dashboard Cite

We report direct numerical simulations (DNS) of the Nusselt number $Nu$ , the vertical profiles of mean temperature $\varTheta (z)$ and temperature variance $\varOmega (z)$ across the thermal boundary layer (BL) in closed turbulent Rayleigh–Bénard convection (RBC) with slippery conducting surfaces ( $z$ is the vertical distance from the bottom surface). The DNS study was conducted in three RBC samples: a three-dimensional cuboid with length $L = H$ and width $W = H/4$ ( $H$ is the sample height), and two-dimensional rectangles with aspect ratios $\varGamma \equiv L/H = 1$ and $10$ . The slip length $b$ for top and bottom plates varied from $0$ to $\infty$ . The Rayleigh numbers $Ra$ were in the range $10^{6} \leqslant Ra \leqslant 10^{10}$ and the Prandtl number $Pr$ was fixed at $4.3$ . As $b$ increases, the normalised $Nu/Nu_0$ ( $Nu_0$ is the global heat transport for $b = 0$ ) from the three samples for different $Ra$ and $\varGamma$ can be well described by the same function $Nu/Nu_0 = N_0 \tanh (b/\lambda _0) + 1$ , with $N_0 = 0.8 \pm 0.03$ . Here $\lambda _0 \equiv L/(2Nu_0)$ is the thermal boundary layer thickness for $b = 0$ . Considering the BL fluctuations for $Pr>1$ , one can derive solutions of temperature profiles $\varTheta (z)$ and $\varOmega (z)$ near the thermal BL for $b \geqslant 0$ . When $b=0$ , the solutions are equivalent to those reported by Shishkina et al. (Phys. Rev. Lett., vol. 114, 2015, 114302) and Wang et al. (Phys. Rev. Fluids, vol. 1, 2016, 082301(R)), respectively, for no-slip plates. For $b > 0$ , the derived solutions are in excellent agreement with our DNS data for slippery plates.

show abstract

Aspect Ratio Dependence of Heat Transfer in a Cylindrical Rayleigh-Bénard Cell

Cited by 32 publications

References 72 publications

Experimental evidence for the boundary zonal flow in rotating Rayleigh–Bénard convection

Experimental evidence for the boundary zonal flow in rotating Rayleigh–Bénard convection

Multiple heat transport maxima in confined-rotating Rayleigh–Bénard convection

Heat transport and temperature boundary-layer profiles in closed turbulent Rayleigh–Bénard convection with slippery conducting surfaces

Contact Info

Product

Resources

About