Heat transport by turbulent Rayleigh–Bénard convection in cylindrical cells with aspect ratio one and less

By A. Nikolaenko, Eric Brown, D. Funfschilling, G. Ahlers. Journal of Fluid Mechanics, 2004

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We present high-precision measurements of the Nusselt number $\cal N$ as a function of the Rayleigh number $R$ for cylindrical samples of water (Prandtl number $\sigma \,{=}\, 4.4$) with a diameter $D$ of 49.7 cm and heights $L \,{=}\, 116.3, 74.6$, and 50.6 cm, as well as for $D \,{=}\, 24.8$ cm and $L \,{=}\, 90.2$ cm. For each aspect ratio $\Gamma \,{\equiv}\, D/L \,{=}\, 0.28, 0.43, 0.67$, and 0.98 the data cover a range of a little over a decade of $R$. The maximum $R \,{\simeq}\, 10^{12}$ and Nusselt number ${\cal N} \,{\simeq}\, 600$ were reached for $\Gamma \,{=}\, 0.43$ and $D \,{=}\, 49.7$. The data were corrected for the influence of the finite conductivity of the top and bottom plates on the heat transport in the fluid to obtain estimates of $\cal N_{\infty}$ for plates with infinite conductivity. The results for ${\cal N}_{\infty}$ and $\Gamma \,{\geq}\, 0.43$ are nearly independent of $\Gamma$. For $\Gamma \,{=}\, 0.275$ ${\cal N}_{\infty}$ falls about 2.5% below the other data. For $R \,{\lesssim}\,10^{11}$, the effective exponent $\gamma_{\hbox{\scriptsize\it eff}}$ of ${\cal N}_{\infty} \,{=}\, N_0 R^{\gamma_{\hbox{\scriptsize\it eff}}}$ is about 0.32, larger than those of the Grossmann–Lohse model with its current parameters by about 0.01. For the largest Rayleigh numbers covered for $\Gamma \,{=}\, $0.98, 0.67, and 0.43, $\gamma_{\hbox{\scriptsize\it eff}}$ saturates at the asymptotic value $\gamma \,{=}\, 1/3$ of the Grossmann–Lohse model. The data do not reveal any crossover to a Kraichnan regime with $\gamma_{\hbox{\scriptsize\it eff}} \,{>}\, 1/3$.

Subfields: Computational Mechanics, Environmental Engineering, Global and Planetary Change

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Citations in the corpus

Aspect ratio dependence of heat transfer and large-scale flow in turbulent convection (2010, unknown): “[18] Funfschilling, D.”
Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection (2008, methodology): “e (2008). E. The aspect-ratio dependence of the Nusselt number Several experiments (Ahlers and Xu (2001), Fleischer and Goldstein (2002), Funfschilling et al. (2005), Niemela and Sreenivasan (2006a), Nikolaenko et al. (2005), Sun et al. (2005a), Wu and Libchaber (1992), Xu et al. (2000)) have probed”
Non-Oberbeck–Boussinesq effects in strongly turbulent Rayleigh–Bénard convection (2005, background): “…the large and medium cells were corrected for the effect of the finite conductivity of the copper top and bottom plates (Chaumat, Castaing & Chillà 2002; Verzicco 2004; Brown et al. 2005; Nikolaenko et al. 2005) on the heat transport in the fluid (no correction was needed for the small cell case).”
Radial boundary layer structure and Nusselt number in Rayleigh–Bénard convection (2009, background): “Experimental results are controversial (Heslot, Castaing & Libchaber 1987; Chavanne et al. 1997; Niemela et al. 2000, 2001; Roche et al. 2002; Niemela & Sreenivasan 2003; Funfschilling et al. 2005; Nikolaenko et al. 2005; Funfschilling, Bodenschatz & Ahlers 2009), so that the asymptotic behavior of ”
Heat transport by turbulent Rayleigh–Bénard convection in cylindrical samples with aspect ratio one and larger (2005, background): “For 3.62 <σ < 5.42, Γ = 0.67, and R 1011 we have N ∝ σ −0.044 (Nikolaenko et al. 2005).”