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# Thermal BL thickness δ θ = H/(2 Nu) (open symbols, black crosses) and viscous BL thickness δ u based on slope criterion (filled symbols, blue crosses, red pluses) vs the Rayleigh number. The dashed and dash-dotted lines show the theoretical scaling law δ ∼ Ra −0.25 for both BLs. The insets show the compensated data. Experimental data for Γ = 3 (pluses) and Γ = 5 the (crosses). DNS data (circles, squares, triangles) as in figure 4.

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Article
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Using complementary experiments and direct numerical simulations, we study turbulent thermal convection of a liquid metal (Prandtl number $\textit {Pr}\approx 0.03$ ) in a box-shaped container, where two opposite square sidewalls are heated/cooled. The global response characteristics like the Nusselt number ${\textit {Nu}}$ and the Reynolds number...

## Contexts in source publication

Context 1
... denote quantities that are based on L or H with the subscript L or H, respectively, and they convert as A comparison of the length scales for the Nusselt number is shown in figure 4(a,b) and the data collapse for the length scale L, while they do not do so for length scale H. In general, one can see this collapse for the Reynolds numbers in figure 5(a,b) and the BL thickness in figure 6. This means, that the relevant length scale in VC is the plate size, L, rather than the plate distance, H, for global quantities like Nu and Re. ...
Context 2
... thickness of the thermal and viscous BLs can be obtained from Prandtl 1905), respectively. In figure 6 we show the respective BLs, and, while the thermal BL thickness is obtained straightforwardly, the viscous BL needs an estimation of the parameter a which is widely accepted in case of RBC to be ≈0.482 for a cylindrical cell of unit aspect ratio ( Grossmann & Lohse 2002), but in general dependent on Γ . From the DNS data, using Re L , we can estimate this parameter for Γ = 5 to be a ≈ 0.38 and then apply this value of a to the experimental data for both aspect ratios Γ = 3 and 5. Thus, we calculate the average ratio of Re L −1/2 and δ u , which is obtained by (2.8). ...
Context 3
... the DNS data, using Re L , we can estimate this parameter for Γ = 5 to be a ≈ 0.38 and then apply this value of a to the experimental data for both aspect ratios Γ = 3 and 5. Thus, we calculate the average ratio of Re L −1/2 and δ u , which is obtained by (2.8). The estimate of a works well for both aspect ratios Γ = 3 and 5 used by the experiments ( figure 6). This gives an estimate that the viscous BL at Ra L ≈ 10 7 has a thickness of approximately 1 mm, while the distance between the plates is H = 40 mm (Γ = 5). ...

## Citations

... The work devoted to the study of natural convection in liquid gallium for the crystal growth applications can be distinguished as one of the early ones [20]. In some studies on inclined convection, the position of a cylindrical container at the extreme horizontal point will also correspond to the case of vertical convection [8,9] The most complete study from the fluid mechanics point of view on vertical convection of liquid metal in a box-shaped container was published in [21]. ...
... Lx/H = 8; Ly/H = 4 -∼ 10 2 − 10 4 [19] 10 −2 < P r < 30 10 5 < Ra < 10 10 L/D= 1 ∼ 10 0 − 10 2 < 1.8 [26] 10 −3 < P r < 10 10 3 < Gr < 5 · 10 7 L/H = 10/6 -- [9] P r ∼ 0.009 Ra > 10 7 L/D = 1 ∼ 6 − 7 ∼ 10 4 [5] P r = 10 10 7 < Ra < 10 14 H/L = 1 17 − 1908 ∼ 10 1 − 10 4 [21] P r = 0.03 5 · 10 3 < Ra < 10 8 1, 2, 3 and 5. ∼ 1 − 20 ∼ 10 2 − 2 · 10 4 ...
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Heat and momentum transfer of low-Prandtl-number fluid ($Pr=0.029$) in a closed rectangular cavity ($100\times60\times10$ mm$^3$) heated at one side and cooled at the opposite side are analyzed. The electromagnetic forces into the liquid metal are generated by the travelling magnetic field inductor and directed towards buoyancy forces. Large eddy simulations are performed with the Grashof number $Gr$ from $1.9\cdot 10^5$ to $7.6\cdot 10^7$ and the electromagnetic forcing parameter $F$ from $2.6\cdot 10^4$ to $2.6\cdot10^6$. An experimental validation of the simulation results of vertical convection and electromagnetically driven flow using GaInSn alloy has been performed. Three types of flow patterns are obtained for different interaction parameters $N = F / Gr$: counterclockwise flow, clockwise flow, and coexistence of two vortices. Analysis of the Reynolds number shows that the transition zone from natural convection to electromagnetic stirring lies in the range $0.02<F/Gr<0.07$ and two braking modes are found. The transition point between the convective heat transfer regimes is found for $F / Gr$ around 1. The analysis of isotherms deformation showed that in such convective systems it is possible to achieve minimum deviation of the isotherm shape from a straight line in the range of $0.05 <F/Gr <0.2$.
Article
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.