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Sketch of the experimental facility, which consists of: (1) a cylindrical convection cell, (2) a hot heat exchanger chamber, (3) a cold heat exchanger chamber, (4) a heated copper plate, (5) a cooled copper plate and (6) inductor coils. The convection cell (1) and heat exchangers (2, 3) are filled with liquid sodium. D is the diameter and L the length of the cylindrical convection cell (1), β is the cell inclination angle, Θ the temperature drop between the hot and cold heat exchanger chambers, ∆ the resulting temperature drop between the inner surfaces of the heated and cooled plates of the convection cell (1).

Sketch of the experimental facility, which consists of: (1) a cylindrical convection cell, (2) a hot heat exchanger chamber, (3) a cold heat exchanger chamber, (4) a heated copper plate, (5) a cooled copper plate and (6) inductor coils. The convection cell (1) and heat exchangers (2, 3) are filled with liquid sodium. D is the diameter and L the length of the cylindrical convection cell (1), β is the cell inclination angle, Θ the temperature drop between the hot and cold heat exchanger chambers, ∆ the resulting temperature drop between the inner surfaces of the heated and cooled plates of the convection cell (1).

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Preprint
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Inclined turbulent thermal convection by large Rayleigh numbers in extremely small-Prandtl-number fluids is studied based on results of both, measurements and high-resolution numerical simulations. The Prandtl number $Pr\approx0.0093$ considered in the experiments and the Large-Eddy Simulations (LES) and $Pr=0.0094$ considered in the Direct Numeric...

Contexts in source publication

Context 1
... inner length of the convection cell is L = 216 mm and the inner diameter D = 212 mm. Both end faces of the convection cell are separated from the heat exchanger chambers by 1 mm thick copper discs, see a sketch in figure 1. The convection cell is filled with liquid sodium. ...
Context 2
... entire setup is placed on a swing frame, so that the convection cell can be tilted from a vertical position to a horizontal one. Inclination of the convection cell is then characterised by the angle β between the vertical and the cylinder axis, see figure 1. Obviously, the boundary conditions in a real liquid-metal experiment and the idealised boundary conditions that are considered in numerical simulations, are different. ...
Context 3
... massive copper plates would not provide a uniform temperature at the surfaces of the plates [43]. To avoid this undesirable inhomogeneity, in our experiment, instead of thick copper plates, we use rather thin ones, which are intensively washed from the outside by liquid sodium of prescribed temperature (see figure 1). The latter process takes place in two heat exchanger chambers, a hot one and a cold one, which are equipped with induction coils. ...
Context 4
... C, for which the Prandtl number equals Pr ≈ 0.0093. Each experiment is performed for a prescribed and known applied temperature difference Θ = T hot − T cold , where T hot and T cold are the timeaveraged temperatures of sodium in, respectively, the hot and cold heat exchanger chambers, which measured close to the copper plates (see figure 1). ...
Context 5
... is present in the RBC case (figures 8 a, b) and for the inclination angles β = 20 • (figure 8 c) and β = 36 • ( figure 8 d). figure 10 are taken. The phases θ 1 (t) and θ 5 (t) in (b) have a period of T θ = 7.6 t f , which is determined by the Fourier analysis. ...
Context 6
... when at the location B3 the fluid is extremely hot, the lowest temperature is obtained near D3, which is located only 90 • azimuthally below B3. Analogously, when the fluid is hot at the location H3, its lowest temperature is obtained near the location F3, which is 90 • below H3 (see also figure 10). These events happen at the times t/t f = 17 and t/t f = 21 in figure 9, respectively. ...
Context 7
... figure 10, the above described process, namely, the azimuthal movement of the hot and cold batches of fluid in a form of an oscillatory motion against each other, is illustrated with three-dimensional side views in two perpendicular directions. Additionally, the corresponding horizontal cross-sections of the instantaneous temperature fields at the mid-height of the cylinder are presented there. ...
Context 8
... figure 11a the standard deviations of the phases θ i in the circles i = 1, 3 and 5 are presented, while figure 11b shows the corresponding time-averaged strengths of the LSC, δ i t , as they are obtained in the liquid-sodium measurements and DNS. The measurements show that the standard deviations of the phases θ 1 (near the heated plate) and θ 5 (near the cooled plate) are relatively large for small inclination angles, while being small for large inclination angles. ...
Context 9
... figure 11a the standard deviations of the phases θ i in the circles i = 1, 3 and 5 are presented, while figure 11b shows the corresponding time-averaged strengths of the LSC, δ i t , as they are obtained in the liquid-sodium measurements and DNS. The measurements show that the standard deviations of the phases θ 1 (near the heated plate) and θ 5 (near the cooled plate) are relatively large for small inclination angles, while being small for large inclination angles. ...
Context 10
... standard deviations of θ 1 , θ 3 and θ 5 , obtained in the DNS, show generally a similar behaviour as those measured in the experiments, but due to only a few considered inclination angles in the DNS, it is impossible to resolve the sudden drop which is observed in the measurements. Also one should notice that the data in figure 11 are very sensitive to the time of statistical averaging, which is extremely short in the DNS compared to the experiment. ...
Context 11
... results for the time-averaged strengths of the LSC, δ i t , obtained in the measurements and DNS ( figure 11b) show good agreement. In the RBC case (β = 0 • ), the LSC strength is small and grows smoothly with the inclination angle β. ...
Context 12
... figure 12a, the time-averaged temperature profiles along the cylinder axis at the positions A to H are presented for the inclination angles β = 36 • (DNS) and β = 40 • (LES and experiments). Figure figure 12b shows analogous profiles for the inclination angles β = 72 • (DNS) and β = 70 • (LES and experiments). ...
Context 13
... figure 12a, the time-averaged temperature profiles along the cylinder axis at the positions A to H are presented for the inclination angles β = 36 • (DNS) and β = 40 • (LES and experiments). Figure figure 12b shows analogous profiles for the inclination angles β = 72 • (DNS) and β = 70 • (LES and experiments). In both figures, the profiles at the positions A and E are presented, as well as the average of the profiles at the positions B and H, the average of the profiles at the positions D and F and the average of the C-profile and G-profile. ...
Context 14
... figure 13, the time-averaged profiles along the cylinder axis of the velocity component u z are presented for the same inclinations angles, as in figure 12. Again, a very good agreement between the DNS, LES and experiments is obtained. The velocity estimates at the locations between the neighbouring thermocouples, which are derived from the correlation times obtained in the temperature measurements, are found to be in a very good agreement with the DNS and LES data. ...
Context 15
... figure 13, the time-averaged profiles along the cylinder axis of the velocity component u z are presented for the same inclinations angles, as in figure 12. Again, a very good agreement between the DNS, LES and experiments is obtained. ...
Context 16
... inner length of the convection cell is L = 216 mm and the inner diameter D = 212 mm. Both end faces of the convection cell are separated from the heat exchanger chambers by 1 mm thick copper discs, see a sketch in figure 1. The convection cell is filled with liquid sodium. ...
Context 17
... entire setup is placed on a swing frame, so that the convection cell can be tilted from a vertical position to a horizontal one. Inclination of the convection cell is then characterised by the angle β between the vertical and the cylinder axis, see figure 1. Obviously, the boundary conditions in a real liquid-metal experiment and the idealised boundary conditions that are considered in numerical simulations, are different. ...
Context 18
... massive copper plates would not provide a uniform temperature at the surfaces of the plates [43]. To avoid this undesirable inhomogeneity, in our experiment, instead of thick copper plates, we use rather thin ones, which are intensively washed from the outside by liquid sodium of prescribed temperature (see figure 1). The latter process takes place in two heat exchanger chambers, a hot one and a cold one, which are equipped with induction coils. ...
Context 19
... C, for which the Prandtl number equals Pr ≈ 0.0093. Each experiment is performed for a prescribed and known applied temperature difference Θ = T hot − T cold , where T hot and T cold are the timeaveraged temperatures of sodium in, respectively, the hot and cold heat exchanger chambers, which measured close to the copper plates (see figure 1). ...
Context 20
... is present in the RBC case (figures 8 a, b) and for the inclination angles β = 20 • (figure 8 c) and β = 36 • ( figure 8 d). figure 10 are taken. The phases θ 1 (t) and θ 5 (t) in (b) have a period of T θ = 7.6 t f , which is determined by the Fourier analysis. ...
Context 21
... when at the location B3 the fluid is extremely hot, the lowest temperature is obtained near D3, which is located only 90 • azimuthally below B3. Analogously, when the fluid is hot at the location H3, its lowest temperature is obtained near the location F3, which is 90 • below H3 (see also figure 10). These events happen at the times t/t f = 17 and t/t f = 21 in figure 9, respectively. ...
Context 22
... figure 10, the above described process, namely, the azimuthal movement of the hot and cold batches of fluid in a form of an oscillatory motion against each other, is illustrated with three-dimensional side views in two perpendicular directions. Additionally, the corresponding horizontal cross-sections of the instantaneous temperature fields at the mid-height of the cylinder are presented there. ...
Context 23
... figure 11a the standard deviations of the phases θ i in the circles i = 1, 3 and 5 are presented, while figure 11b shows the corresponding time-averaged strengths of the LSC, δ i t , as they are obtained in the liquid-sodium measurements and DNS. The measurements show that the standard deviations of the phases θ 1 (near the heated plate) and θ 5 (near the cooled plate) are relatively large for small inclination angles, while being small for large inclination angles. ...
Context 24
... figure 11a the standard deviations of the phases θ i in the circles i = 1, 3 and 5 are presented, while figure 11b shows the corresponding time-averaged strengths of the LSC, δ i t , as they are obtained in the liquid-sodium measurements and DNS. The measurements show that the standard deviations of the phases θ 1 (near the heated plate) and θ 5 (near the cooled plate) are relatively large for small inclination angles, while being small for large inclination angles. ...
Context 25
... standard deviations of θ 1 , θ 3 and θ 5 , obtained in the DNS, show generally a similar behaviour as those measured in the experiments, but due to only a few considered inclination angles in the DNS, it is impossible to resolve the sudden drop which is observed in the measurements. Also one should notice that the data in figure 11 are very sensitive to the time of statistical averaging, which is extremely short in the DNS compared to the experiment. ...
Context 26
... results for the time-averaged strengths of the LSC, δ i t , obtained in the measurements and DNS ( figure 11b) show good agreement. In the RBC case (β = 0 • ), the LSC strength is small and grows smoothly with the inclination angle β. ...
Context 27
... figure 12a, the time-averaged temperature profiles along the cylinder axis at the positions A to H are presented for the inclination angles β = 36 • (DNS) and β = 40 • (LES and experiments). Figure figure 12b shows analogous profiles for the inclination angles β = 72 • (DNS) and β = 70 • (LES and experiments). ...
Context 28
... figure 12a, the time-averaged temperature profiles along the cylinder axis at the positions A to H are presented for the inclination angles β = 36 • (DNS) and β = 40 • (LES and experiments). Figure figure 12b shows analogous profiles for the inclination angles β = 72 • (DNS) and β = 70 • (LES and experiments). In both figures, the profiles at the positions A and E are presented, as well as the average of the profiles at the positions B and H, the average of the profiles at the positions D and F and the average of the C-profile and G-profile. ...
Context 29
... figure 13, the time-averaged profiles along the cylinder axis of the velocity component u z are presented for the same inclinations angles, as in figure 12. Again, a very good agreement between the DNS, LES and experiments is obtained. The velocity estimates at the locations between the neighbouring thermocouples, which are derived from the correlation times obtained in the temperature measurements, are found to be in a very good agreement with the DNS and LES data. ...
Context 30
... figure 13, the time-averaged profiles along the cylinder axis of the velocity component u z are presented for the same inclinations angles, as in figure 12. Again, a very good agreement between the DNS, LES and experiments is obtained. ...

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