![Page 1: Victor Steinberg and Enrico Segre, Yuri Burnishev](https://reader036.vdocuments.us/reader036/viewer/2022062810/56815c7e550346895dca9404/html5/thumbnails/1.jpg)
Strong symmetrical non-Oberbeck-Boussinesq turbulent convection and a possible role of
compressibility
Victor Steinberg and Enrico Segre, Yuri Burnishev
Department of Physics of Complex Systems
![Page 2: Victor Steinberg and Enrico Segre, Yuri Burnishev](https://reader036.vdocuments.us/reader036/viewer/2022062810/56815c7e550346895dca9404/html5/thumbnails/2.jpg)
Goals of the experiment
• Can strong but symmetric variations of fluid properties with respect to a cell mid-plane alter a scaling of Nu versus Ra?
• Is Pr-dependence of Nu so different from OB-case and strong?
• What is a possible source of this strong Pr-dependence?
![Page 3: Victor Steinberg and Enrico Segre, Yuri Burnishev](https://reader036.vdocuments.us/reader036/viewer/2022062810/56815c7e550346895dca9404/html5/thumbnails/3.jpg)
Phase diagram of SF6 in the reduced variablesThree isobars are at P=38.2, 37.7, 37.6 bars and at Pr=36,122, 180, respectively (from top to bottom)
Region near CP of the average T in the cellExplored in the experiment
Thick lines on the isobars define the T and ρ distributions at Δused in the experiment
Phase diagram of SF6
![Page 4: Victor Steinberg and Enrico Segre, Yuri Burnishev](https://reader036.vdocuments.us/reader036/viewer/2022062810/56815c7e550346895dca9404/html5/thumbnails/4.jpg)
Schematic drawing of a convective cell and thermistor suspension for local T measurements in cylindrical cell and without the probe in square cell.
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Variations of a simplified non-OB criterion vs Ra for different PrInset: Fractional deviations of δβ and δCp vs Ra
![Page 6: Victor Steinberg and Enrico Segre, Yuri Burnishev](https://reader036.vdocuments.us/reader036/viewer/2022062810/56815c7e550346895dca9404/html5/thumbnails/6.jpg)
(a) The temperature distributions of the gas propertiesβ and Cp along the cell height, normalized by their values at the cell mid-plane.
(b) Upper plot: the dependence of λ normalized by its value at the cell mid-plane, for ethane and butane. Lower plot: the temperature distribution of λ for SF6 along the cell height, normalized by the values at thecell mid-plane as a function of T-Tm.
Variations of fluid properties
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The ratio of the temperature drops across the top and bottom halves of the cell, versus Ra, for four values of Pr.bt /
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Temperature profiles in turbulent convection of SF6 near CP: (a) Ra = Pr = 36,¢ = 45 mK. Inset: zoom in of the bottom thermal boundary layer. (b) Ra = Pr = 95,¢ = 25 mK. Inset: zoom in of the bottom thermal boundary layer.
12101.3 13109.1
Measurements of thermal boundary layer and its scaling with Ra and Pr
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L/2δ versus Ra for supercritical SF6 far away from CP at three values of Pr = 0.8; 1.5; 3.
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The same data in compensated presentation versus Ra for three values of Pr.
01.031.0)2/( RaL
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L/2δ versus Ra for SF6 near CP at four values of Pr.
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The same data in compensated presentation versus Ra for four values of Pr. Inset: Pr dependence of for four values of Pr.
01.032.0)2/( RaL 01.032.0)2/( RaL
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Presentation of the whole dataset on a single plot in the scaled variables: versus Ra.01.023.0Pr)2/( L
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Convergence of the iteration procedure to calculate the corrected value of Nu versus the number of iterations N.
Heat transfer measurements
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The corrected values of Nu versus Ra for supercritical SF6 far away from CP, for three values of Pr=0.8, 1.5, and 3.
![Page 16: Victor Steinberg and Enrico Segre, Yuri Burnishev](https://reader036.vdocuments.us/reader036/viewer/2022062810/56815c7e550346895dca9404/html5/thumbnails/16.jpg)
The same data shown in compensated presentation versus Ra, together withthe data of others, taken from literature. Symbols: ■- Niemela1 Γ= 1=2; Pr = 0:7; □ - Niemela2Γ= 1; Pr = 0:7 ; ●-Roche Γ = 1/2; Pr = 1.5 (from Ref.[1]); ○ - Chavanne Γ= 1/2; 0.7 < Pr < 2.0;▲- Ahlers1 0.43 <·Γ<0.98; Pr = 4.4; ∆- Ahlers2 Γ= 0.28; Pr = 4.4 (from Ref. [2]). Our data -- Pr = 0.8, open star - Pr = 1.5, - Pr = 3.0.
309.0NuRa
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The corrected values of Nu versus Ra for many values of Pr obtained in the cell with L = 9 cm and the stainless steel top and aluminum bottom plates only.
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Corrected values of Nu versus Ra for comparison among cells: stainless steel (SS) (top) and aluminum (bottom), versus copper (Cu) plates at Pr = 4 - upper, Pr = 36 - middle, and Pr = 126 - lower plots.
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Corrected values of Nu versus Ra for comparison between the cells with copper plates but different cell heights: L = 9 cm versus L = 4.5 cm at Pr = 4 - upper, Pr = 35 - middle, and Pr = 128 - lower plots.
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Compensated plot for the entire data set in the scaled variables versus Ra. Inset: minimization procedure to get the scaling exponent α for Pr dependence.
003.0302.0 NuRa
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Pr dependence of the scaled variable for the entire data with Tc =318.733Ktaken from NIST , and the same data with Tc = 318.717 K taken from [23]. We alsoadded on the same plot three data points for Pr = 0.8; 1.5; 3 obtained for SF6 far away from CP.
003.0302.0 NuRa
![Page 22: Victor Steinberg and Enrico Segre, Yuri Burnishev](https://reader036.vdocuments.us/reader036/viewer/2022062810/56815c7e550346895dca9404/html5/thumbnails/22.jpg)
The entire set of the data collapses onto one line in the scaled variables versus Ra with Tc = 318.733 K taken from NIST007.020.0Pr Nu
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Scaling for Nu(Ra,Pr)
007.020.0003.0302.0 Pr)01.0(18.0 RaNuFor Pr in the range 4 - 354
01.023.001.032.0 Pr)05.0(8.02
Ral
L
Scaling for thermal boundary layer L/2l(Ra,Pr)
For Pr in the range11 - 95
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Conclusions
• In spite of strong variations of the fluid properties across the cell height, symmetric non-OB turbulent convection exhibits the same scaling of Nu with Ra as the OB turbulent convection but a much stronger Pr dependence.
• The influence of the non-OB effect on the heat transport and found that, for the same Pr, an eight-fold larger non-OB effect does not alter either the value of Nu nor its scaling with respect to Ra.
• Strong symmetric non-OB effect by itself is not responsible for the strong Pr dependence of the heat transport near CP. The possible source of this Pr-dependence is the strongly enhanced isothermal compressibility in the vicinity of CP, which can affect the dynamics of plumes and so the heat transport close to the CP