Heat transfer in cryogenic helium gas by turbulent Rayleigh–Bénard convection in a cylindrical cell of aspect ratio 1

Abstract

We present experimental results on the heat transfer efficiency of cryogenic turbulent Rayleigh-Bénard convection (RBC) in a cylindrical cell 0.3 m in both diameter and height which has improvements with respect to various corrections connected with finite thermal conductivity of sidewalls and plates. The heat transfer efficiency described by the Nusselt number Here H is the total convective heat flux density, g stands for the acceleration due to gravity, and ΔT is the temperature difference between the parallel top and the bottom plates separated by the vertical distance L. The properties of the working fluid are characterized by the thermal conductivity, λ, and by the combination α νκ ( ) , where α is the isobaric thermal expansion, ν is the kinematic viscosity, and κ denotes the thermal diffusivity. New J. Phys. 16 (2014) 053042 P Urban et al New J. Phys. 16 (2014) 053042 P Urban et al New J. Phys. 16 (2014) 053042 P Urban et al 4 New J. Phys. 16 (2014) 053042 P Urban et al 5 3 Note that our Brno cryogenic data recently published in two Letters [43, 44] are erroneously treated by the authors as aspect ratio Γ = 1 2 data, while they have all been obtained for the Γ = 1 cell. New J. Phys. 16 (2014) 053042 P Urban et al 6 Figure 1. Schematic drawing of the helium cryostat [55] containing the cylindrical aspect ratio Γ = 1 RBC cell. New J. Phys. 16 (2014) 053042 P Urban et al 7 W K 1 25 38 50 New J. Phys. 16 (2014) 053042 P Urban et al 9 Pr Pr Ra c c c (white filled red circles). The black line illustrates the slope ∝ Pr Ra 0.5 . New J. Phys. 16 (2014) 053042 P Urban et al New J. Phys. 16 (2014) 053042 P Urban et al 13 New J. Phys. 16 (2014) 053042 P Urban et alWe thank many colleagues for help and stimulating discussions, especially S Babuin, X He, M Jackson, R du Puits, P-E Roche, J Salort, and D Schmoranzer. This work was supported by the GAČR 203/12/P897, and the work of MLM and LS by GAČR P203/11/0442. Appendix. Tabulated experimental dataIn tables A1 and A2, values of Ra corr and Nu corr represent the corrected data, with corrections applied as discussed in the text. All remaining values of Rayleigh, Prandtl and Nusselt numbers are not corrected in any way.New J. Phys. 16 (2014) 053042 P Urban et al

Temperature profiles measurements in turbulent Rayleigh-Bénard convection by optical fibre system at the Barrel of II-menau

“…The shift of the side position profile to higher temperatures is expected as a result of upward convection flow near the side wall. The differences between the time-averaged temperatures T Pt (z) and the mean temperature T m in the region of turbulent core can be ascribed to the NOB effects [3,5]. The situation corresponds to the schematic illustration in Fig.…”

“…Breaking these conditions leads to Non-Oberbeck-Boussinesq (NOB) effects. e-mail: drahotsky@isibrno.cz The principal motivation of our long-term work is to shed light on the discrepancies among published results on heat transfer efficiency by RBC for Ra values above 10 11 [2][3][4] and influence of NOB effects on RBC, especially on a possible transition of RBC to the ultimate regime [5,6]. It was observed experimentally that NOB effects do lead to asymmetry of the thermal boundary layers adjacent to the EPJ Web of Conferences 180, 02020 (2018) https://doi.org/10.1051/epjconf/201818002020 EFM 2017 top and bottom plates (see schematic illustration in Fig.…”

Thermal radiation in Rayleigh-Bénard convection experiments

“…Let us emphasize that for high Ra RBC experiments utilizing cryogenic helium gas and performed at temperatures of a few kelvin [3,6,7,[24][25][26][27][28][29][30][31][32] the FF radiative heat transfer is completely negligible, thanks to its strong temperature dependence (∝ T 4 ). This is confirmed by two examples of corrections calculated for our own Γ = 1 cell 30 cm in diameter used in most Brno RBC experiments, .…”

“…In RBC experiments, extreme care must be taken to correctly evaluate Nu and Ra in order to account for * urban@isibrno.cz † skrbek@fzu.cz the influence of various factors [3], such as parasitic heat leaks, finite thermal conductivity and capacity of plates [4] and walls [5] of the RBC cell, non Oberbeck-Boussinesq effects, adiabatic gradient in the working fluids as well as uncertainties in their physical properties, especially in the vicinity of the equilibrium saturation curve [6] and the critical point [7] of the working fluid. This is usually done via corrections that follow various models of heat flow in a particular RBC cell.…”

Heat transfer in rough-wall turbulent thermal convection in the ultimate regime

“…He experimentally found such a transition around Ra ∼ 10 14 [15][16][17], Chavanne, Roche et al [18][19][20] observed it at lower Ra ∼ 10 11 − 10 12 and others still do not find such a transition at all [21][22][23]. To clarify this question, major numerical efforts are undertaken to solve the underlying Boussinesq equations in this large Ra regime.…”