Cryogenic Rayleigh–Bénard convection (RBC) at very high Rayleigh numbers (Ra) serves as a key system for understanding buoyancy-driven industrial and large-scale natural flows and for testing theories of turbulent convective heat transport. The central measured response is the Nusselt number (Nu), which quantifies the convective heat transfer efficiency, i.e., the enhancement of heat transport relative to the purely conductive state. Cryogenic helium experiments allow one to reach extremely high Ra under well-controlled laboratory conditions; however, interpretation of the resulting Nu(Ra) scalings remains sensitive to non-Oberbeck–Boussinesq (NOB) effects, experimental uncertainties, and corrections that must be applied to raw data. We present an analysis of experimental uncertainties and data correction procedures applicable to cryogenic RBC experiments, specifically to those performed in the present, newly built cylindrical RBC cell in Brno. For a representative set of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$^{4}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>4</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>He working points in the p–T diagram, we examine how the evaluated Nu(Ra) dependence is affected by measurement uncertainties, corrections for the adiabatic temperature gradient, parasitic heat leaks, finite thermal conductivity of the plates and sidewalls, and by the choice of thermophysical property database used to determine the relevant properties of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$^{4}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>4</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>He at the selected working points. The analysis shows that uncertainties and offset corrections associated with the temperature difference across the cell have the strongest local impact on the evaluated Nu(Ra) dependence, while sidewall corrections and the choice of thermophysical property database mainly affect the global scaling behavior. Our study highlights the necessity of rigorous uncertainty and correction analysis when assessing experimental evidence for a transition to the ultimate regime of RBC, since apparent changes in scaling may also arise from NOB effects and experimental imperfections.

Experimental Challenges in Determining Heat Transfer Efficiency Scaling in Highly Turbulent Cryogenic Rayleigh–Bénard Convection

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发表日期：

2026年7月21日

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P. Urban,
V. Musilová,
P. Hanzelka,
T. Králík,
M. Macek,
L. Skrbek

摘要

Cryogenic Rayleigh–Bénard convection (RBC) at very high Rayleigh numbers (Ra) serves as a key system for understanding buoyancy-driven industrial and large-scale natural flows and for testing theories of turbulent convective heat transport. The central measured response is the Nusselt number (Nu), which quantifies the convective heat transfer efficiency, i.e., the enhancement of heat transport relative to the purely conductive state. Cryogenic helium experiments allow one to reach extremely high Ra under well-controlled laboratory conditions; however, interpretation of the resulting Nu(Ra) scalings remains sensitive to non-Oberbeck–Boussinesq (NOB) effects, experimental uncertainties, and corrections that must be applied to raw data. We present an analysis of experimental uncertainties and data correction procedures applicable to cryogenic RBC experiments, specifically to those performed in the present, newly built cylindrical RBC cell in Brno. For a representative set of $^{4}$ $^{4}$ He working points in the p–T diagram, we examine how the evaluated Nu(Ra) dependence is affected by measurement uncertainties, corrections for the adiabatic temperature gradient, parasitic heat leaks, finite thermal conductivity of the plates and sidewalls, and by the choice of thermophysical property database used to determine the relevant properties of $^{4}$ $^{4}$ He at the selected working points. The analysis shows that uncertainties and offset corrections associated with the temperature difference across the cell have the strongest local impact on the evaluated Nu(Ra) dependence, while sidewall corrections and the choice of thermophysical property database mainly affect the global scaling behavior. Our study highlights the necessity of rigorous uncertainty and correction analysis when assessing experimental evidence for a transition to the ultimate regime of RBC, since apparent changes in scaling may also arise from NOB effects and experimental imperfections.