Thermal convection at high Rayleigh numbers in compressed gases.

Abstract

This study focuses on the heat transfer relationship for turbulent convection in a layer of fluid heated from below. Results are presented in the form of the Nusselt number as a function of the Rayleigh number, for Rayleigh numbers ranging from 2 × 10 9 to 3.1 × 10 12 . High Rayleigh numbers are attained by pressurizing nitrogen, argon and krypton to pressures of up to 80 bar. The experimental apparatus is designed with close attention to the effects of conduction through the insulating sidewalls at low Rayleigh number, and to the effects of variable properties that may affect the Boussinesq approximation at high Rayleigh numbers.

The results show a relationship between the Nusselt and Rayleigh numbers that is close to a power-law with an exponent of 1/3 for the Rayleigh number. There is no visible transition, or incipient transition to a power-law regime with an exponent of 1/2, as has been theoretically predicted by some investigators. It is argued that various other values of the exponent that are found in the literature are either due to conduction effects at low Rayleigh numbers (leading to a lower exponent) or variable properties (leading to a higher exponent) at high Rayleigh numbers. However, the precise mechanism of energy transport that leads to an exponent of 1/3 remains unclear. While a large-scale recirculation has been observed in experimental apparatuses, there remains uncertainty as to the manner in which this flow affects the stability of the thermal boundary layer.

Local temperature measurements were taken using a 76μ m thermocouple probe. The temperature measurements are at significant variance from the expected temperature distribution in the thermal boundary layer. Conduction effects in the probe are shown to be significant. Temperature statistics measured with the probe show some averaging over high frequencies.