hide
Free keywords:
Rayleigh-Bénard convection; turbulent convection
Abstract:
Recent experiments by Vasil’ev et al. (2015a) using liquid sodium as working fluid inside an extremely slender Rayleigh-Bénard convection (RBC) cell of the diameter-to-height aspect ratio Γ = 1/20, which was inclined with respect to gravity, showed astonishing results: the heat transport through the system can be tenfold stronger for an inclination of β ≈ 65◦ , compared to classical RBC without inclination, β = 0◦. As liquid metals are opaque and the flow structure is hardly accessible by experimental means, the main objective of this work is to conduct high-fidelity direct numerical simulations (DNS), where the full temperature and velocity fields are available, and to understand the complex relationship between the flow structures and the heat transport. It is found that inside slender cylinders of Γ = 1/5 at Prandtl numbers 1 and 0.1, the heat transport is generally enhanced through inclination. This enhancement is related to a stronger single large-scale circulation (LSC) roll, which helps to create a hot and a cold plume column that eventually span the whole cylinder and impinge on the opposite boundary layer. Furthermore, for low-Prandtl-number fluids (Pr = 0.1) and slender cylinders (Γ = 1/5), the DNS reveal a global flow structure, that consists of up to four distinguishable rolls on top of each other. The heat transport is strongly determined by the number of rolls and decreases significantly as the number of rolls increases. Additionally, the elliptical instability is identified as the mechanism to break up the single-roll flow structure into multiple rolls. Finally, DNS for Γ = 1, extremely low Prandtl number (Pr = 0.0094) and Ra = 1.67 × 10^7 are directly compared to measurements in liquid sodium. The study demonstrates a quantitative agreement of the experimental and numerical results, in particular with respect to the global heat and momentum transport, temperature and velocity profiles, as well as the dynamics of the LSC. The DNS reveal that the twisting and sloshing of the LSC at small inclination angles periodically affects the instantaneous heat transport (with a variation of up to ±44 % of the mean heat transport). The twisted LSC is associated with a weak heat transport, while the sloshing mode that brings together the hot and cold streams of the LSC is associated with a strong heat transport.
