Experimental investigation on the influence of rotation on thermal convection

by Marcel Frederik Wedi
Doctoral thesis
Date of Examination:2022-02-14
Date of issue:2022-10-18
Advisor:Dr. Stephan Weiss
Referee:Prof. Dr. Stefan Dreizler
Referee:PD Dr. Olga Shishkina
Persistent Address: http://dx.doi.org/10.53846/goediss-9502

 

 

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Abstract

English

We report on experimental measurements of rotating Rayleigh-Bénard convection to study the influence of the Coriolis force on the heat transport and the flow structure. Two experimental setups were used. The first is a 2.24 m tall cylindrical cell with an aspect ratio between its diameter (D) and its height H, Γ = D/H = 0.5. It is filled with either nitrogen or pressurized gaseous sulfur hexafluoride to achieve Rayleigh numbers 7.5 × 10^9 ≤ Ra ≤ 7.5 × 10^14, while the Prandtl number Pr remained fairly constant at 0.72 ≤ Pr ≤ 0.96. We performed heat flux measurements (i.e. the Nusselt number Nu) and obtain scaling relations as function of Ra and the rotation rate in form of the inverse Rossby number 1/Ro. We find Nu_0 ∝ Ra^0.315 for the non-rotating and a collapse of Nu/Nu_0(1/Ro) for the rotating case. For sufficiently large 1/Ro, we find Nu/Nu_0 ∝ 1/Ro^-0.42. Three regimes were determined, with increasing influence of rotation. Their transitional values 1/Ro^*_1 = 0.8 and 1/Ro^*_1 = 4 could be found in numerous quantities throughout the analysis, where we relied on point-wise temperature measurements distributed throughout the cell. 1/Ro^*_1 was found as the onset of a travelling temperature wave around the circumference close to the sidewall, referred to as boundary zonal flow (BZF). This structure with wave number k_BZF = 1 drifts in counter-rotating direction with a frequency ω/Ω ∝ 1/Ro^-3/4. In the smaller, optically accessible setup, we performed particle image velocimetry (PIV). It consists of a H = 0.196 m, Γ = 1, transparent setup made out of acrylic glass. With mixtures of water and glycerol at different mass concentrations we achieved 6.55 ≤ Pr ≤ 76 at various combinations of Ra and the dimensionless rotation rate (Ekman number - Ek ). We focussed on an horizontal layer at half-height, where we investigated the BZF in the velocity field. We found a thickness scaling relation δ_0 ∝ Ek^1/2, while the distance from the sidewall to the maximum azimuthal velocity was found to scale as δ^max_φ ∝ Ek^3/2Ra^1/2Pr^-0.8.
Keywords: rotating flows; convection; Rayleigh-Bénard; rotating turbulence
 
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