Rotating Rayleigh-Bénard convection in cylindrical cells with aspect ratios one and two

Abstract

Turbulent thermal convection occurs in numerous situations, for example in the Earth's atmosphere, in the Earth's liquid outer core and in turbo machinery. These systems can be represented by the rotating Rayleigh-Bénard problem, which is investigated experimentally with a newly designed cylindrical convection cell. The aspect ratio ? of the cylindrical volume is defined as the ratio of its diameter and its height. Of interest in this study are the enhancement of heat transport between the upper and lower boundary due to rotation and the presence of a large-scale circulation in the contained fluid. For this purpose, a new experimental setup is constructed, with an inner diameter of 250 mm and two different sidewall heights, resulting in aspect ratios ?=1 and ?=2. The lower boundary is a copper plate heated electrically, while the upper boundary is a copper plate cooled with water. Heat loss at the sidewalls is minimized with active and passive isolation. The profile of the large-scale circulation is measured using 16 or 24 temperature sensors in the sidewall and the heat transported is measured from the input power of the lower plate. The experiments with both aspect ratios are performed with water at a fixed Prandtl number of 4.38, at three different Rayleigh numbers of 2.99·108, 5.88·108 and 1.16·109. Non-rotating measurements of heat transport for ?=1 agree very well with measurements found in literature. The heat transport in ?=2 is 6% lower, which is attributed to the more elliptical shape of the large-scale circulation. Heat transport is increased with up to 15% by rotation for ?=1, which agrees with literature data in terms of position and magnitude, and up to 20% for ?=2. The onset of rotational enhancement of heat transport is located at Ro?2 for ?=1, but at Ro?7 for ?=2. This is likely caused by the weaker large-scale circulation being more easy to overcome by Ekman pumping in the ?=2 case, shifting the transition to higher Rossby numbers for higher aspect ratios. The single-roll large-scale circulation is dominant in both aspect ratios at none to weak rotation. The disappearance of this mode coincides with the onset of rotational enhancement of heat transport, with the transition being sharper in ?=2 than in ?=1. Overall, rotational heat transport enhancement showed expected behaviour for ?=1, but revealed a so far undocumented aspect ratio dependence as supported by the ?=2 measurements.

Date of Award	31 Aug 2010
Original language	English
Supervisor	Herman J.H. Clercx (Supervisor 1) & R.J.A.M. Stevens (Supervisor 2)