Suppression of free convection effects for spherical 1 kg mass prototype

• Published in: International journal of heat and mass transfer 2021-05, Vol.170, p.121037, Article 121037
• Main Authors: Sachs, Sebastian, Fröhlich, Thomas, Schumacher, Jörg
• Format: Article
• Language: English
• Subjects: Boundary conditions; Boussinesq equations; Chambers; Complexity; Direct numerical simulation; Flow distribution; Free convection; Hemispherical shells; Mathematical models; Secondary flow; Simulation; Spectral element method; Temperature effects; Temperature gradients; Two dimensional models; Uncertainty; Updraft
• ISSN: 0017-9310; 1879-2189
• DOI: 10.1016/j.ijheatmasstransfer.2021.121037

•Simulations of free convection around a sphere applying the spectral element method.•Mass differences due to updraft forces lead to uncertainties in precision weighing.•Additional built-ins for counter heating can suppress these updraft forces. [Display omitted] We investigate the free convection processes in the vicinity of a spherical 1 kg mass standard by two- and three-dimensional direct numerical simulations using a spectral element method. Our focus is on the determination and suppression of updraft forces in a high-precision mass comparator which are caused by temperature differences between mass standard and its environment in the millikelvin range – a source of systematic uncertainties in the high-precison mass determination. A two-dimensional model is presented first, which obtains a good agreement with previous laboratory measurements for the smaller temperature differences up to 15 mK. The influence of different boundary conditions and side lengths of the square domain is discussed for the mass standard positioned in the center of the chamber. The complexity is increased subsequently in configurations with additional built-ins for counter heating in form of planar plates or hemispherical shells above the mass standard. The latter ones lead to a full compensation of the updraft force. Three-dimensional simulations in a closed cubic chamber confirm the two-dimensional findings and additionally reveal complex secondary flow patterns in the vicinity of the mass standard. The reduction of the heat transfer due to the built-ins is also demonstrated by a comparison of the Nusselt numbers as a function of the Rayleigh number in the chosen parameter range. Our simulations suggest that such additional constructive measures can enhance the precision of the mass determination by suppression of free convection and related systematic uncertainties.