Performance analysis of natural convection correlations for spheres at high Rayleigh numbers

Abstract There are industrial applications, such as spherical tanks under very low wind conditions, in which natural convection from spheres at high Rayleigh numbers can be of great importance. Due to different limitations, this problem has been studied either experimentally or numerically for Rayleigh numbers smaller than 1011, approximately. Furthermore, just a few correlating equations are available in scientific literature beyond that limit. Thus, a CFD model has been developed to estimate the overall heat transfer to large spheres with Rayleigh numbers ranging from 4·108 to 2·1014. A set of 48 cases of spheres with different diameters (1m–40 m) and under different air and sphere surface temperatures were numerically simulated. Besides, the results of the average Nusselt number provided by the CFD model and the available correlating equations were compared and deviations quantified. At the model validation stage, CFD estimations of the overall Nusselt number showed good agreement with experimental observations (7.1% of average relative error) while correlating equations deviated up to more than 28% on average. From the cases studied, CFD results suggest that Kitamura et al.‘s correlating equation could be extended beyond its reported limits of validity. A comparison analysis has also shown high discrepancies, up to 40%, among correlations.