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.

[1]  H. Merk,et al.  Thermal convection in laminar boundary layers III , 1954 .

[2]  S. Dash,et al.  Natural convection heat transfer from a finned sphere , 2015 .

[3]  A. Cornish,et al.  Numerical solution of steady-state free convective heat transfer from a solid sphere , 1981 .

[4]  T. Yuge,et al.  Experiments on Heat Transfer From Spheres Including Combined Natural and Forced Convection , 1960 .

[5]  G. Schütz.  Natural convection mass-transfer measurements on spheres and horizontal cylinders by an electrochemical method , 1963 .

[6]  Kuang C. Lin,et al.  3D-CFD investigation into free convection flow above a heated horizontal cylinder: Comparisons with experimental data , 2017 .

[7]  B. Chung,et al.  Visualization of natural convection heat transfer on a sphere , 2017 .

[8]  A. Cornish,et al.  Numerical simulation of free convective heat transfer from a sphere , 1982 .

[9]  T. Misumi,et al.  Fluid flow and heat transfer of natural convection around large horizontal cylinders: Experiments with air , 2003 .

[10]  M. Weber,et al.  Natural convection mass transfer to nonspherical objects at high rayleigh number , 1984 .

[11]  Joel H. Ferziger,et al.  Computational methods for fluid dynamics , 1996 .

[12]  I. Miroshnichenko,et al.  Turbulent natural convection heat transfer in rectangular enclosures using experimental and numerical approaches: A review , 2018 .

[13]  C. Tien,et al.  Laminar Free Convection From a Sphere , 1964 .

[14]  Florian Menter,et al.  The SST Turbulence Model with Improved Wall Treatment for Heat Transfer Predictions in Gas Turbines , 2003 .

[15]  Y. R. Mayhew,et al.  Free convection from a sphere in air , 1962 .

[16]  G. Gogos,et al.  Numerical study of transient laminar natural convection over an isothermal sphere , 2007 .

[17]  Stuart W. Churchill,et al.  A general expression for the correlation of rates of transfer and other phenomena , 1972 .

[18]  Takashi Suzuki,et al.  Fluid flow and heat transfer of high-Rayleigh-number natural convection around heated spheres , 2015 .

[19]  A. Campo.  Correlation equation for laminar and turbulent natural convection from spheres , 1980 .

[20]  Stuart W. Churchill,et al.  COMPREHENSIVE, THEORETICALLY BASED, CORRELATING EQUATIONS FOR FREE CONVECTION FROM ISOTHERMAL SPHERES , 1983 .

[21]  J. Schenk,et al.  Thermal free convection from a solid sphere , 1965 .

[22]  George Gogos,et al.  Laminar natural convection heat transfer from isothermal spheres , 1996 .

[23]  Y. Jaluria,et al.  On the buoyancy-induced flow arising from a heated hemisphere , 1975 .

[24]  J. Lienhard,et al.  On the commonality of equations for natural convection from immersed bodies , 1973 .