Fluid flow and heat transfer of high-Rayleigh-number natural convection around heated spheres

Experimental investigations were carried out on the natural convective flows of water and air induced around heated spheres. A keen interest was directed to high-Rayleigh-number flows that undergo turbulent transition. For the sake of this, spheres with different diameters, d = 50 to 1000 mm, were fabricated and tested, and this enabled the experiments in the wide and high ranges of Rayleigh numbers, 5 × 106 < Rad < 4 × 1010 for water and 4 × 105 < Rad < 4 × 109 for air. In particular, the present maximum Rayleigh numbers are one or two decades higher than those of the prior experiments. The flows ascending along the heated spheres were first visualized to investigate the mechanisms of turbulent transition and the critical Rayleigh numbers. The results showed that the turbulent transition begins at the top of the sphere when the Rayleigh numbers are at around 3.0 × 108 for water and 3.5 × 108 for air. Then, the transition points move from the top to the side of the sphere with further increase in the Rayleigh numbers. The average Nusselt numbers from the spheres were subsequently measured and correlated with the Rayleigh numbers. The result showed that the present Nusselt numbers coincide fairly well with the prior laminar correlations in the range of the Rayleigh numbers less than the above critical. On the other hand, they showed a considerable deviation from the prior turbulent correlation when the Rayleigh numbers beyond the critical.