Natural convection experiments around an upper dome varying Rayleigh number and truncation angle

Abstract

We carried out natural convection heat transfer experiments around upper domes varying truncation angles (θ = 90°, 70°, 50°, and 30°) over a wide range of Rayleigh number (Ra_Db = gβΔTD_b³/αν, 2.63 × 10⁹ ≤ Ra_Db ≤ 1.08 × 10¹³). The shape of a dome is close to the hemisphere as θ is 90° and to flat plate as θ is 0°. To achieve high Ra_Db condition, mass transfer experiments using H₂SO₄–CuSO₄ copper electroplating system were employed. Mass transfer rates were measured by electric current, and flows were observed by the Particle Image Velocimetry (PIV). The measured average Nusselt number (Nu_Db = h_mD_b/k) increased as Ra_Db increased and as the θ decreased. The enhancement was more significant at lower Ra_Db values, which is attributed to variations in the location of flow transition to turbulence and separation. At a relatively low Ra_Db (1.08 × 10¹⁰), flow remains attached but undergoes an early transition to turbulence when the θ is small. Meanwhile, when the θ becomes large, flow separation occurs without prior transition. As Ra_Db increases, however, flow separation occurs irrespective of the θ. Nu_Db of dome with θ = 30° had 35 % higher than the dome with θ = 90° at Ra_Db = 1.08 × 10¹⁰ until 18 % higher at Ra_Db = 1.08 × 10¹³. The Nu_Db correlation for an upper dome was developed. This work contributes not only to a deeper phenomenological understanding of natural convection heat transfer around upper domes but to the application to passive cooling of SMR outer containments.