Turbulent Rayleigh–Bénard convection in low Prandtl–number fluids

Abstract

An experimental investigation of Rayleigh–Bénard convection in liquid sodium has been performed in cylindrical test cells with aspect ratios between 20 and 4.5 for a range of Rayleigh numbers 10 4< Ra<5×10 6. The Prandtl number is between 6.0×10 −3±0.1×10 −3. For low Rayleigh number Ra<10 4 the dimensionless heat flux, Nu is mainly conduction controlled and close to 1; a correlation Nu=0.115 × Ra 0.25 describes the observations adequately for 2×10 4< Ra<5×10 6. It is shown that the Nusselt numbers are smaller for sodium than for other fluids with larger Prandtl numbers such as mercury and helium. This contrasts with the relation Nu∼ Ra 2/7 Pr 1/7 recently proposed by Siggia [High Rayleigh number convection. Ann. Rev. Fluid Mech. (1994)] but conforms with a relation Nu∼( Ra Pr) 1/4 for low Prandtl number fluids derived by Jones et al. [Axisymmetric convection in a cylinder. J. Fluid Mech. 73 (1976) 353–358] and with recent numerical simulations of low Prandtl number convection by Vercicco and Camussi [Transitional regimes of low-Prandtl thermal convection in a cylindrical cell. Phys. Fluids 9 (5) (1997) 1287–1295]. The heat transfer as well as the statistical properties of the turbulent convection are significantly influenced by mode transitions in the test cell of small aspect ratio. The formation of thermal boundary layers occurs only at high Rayleigh numbers of the order Ra≳10 6. An instability in these thermal boundary layers triggers a new mode of large scale fluctuating motion. The analysis of the temperature time signals shows that the temperature field behaves essentially dissipative up to Rayleigh numbers Ra∼5×10 6.