Influence of the Lateral Walls on the Thermal Plumes in Turbulent Rayleigh-Benard Convection in Rectangular Containers

摘要

Turbulent Rayleigh-Benard (RB) convection is one of the classical problems in fluid mechanics, where fluid with a Prandtl number Pr = v/k is exposed to a vertical temperature gradient between a hot lower and a cold upper surface. The Rayleigh number Ra = αgH~3 ΔT/(vk) is a non-dimensional parameter to specify the ratio between the buoyancy and viscous forces, where α, v and κ denote the thermal expansion coefficient, kinematic viscosity and thermal diffusivity, respectively. ΔT is the vertical temperature gradient between the two bounding surfaces, H the height of the fluid layer and g the gravitational acceleration. For high enough Ra the thermal plumes that are rising and falling from the respective hot and cold surfaces become increasingly irregular. In recent years many fundamental studies dealt with the Rayleigh-Benard problem in order to gain deeper knowledge of the underling mechanisms driving the convective flow and the heat transport. Verzicco and Sreenivasan [10] investigated the influence of an isothermal and a constant heat flux bottom plate in a cylindrical geometry on the heat transport for Rayleigh numbers up to 10~(13). They concluded that the unsteady ejection of thermal plumes with a constant heat flux boundary is closer to experimental conditions. The thermal plumes are, however, a subject area that attracted a lot of attention in the field of thermal convection. Shishkina and Wagner [9] also performed direct numerical simulations (DNS) in a cylindrical geometry and analysed the geometrical properties of sheet-like thermal plumes in horizontal slices through the bulk flow. Zhou and Xia [11] conducted experiments showing that the skewness of the temperature signal can be taken to separate the flow field into three regions: bulk, boundary and mixing layers.