Journal of Fluid Mechanics

Papers

Analysis of sheet-like thermal plumes in turbulent Rayleigh–Bénard convection

OLGA SHISHKINAa1 and CLAUS WAGNERa1

a1 DLR – Institute for Aerodynamics and Flow Technology, Bunsenstraße 10, 37073 Göttingen, Germany

Abstract

Sheet-like thermal plumes are investigated using time-dependent and three-dimensional flow fields obtained from direct numerical simulations and well-resolved large-eddy simulations of turbulent Rayleigh–Bénard convection in water (Prandtl number Pr=5.4) in a cylindrical container with the aspect ratio Γ=1 and for the Rayleigh numbers Ra=2×109 and 2×1010.

To analyse quantitatively the physical properties of the sheet-like thermal plumes and the turbulent background and to obtain the temperature threshold which separates these two different flow regions, the temperature dependences of the conditionally averaged local heat flux, thermal dissipation rate and selected components of the velocity and vorticity fields are studied. It is shown that the sheet-like plumes are characterized by high values of the local heat flux and relatively large absolute values of the vertical components of the vorticity and velocity fields. The borders of these plumes are indicated by large values of the thermal dissipation rate and large absolute values of the horizontal vorticity components. In contrast to the sheet-like thermal plumes, the turbulent background is characterized by low values of the thermal dissipation rate, local heat flux and vertical vorticity component. The highest values of the local heat flux and the highest absolute values of the vertical vorticity component are found in the regions where the sheet-like plumes strike against each other. Fluid swirling at these places forms the stems of the mushroom-like thermal plumes which develop in the bulk of the Rayleigh–Bénard cell.

Further, formulae to calculate the curvature, thickness and length of the plumes are introduced. Geometrical properties such as plume area, diameter, curvature, thickness and aspect ratio together with the physical properties of the sheet-like plumes such as temperature, heat flux, thermal dissipation rate, velocity and vorticity are investigated.

(Received June 14 2007)

(Revised December 03 2007)

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