Numerical Study on Natural Convection and Radiation From a Square Disk

In this paper, a numerical study of natural convection from a disk is presented. The disk is placed vertically in a closed cavity (cylinder) and has a constant heat flux. Different numerical simulations of this test case are executed at various gravity accelerations (=g) inside the cavity. The accelerations are varied from 9.81 m/s² to 53 m/s². The Rayleigh number changes with these accelerations. The flow pattern and the temperature distribution inside the cavity are visualized. For natural convection inside a cavity, a vortex is expected in the air flow: a plume of warm rising air at the centre of the cylinder above the heated square disk and descending colder air at the walls of the cavity. The air velocity is higher in the central plume. At w = 9.81 m/s², the maximum air velocity is 0.05 m/s. This velocity increases with increasing acceleration w till 0.6 m/s at w = 53 m/s². At low w, the flow pattern exists of a stable vortex and thus a steady-state flow. At w = 15 m/s², the vortex becomes more unstable and is swirling. At w = 27 m/s², the vortex is even more swirling and the following periodical phenomenon takes place: first the vortex starts to dissolve in a small vortex at the top of the cylinder and a vortex below this around the square disk. Then, the lower vortex starts to increase again and the upper vortex is fading. So there is again one big vortex with a central, unstable plume that reaches the top of the cylinder. After a few seconds, the plume dissolves again. This phenomenon has no constant period. The higher w, the faster this phenomenon happens and thus the shorter the period. At w = 53m/s², the vortex seems more turbulent than laminar, however the Rayleigh number is still in the laminar range (Ra<10⁶). The numerical simulations are verified with existing correlations. There was a good agreement between correlations and numerical simulation.