Numerical simulation of flow pattern formation in a bottom heated cylindrical fluid layer

Abstract

The temporal formation of the buoyancy-driven flow structures in a bottom heated, shadow, cylindrical fluid layer was numerically studied. The unsteady three-dimensional Navier-Stokes and energy equations were discretized by the power law scheme and solved by the fully implicit Marker-and-Cell method. Computations were carried out for the pressurized argon (Pr = 0.69) and wafer (Pr = 6.1) layers for various Rayleigh numbers and heating rates of the layer. ln the pressurized argon layer at a slightly supercritical Rayleigh number with Ra-f = 1.05Ra(c), a steady straight roll pattern was formed when the heating rate was very slow (a = 0.001) after a long transient stage. When the heating rate was raised to a = 0.01, a very different structure like U-rolls was formed at steady state. In the water layer with Ra-f = 1.05Ra(c), a straight roll pattern was again formed, hut at a = 0.01. At Ra-f = 1.13Ra(c), curved rolls with the three foci at the sidewall were formed for a = 0.01. A pattern in the form of U-rolls appears at a = 0.01. Regular concentric circular rods prevail at a = 1.0. When the Rayleigh number is further raised to 1.23Ra(c), the resulting steady flow is dominated by incomplete circular rolls with open ends near theta = 0 degrees.