An Analysis of the Effect of Rectangular Geometries on the Large-scale Circulation in Turbulent Rayleigh-B?nard Convection

In this research we have explored the behavior of Rayleigh-B?nard convection in a rectangular enclosed cell whose length is twice as big as its depth. In Rayleigh-B?nard convection, a fluid-filled cell is heated from the bottom plate while simultaneously being cooled from the top plate. This simultaneous cooling and heating forms a large scale circulation (LSC) that the fluid follows within the cell. Rayleigh-B?nard convection has two dimensionless parameters to specify the fluid and heat input, the Prandtl number and the Rayleigh number. The Prandtl number sets the ratio of the kinematic viscosity to the thermal diffusivity. The Rayleigh number sets the heat transfer within the cell. Our simulated cell characterized the Prandtl number of mercury. We ran four simulations using Nek5000, a program designed by Paul Fischer at Argonne National Laboratory that simulates fluid dynamics. We used Rayleigh numbers 1x106, 5x106, 1x107 and 5x107. We focused on the behavior of the large scale circulation as well as on the heat transport due to convection, which is described by the Nusselt number. We also created animations of the circulation to observe the LSC path as time evolved and tracked the z-component of the velocity at various locations within the cell. We then compared the results from the rectangular cell to results for simulations of the same Rayleigh numbers but for a cylindrical cell of length equal to its depth