Heat Transfer and Flow Visualization in Natural Convection in Rapidly Spinning Systems

The design of airborne superconducting generators for intermittent duty requires the understanding of some unique free-convection processes in the spinning helium bath. Toward that end, some fundamental experiments on steady and transient free convection in rotating containers of representative geometries have been performed. Heat transfer data from heaters of various geometries mounted on the outer container surface to several fluids are reported. A correlation for steady-state Nusselt number is presented for a wide range of Rayleigh and Prandtl numbers. The heat transfer coefficient was found to be independent of heater size, geometry, and fluid viscosity. Heat transfer measurements during simultaneous thermal transients and sudden increases in rotational speed were also made. They show an enhancement of heat transfer due to the relative counterrotation of the fluid following the acceleration of the container. This persists for a period well below that for fluid spinup. A model based upon the submergence of the thermal boundary layer by the diffusive wave from the wall was successful in correlating this period. Quasi-steady flow visualization experiments indicate that the thermal plumes generate two-dimensional, axially invariant flow fields. Their trajectories are radial relative to the spinning container. Those observations are shown to be consistent with the fact that weak buoyant plumes in containers rotating at small Ekman numbers result in low Rossby number motions. Those are two dimensional according to the Taylor–Proudman theorem. It is shown that the Coriolis and pressure forces on such a thermal column are in azimuthal equilibrium, hence the radial trajectory. Flow visualization following impulsive acceleration in an off-axis, nonaxisymmetric container shows that the flow field is dominated by vortices expelled from corners. The fluid spinup time, however, was found to be the same as that for an on-axis circular cylinder of the same characteristic diameter.