Thermally, mechanically or externally driven flows in a gas centrifuge with insulated horizontal end plates

Abstract

The axisymmetric motion of a compressible fluid in a rapidly rotating cylinder is considered using a linear approach and boundary-layer techniques. The deviation of the fluid motion from rigid-body rotation is caused either by an applied temperature distribution on the side wall, a differential rotation of the top and bottom end plates or sources and sinks of fluid distributed on the end plates. The horizontal end plates are assumed to be thermally insulated, while the side wall is conducting. The critical parameter governing the problem is found to be E−½(γ − 1) PrG0/4γ, where E is the Ekman number, γ the ratio of specific heats, Pr the Prandtl number and G0 the square of a rotational Mach number. If this parameter is larger than unity, the coupled effect of the compressibility of the fluid and the thermal condition on the end plates suppresses the flow in the cylinder. The flow in the inner inviscid core is strongly coupled with the Ekman-layer flow through the boundary conditions on the end plates, something which does not occur if the fluid is Boussinesq nor if the fluid is compressible and the end plates are conducting.