Properties of Boundary Layers Generated by Mechanically and Thermally Driven Flows in a Centrifuge

摘要

The flow of a compressible viscous perfect gas in a rotating cylinder closed at both ends is investigated by the linear theory. The Mach number is assumed to be of unit order and the Ekman number epsilon small enough so that boundary layers occur and asymptotic methods are valid. Matching conditions between adjacent areas are usually derived from the theory of singular perturbations. Here, a self-consistent set of matching, conditions is obtained from the system itself for fixed epsilon and will be then applied to the case epsilon implies 0. The elimination of the pressure reduces to 4 the number of unknown functions for which a set of matching conditions equivalent to the initial one is given. It is then shown that the main properties of the flow depend only upon the boundary conditions for the 'thermal wind quantity' Y=xT-2v where x is the radial coordinate, T the temperature and v the azimuthal velocity. These results are then applied to a symmetric case, showing the relation between the Stewartson's layers and the properties of the boundary conditions. In particular, the case of a jump of temperature or azimuthal velocity, or both (in fact a jump of Y) between the end-cap and the side wall is investigated. (Atomindex citation 11:522515)