Some Aspects of Compressible Rayleigh’s Problem in a Rotating Cylinder

Abstract

The Rayleigh problem of a compressible gas contained in an infinitely long cylinder is considered. The time-dependent flow of the initially motionless gas driven by the rapidly rotating cylindrical sidewall is described. The flow field is determined by the two principal dynamic mechanisms: the compressible Rayleigh effect and the curvature effect. Comprehensive numerical calculations have been performed to solve the governing complete, time-dependent, compressible Navier-Stokes equations formulated in cylindrical coordinates. The details of the evolutions of flow and temperature fields are presented. Unlike the Rayleigh problem about a flat plate, the centrifugal compression causes a small radially-outward normal velocity component in a narrow region very close to the sidewall. Also, due to the boundedness of the flow domain, the propagating compression wave is reflected at the central axis. The importance of the curvature effect relative to the compressible Rayleigh effect decreases as E·M decreases, where E and M denote respectively the Ekman number and the Mach number. Numerical results are exhibited to corroborate this assertion.