Choking conditions for nonuniform viscous flows

Abstract

The laminar viscous compressible flow of a gas in a pipe of -*constant cross section joining two reservoirs is considered. As it is well known, the pipe flow becomes independent of the discharge pressure if this is lower than a critical value. Then it is found that the parabolic equations describing the high Reynolds number flow in the interior of the pipe tend to develop a singularity at the outlet, where the limiting temperature and velocity profiles satisfy a criticality condition. The structure of the nonuniform flow near the outlet consists of an effectively inviscid vortical bulk region and a viscous boundary layer of low velocity, whose thickness tends to zero at the outlet. Matching between these two regions determines the strength of the singularity. This two-layered structure is thought to be generic for nonuniform viscous flows having to satisfy a no-slip'boundary condition; in particular, the thin viscous layer is universal.