Confined axisymmetric laminar jets with large expansion ratios

Abstract

This paper investigates the steady round laminar jet discharging into a coaxial duct when the jet Reynolds number, Re/sub j/, is large and the ratio of the jet radius to the duct radius, epsiv, is small. The analysis considers the distinguished double limit in which the Reynolds number Re/sub a/=Re/sub j/epsiv for the final downstream flow is of order unity, when four different regions can be identified in the flow field. Near the entrance, the outer confinement exerts a negligible influence on the incoming jet, which develops as a slender unconfined jet with constant momentum flux. The jet entrains outer fluid, inducing a slow backflow motion of the surrounding fluid near the backstep. Further downstream, the jet grows to fill the duct, exchanging momentum with the surrounding recirculating flow in a slender region where the Reynolds number is still of the order of Re/sub j/. The streamsurface bounding the toroidal vortex eventually intersects the outer wall, in a non-slender transition zone to the final downstream region of parallel streamlines. In the region of jet development, and also in the main region of recirculating flow, the boundary-layer approximation can be used to describe the flow, while the full Navier-Stokes equations are needed to describe the outer region surrounding the jet and the final transition region, with Re/sub a/=Re/sub j/epsiv entering as the relevant parameter to characterize the resulting non-slender flows.