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_j, is large and the ratio of the jet radius to the duct radius, ε, is small. The analysis considers the distinguished double limit in which the Reynolds number Re_a = Re_jε 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 back flow 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_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_a = Re_jε entering as the relevant parameter to characterize the resulting non-slender flows.