Near Critical Swirling Flow in a Slightly Contracting Pipe

Abstract

The development of an inviscid, incompressible, axisymmetric, and near-critical swirling jet entering a slightly contracting finite-length pipe is studied. Certain flow conditions that can reflect the physical situation are prescribed along the pipe inlet, outlet, centerline, and wall. To understand the nature of the flows near the critical swirl level, a nonlinear small-disturbance analysis is developed from the governing equations of motion. It shows that a small but finite pipe contraction causes the flow to accelerate near the centerline and decelerate along the wall. For certain inlet swirl levels and pipe contractions, the flow on the wall at the pipe outlet can stagnate. The analysis indicates for the first time that a wall separation zone can appear in pipes at rotation levels below the critical swirl for vortex breakdown and compete with the appearance of the breakdown zones. Increasing the vortex core radius, the speed of the axial jet, and the pipe length promotes the wall separation phenomenon at swirl levels below the critical swirl for a fixed pipe contraction or at a smaller pipe contraction for a fixed swirl level. Based on the present results and previous studies, the interaction between wall separation zones and vortex breakdown zones is discussed. This investigation might be relevant for high-Reynolds-number laminar flows in pipes and as long as the boundary layers remain thin and attached to the pipe wall.