Swirl boundary layer and flow separation at the inlet of a rotating pipe

Abstract

When a fluid enters a rotating circular pipe, an angular momentum or swirl boundary layer appears at the wall and interacts with the axial momentum boundary layer. In the centre of the pipe, the fluid is free of swirl and is accelerated due to boundary layer growth. Below a critical flow number, defined as the ratio of average axial velocity to circumferential velocity of the pipe, there is flow separation, known in the turbomachinery context as part load recirculation. To describe this phenomenon analytically, we extended boundary layer theory to a swirl boundary layer interacting with the axial momentum boundary layer. The solution of the resulting generalized von Kármán momentum equation takes into account the influence of the Reynolds number and flow number. We show the impact of swirl on the axial boundary layer and conduct experiments in which we vary Reynolds number, flow number and surface roughness to validate the analytical results. The extended boundary layer theory predicts a critical flow number which is analytically derived and validated. Below this critical flow number, separation is expected.

A Second Turbulent Regime When a Fully Developed Axial Turbulent Flow Enters a Rotating Pipe

“…When a thin laminar boundary layer enters a rotating pipe for ϕ > 0.71, the circumferential velocity profile transforms and both boundary layers are thickened at the inlet of a rotating pipe [6]. There, for a smaller flow number with a thin or fully developed turbulent or a thin laminar axial boundary layer, the circumferential velocity profile follows u φ = (1 − y/δ S ) 2 for an attached flow [1,2,4,5]. For the fully developed axial turbulent flow, the swirl boundary layer thickness follows…”

“…For a thin axial boundary layer, the constant C is approximately 4.64 and m 1 ≈ −0.46, m 2 ≈ −0.49 and m 3 ≈ 0.44 [2]. The swirl boundary layer becomes independent of the Reynolds number for a hydrauliclly rough flow but still depends on the flow number [1,2]. For a hydraulically rough flow, the circumferential velocity profile follows more or less…”

“…At part load of a turbo machine below a critical flow number ϕ :=Ũ/(RΩ) < ϕ c , with the average axial velocityŨ and circumferential velocity of the pipeRΩ, flow separation occurs, the so called part load recirculation. This flow separation is caused by the swirl, i.e., centrifugal force [1,2]. Thus, there is an interdependency of axial momentum and swirl.…”

“…By rotating the pipe, a second boundary layer in circumferential direction is produced by viscosity and develops. It is the so called swirl boundary layer with thicknessδ S [1][2][3][4][5]; see Fig. 1.…”

“…Inside the swirl boundary layer is a circumferential velocity componentũ φ , outside, the flow is swirl-free. Due to centrifugal force, there is a non-negligible radial pressure distribution inside the swirl boundary layer for ϕ 1 [1,2]. The Reynolds number Re := 2R 2Ω /ν with the kinematic viscosityν, the flow number ϕ and the averaged surface roughnessR z influence the boundary layers evolution.…”