Two turbulent flow regimes at the inlet of a rotating pipe

Abstract

When a fluid enters a rotating circular pipe a swirl boundary layer with thickness ofδ S appears at the wall and interacts with the axial momentum boundary layer with thickness ofδ. We investigate the turbulent flow applying Laser-Doppler-Anemometry to measure the circumferential velocity profile at the inlet of a rotating pipe. The measured swirl boundary layer thickness follows a power law taking Reynolds number and flow number into account. A critical combination of Reynolds number, flow number and axial position causes a transition of the swirl boundary layer development in the turbulent regime. At this critical combination, the swirl boundary layer thickness as well as the turbulence intensity increase and the latter yields a self-similarity. The circumferential velocity profile changes to a new presented self-similarity. A method is established to define the transition inlet length, when the transition appears and a stability map for two regimes is given.

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 high Reynolds number as well as high flow number Eqn. 1 is not longer valid because a second transition of the swirl boundary layer occurs in the turbulent regime [2,5], which is the main focus of this paper. By this transition (Re, ϕ, z) > (Re, ϕ, z) t , the circumferential velocity profile transforms from the parabolic profile u φ = (1 − y/δ S ) 2 of regime I into…”

“…These findings are done when a thin axial turbulent boundary layer, i.e., configuration I, streams into the rotating pipe [5]. The transition occurs as well as when a fully developed axial turbu- lent flow, i.e., configuration II, enters the rotating pipe [5], but this is not fully analysed. This is the task of this paper.…”

“…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.…”

“…We observe a transition in the turbulent regime of the swirl boundary layer including a profile transformation and an increase of the turbulence intensity for a parameter combination (Re, ϕ, z) t . By doing so, we measure the circumferential velocity profile by Laser-Doppler-Anemometry (LDA) and analyse the profile to indicate the turbulent regimes and the transition inlet length as it is done in our previous work [5]. Throughout this investigation, we nondimensionlise length with the pipe radiusR and velocities with the pipe circumferential velocityRΩ.…”