Vortex Structure and Kinematics of Encased Axial Turbomachines

Abstract

This paper models the kinematics of the vortex system of an encased axial turbomachine at part load and overload applying analytical methods. Thus far, the influence of the casing and the tip clearance on the kinematics have been solved separately. The vortex system is composed of a hub, bound and tip vortices. For the nominal operating point φ ≈ φ opt and negligible induction, the tip vortices transform into a screw. For part load operation φ → 0 the tip vortices wind up to a vortex ring, i.e., the pitch of the screw vanishes. The vortex ring itself is generated by bound vortices rotating at the angular frequency Ω . The hub vortex induces a velocity on the vortex ring causing a rotation at the sub-synchronous frequency Ω ind = 0.5 Ω . Besides, the vortex ring itself induces an axial velocity. Superimposed with the axial main flow this results in a stagnation point at the tube wall. This stagnation point may wrongly be interpreted as dynamic induced wall stall. For overload operation φ → ∞ the vortex system of the turbomachine forms a horseshoe, i.e., the pitch of the screw becomes infinite. Both hub and tip vortices are semi-infinite, straight vortex filaments. The tip vortices rotate against the rotating direction of the turbomachine due to the induction of the hub vortex yielding the induced frequency Ω ind = − 0.5 Ω / s with the tip clearance s.