**Structure and Kinematics of the Vortex System in Axial Turbomachines**

Development of Analytical and Computational Methods

This investigation models the kinematics of the vortex system of an encased axial turbomachine depending on the operation point applying vortex theory and potential flow theory. By doing so, the physical understanding of compressor and fan stall at the housing, surge, spill forward and noise generation is enlarged. The total change in circulation along the plane of the machine is linked to the flow number φ ∶= U / (Ωa) by Euler's turbine equation, with U the axial free-stream velocity, Ω the angular frequency of the turbomachine and a the radius of the housing. Depending on the operating point, the vortex system of an axial turbomachine changes. For the nominal operating point φ ≈ φ_opt and negligible induction, the tip vortices transform into a screw with a pitch of 2πφa. The most relevant operating point for practical applications is part load operation. For this case, i.e. small flow numbers φ → 0, the tip vortices roll up to a vortex ring with increasing circulation due to Helmholtz's theorems. The vortex ring itself is generated by bound vortices rotating with the angular frequency Ω.

Two results emerge out of the analytic research concerning the vortex system of an axial turbomachine at part load: first, the analysis shows an induced movement of the tip vortices in the same rotating direction as the turbomachine. The vortex ring rotates at the sub-synchronous frequency Ω_ind < Ω/2. Second, the vortex ring itself induces an axial velocity at the tube wall. Superimposed with the axial main flow, this results in a stagnation point. Since the vortex strength increases in time, the stagnation point moves upstream. This effect may falsely be interpreted as a dynamic boundary layer separation. Hence, the results may give new insights into transient stall phenomena in axial turbomachinery. For overload φ → ∞ the hub, the bound and the tip vortices form a horseshoe. Both, hub and tip vortices are semi-infinite, straight vortex filaments generated by bound vortices. The analysis yields an induced movement of the tip vortices against the rotating direction of the turbomachine at heavy overload.