Archive of Applied Mechanics

, Volume 89, Issue 2, pp 307–312 | Cite as

Vortex-induced transient stall

  • P. F. PelzEmail author
  • P. Taubert


This study analyzes the induced flow by a coaxial vortex ring inside a circular tube applying vortex theory and potential flow theory. The vortex ring itself is generated by bound vortices rotating with the angular frequency \({\varOmega }\). Two results emerge out of the analytic research: first it is shown that induction causes the rotation of the vortex ring. It rotates at the sub-synchronous frequency \({\varOmega }_\mathrm {ind}<0.5\,{\varOmega }\). Second, the ring vortex 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 kinematic 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.


Analytical methods Fluid dynamics Kinematic stall Potential theory Turbomachinery Vortex dynamics 



  1. 1.
    Betz, A.: Schraubenpropeller mit geringstem Energieverlust. Mit einem Zusatz von L. Prandtl. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, pp. 193–217 (1919)Google Scholar
  2. 2.
    Brennen, C.E.: Hydrodynamics of Pumps. Oxford Science Publications. Concepts ETI; Oxford University Press, Norwich (1994)Google Scholar
  3. 3.
    Cloos, F.J., Stapp, D., Pelz, P.F.: Swirl boundary layer and flow separation at the inlet of a rotating pipe. J. Fluid Mech. 811, 350–371 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Dixon, S.L.: Some Three Dimensional Effects of Rotating Stall. HM Stationery Office, Richmond (1962)Google Scholar
  5. 5.
    Gharib, M., Rambod, E., Shariff, K.: A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121–140 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Glauert, H.: Die Grundlagen der Tragflügel- und Luftschraubentheorie. Springer, Berlin (1929)CrossRefzbMATHGoogle Scholar
  7. 7.
    Goldstein, S.: On the vortex theory of screw propellers. Proc. R. Soc. Lond. Ser. A 123(792), 440–465 (1929)CrossRefzbMATHGoogle Scholar
  8. 8.
    Greitzer, E.M.: Review-axial compressor stall phenomena. J. Fluids Eng. 102(2), 134–151 (1980)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Pelz, P.F., Spurk, J.H., Müller, H.D.J.: Reducing mixing at the outlet bore of a cylinder. Arch. Appl. Mech. 68(6), 395–406 (1998)CrossRefzbMATHGoogle Scholar
  10. 10.
    Prandtl, L.: Über die Entstehung von Wirbeln in der idealen Flüssigkeit, mit Anwendung auf die Tragflügeltheorie und andere Aufgaben. In: Vorträge aus dem Gebiete der Hydro-und Aerodynamik, pp. 18–33. Springer, Innsbruck (1924)Google Scholar
  11. 11.
    van Kuik, G.: The relationship between loads and power of a rotor and an actuator disc. J. Phys. Conf. Ser. 555, 012,101 (2014)CrossRefGoogle Scholar

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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Chair of Fluid SystemsTechnische Universität DarmstadtDarmstadtGermany

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