Abstract
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.
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Notes
The maximal flow number \({\hat{\varphi }}\) equals the tangent of the blade’s trailing edge angle.
References
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)
Brennen, C.E.: Hydrodynamics of Pumps. Oxford Science Publications. Concepts ETI; Oxford University Press, Norwich (1994)
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)
Dixon, S.L.: Some Three Dimensional Effects of Rotating Stall. HM Stationery Office, Richmond (1962)
Gharib, M., Rambod, E., Shariff, K.: A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121–140 (1998)
Glauert, H.: Die Grundlagen der Tragflügel- und Luftschraubentheorie. Springer, Berlin (1929)
Goldstein, S.: On the vortex theory of screw propellers. Proc. R. Soc. Lond. Ser. A 123(792), 440–465 (1929)
Greitzer, E.M.: Review-axial compressor stall phenomena. J. Fluids Eng. 102(2), 134–151 (1980)
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)
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)
van Kuik, G.: The relationship between loads and power of a rotor and an actuator disc. J. Phys. Conf. Ser. 555, 012,101 (2014)
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Pelz, P.F., Taubert, P. Vortex-induced transient stall. Arch Appl Mech 89, 307–312 (2019). https://doi.org/10.1007/s00419-018-1468-5
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DOI: https://doi.org/10.1007/s00419-018-1468-5