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Onset conditions for vortex breakdown in supersonic flows

Published online by Cambridge University Press:  06 February 2018

Toshihiko Hiejima Open the ORCID record for Toshihiko Hiejima [Opens in a new window]
Toshihiko Hiejima*
Affiliation:
Department of Aerospace Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Nakaku, Sakai, Osaka 599-8531, Japan
*
†Email address for correspondence: [email protected]
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Abstract

This study proposes an onset condition of shock-free supersonic vortex breakdown from the axial momentum variation, which applies in the presence or absence of a stagnation point. The condition is derived from a comprehensive approach to vortex breakdown. Supersonic breakdown appeared when the swirl parameter and Mach number were small. Moreover, bubble-type breakdowns with a stagnation point, which occur in subsonic conditions, could not occur under the supersonic condition in the present analysis. The predicted breakdowns under this condition were consistent with the results of the three-dimensional numerical simulations for Mach numbers ranging from 1.5 to 5.0. Supersonic vortex breakdowns were clearly captured by the helicity contours in the numerical results. The threshold of the downstream Mach number required for spiral breakdown with no stagnation point was also theoretically derived and verified in numerical results. These findings provide new insights into vortex breakdown in supersonic flows.

JFM classification

Compressible Flows: Compressible Flows Vortex Flows: Vortex breakdown Vortex Flows: Vortex Flows
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 840 , 10 April 2018 , R1
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Copyright
© 2018 Cambridge University Press 

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