Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-12-01T04:31:21.207Z Has data issue: false hasContentIssue false
  • English
  • Français

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]
Get access Rights & Permissions [Opens in a new window]

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
Check for updates
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abid, M. 2008 Nonlinear mode selection in a model of trailing line vortices. J. Fluid Mech. 605, 19–45.Google Scholar
Batchelor, G. K. 1964 Axial flow in trailing line vortices. J. Fluid Mech. 20, 645–658.CrossRefGoogle Scholar
Benjamin, T. B. 1962 Theory of the vortex breakdown phenomenon. J. Fluid Mech. 14 (4), 593–629.Google Scholar
Broadhurst, M. S. & Sherwin, S. J. 2008 Helical instability and breakdown of a Batchelor trailing vortex. In Progress in Industrial Mathematics at ECMI 2006, Mathematics in Industry, pp. 191–195. Springer.Google Scholar
Brown, G. L. & Lopez, J. M. 1990 Axisymmetric vortex breakdown. Part 2. Physical mechanisms. J. Fluid Mech. 221, 553–576.Google Scholar
Darmofal, D. L., Khan, R., Greitzer, E. M. & Tan, C. S. 2001 Vortex core behaviour in confined and unconfined geometries: a quasi-one-dimensional model. J. Fluid Mech. 449, 61–84.CrossRefGoogle Scholar
Delery, J. M. 1994 Aspects of vortex breakdown. Prog. Aerosp. Sci. 30, 1–59.Google Scholar
Escudier, M. 1988 Vortex breakdown: observations and explanations. Prog. Aerosp. Sci. 25 (2), 189–229.CrossRefGoogle Scholar
Hall, M. G. 1972 Vortex breakdown. Annu. Rev. Fluid Mech. 4, 195–218.CrossRefGoogle Scholar
Herrada, M. A. & Fernandez-Feria, R. 2006 On the development of three-dimensional vortex breakdown in cylindrical regions. Phys. Fluids 18 (8), 084105.Google Scholar
Herrada, M. A., Pérez-Saborid, M. & Barrero, A. 2003 Vortex breakdown in compressible flows in pipes. Phys. Fluids 15 (8), 2208–2218.Google Scholar
Hiejima, T. 2013 Linear stability analysis on supersonic streamwise vortices. Phys. Fluids 25, 114103.CrossRefGoogle Scholar
Hiejima, T. 2014 Spatial evolution of supersonic streamwise vortices. Phys. Fluids 26, 074102.Google Scholar
Hiejima, T. 2016 Effects of streamwise vortex breakdown on supersonic combustion. Phys. Rev. E 93, 043115.Google Scholar
Hiejima, T. 2017 Streamwise vortex breakdown in supersonic flows. Phys. Fluids 29, 054102.Google Scholar
Keller, J. J. 1994 On the practical application of vortex breakdown theory to axially symmetrical and three-dimensional compressible flows. Phys. Fluids 6 (4), 1515–1523.CrossRefGoogle Scholar
Leibovich, S. 1978 The structure of vortex breakdown. Annu. Rev. Fluid Mech. 10, 221–246.CrossRefGoogle Scholar
Lucca-Negro, O. & O’Doherty, T. 2001 Vortex breakdown: a review. Prog. Energy Combust. Sci. 27, 431–481.Google Scholar
Luginsland, T. & Kleiser, L. 2015 Mach number influence on vortex breakdown in compressible, subsonic swirling nozzle-jet flows. In Direct and Large-Eddy Simulation IX, pp. 311–317. Springer.Google Scholar
Mager, A. 1972 Dissipation and breakdown of a wing-tip vortex. J. Fluid Mech. 55 (4), 609–628.Google Scholar
Mahesh, K. 1996 A model for the onset of breakdown in an axisymmetric compressible vortex. Phys. Fluids 8 (12), 3338–3345.CrossRefGoogle Scholar
Nelson, R. C. & Pelletier, A. 2003 The unsteady aerodynamics of slender wings and aircraft undergoing large amplitude maneuvers. Prog. Aerosp. Sci. 39 (2), 185–248.CrossRefGoogle Scholar
Oberleithner, K., Paschereit, C. O., Seele, R. & Wygnanski, I. 2012 Formation of turbulent vortex breakdown: intermittency, criticality, and global instability. AIAA J. 50 (7), 1437–1452.Google Scholar
Ruith, M. R., Chen, P., Meiburg, E. & Maxworthy, T. 2003 Three-dimensional vortex breakdown in swirling jets and wakes: direct numerical simulation. J. Fluid Mech. 486, 331–378.Google Scholar
Rusak, Z. & Lee, J. H. 2002 The effect of compressibility on the critical swirl of vortex flows in a pipe. J. Fluid Mech. 461, 301–319.Google Scholar
Shtern, V. & Hussain, F. 1999 Collapse, symmetry breaking, and hysteresis in swirling flows. Annu. Rev. Fluid Mech. 31 (1), 537–566.Google Scholar
Visbal, M. R. & Gordnier, R. E. 1995 Compressibility effects on vortex breakdown onset above a 75° sweep delta wing. J. Aircraft 32, 936–942.Google Scholar