Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-19T15:08:55.387Z Has data issue: false hasContentIssue false
  • English
  • Français

Secondary instability of crossflow vortices: validation of the stability theory by direct numerical simulation

Published online by Cambridge University Press:  04 July 2007

GIUSEPPE BONFIGLI  and
MARKUS KLOKER
GIUSEPPE BONFIGLI
Affiliation:
Institut für Aerodynamik und Gasdynamik, Universität Stuttgart, Pfaffenwaldring 21, D-70550 Stuttgart, Germany
MARKUS KLOKER
Affiliation:
Institut für Aerodynamik und Gasdynamik, Universität Stuttgart, Pfaffenwaldring 21, D-70550 Stuttgart, Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

Detailed comparison of spatial direct numerical simulations (DNS) and secondary linear stability theory (SLST) is provided for the three-dimensional crossflow-dominated boundary layer also considered at the DLR-Göttingen for experiments and theory. Secondary instabilities of large-amplitude steady and unsteady crossflow vortices arising from one single primary mode have been analysed. SLST results have been found to be reliable with respect to the dispersion relation and the amplitude distribution of the modal eigenfunction in the crosscut plane. However, significant deviations have been found in the amplification rates, the SLST results being strongly dependent on the necessarily simplified representation of the primary state. The secondary instability mechanisms are shown to be local, i.e. robust with respect to violations of the periodicity assumption made in the SLST for the wall-parallel directions. Perturbations associated with different local maxima of the spanwise periodic eigenfunctions develop independently from each other interacting only with the primary vortices next to them. Characteristic structures induced by different secondary instability modes have been analysed and an analogy with the Kelvin–Helmholtz instability mechanism has been highlighted.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 583 , 25 July 2007 , pp. 229 - 272
Copyright
Copyright © Cambridge University Press 2007

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

REFERENCES

Balachandar, S., Streett, C. L. & Malik, M. R. 1992 Secondary instability in rotating-disk flow. J. Fluid Mech. 242, 323–347.CrossRefGoogle Scholar
Bippes, H. 1999 Basic experiments on transition in three-dimensional boundary layers dominated by crossflow instability. Prog. Aerospace Sci. 35, 363–412.CrossRefGoogle Scholar
Bonfigli, G.. 2006 Numerical simulation of transition and early turbulence in a 3-d boundary layer perturbed by superposed stationary and traveling crossflow vortices. Dissertation, Universität Stuttgart.Google Scholar
Bonfigli, G. & Kloker, M. 1999 Spatial Navier–Stokes simulation of crossflow-induced transition in a three-dimensional boundary layer. In New Results in Numerical and Experimental Fluid Mechanics II (ed. Nitsche, W., Heinemann, H. J. & Hilbig, R.), NNFM, vol. 72. 11th AG STAB-DGLR Symposium, Berlin, Germany, 1998. Vieweg.CrossRefGoogle Scholar
Chernoray, V. G., Dovgal, A. V., Kozlov, V. V. & Löfdahl, L. 2005 Experiments on secondary instability of streamwise vortices in a swept-wing boundary layer. J. Fluid Mech. 534, 295–325.CrossRefGoogle Scholar
Drazin, P. G. & Reid, W. H. 2004 Hydrodynamic Stability, 2nd edn. Cambridge University Press.CrossRefGoogle Scholar
Hein, S. 2004 Nonlinear nonlocal transition ansalysis. Dissertation, Universität Stuttgart.Google Scholar
Högberg, M. & Henningson, D. 1998 Secondary instability of cross-flow vortices in Falkner–Skan–Cooke boundary layers. J. Fluid Mech. 368, 339–357.CrossRefGoogle Scholar
Janke, E. & Balakumar, P. 2000 On the secondary instability of three-dimensional boundary layers. Theoret. Comput. Fluid Dyn. 14, 167–194.CrossRefGoogle Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
Kawakami, M., Kohama, Y. & Okutsu, M. 1999 Stability characteristics of stationary crossflow vortices in three-dimensional boundary layer. AIAA Paper 99–0811.CrossRefGoogle Scholar
Kloker, M. 1993 Direkte Numerische Simulation des laminar-tur-bulenten Strö-mungs-um-schlages in einer stark ver-zögerten Grenz-schicht. Dissertation, Universität Stuttgart.Google Scholar
Koch, W. 2002 On the spatio-temporal stability of primary and secondary crossflow vortices in a three-dimensional boundary layer. J. Fluid Mech. 456, 85–111.CrossRefGoogle Scholar
Koch, W., Bertolotti, F. P., Stolte, A. & Hein, S. 2000 Nonlinear equilibrium solutions in a three-dimensional boundary layer and their secondary stability. J. Fluid Mech. 406, 131–174.CrossRefGoogle Scholar
Lerche, T. 1997 Experimentelle Untersuchung nichtlinearer Strukturbildung im Transitionsproze einer instabilen dreidimensionalen Grenzschicht. Dissertation, Universität Göttingen.Google Scholar
Linnick, M. & Rist, U. 1999 Vortex identification and extraction in a boundary-layer flow. In Vision, Modelling, and Visualization 2005 (ed. Greiner, G., Hornegger, J., Niemann, H. & Stamminger, M.), pp. 9–16. Akad. Verl.-Ges. Aka, November 16–18 2005. Erlangen, Germany.Google Scholar
Malik, M. R. & Chang, C. L. 1994 Crossflow disturbances in three-dimensional boundary layers: nonlinear development, wave interaction and secondary instability. J. Fluid Mech. 268, 1–36.CrossRefGoogle Scholar
Malik, M. R., Li, F., Choudhari, M M.. & Chang, C. L. 1999 Secondary instability of crossflow vortices and swept-wing boundary-layer transition. J. Fluid Mech. 399, 85–115.CrossRefGoogle Scholar
Messing, R. 2004 Direkte Numerische Simulationen zur diskreten Absaugung in einer dreidimensionalen Grenzschichtströmung. Dissertation, Universität Stuttgart.Google Scholar
Meyer, F. 1989 Numerische Simulation der Transition in dreidimensionalen Grenzschichten. Dissertation, Universität Göttingen.Google Scholar
Michalke, A. 1964 On the inviscid instability of the hyperbolic-tangent velocity profile. J. Fluid Mech. 19, 543–556.CrossRefGoogle Scholar
Michalke, A. 1982 On the inviscid instability of a circular jet with external flow. J. Fluid Mech. 114, 343–359.CrossRefGoogle Scholar
Müller, B. 1990 Experimentelle Untersuchung der Querströmungsinstabilität im linearen und nichtlinearen Bereich des Transitionsgebietes. Dissertation, Universität Göttingen.Google Scholar
Müller, W. 1995 Numerische Untersuchung räumlicher Umschlagvorgänge in dreidimensionalen Grenzschichtströmungen. Dissertation, Universität Stuttgart.Google Scholar
Radeztsky, R. H., Reibert, M. S. & Saric, W. S. 1999 Effect of isolated micro-sized roughness on transition in swept-wing flows. AIAA J. 38, 1370–1377.CrossRefGoogle Scholar
Reed, H. L. & Saric, W. S. 1989 Stability of three-dimensional boundary layers. Annu. Rev. Fluid Mech. 21, 235–284.CrossRefGoogle Scholar
Saric, W. S., Reed, H. L. & White, E. B. 2003 Stability and transition of three-dimensional boundary layers. Annu. Rev. Fluid Mech. 35, 413–440.CrossRefGoogle Scholar
Wassermann, P. & Kloker, M. 2002 Mechanisms and passive control of crossflow-vortex-induced transition in a three-dimensional boundary layer. J. Fluid Mech. 456, 49–84.CrossRefGoogle Scholar
Wassermann, P. & Kloker, M. 2003 Transition mechanisms induced by travelling crossflow vortices in a three-dimensional boundary layer. J. Fluid Mech. 483, 67–89.CrossRefGoogle Scholar
Wassermann, P. & Kloker, M. 2005 Transition mechanisms in a three-dimensional boundary-layer flow with pressure-gradient changeover. J. Fluid Mech. 530, 265–293.CrossRefGoogle Scholar
White, E. B. & Saric, W. S. 2005 Secondary instability of crossflow vortices. J. Fluid Mech. 525, 275–308.CrossRefGoogle Scholar
White, E. B., Saric, W. S., Gladden, R. D. & Gabet, P. M. 2001 Stages of swept-wing transition. AIAA Paper 2001–0271.CrossRefGoogle Scholar
Wintergerste, T. 2002 Numerische Untersuchung der Spätstadien der Transition in einer dreidimensionalen Grenzschicht. Dissertation, Eidgenössische Technische Hochschule Zürich.Google Scholar