Skip to main content
SpringerLink
Log in
Book cover

New Results in Numerical and Experimental Fluid Mechanics XI pp 219–228Cite as

Linear and Nonlinear Growth of Secondary Instabilities of Stationary Crossflow Vortices Studied by Parabolized Stability Equations

  • Conference paper
  • First Online:

  • 2149 Accesses

Part of the book series: Notes on Numerical Fluid Mechanics and Multidisciplinary Design ((NNFM,volume 136))

Abstract

Laminar–turbulent transition in (quasi–) three–dimensional boundary layers dominated by stationary crossflow vortices is studied for the setup of the DLR swept–flat plate experiment. The linear and subsequent nonlinear development of both the stationary crossflow vortices and their high–frequency secondary instabilities are modelled by nonlinear parabolized stability equations (PSE). In contrast to previous work, secondary instability theory is used only for initialization of secondary instabilities within the PSE analysis. Thereby, the nonlinear development of secondary instabilities including the generation of higher harmonics could be studied up to the stages where the feedback of the finite–amplitude secondary instability modes on the stationary crossflow vortices is no longer negligible and the skin–friction coefficient starts to deviate from that due to the mean flow distortion caused by the stationary crossflow modes alone. Moreover, the present approach allows rather efficient studies on the nonlinear development of secondary instabilities independent of their frequency.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    Note that the DLR swept flat plate experiment recently has been re–established with a slightly increased chord length and a modified shape of the displacement body which imposes a different pressure distribution on the flat plate (see [1]).

References

  1. Barth, H.P., Hein, S., Rosemann, H.: Redesigned swept flat-plate experiment for crossflow-induced transition studies. In: Proceedings 20. DGLR-Fach-Symposium der STAB, 8.+9. Nov. 2016, Braunschweig

    Google Scholar 

  2. Deyhle, H., Bippes, H.: Disturbance growth in an unstable three-dimensional boundary layer and its dependence on environmental conditions. J. Fluid Mech. 316, 73–113 (1996)

    Article  Google Scholar 

  3. Hein, S.: Nonlinear nonlocal transition analysis. DLR-FB 2005-10 (2005)

    Google Scholar 

  4. Hein, S.: Nonlinear nonlocal analysis of crossflow–dominated transition scenarios using DNS–like resolution. In: Govindarajan, R. (ed.) Proceedings Sixth IUTAM Symposium on Laminar–Turbulent Transition, 13-17 December 2004, Bangalore, India. Fluid Mech. Appl. 78, pp. 281–286. Springer (2006)

    Google Scholar 

  5. Hein, S., Koch, W.: Secondary instability theory applied to the Fokker 100 flight experiment. ALTTA Technical Report No. 82 (2003)

    Google Scholar 

  6. Hein, S., Bertolotti, F.P., Simen, M., Hanifi, A., Henningson, D.: Linear nonlocal instability analysis—The linear NOLOT code–. DLR-IB A56, 223–294 (1995)

    Google Scholar 

  7. Janke, E., Balakumar, P.: On the secondary instability of three-dimensional boundary layers. Theor. Comput. Fluid Dyn. 14, 167–194 (2000)

    Article  MATH  Google Scholar 

  8. Koch, W., Bertolotti, F.P., Stolte, A., Hein, S.: Nonlinear equilibrium solutions in a three-dimensional boundary layer and their secondary instability. J. Fluid Mech. 406, 131–174 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  9. Li, F., Choudhari, M.M.: Spatially developing secondary instabilities in compressible swept airfoil boundary layers. Theor. Comput. Fluid Dyn. 25, 65–84 (2011)

    Article  MATH  Google Scholar 

  10. Malik, M.R., Li, F., Chang, C.L.: Crossflow disturbances in three-dimensional boundary layers: nonlinear development, wave interaction and secondary instability. J. Fluid Mech. 268, 1–36 (1994)

    Article  MATH  Google Scholar 

  11. Malik, M.R., Li, F., Choudhari, M.M., Chang, C.L.: Secondary instability of crossflow vortices and swept-wing boundary-layer transition. J. Fluid Mech. 399, 85–115 (1999)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. DLR—Institute of Aerodynamics and Flow Technology, Bunsenstr.10, 37073, Göttingen, Germany

    Stefan Hein

Authors
  1. Stefan Hein
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stefan Hein .

Editor information

Editors and Affiliations

  1. Institut für Aerodynamik und Strömungstechnik, Deutsches Zentrum für Luft- und Raumfahrt, Göttingen, Germany

    Andreas Dillmann

  2. Airbus Deutschland, Bremen, Germany

    Gerd Heller

  3. Institut für Aerodynamik und Gasdynamik, Universität Stuttgart, Stuttgart, Germany

    Ewald Krämer

  4. Institut für Aerodynamik und Strömungstechnik, Deutsches Zentrum für Luft- und Raumfahrt, Göttingen, Germany

    Claus Wagner

  5. Institut für Strömungsmechanik, Technische Universität Braunschweig, Braunschweig, Germany

    Stephan Bansmer

  6. Institut für Strömungsmechanik, Technische Universität Braunschweig, Braunschweig, Germany

    Rolf Radespiel

  7. Institut für Strömungsmechanik, Technische Universität Braunschweig, Braunschweig, Germany

    Richard Semaan

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Hein, S. (2018). Linear and Nonlinear Growth of Secondary Instabilities of Stationary Crossflow Vortices Studied by Parabolized Stability Equations. In: Dillmann, A., et al. New Results in Numerical and Experimental Fluid Mechanics XI. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 136. Springer, Cham. https://doi.org/10.1007/978-3-319-64519-3_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-64519-3_20

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-64518-6

  • Online ISBN: 978-3-319-64519-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation