Skip to main content
SpringerLink
Log in

Local receptivity in non-parallel boundary layer

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

The research on boundary-layer receptivity is the key issue for the laminarturbulent transition prediction in fluid mechanics. Many of the previous studies for local receptivity are on the basis of the parallel flow assumption which cannot accurately reflect the real physics. To overcome this disadvantage, local receptivity in the non-parallel boundary layer is studied in this paper by the direct numerical simulation (DNS). The difference between the non-parallel and parallel boundary layers on local receptivity is investigated. In addition, the effects of the disturbance frequency, the roughness location, and the multiple roughness elements on receptivity are also determined. Besides, the relations of receptivity with the amplitude of free-stream turbulence (FST), with the roughness height, and with the roughness length are ascertained as well. The Tollmien- Schlichting (T-S) wave packets are excited in the non-parallel boundary layer under the interaction of the FST and the localized wall roughness. A group of T-S waves are separated by the fast Fourier transform. The obtained results are in accordance with Dietz’s measurements, Wu’s theoretical calculations, and the linear stability theory (LST).

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Chen, L., Tang, D. B., and Liu, C, Numerical studies on evolution of secondary streamwise vortices in transitional boundary layers. Numerical studies on evolution of secondary streamwise vortices in transitional boundary layers 32, 449–458 (2011)

    MathSciNet  MATH  Google Scholar 

  2. Wu, W. Z. and Tang, D. B. Studies on nonlinear stability of three-dimensional H-type disturbance. Acta Mechanica Sinica, 19, 517–526 (2003)

    Article  MathSciNet  Google Scholar 

  3. Zheng, X. B. and Jiang, N, The spatial-temporal evolution of coherent structures in log law region of turbulent boundary layer. The spatial-temporal evolution of coherent structures in log law region of turbulent boundary layer 31, 16–24 (2015)

    MathSciNet  Google Scholar 

  4. Saric, W. S., Reed, H. L., and Kerschen, E. J. Boundary-layer receptivity to freestream disturbances. Annual Review of Fluid Mechanics, 34, 291–319 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  5. Goldstein, M. E. The evolution of Tollmien-Schlichting waves near a leading edge. Journal of Fluid Mechanics, 127, 59–81 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  6. Goldstein, M. E. Scattering of acoustic waves into Tollmien-Schlichting waves by small streamwise variations in surface geometry. Journal of Fluid Mechanics, 154, 509–529 (1985)

    Article  MATH  Google Scholar 

  7. Ruban, A. I. On the generation of Tollmien-Schlichting waves by sound. Fluid Dynamics, 19, 709–717 (1984)

    Article  MATH  Google Scholar 

  8. Saric, W. S., Hoos, J. A., and Radeztsky, R. H. Boundary-layer receptivity of sound with roughness. Boundary Layer Stability and Transition to Turbulence, 1, 17–22 (1991)

    Google Scholar 

  9. Wiegel, M. and Wlezien, R. Acoustic receptivity of laminar boundary layers over wavy walls. The 3rd Shear Flow Conference, American Institute of Aeronautics and Astronautics, Reston (1993)

    Google Scholar 

  10. Würz, W., Herr, S., Wörner, A., Rist, U., Wagner, S., and Kachanov, Y. S. Three-dimensional acoustic-roughness receptivity of a boundary layer on an airfoil: experiment and direct numerical simulations. Journal of Fluid Mechanics, 478, 135–163 (2003)

    Article  MATH  Google Scholar 

  11. Choudhari, M. Boundary-layer receptivity to three-dimensional unsteady vortical disturbances in free stream. The 34th Aerospace Sciences Meeting and Exhibit, American Institute of Aeronautics and Astronautics, Reston (1996)

    Google Scholar 

  12. Duck, P. W., Ruban, A. I., and Zhikharev, C. N. The generation of Tollmien-Schlichting waves by free-stream turbulence. Journal of Fluid Mechanics, 312, 341–371 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  13. Dietz, A. J. Distributed boundary layer receptivity to convected vorticity. Fluid Dynamics Conference, American Institute of Aeronautics and Astronautics, Reston (1996)

    Book  Google Scholar 

  14. Dietz, A. J. Boundary-layer receptivity to transient convected disturbances. AIAA Journal, 36, 1171–1177 (1998)

    Article  Google Scholar 

  15. Dietz, A. J. Local boundary-layer receptivity to a convected free-stream disturbance. Journal of Fluid Mechanics, 378, 291–317 (1999)

    Article  MathSciNet  Google Scholar 

  16. Wu, X. S. On local boundary-layer receptivity to vortical disturbances in the free stream. Journal of Fluid Mechanics, 449, 373–393 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  17. Wu, X. S. Receptivity of boundary layers with distributed roughness to vortical and acoustic disturbances: a second-order asymptotic theory and comparison with experiments. Journal of Fluid Mechanics, 431, 91–133 (2001)

    Article  MATH  Google Scholar 

  18. Zhang, Y. M. and Zhou, H, Numerical study of local boundary layer receptivity to freestream vortical disturbances. Numerical study of local boundary layer receptivity to freestream vortical disturbances 265, 547–554 (2005) DOI 10.1007/BF02466327

    MATH  Google Scholar 

  19. Shen, L. Y. and Lu, C. G. Boundary-layer receptivity under the interaction of free-stream turbulence and localized wall roughness. Applied Mathematics and Mechanics (English Edition), 373, 349–360 (2016) DOI 10.1007/s10483-016-2037-6

    Article  Google Scholar 

  20. Ricco, P, The pre-transitional Klebanoff modes and other boundary-layer disturbances induced by small-wavelength free-stream vorticity. The pre-transitional Klebanoff modes and other boundary-layer disturbances induced by small-wavelength free-stream vorticity 638, 267–303 (2009)

    MATH  Google Scholar 

  21. Zuccher, S. and Luchini, P, Boundary-layer receptivity to external disturbances using multiple scales. Boundary-layer receptivity to external disturbances using multiple scales 49, 441–467 (2014)

    MathSciNet  MATH  Google Scholar 

  22. Shen, L. Y., Lu, C. G., Wu, W. G., and Xue, S. F. A high-order numerical method to study threedimensional hydrodynamics in a natural river. Advances in Applied Mathematics and Mechanics, 7, 180–195 (2015)

    Article  MathSciNet  Google Scholar 

  23. Lu, C. G., Cao, W. D., Zhang, Y., and Peng, J, Large eddies induced by local impulse at wall of boundary layer with pressure gradients. Large eddies induced by local impulse at wall of boundary layer with pressure gradients 18, 873–878 (2008)

    Google Scholar 

  24. Zhang, Y. M., Zaki, T., Sherwin, S., and Wu, X. S. Nonlinear response of a laminar boundary layer to isotropic and spanwise localized free-stream turbulence. The 6th AIAA Theoretical Fluid Mechanics Conference, American Institute of Aeronautics and Astronautics, Reston (2011)

    Google Scholar 

  25. Bodonyi, R. J. Nonlinear triple-deck studies in boundary-layer receptivity. Applied Mechanics Reviews, 43, S158–S166 (1990)

    Article  Google Scholar 

  26. Zhou, M. D., Liu, D. P., and Blackwelder, R. F. An experimental study of receptivity of acoustic waves in laminar boundary layers. Experiments in Fluids, 17, 1–9 (1994)

    Article  Google Scholar 

  27. Lu, C. G. and Shen, L. Y. Numerical study on boundary-layer receptivity with localized wall blowing/suction (in Chinese). Acta Physica Sinica, 64, 224702 (2015)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Atmospheric Science, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Luyu Shen

  2. School of Marine Science, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Changgen Lu

Authors
  1. Luyu Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Changgen Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Changgen Lu.

Additional information

Project supported by the National Natural Science Foundation of China (No. 11172143) and the Research Innovation Program for College Graduates of Jiangsu Province (No.CXZZ130518)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shen, L., Lu, C. Local receptivity in non-parallel boundary layer. Appl. Math. Mech.-Engl. Ed. 37, 929–940 (2016). https://doi.org/10.1007/s10483-016-2092-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-016-2092-9

Keywords

Chinese Library Classification

2010 Mathematics Subject Classification

Search

Navigation