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Numerical studies on evolution of secondary streamwise vortices in transitional boundary layers

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Abstract

Formation and evolution of secondary streamwise vortices in the compressible transitional boundary layers over a flat plate are studied using a direct numerical simulation method with high-order accuracy and highly effective non-reflecting characteristic boundary conditions. Generation and development processes of the secondary streamwise vortices in the complicated transitional boundary flow are clearly analyzed based on the of numerical results, and the effects on the formation of the ring-like vortex that is vital to the boundary layer transition are explored. A new mechanism forming the ring-like vortex through the mutual effect of the primary and secondary streamwise vortices is expressed.

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References

  1. Borodulin, V. I., Gaponenko, V. R., Kachanov, Y. S., Meyer, D. G. W., Rist, U., Lian, Q. X., and Lee, C. B. Late-stage transitional boundary-layer structures: direct numerical simulation and experiment. Theoret. Comput. Fluid Dynamics, 15, 317–337 (2002)

    Article  MATH  Google Scholar 

  2. Tang, D. B. and Xia, H. Nonlinear evolution analysis of T-S disturbance wave at finite amplitude in nonparallel boundary layers. Applied Mathematics and Mechanics (English Edition), 23(6), 660–669 (2002) DOI 10.1007/BF02437650

    Article  MATH  Google Scholar 

  3. Kachanov, Y. S. Physical mechanisms of laminar-boundary-layer transition. Annu. Rev. Fluid Mech., 26, 411–482 (2002)

    Article  Google Scholar 

  4. Borodulin, V. I., Kachanov, Y. S., and Koptsev, D. B. Experimental study of resonant interactions of instability waves in self-similar boundary layer with an adverse pressure gradient. J. Turbulence, 3, 62–64 (2002)

    Google Scholar 

  5. Kachanov, Y. S. On a universal mechanism of turbulence production in wall shear flows. Recent Results in Laminar-Turbulent Transition, Springer, Berlin, Vol. 86, 1–12 (2003)

    Google Scholar 

  6. Bake, S., Meyer, D. G. W., and Rist, U. Turbulence mechanism in Klebanoff transition: a quantitative comparison of experiment and direct numerical simulation. J. Fluid Mech., 459, 217–243 (2002)

    Article  MATH  Google Scholar 

  7. Zhang, Y. M. and Zhou, H. PSE as applied to problems of transition in compressible boundary layers. Applied Methematics and Mechanics (English Edition), 29(7), 833–840 (2008) DOI 10.1007/s10483-008-0701-8

    Article  MATH  Google Scholar 

  8. Guo, X. and Tang, D. B. Nonlinear stability of supersonic nonparallel boundary layer flows. Chinese Journal of Aeronautics, 23, 283–289 (2010)

    Article  Google Scholar 

  9. Huang, Z. F., Can, W., and Zhou, H. The mechanism of breakdown in laminar-turbulent transition of a supersonic boundary layer on a flat plate-temporal mode. Science in China, Series G: Physics, Mechanics & Astronomy, 48(5), 614–625 (2005)

    Article  Google Scholar 

  10. Li, X. L., Fu, D. X., and Ma, Y. W. DNS of compressible turbulent boundary layer over a blunt wedge. Science in China, Series G: Physics, Mechanics & Astronomy, 48(2), 129–141 (2005)

    Article  Google Scholar 

  11. Sergio, P., Matteo, B., and Francesco, G. Characterization of coherent vortical structures in a supersonic turbulent boundary layer. J. Fluid Mech., 613, 205–231 (2008)

    MATH  Google Scholar 

  12. Robinson, S. K. Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech., 23, 601–639 (1991)

    Article  Google Scholar 

  13. Doligalski, T. L. and Walker, J. D. A. The boundary layer induced by a convected two-dimensional vortex. J. Fluid Mech., 139, 1–28 (1984)

    Article  MATH  Google Scholar 

  14. Lee, C. B. and Wu, J. Z. Transition in wall-bounded flows. Applied Mechanics Reviews, 61(3), 030802 (2008)

    Article  MathSciNet  Google Scholar 

  15. Acarlar, M. S. and Smith, C. R. A study of hairpin vortices in a laminar boundary layer, part II: hairpin vorices generated by fluid injection. J. Fluid Mech., 175, 43–83 (2002)

    Article  Google Scholar 

  16. Lee, C. B. On the formation of the streamwise vortex in a transitioanal boundary layer. Acta Physica Sinica, 50(1), 182–184 (2001)

    Google Scholar 

  17. Moin, P. and Mahesh, K. Direct numerical simulation: a tool in turbulence research. Annu. Rev. Fluid Mech., 30, 539–578 (1998)

    Article  MathSciNet  Google Scholar 

  18. Jiang, L., Shan, H., and Liu, C. Direct numerical simulation of boundary-layer receptivity for subsonic flow around airfoil. Proceedings of the Second AFOSR International Conference on DNS/LES, The State University of New Jersey, New Brunswick (1999)

    Google Scholar 

  19. Lele, S. K. Compact finite difference schemes with spectral-like resolution. Journal of Computational Physics, 103, 16–42 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  20. Shu, C. W. and Osher, S. Efficient implementation of essentially non-oscillatory shock-capturing scheme. Journal of Computational Physics, 77, 39–471 (1988)

    Article  MathSciNet  Google Scholar 

  21. Malik, M. R. Numerical methods for hypersonic boundary layer stability. Journal of Computational Physics, 86, 376–413 (1990)

    Article  MATH  Google Scholar 

  22. Jiang, L., Shan, H., and Liu, C. Non-reflecting boundary conditions for DNS in curvilinear coordinates. Proceedings of the Second AFOSR International Conference on DNS/LES, The State University of New Jersey, New Brunswick (1999)

    Google Scholar 

  23. Chen, L., Tang, D. B., and Guo, X. Numerical simulation of free vortex with modified Navier-Stokes characteristic boundary conditions. Modern Physics Letters B, 24(13), 57–60 (2010)

    Google Scholar 

  24. Wu, J. Z., Ma, H. Y., and Zhou, M. D. Vorticity and Vortex Dynamics, Springer, Berlin (2006)

    Book  Google Scholar 

  25. Jeong, J. and Hussain, F. On the identification of a vortex. J. Fluid Mech., 285, 69–94 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  26. Chen, L., Tang, D. B., Liu, X. B., Oliveira, M., and Liu, C. Q. Evolution of the ring-like vortices and spike structure in transitional boundary layers. Science in China, Series G: Physics, Mechanics & Astronomy, 53(3), 514–520 (2010)

    Article  Google Scholar 

  27. Chen, L. and Liu, C. Numerical study on mechanisms of second sweep and positive spikes in transitional flow on a flat plate. Computers & Fluids, 40, 28–41 (2011)

    Article  Google Scholar 

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Correspondence to Deng-bin Tang  (唐登斌).

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Project supported by the National Natural Science Foundation of China (No. 10772082) and AFOSR (No.FA9550-08-1-0201)

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Chen, L., Tang, Db. & Liu, Cq. Numerical studies on evolution of secondary streamwise vortices in transitional boundary layers. Appl. Math. Mech.-Engl. Ed. 32, 449–458 (2011). https://doi.org/10.1007/s10483-011-1429-9

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  • DOI: https://doi.org/10.1007/s10483-011-1429-9

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Chinese Library Classification

2010 Mathematics Subject Classification

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