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Nonlinear Crossflow Disturbances and Secondary Instabilities in Swept-Wing Boundary Layers

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Part of the book series: Fluid Mechanics and Its Applications ((FMIA,volume 35))

Abstract

We numerically solve the governing partial differential equations to study nonlinear evolution of crossflow disturbances in incompressible as well as compressible boundary layers. When the amplitude of these disturbances become sufficiendy large, the flow field becomes highly inflectional and unstable to high-frequency oscillations (secondary instability) which lead to breakdown to turbulence in three-dimensional boundary layers. Using the 2D eigenvalue approach, we consider secondary instability of crossflow vortices in swept-wing flows, discuss their structure and the associated production mechanism. The results for a swept-cylinder show the existence of secondary oscillations of about 17 kHz yielding good agreement with the experiments of Poll (1985). Calculations for a supersonic boundary layer show secondary oscillations approaching frequencies of 1 MHz.

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References

  • Balachandar, S., Streett, C. L., and Malik, M. R. (1992) Secondary instability in a rotating disk flow, J. Fluid Mech. 242, 323–347.

    Article  ADS  Google Scholar 

  • Bertolotti, F. P., Herbert, Th. and Spalart, P. R. (1992) Linear and nonlinear stability of the Blasius boundary layer, J. Fluid Mech. 242, 441–474.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Chang, C.-L. and Malik, M. R. (1994) Oblique-mode breakdown and secondary instability in supersonic boundary layers, J. Fluid Mech. 273, 323–359.

    Article  ADS  MATH  Google Scholar 

  • Chang, C. -L., Malik, M. R., Erlebacher, G. and Hussaini, M. Y. (1991) Compressible stability of growing boundary layers using parabolized stability equations, AIAA Paper 91–1636.

    Google Scholar 

  • Chang, C. -L., Malik, M. R„ and Vinh, H. (1995) Linear and Nonlinear Stability of Compressible Swept-Wing Boundary Layers, AIAA Paper 95–2278.

    Google Scholar 

  • Creel, T. R., Jr., Malik, M. R., and Beckwith, I. E. (1987) Experimental and theoretical investigation of boundary-layer instability mechanisms on a swept leading edge at Mach 3.5, Research in Natural Laminar Flow and Laminar-Flow Control, NASA Conference Publication 2487, Part 3, 981–995.

    Book  Google Scholar 

  • Gregory, N., Stuart, J. T., and Walker, W. S., (1955) On the stability of three-dimensional boundary layers with application to the flow due to a rotating disk,” Phil. Trans, Roy. Soc. A 248, 155–199.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Herbert, Th. (1991) Boundary-layer transition — analysis and prediction revisited, AIAA Paper No. 91–0737.

    Google Scholar 

  • Li, F. and Malik, M. R. (1995) Fundamental and subharmonic secondary instabilities of Görtier vortices, J. Fluid Mech. in press.

    Google Scholar 

  • Kohama, Y. (1984) Study on boundary-layer transition of a rotating disk, Acta Mechanica 50, 193–199.

    Article  ADS  Google Scholar 

  • Kohama, Y, Saric, W. S., and Hoos, J. A. (1991) A hjigh-frequency, secondary instability of crossflow vortices that leads to transition, Proc. of The Royal Aeronautical Society Conf. on Boundary Layer Transition & Control, Cambridge, UK, pp. 4.1–4.13.

    Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  • Poll, D. I. A., (1985) Some observations of the transition process on the windward face of a long yawed cylinder, J. Fluid Mech. 150, 329–356.

    Article  ADS  Google Scholar 

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© 1996 Kluwer Academic Publishers

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Malik, M.R., Li, F., Chang, CL. (1996). Nonlinear Crossflow Disturbances and Secondary Instabilities in Swept-Wing Boundary Layers. In: Duck, P.W., Hall, P. (eds) IUTAM Symposium on Nonlinear Instability and Transition in Three-Dimensional Boundary Layers. Fluid Mechanics and Its Applications, vol 35. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1700-2_25

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  • DOI: https://doi.org/10.1007/978-94-009-1700-2_25

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7261-8

  • Online ISBN: 978-94-009-1700-2

  • eBook Packages: Springer Book Archive

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