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Neutral stability curves of low-frequency Görtler flow generated by free-stream vortical disturbances

Published online by Cambridge University Press:  20 April 2018

Samuele Viaro Open the ORCID record for Samuele Viaro [Opens in a new window]  and
Pierre Ricco Open the ORCID record for Pierre Ricco [Opens in a new window]
Samuele Viaro*
Affiliation:
Department of Mechanical Engineering, The University of Sheffield, Sheffield, S1 3JD, UK
Pierre Ricco
Affiliation:
Department of Mechanical Engineering, The University of Sheffield, Sheffield, S1 3JD, UK
*
†Email address for correspondence: sviaro1@sheffield.ac.uk
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Abstract

The neutral curves of the boundary layer Görtler-vortex flow generated by free-stream disturbances, i.e., curves that distinguish the perturbation flow conditions of growth and decay, are computed through a receptivity study for different Görtler numbers, wavelengths, and low frequencies of the free-stream disturbance. The perturbations are defined as Klebanoff modes or strong and weak Görtler vortices, depending on their growth rate. The critical Görtler number below which the inviscid instability due to the curvature never occurs is obtained and the conditions for which only Klebanoff modes exist are thus revealed. A streamwise-dependent receptivity coefficient is defined and we discuss the impact of the receptivity on the $N$ -factor approach for transition prediction.

JFM classification

Boundary Layers: Boundary Layers Boundary Layers: Boundary layer receptivity Boundary Layers: Boundary layer stability

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Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 845 , 25 June 2018 , R1
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Copyright
© 2018 Cambridge University Press 

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References

Bassom, A. P. & Seddougui, S. O. 1995 Receptivity mechanisms for Görtler vortex modes. Theor. Comput. Fluid Dyn. 7 (5), 317–339.Google Scholar
Boiko, A. V., Ivanov, A. V., Kachanov, Y. S. & Mischenko, D. A. 2010 Steady and unsteady Görtler boundary-layer instability on concave wall. Eur. J. Mech. (B/Fluids) 29 (2), 61–83.CrossRefGoogle Scholar
Boiko, A. V., Ivanov, A. V., Kachanov, Y. S., Mischenko, D. A. & Nechepurenko, Y. M. 2017 Excitation of unsteady Görtler vortices by localized surface nonuniformities. Theor. Comput. Fluid Dyn. 31 (1), 67–88.Google Scholar
Goldstein, M. E. 1983 The evolution of Tollmien–Schlichting waves near a leading edge. J. Fluid Mech. 127, 59–81.Google Scholar
Görtler, H. 1940 Über eine dreidimensionale Instabilität Laminarer Grenzschichten an konkaven Wänden. Naschr Wiss Gas, Gottingen Math Phys Klasse 2 (1) ; translated as ‘On the three-dimensional instability of laminar boundary layers on concave walls’. NACA TM 1375, 1954.Google Scholar
Hall, P. 1982 Taylor–Görtler vortices in fully developed or boundary-layer flows: linear theory. J. Fluid Mech. 124, 475–494.Google Scholar
Hall, P. 1983 The linear development of Görtler vortices in growing boundary layers. J. Fluid Mech. 130, 41–58.CrossRefGoogle Scholar
Hall, P. 1990 Görtler vortices in growing boundary layers: the leading edge receptivity problem, linear growth and the nonlinear breakdown stage. Mathematika 37 (74), 151–189.Google Scholar
Jaffe, N. A., Okamura, T. T. & Smith, A. M. O. 1970 Determination of spatial amplification factors and their application to predicting transition. AIAA J. 8 (2), 301–308.CrossRefGoogle Scholar
Leib, S. J., Wundrow, D. W. & Goldstein, M. E. 1999 Effect of free-stream turbulence and other vortical disturbances on a laminar boundary layer. J. Fluid Mech. 380, 169–203.CrossRefGoogle Scholar
Malik, M. R., Li, F., Choudhari, M. M. & Chang, C. 1999 Secondary instability of crossflow vortices and swept-wing boundary layer transition. J. Fluid Mech. 399, 85–115.Google Scholar
Ricco, P. 2009 The pre-transitional Klebanoff modes and other boundary layer disturbances induced by small-wavelength free-stream vorticity. J. Fluid Mech. 638, 267–303.Google Scholar
Ricco, P. & Wu, X. 2007 Response of a compressible laminar boundary layer to free-stream vortical disturbances. J. Fluid Mech. 587, 97–138.Google Scholar
Sescu, A. & Thompson, D. 2015 On the excitation of Görtler vortices by distributed roughness elements. Theor. Comput. Fluid Dyn. 29 (1–2), 67–92.Google Scholar
Smith, A. M. O. 1955 On the growth of Taylor–Görtler vortices along highly concave walls. Quart. J. Math. 13 (3), 233–262.Google Scholar
Squire, H. B. 1933 On the stability for three-dimensional disturbances of viscous fluid flow between parallel walls. Proc. R. Soc. Lond. A 142, 621–628.Google Scholar
Tollmien, W. 1929 Uber die Entstehung der Turbulenz 1. Mitteilung. Nach. Ges. Wiss. Göttingen, Math. Phys. Kl. 21–44. Translated into English as NACA TM 609 (1931).Google Scholar
Ustinov, M. V. 2013 Boundary layer receptivity to the nonlinearly developing freestream turbulence. Fluid Dyn. 48 (5), 621–635.Google Scholar
Van Ingen, J. L.1956 A suggested semi-empirical method for the calculation of the boundary layer transition region. PhD thesis, Technische Hogeschool Delft, Vliegtuigbouwkunde, Rapport VTH-74.Google Scholar
Wu, X., Zhao, D. & Luo, J. 2011 Excitation of steady and unsteady Görtler vortices by free-stream vortical disturbances. J. Fluid Mech. 682, 66–100.Google Scholar
Xu, D., Zhang, Y. & Wu, X. 2017 Nonlinear evolution and secondary instability of steady and unsteady Görtler vortices induced by free-stream vortical disturbances. J. Fluid Mech. 829, 681–730.Google Scholar