Abstract
The present study is devoted to the investigation of several, presumably most efficient, mechanisms of the production of non-stationary Görtler vortices in a laminar boundary layer on a concave wall due to scattering of 2D and 3D free-stream vortices by streamwise localized 3D and 2D surface and flow non-uniformities. The experiments were carried out by means of the method of controllable non-stationary disturbances. The interaction of downstream-propagating 3D free-stream vortices with the growing boundary layer, presenting natural 2D bas-flow non-uniformity, was found to lead to a rather efficient excitation of unsteady Görtler modes. This mechanism of distributed receptivity is able to modify considerably the growth rates of the excited Görtler vortices in comparison with the linear stability laws. In the present paper, definitions of the coefficients of distributed vortical receptivity are given and some estimates of values of these coefficients are reported. In spite of a high measurement accuracy and a rather broad range of examined parameters, no excitation of Görtler vortices due to other examined mechanisms was identified.
Similar content being viewed by others
References
J.M. Floryan, On the Görtler instability of boundary layers, J. Aerosp. Sci., 1991, Vol. 28, P. 235–271.
A.V. Boiko, A.V. Ivanov, Y.S. Kachanov, and D.A. Mischenko, Steady and unsteady Görtler boundary-layer instability on concave wall, Eur. J. Mech. B/Fluids, 2010, Vol. 29, P. 61–83.
X. Wu, D. Zhao, and J. Luo, Excitation of steady and unsteady Görtler vortices by free-stream vortical disturbances, J. Fluid Mech., 2011, Vol. 682, P. 66–100, DOI: 10.1017/jfm.2011.224.
Y.S. Kachanov, Three-dimensional receptivity of boundary layers, Eur. J. Mech. B/Fluids, 2000, Vol. 19, No. 5, P. 723–744.
V.R. Gaponenko, A.V. Ivanov, Y.S. Kachanov, and J.D. Crouch, Swept-wing boundary-layer receptivity to surface non-uniformities, J. Fluid Mech., 2002, Vol. 461, P. 93–126.
V.I. Borodulin, A.V. Ivanov, Y.S. Kachanov, and V.Yu. Komarova, Distributed two-dimensional boundarylayer receptivity to non-stationary vortical disturbances in the presence of surface roughness, Thermophysics and Aeromechanics, 2006, Vol. 13, No. 2, P. 183–208.
V.I. Borodulin, A.V. Ivanov, Y.S. Kachanov, and A.A. Fedenkova, Three-dimensional distributed receptivity of a boundary layer to unsteady vortex disturbances, in: Proc. XIII Int. Conf. on Methods of Aerophysical Research, Part III, Parallel Publ. House, Novosibirsk 2007, P. 45–50.
V.I. Borodulin, A.V. Ivanov, and Y.S. Kachanov, Distributed receptivity of swept-wing boundary layer to streamwise vortices. Part. 1. Experimental approach, in: Proc. XV Int. Conf. on Methods of Aerophysical Research, ISBN 978-5-98901-085-1 / V.M. Fomin (Editor), Novosibirsk, ITAM SB RAS, 2010.
V.I. Borodulin, A.V. Ivanov, and Y.S. Kachanov, Distributed receptivity of swept-wing boundary layer to streamwise vortices. Part. 2. Receptivity characteristics, in: Proc. XV Int. Conf. on Methods of Aerophysical Research, ISBN 978-5-98901-085-1, V.M. Fomin (Editor), ITAM SB RAS, Novosibirsk, 2010.
V.I. Borodulin, Y.S. Kachanov, A.P. Roschektayev, and S. Bake, Experimental study of 3D receptivity of a boundary layer to free-stream vortices during their scattering on localized surface vibrations, Thermophysics and Aeromechanics, 2004, Vol. 11, No. 2, P. 185–198.
V.I. Borodulin, A.V. Ivanov, Y.S. Kachanov, and A.P. Roschektayev, Receptivity coefficients at excitation of cross-flow waves by free-stream vortices in the presence of surface roughness, J. Fluid Mech., 2013, Vol. 716, P. 487–527, DOI: 10.1017/jfm.2012.555.
V.I. Borodulin, A.V. Ivanov, Y.S. Kachanov, and A.P. Roschektayev, Vortex receptivity of a swept-wing boundary layer in the presence of surface vibrations, in: Proc. XIV Intern. Conf. on Methods of Aerophysical Research. June 30–July 6, 2008, V.M. Fomin (Editor), Novosibirsk, ITAM SB RAS, 2008, p. 10.
A.V. Ivanov, Y.S. Kachanov, and D.A. Mischenko, Generation of non-stationary Görtler vortices by localized surface non-uniformities. Receptivity coefficients, Thermophysics and Aeromechanics, 2012, Vol. 19, No. 4, P. 523–539.
H. Bippes and H. Görtler, Dreidimensionale Störungen in der Grenzschicht an einer konkaven Wand, Acta Mech., 1972, Vol. 14, P. 251–267.
J.D. Swearingen and R.F. Blackwelder, The growth and breakdown of streamwise vortices in the presence of a wall, J. Fluid Mech., 1987, Vol. 182, P. 255–290.
V. Kottke, On the instability of laminar boundary layers along concave walls towards Görtler vortices, in: Propagation in Non-Equilibrium Systems, J.E. Wesfreid & H. Brand (Eds.), Springer, 1988, P. 390–398.
L.S. Pontryagin, Ordinary Differential Equations, Addison-Wesley Publishing Company, London, 1962.
J. Nocedal and S.J. Wright, Numerical Optimization, Springer Science & Business Media, LLC, 2006.
M. Gen and R. Cheng, Genetic Algorithms and Engineering Optimization, John Wiley & Sons, 2000.
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was financially supported by the Russian Foundation for Basic Research (Grant No. 10-01-00109).
Rights and permissions
About this article
Cite this article
Ivanov, A.V., Kachanov, Y.S. & Mischenko, D.A. Mechanisms of distributed and localized excitation of unsteady Görtler modes by free-stream vortices. Thermophys. Aeromech. 21, 663–678 (2014). https://doi.org/10.1134/S0869864314060018
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0869864314060018