Abstract
The interaction of disturbances in supersonic boundary layer is considered within the framework of the weakly nonlinear stability theory for the Mach number M = 2 on the solid and porous surfaces. The interrelations in several triplets composed of two- and three-dimensional waves at the frequencies related by the phase synchronization conditions were modelled. It was found that their interactions on the solid surface are much stronger in the asymmetric triplet. It was found that on a porous surface, the linear increments of vortex disturbances increase considerably, the region of dangerous frequencies widens, and the spatial extension of the existence of growing oscillations increases. Nonlinear interactions are, as a rule, much more intense in comparison with the case of an solid surface; they realize in a broad frequency range, which results to a broadband growth of the Tollmien — Schlichting subharmonic vortex waves. An increase in the surface porosity leads to the intensification of nonlinear processes.
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S.A. Gaponov, N.M. Terekhova, and B.V. Smorodsky, Three-wave interaction of disturbances in hypersonic boundary layer, Vestnik NGU, Ser. Fizika, 2008, Vol. 3, Iss. 3, P. 39–45.
S.A. Gaponov and N.M. Terekhova, Three-wave interactions between disturbances in the hypersonic boundary layer on impermeable and porous surfaces, Fluid Dyn., 2009, Vol. 44, No. 3, P. 362–371.
D.A. Bountin, A.N. Shiplyuk, A.A. Maslov, and N. Chokani, Nonlinear aspects of hypersonic boundary layer stability on a porous surface, in: 42nd AIAA Aerospace Sci. Meeting and Exhibit, 2004/Reno, NV; AAIA Paper, 2004, No. 0258.
S.A. Gaponov and I.I. Maslennikova, Subharmonic instability of supersonic boundary layer, Thermophysics Aeromechanics, 1997, Vol. 4, No. 1, P. 1–10.
S.A. Gaponov and N.M. Terekhova, Evolution of disturbances of elevated intensity in supersonic boundary layer, Aeromekhanika i gazovaya dinamika, 2003, No. 1, P. 28–38.
A. Tumin, Nonlinear interaction of wave trains in a supersonic boundary layer, Phys. Fluids, 1996, Vol. 8, No. 9, P. 2552–2554.
S.A. Gaponov, Influence of gas compressibility on the stability of a boundary layer above a permeable surface at subsonic speeds, Prikl. mekh. techn. fiz., 1975, No. 1, P. 121–125.
S.A. Gaponov, Influence of the porous coating properties on the boundary layer stability, Izv. SO AN SSSR, Ser. tekhn. nauk, 1971, No. 3, Iss. 1, P. 21–23.
F.B. Daniels, On the propagation of sound waves in a cylindrical conduit, J. Acoust. Soc. Amer., 1950, Vol. 22, No. 5, P. 563–564.
M.B. Zelman, On the nonlinear development of disturbances in plane-parallel flows, Izv. SO AN SSSR. Ser. tekhn. nauk, 1974, Iss. 3, No. 13, P. 16–21.
A.D. Kosinov, N.V. Semionov, and S.G. Shevelkov, Investigation of supersonic boundary layer stability and transition using controlled disturbances, in: Proc. Int. Conf. on Methods of Aerophys. Research. Pt. 2, Novosibirsk, 1994, P. 159–166.
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The work was financially supported by the President of Russian Federation (NSh 454.2008.1) and by the Russian Foundation for Basic Research (Grant No. 08-01-00038a).
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Gaponov, S.A., Terekhova, N.M. Three-wave nonlinear interactions of disturbances in supersonic boundary layer on the solid and porous surfaces. Thermophys. Aeromech. 16, 335–346 (2009). https://doi.org/10.1134/S0869864309030020
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DOI: https://doi.org/10.1134/S0869864309030020