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Influence of Damping of a Compliant Surface on Inviscid Instability of Overlying Incompressible Boundary Layer
- Authors: Savenkov I.V.1
-
Affiliations:
- Dorodnicyn Computing Center, Federal Research Center “Computer Science and Control,” Russian Academy of Sciences
- Issue: Vol 63, No 9 (2023)
- Pages: 1565-1574
- Section: Mathematical physics
- URL: https://journal-vniispk.ru/0044-4669/article/view/136214
- DOI: https://doi.org/10.31857/S0044466923090144
- EDN: https://elibrary.ru/SGZLHK
- ID: 136214
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Abstract
The instability of an incompressible boundary layer on a compliant plate with respect to inviscid perturbations in the limit of high Reynolds numbers is analyzed using triple-deck theory. It is shown that unstable inviscid perturbations can exist only if the inertia and/or damping of the plate are taken into account. A twofold role of damping is revealed: it suppresses instability under certain conditions, while leading to its generation under other conditions.
About the authors
I. V. Savenkov
Dorodnicyn Computing Center, Federal Research Center “Computer Science and Control,” Russian Academy of Sciences
Author for correspondence.
Email: isavenkov@mail.ru
119333, Moscow, Russia
References
- Kramer M.O. Boundary-layer stabilization by distributed damping // J. Aeronaut. Sci. 1957. V. 24. P. 458–460.
- Benjamin T.B. Effects of a flexible boundary on hydrodynamic stability // J. Fluid Mech. 1960. № 9. P. 513–532.
- Benjamin T.B. The threefold classification of unstable disturbances in flexible surfaces bounding inviscid flows // J. Fluid Mech. 1963. № 16. P. 436–450.
- Landahl M.T. On the stability of a laminar incompressible boundary layer over a flexible surface// J. Fluid Mech. 1962. № 13. P. 609–632.
- Carpenter P.W., Garrad A.D. The hydrodynamic stability of flow over Kramer-type compliant surfaces. Part 1. Tollmien-Schlichting instabilities // J. Fluid Mech. 1985. V. 155. P. 465–510.
- Riley J.J., Gad-el-Hak, Metcalfe R.W. Compliant coatings// Ann. Rev. Fluid Mech. 1988. № 20. P. 393–420.
- Flow Past Highly Compliant Boundaries and in Collapsible Tubes // Proc. of the IUTAM Symp., University of Warwick, UK, 26–30 March 2001. Kluwer Acad. Publ., 2003.
- Gad-el-Hak M. Compliant coatings for drag reduction // Progress in Aerospace Sciences. 2002. V. 38. Iss. 1. January 2002. P. 77–99.
- Carpenter P.W. Recent progress in the use of compliant walls for laminar flow control // Progress in Industrial Mathematics at ECMI 2006. Math. in Industry. 2008. № 12. P. 178.
- Нейланд В.Я. К теории отрыва ламинарного пограничного слоя в сверхзвуковом потоке // Изв. АН СССР. Сер. механ. жидкости и газа. 1969. № 4. С. 53–58.
- Stewartson K., Williams P.G. Self-induced separation // Proc. Roy. Soc. A. 1969. V. 312. № 1509. P. 181–206.
- Messiter A.F. Boundary-layer flow near the trailing edge of a flat plate // SIAM J. Appl. Math. 1970. V. 18. № 1. P. 241–257.
- Савенков И.В. Подавление роста нелинейных волновых пакетов упругостью обтекаемой поверхности // Ж. вычисл. матем. и матем. физ. 1995. Т. 35. № 1. С. 95–103.
- Савенков И.В. Об абсолютной неустойчивости несжимаемого пограничного слоя на податливой поверхности // Ж. вычисл. матем. и матем. физ. 2018. Т. 58. № 2. С. 281–290.
- Савенков И.В. Влияние инерционности податливой поверхности на вязкую неустойчивость несжимаемого пограничного слоя// Ж. вычисл. матем. и матем. физ. 2019. Т. 59. № 4. С. 707–715.
- Walker J.D.A., Fletcher A., Ruban A.I. Instabilities of a flexible surface in supersonic flow // Q. Jl Mech. Appl. Math. 2006. V. 59. № 2. P. 253–276.
- Савенков И.В. Невязкая неустойчивость несжимаемого пограничного слоя на податливой поверхности // Ж. вычисл. матем. и матем. физ. 2020. Т. 60. № 7. С. 1268–1280.
- Жук В.И. Волны Толлмина–Шлихтинга и солитоны. М.: Наука, 2001. 167 с.
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