Plenary Lecture

Instability and Three-Wave Interactions in Supersonic Boundary Layers

Professor Sergey A. Gaponov
co-author N. M. Terekhova
Khristianovich Institute of Theoretical and Applied Mechanics (ITAM)
E-mail: gaponov@itam.nsc.ru

Abstract: The problem of laminarization of viscous flows became topical in connection with an important practical problem, namely, the problem of reducing friction drag. As a rule, laminar-turbulent transition is initiated by unstable oscillations growing downstream, and therefore suppression of the instability wave leads to an increase in the length of the laminar flow section. In the paper the disturbances development in supersonic boundary layer is considered within the framework of the linear and weakly nonlinear stability theory for the Mach number M = 2; 5.3 on the soled, porous and flexible surfaces. The special attention is paid to three - wave interaction. On a porous surface at M = 5.3 acoustic and vortex waves in resonant three-wave systems are found to interact in the weak redistribution mode, which leads to weak decay of the acoustic component and weak amplification of the vortex component. Three-dimensional vortex waves are demonstrated to interact more intensively than two-dimensional waves. Vanishing of the pumping wave, which corresponds to a plane acoustic wave on a solid surface, is found to assist in increasing the length of the regions of linear growth of disturbances and the laminar flow regime. At M = 2.0 it was established that three-wave resonant interaction is stronger for non-symmetric triplet at M=2 on the impermeable surface, and such nonlinear interactions become even stronger on the porous surface in comparison to impermeable surface. For flexible coverings it was established that them an influence on a stability of a boundary layer considerably even in case of a gas stream. At moderate supersonic speeds application of thin flexible coverings leads to flow stabilization, at least, in the field of large Reynolds's numbers. At high Mach numbers, for example for М=5.3, the area of low Reynolds's numbers where destabilization of the second mode is observed, extends in comparison with case М=2.0. However at Reynolds's numbers answering to the greatest instability at a rigid surface, the flexible covering stabilizes a flow. As a whole flexible covering destabilizes vortical and stabilizes acoustic disturbance both on linear and on nonlinear development stages.

Brief Biography of the Speaker: Sergey Gaponov graduated from the Physics Department of Novosibirsk State University, Russia in 1964. With 1965 till April he works in the Khristianovich Institute of Theoretical and Applied Mechanics of Siberian Branch of Russian Academy of Science as Junior and Senior Scientific Researcher, Head of Laboratory. Now he is Main researcher of the same Institute. With 1992 he works also as Professor of the Department of Theoretical Mechanics, Novosibirsk State University of Architecture and Civil Engineering. S. Gaponov is the expert in a field of the fluid and gas mechanics. The basic directions of his scientific activity are connected with researches of hydrodynamic stability, non-stationary processes and the turbulence occurrence in supersonic gas flows. He defended the candidate thesis "Stability of the incompressible boundary layer on a permeable Surface" (1971) and doctor thesis (physics and mathematics) “Development of disturbances in a supersonic boundary layer” (1987). He is member of Council on a defence of doctoral theses at Institute of Theoretical and Applied Mechanics, member of Russian National Committee on Theoretical and Applied Mechanics, member of the International Scientific Committee on Fluid Mechanics and Aerodynamics. The prize of Zhukovsky was awarded to him. There are many grants for fundamental research in which he took part: Grant of International Science and Technology Center: ISTC-128-96 investigator, Grants of Russian Foundation for Basic Research (team leader.) He took part in work of numerous scientific conferences, including the Fluid Mechanics and Aerodynamics conferences. Number of his papers in refereed journals is more than140. Two books were published.

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