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Plenary Lecture
Instability and Receptivity of a Compressible
Boundary Layer
Sergey A. Gaponov
Institute of Theoretical and Applied Mechanics (ITAM),
SB RAS, 630090, Novosibirsk,
RUSSIA
Fax: +7(383)3307268
E-mail: gaponov@itam.nsc.ru
Web site: http://www.itam.nsc.ru/
Abstract:
A strong international interest in problems receptivity and stability exists
in connection with studies of the laminar- turbulent transition in
wall-bounded shear layers of gas-turbine-engine blades and vanes,
low-Reynolds-number vehicles, submarines and torpedoes, subsonic and
supersonic civil transports and reentry vehicles. The onset of turbulence in
the boundary layer comprises three main stages: (a) receptivity, (b) linear
stability, and (c) nonlinear breakdown.
During the first stage, in the region of relatively low local Reynolds
number, instability waves are generated. The problem of generating these
waves by perturbations (which include acoustic, vortical, temperature) is
referred to as the problem of boundary-layer receptivity to external
disturbances. This aspect of the transition process was clearly formulated
for the first time by Morkovin as the problem of transformation of external
disturbances into eigen boundary-layer oscillations.
The second stage of transition corresponds to the propagation of
small-amplitude instability waves down the boundary layer, which are either
amplified, if the flow is unstable to them, or attenuated. This stage is
described by linear hydrodynamic stability theory.
The objective of this paper is to provide a critical evaluation of stability
and receptivity for the compressible boundary layer (mainly for supersonic
flows).
Receptivity of supersonic boundary layer to acoustic, vorticity and thermal
disturbances is considered too. Boundary layer internal eigen oscillations
are mostly excited by acoustic waves with finite angles of incidence whose
wave fronts are parallel to plate leading edge. For angle of incidence
equals to zero, the most intensive fluctuations are excited by oblique
waves. The exact value of this angle slowly depends on basic flow and
acoustic wave parameters. The intensity of internal disturbances exceeds
much the amplitude of external acoustic wave. As concern to the boundary
layer interaction with external perturbations, which are transferred by a
mean flow, it was found that the efficiency of the eigen boundary layer
disturbances excitation is much higher for three-dimensional (3D) waves
comparing to 2D one and it is increasing with decreasing frequency. So the
maximal flow distortion was found for steady disturbances, which induce
stream-wise structures inside the boundary layer.
The linear stability analysis of supersonic boundary layers uncovers some
differences between supersonic instability and the subsonic one. The
extension of the Rayleigh inflection-point criterion to compressible
boundary layers has an important change from incompressible boundary layers.
Lees & Lin and Mack classified the disturbance according to the disturbance
phase speed relative to the boundary-layer edge velocity: 1) subsonic, 2)
sonic and 3) supersonic. One of the most significant developments in
compressible theory consists in detection of new unstable waves. At moderate
Mach numbers most unstable are the three-dimensional (3-D, inclined) waves
of the first mode. The lowest-frequency the so-called second mode is found
to be the dominant instability for Mach number greater than about 4; it is
more unstable than either the 3-D first mode.
When the amplitudes of instability waves reach considerable values the flow
enters a phase of nonlinear breakdown, randomization, and a final transition
into a turbulent state. In the case of a weak non- linearity it is watched
the development of non-symmetrical triads, because of the primary unstable
mode is three-dimensional in the supersonic boundary layer. If the
amplitudes are large enough the three-dimensional disturbances could be
degenerate into two- dimensional.
All this problem will be consider in the report.
Brief Biography of the Speaker:
Field of
research:
Fluid dynamics, laminar- turbulent
transition in wall-bounded shear layers.
Surname: Gaponov
First name:
Sergey
Date of
birth:
August 20,
1940
Affiliation:
Laboratory
wave processes in supersonic viscous flows,
Institute of Theoretical and Applied Mechanics of Siberian Branch of Russian
Academy of Science (ITAM SB RAS); Professor at the Department of Theoretical
Mechanics, Novosibirsk State
University of Architecture and Civil Engineering
(NSUACE).
Address:
Institutskaya Street, 4/1, 630090 Novosibirsk, Russia
Phone:
+7(383)3301228
Fax:
+7(383)3307268
E-mail:
gaponov@itam.nsc.ru
Education:
Graduated from Physics Department of Novosibirsk State University
(NSU), 1964.
Brief
description of professional career
(including the title of the dissertation work, the year and the Institution
where it has been defended):
1.
Junior and
Senior Scientific Researcher, Head of Laboratory
of the
Institute
of Theoretical and Applied Mechanics SB RAS, January 1965 – till now.
2.
Professor
at the Department of Theoretical Mechanics,
Novosibirsk State University of Architecture
and Civil Engineering (NSUACE),
1992-till now.
Ph.D.
Thesis:
"Stability
of the Incompressible Boundary
Layer on a
Permeable Surface", 1971, Institute of Theoretical and Applied Mechanics of
Siberian Branch of Russian Academy of Science (ITAM SB RAS).
Degree of
Doctor (Physics and Mathematics):
«Development of disturbances in a supersonic boundary layer», 1987, Moscow
Physical-Technical Institute.
Other
fields:
Member of
Council on Defence of doctoral Thesis’s at Institute of Theoretical and
Applied Mechanics, Member of Russian National Committee on Theoretical and
Applied Mechanics, Prize-Winner of Professor Joukovski
List of
recent grants for fundamental research:
Grant of
International Science and Technology Center: ISTC-128-96 (1996-1999,
investigator). Grants of Russian Foundation for Basic Research (1994-95,
1996-98, 1999-01, 2002-04, 2005-07, team leader.)
Publications:
Number of
communications to scientific meetings exceed hundred. Number of papers in
refereed journals: 130. Two books are published.
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