Some physical aspects of shock wave/boundary layer interactions Jean Délery · Jean-Paul Dussauge
Received: 9 February 2009 / Accepted: 29 June 2009 / Published online: 26 July 2009 © Springer-Verlag 2009
Abstract When the ﬂow past a vehicle ﬂying at high velocity becomes supersonic, shock waves form, caused either by a change in the slope of a surface, a downstream obstacle or a back pressure constraining the ﬂow to become subsonic. In modern aerodynamics, one can cite a large number of circumstances where shock waves are present. The encounter of a shock wave with a boundary layer results in complex phenomena because of the rapid retardation of the boundary layer ﬂow and the propagation of the shock in a multilayered structure. The consequence of shock wave/ boundary layer interaction (SWBLI) are multiple and often critical for the vehicle or machine performance. The shock submits the boundary layer to an adverse pressure gradient which may strongly distort its velocity proﬁle. At the same time, in turbulent ﬂows, turbulence production is enhanced which ampliﬁes the viscous dissipation leading to aggravated performance losses. In addition, shock-induced separation most often results in large unsteadiness which can damage the vehicle structure or, at least, severely limit its performance. The article ﬁrst presents basic and well-established results on the physics of SWBLI corresponding to a description in terms of an average two-dimensional steady ﬂow. Such a description allows apprehending the essential properties of SWBLIs and drawing the main features of the overall ﬂow structure associated with SWBLI. Then, some emphasis is placed on unsteadiness in SWBLI which constitutes a salient feature of Communicated by A. Hadjadj. J. Délery ONERA/DAFE, Centre de Meudon, Meudon, France e-mail: email@example.com J.-P. Dussauge (B) IUSTI, UMR 6595 CNRS-Université d’Aix Marseille, Marseille, France e-mail: firstname.lastname@example.org
this phenomenon. In spite of their importance, ﬂuctuations in SWBLI have been considered since a relatively recent date although they represent a domain which deserves a special attention because of its importance for a clear physical understanding of interactions and of its practical consequences as in aeroelasticity. Keywords Shock wave/boundary layer interaction · Shock polar · Triple deck structure · Rotational ﬂow · Separated ﬂow · Shock-shock interference · Unsteadiness · Turbulence · Strouhal number PACS 47.40Nm · 47.32Ff List of symbols (C) Designates a shock E( f ) Power spectral density f Frequency h Height of the separated bubble L Interaction length M Mach number Convective Mach number Mc Mach number at the boundary layer outer edge Me p Pressure Stagnation pressure pst r Density ratio R Designates the reattachment point s Velocity ratio S Designates the separation point Strouhal number SL T Designates a triple point Flow velocity on the separated ﬂow dividing UD streamline Flow velocity at the boundary layer outer edge Ue Shock displacement velocity Us
J. Délery, J.-P. Dussauge
X0 (Mc ) ϕ δ ( )
Interaction origin Normalized spreading rate of the mixing layer Shock induced deﬂection Boundary layer thickness Designates a shock polar
1 General introduction When the ﬂow past a vehicle ﬂying at high velocity becomes supersonic, shock waves inevitably form, caused either by a change in the slope of a surface, a downstream obstacle or a back pressure constraining the ﬂow to become subsonic. In modern aerodynamics, one can cite a large number of circumstances where shock waves are present. On transport aircraft, a nearly normal shock terminates the supersonic region existing on the wing in certain ﬂight conditions (see Fig. 1a). This transonic situation is also encountered in turbomachine cascades and on helicopter blades. Supersonic aircraft are much affected by shock...