Publisher Summary The chapter reviews subdivisions of the boundary layers that become necessary under the impact of sudden stream wise changes. If the boundary layer is supersonic, a new phenomenon occurs that appears to have no counterpart in subsonic flow. It leads to a greater ease of study of the flow properties and helps to overcome the barrier of separation that appears to hinder progress in the incompressible studies. The phenomenon is the free-interaction boundary layer, first observed by Ackeret and independently by Liepmann in their study of the interaction between a shock wave and a boundary layer and more extensively studied subsequently by Liepmann, Chapman, Hakkinen, and many others. These studies show that when a shock, sufficiently strong to provoke separation, strikes a laminar boundary layer, the boundary layer actually separates ahead of the foot of the shock and the flow features of the separation region are independent of the characteristics of the shock and depend only on the local properties of the flow. The chapter provides example for incompressible boundary layers when the fluid is compressible and explains the modifications necessary to allow this effect.

Multistructured Boundary Layers on Flat Plates and Related Bodies

Great efforts have been dedicated during the last decades to the research and development of hypersonic aircrafts that can fly at several times the speed of sound. These aerospace vehicles have revolutionary applications in national security as advanced hypersonic weapons, in space exploration as reusable stages for access to low Earth orbit, and in commercial aviation as fast long-range methods for air transportation of passengers around the globe. This review addresses the topic of supersonic combustion, which represents the central physical process that enables scramjet hypersonic propulsion systems to accelerate aircrafts to ultra-high speeds. The description focuses on recent experimental flights and ground-based research programs and highlights associated fundamental flow physics, subgrid-scale model development, and full-system numerical simulations.

Supersonic Combustion in Air-Breathing Propulsion Systems for Hypersonic Flight

The problems associated with the prohibitive number of possible system modes for a fluttering compressor or turbine blade row are eliminated by the development that comprises the present report. The existence and uniqueness of extremely simple system flutter modes are proved for blade rows consisting of identical blades equally spaced about a common rotor. These simple system modes, if properly interpreted, have the effect of reducing by a factor of n the number of degrees of freedom necessary to analyze an w-bladed configuration. Stated differently, the system of n blades may be considered, with no loss of generality whatsoever, in terms of a single "equivalent blade." The proof holds under any type of flow and any and all types of interblade coupling, so long as a linear analysis is permissible. Moreover, since it is the flutter-inception point that is of interest in predicting critical velocity or rotational speed, it may well be that the conclusions developed apply even to the onset of stall flutter. Practical application of the method to stall-flutter calculations would, of course, require the availability of aerodynamic stallflutter coefficients. The development is carried out first under the assumption of infinite rotor inertia or, in other words, constant rotor velocity. This restriction is then relaxed, and the treatment is expanded to permit torsional oscillations of the rotor itself. I t is proved that under certain conditions the assumption of infinite rotor inertia introduces no error whatsoever.

System Mode Shapes in the Flutter of Compressor Blade Rows

The principal objective of this paper is to study some unsteady characteristics of an interaction between an incident oblique shock wave impinging on a laminar boundary layer developing on a flat plate. More precisely, this paper shows that some unsteadiness, in particular the low-frequency unsteadiness, originates in a supercritical Hopf bifurcation related to the dynamics of the separated boundary layer. Various direct numerical simulations were carried out of a shock-wave/laminar-boundary-layer interaction (SWBLI). Three-dimensional unsteady Navier–Stokes equations are numerically solved with an implicit dual time stepping for the temporal algorithm and high-order AUSMPW+ scheme for the spatial discretization. A parametric study on the oblique shock-wave angle has been performed to characterize the unsteady behaviour onset. These numerical simulations have shown that starting from the incident shock angle and the spanwise extension, the flow becomes three-dimensional and unsteady. A linearized global stability analysis is carried out in order to specify and to find some characteristics observed in the direct numerical simulation. This stability analysis permits us to show that the physical origin generating the three-dimensional characters of the flow results from the existence of a three-dimensional stationary global instability.

http://jch.robinet.pagesperso-orange.fr/pdf/Robinet_JFM_2006.pdf

Bifurcations in shock-wave/laminar-boundary-layer interaction : global instability approach

: A study is presented of the characteristics of transitional and turbulent layers, and regions of shock wave-turbulent boundary layer interaction in high Reynolds number hypersonic flow. An examination and correlation of skin friction, heat transfer and pressure measurements in laminar, transitional and turbulent boundary layers on sharp flat plates and cones are presented for the Mach range from 3 to 13 at wall-to-free stream temperature ratios from 0.1 to 0. 4.

M. J. Lighthill

Papers

Reflection at a laminar boundary layer of a weak steady disturbance to a supersonic stream, neglecting viscosity and heat conduction