Some Preliminary Thoughts * Part I: Inviscid Hypersonic Flow * Hypersonic Shock and Expansion-Wave Relations * Local Surface Inclination Methods * Hypersonic Inviscid Flowfields: Approximate Methods * Hypersonic Inviscid Flowfields: Exact Methods * Part II: Viscous Hypersonic Flow * Viscous Flow: Basic Aspects, Boundary Layer Results, and Aerodynamic Heating * Hypersonic Viscous Interactions * Computational Fluid Dynamic Solutions of Hypersonic Viscous Flows * Part III: High-Temperature Gas Dynamics * High-Temperature Gas Dynamics: Some Introductory Considerations * Some Aspects of the Thermodynamics of Chemically Reacting Gases (Classical Physical Chemistry) * Elements of Statistical Thermodynamics * Elements of Kinetic Theory * Chemical Vibrational Nonequilibrium * Inviscid High-Temperature Equilibrium Flows * Inviscid High-Temperature Nonequilibrium Flows * Kinetic Theory Revisited: Transport Properties in High-Temperature Gases * Viscous High-Temperature Flows * Introduction to Radiative Gas Dynamics.

Hypersonic and high temperature gas dynamics

The problem of transition from laminar to turbulent flow in viscous bound­ ary layers is of great practical interest. The low skin-friction coefficient of laminar boundary-layer flow is very attractive to those who lay out the engines or pay the fuel for high-speed vehicles such as airplanes. However, the low mixing of fluid properties such as chemical species, heat, or momen­ tum may be intolerable for others who design these engines or cope with the danger of separation in adverse pressure gradients; they may clearly prefer a turbulent state of the flow. Therefore, it would be highly desirable to at least predict, if not to control, whether the flow under consideration is laminar or turbulent. The tremendous efforts of decades of intense research, however, have been to little avail (Reshotko 1976). The empirical en-criterion is still the standard tool in engineering practice, although it is known to ignore essential ingredients of the physics of transition and therefore may dangerously mislead if used beyond the supporting data base. Numerical transition simulations have gained reliability in repro­ ducing the transition process in sufficient detail to extract information unobtainable from laboratory experiments. However, the inherent assumptions of stream wise periodicity and temporal growth of the bound­ ary layer, in addition to the uncertainty of initial conditions, prevent predicting transition in practice. Hence, theory still holds an important place in identifying inherent mechanisms and structures of the transition process and in explaining otherwise unintelligible observations. The past decade saw some important progress in stability theory, slow or fast, depending on the reader's judgment ..

Secondary Instability of Boundary Layers

Most fluid flows are turbulent rather than laminar and the reason for this was studied. One of the earliest explanations was that laminar flow is unstable, and the linear instability theory was first developed to explore this possibility. A series of early papers by Rayleigh produced many notable results concerning the instability of inviscid flows, such as the discovery of inflectional instability. Viscosity was commonly thought to act only to stabilize the flow, and flows with convex velocity profiles appeared to be stable. The investigations that led to a viscous theory of boundary layer instability was reported. The earliest application of linear stability theory to transition prediction calculated the amplitude ratio of the most amplified frequency as a function of Reynolds number for a Blasius boundary layer, and found that this quantity had values between five and nine at the observed Ret. The experiment of Schubauer and Skramstad (1947) completely reversed the prevailing option and fully vindicated the Gottingen proponents of the theory. This experiment demonstrated the existence of instability waves in a boundary layer, their connection with transition, and the quantitative description of their behavior by the theory of Tollmien and Schlichting. It is generally accepted that flow parameters such as pressure gradient, suction and heat transfer qualitatively affect transition in the manner predicted by the linear theory, and in particular that a flow predicted to be stable by the theory should remain laminar. The linear theory, in the form of the e9, or N-factor is today in routine use in engineering studies of laminar flow. The stability theory to boundary layers with pressure gradients and suction was applied. The only large body of numerical results for exact boundary layer solutions before the advent of the computer age by calculating the stability characteristics of the Falkner-Skan family of velocity profiles are given. When the digital computer reached a stage of development which permit the direct solution of the primary differential equations, numerical results were obtained from the linear theory during the next 10 years for many different boundary layer flows: three dimensional boundary layers; free convention boundary layers; compressible boundary layers; boundary layers on compliant walls; a recomputation of Falkner-Skan flows; unsteady boundary layers; and heated wall boundary layers.

Boundary-Layer Linear Stability Theory

▪ Abstract The recent progress in three-dimensional boundary-layer stability and transition is reviewed. The material focuses on the crossflow instability that leads to transition on swept wings and rotating disks. Following a brief overview of instability mechanisms and the crossflow problem, a summary of the important findings of the 1990s is given.

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Stability and transition of three-dimensional boundary layers

The current understanding of boundary-layer receptivity to external acoustic and vortical disturbances is reviewed. Recent advances in theoretical modeling, numerical simulations, and experiments are discussed. It is shown that aspects of the theory have been validated and that the mechanisms by which freestream disturbances provide the initial conditions for unstable waves are better understood. Challenges remain, however, particularly with respect to freestream turbulence

Boundary-layer receptivity to freestream disturbances

: A review is given of boundary layer stability and transition. The normal modes procedures as they apply to boundary layers are briefly reviewed and the mechanism of instability is discussed. It is shown how normal modes results may be used to give guidance regarding the factors affecting transition. Some remarks are made about the prediction of transition and about the fixing of transition. It is concluded that the process of transition from laminar to turbulent flow remains unsolved. However, significant inroads into inroads into the understanding of transition are now possible because of our ability to do sophisticated theoretical and experimental studies of the stability of laminar boundary layers.

Eli Reshotko

Papers

Boundary layer stability and transition