Boundary Value Problems in Physics and Engineering By Frank Chorlton. Pp. 250. (Van Nostrand: London, July 1969.) 70s

Boundary value problems

A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: THE GENERAL THEORY OF ORBITS

Shock wave/turbulent boundary layer interaction and its control

The Wilcox (1988, 1991) k-omega model for eddy-viscosity turbulence does not require damping functions in the viscous sublayer, and its equations are less stiff near the wall. It has been designed to predict the requisite wake length in equilibrium, adverse pressure-gradient boundary-layer flows. When applied to free shear layers, however, a strong dependency of its results on the freestream value of omega has been noted. This feature is presently investigated via the self-similar equations for incompressible equilibrium boundary layers.

Influence of freestream values on k-omega turbulence model predictions

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

Shock-wave strength for separation of a laminar boundary layer at transonic speeds

Similarity Solutions for Plane and Radial Jets Using a k-ε Turbulence Model

In this paper we are concerned with the computation of viscous subsonic and transonic flow over two-dimensional airfoils at high Reynolds numbers where the boundary layers are thin and turbulent over most of the airfoil and wake. Our objective in this work is to develop a fast viscid-inviscid-interaction method that can compute viscous flows over airfoils with extensive regions of flow separation and that can be used to predict the stalling characteristics of airfoils with reasonable accuracy.

The Computation of Viscid-Inviscid Interaction on Airfoils with Separated Flow

In this paper, we investigate the behavior of inviscid supersonic conical flow fields near crossflow stagnation points by constructing coordinate expansions of the exact equations of conical flow. The local cross-flow streamline pattern is shown to be determined primarily by the curvature of the surface pressure distribution (P and by the direction of the surface velocity near the stagnation point. The local streamline pattern at a maximum of the surface pressure is shown to be either a saddle point or a nodal point with cross-flow streamlines normal to the body. The solution corresponding to the node changes to a saddle point at a critical value, (P == — 8, which thus signals the "liftoff" of the vortical singularity first suggested by Ferri. The streamline pattern at a minimum of the pressure distribution is a node with streamlines tangent to the body if (P is less than a critical value, (P = 1, and does not exist if (P > 1. The local solutions are used to infer the general characteristics of the cross-flow streamline pattern generated by yawed circular cones and flat plates. They are also used to analyze the nonuniformity of the small yaw and thin-shock-layer expansions at vortical singularities.

Vortical Singularities in Conical Flow

The method of matched asymptotic expansions is used to analyze the interaction of a normal shock wave with an unseparated turbulent boundary layer on a flat surface at transonic speeds. The theory leads to a three-layer description of the interaction in the double limit of Reynolds number approaching infinity and Mach number approaching unity. The interaction involves an outer, inviscid rotational layer, a constant shear-stress wall layer, and a blending region between them. The pressure distribution is obtained from a numerical solution of the outer-layer equations by a mixed-flow relaxation procedure. An analytic solution for the skin friction is determined from the inner-layer equations. The significance of the mathematical model is discussed with reference to existing experimental data.

R. E. Melnik

Papers

Shock-wave strength for separation of a laminar boundary layer at transonic speeds

Similarity Solutions for Plane and Radial Jets Using a k-ε Turbulence Model

The Computation of Viscid-Inviscid Interaction on Airfoils with Separated Flow

Vortical Singularities in Conical Flow

Analysis of the interaction of a weak normal shock wave with a turbulent boundary layer