Boundary layers in three dimensions

Abstract : Recent adances in the theory of three-dimensional boundary layers are discussed in three main parts. The first part consists of general considerations. The boundary layer equations for laminar compressible flow, and the corresponding momentum integral equations, are written down, in an orthogonal curvilinear system of co-ordinates. Special forms for streamline and geodesic co-rdinates are also given. Cross-flows are then discussed, and this is followed by an account of an axially symmetric analogy and a compressibility correlation that hold when cross-flows are small. In the second part, the extensive exact solutions of Yohner and Hansen for the boundary layer having similar solutions or combinations of similar solutions, and of Sedney - for the boundary layer on a yawed spinning cone, are described. The third part concerns momentum integral methods in which streamline co-ordinates are employed. Works by Timman and Hall are described, and are contrasted as examples of extensions to three dimensions of the Pohlhausen and the Thwaites approaches respectively. The methods of Zaat and Cooke for(liminar) boundary layers with small cross-flow are then presented. (Author)

[1]  J. M. Wild,et al.  The Boundary Layer of Yawed Infinite Wings , 1949 .

[2]  A. M. Kuethe,et al.  Measurements in the boundary layer of a yawed wing , 1949 .

[3]  K. Stewartson,et al.  Correlated incompressible and compressible boundary layers , 1949, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[4]  James P. Johnston.  The Turbulent Boundary Layer at a Plane of Symmetry in a Three-Dimensional Flow , 1960 .

[5]  J. C. Cooke.  Pohlhausen's Method for Three-Dimensional Laminar Boundary Layers , 1951 .

[6]  A. D. Young.  The Calculation of the Profile Drag of Aerofoils and Bodies of Revolution at Supersonic Speeds , 1953 .

[7]  Ching-Sheng Wu,et al.  The three dimensional incompressible laminar boundary layer on a spinning cone , 1959 .

[8]  Franklin K. Moore,et al.  Three-Dimensional Boundary Layer Theory , 1956 .

[9]  James Paul Johnston.  Three-dimensional turbulent boundary layer , 1957 .

[10]  E. C. Maskell.  Flow separation in three dimensions , 1955 .

[11]  R. Sedney.  Laminar Boundary Layer on a Spinning Cone at Small Angles of Attack in a Supersonic Flow , 1957 .

[12]  B. Thwaites,et al.  Approximate Calculation of the Laminar Boundary Layer , 1949 .

[13]  Roberto Vaglio-Laurin,et al.  Turbulent Heat Transfer on Blunt-Nosed Bodies in Two-Dimensional and General Three-Dimensional Hypersonic Flow , 1960 .

[14]  A. G. Hansen,et al.  On possible similarity solutions for three-dimensional incompressible laminar boundary layers III : similarity with respect to stationary polar coordinates for small angle variation , 1957 .

[15]  Arthur Mager,et al.  Generalization of Boundary-Layer Momentum-Integral Equations to Three-Dimensional Flows Including Those of Rotating System , 1952 .

[16]  V. M. F. B.Sc.,et al.  LXXXV. Solutions of the boundary-layer equations , 1931 .

[17]  J. C. Cooke.  On Pohlhausen's Method with Application to a Swirl Problem of Taylor , 1952 .

[18]  H. G. Loos.  A Simple Laminar Boundary Layer with Secondary Flow , 1955 .

[19]  W. Mangler.  Zusammenhang zwischen ebenen und rotationssymmetrischen Grenzschichten in kompressiblen Flüssigkeiten , 1948 .

[20]  H. Herzig.  Experimental and Analytical Investigation of Secondary Flows in Ducts , 1957 .

[21]  J. P. Johnston,et al.  On the Three-Dimensional Turbulent Boundary Layer Generated by Secondary Flow , 1960 .

[22]  L. Howarth.  THE BOUNDARY LAYER IN THREE DIMENSIONAL FLOW. PART II. THE FLOW NEAR A STAGNATION POINT , 1951 .

[23]  I. E. Beckwith,et al.  Compressible laminar boundary layer over a yawed infinite cylinder with heat transfer and arbitrary Prandtl number , 1957 .

[24]  F. Moore,et al.  Three-dimensional compressible laminar boundary-layer flow , 1951 .

[25]  L. Howarth,et al.  Concerning the effect of compressibility on lam inar boundary layers and their separation , 1948, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[26]  L. Howarth,et al.  XXV. The boundary layer in three dimensional flow.—Part I. Derivation of the equations for flow along a general curved surface , 1951 .

[27]  T. Geis.  ``Ahnliche'' dreidimensionale Grenzschichten , 1956 .

[28]  F. Moore.  Laminar boundary layer on a circular cone in supersonic flow at a small angle of attack , 1951 .

[29]  E. Gruschwitz.  Turbulente Reibungsschichten mit Sekundärströmung , 1935 .

[30]  H. G. Pinsent,et al.  APPROXIMATE METHODS FOR CALCULATING THREE-DIMENSIONAL BOUNDARY LAYER FLOW ON WINGS , 1961 .

[31]  J. T. Stuart.  ON THE EFFECTS OF UNIFORM SUCTION ON THE STEADY FLOW DUE TO A ROTATING DISK , 1954 .

[32]  Dean R. Chapman,et al.  Temperature and Velocity Profiles in the Compressible Laminar Boundary Layer with Arbitrary Distribution of Surface Temperature , 1949 .

[33]  A. G. Hansen,et al.  On possible similarity solutions for three-dimensional incompressible laminar boundary layers II : similarity with respect to stationary polar coordinates , 1956 .

[34]  C. R. Illingworth.  XLII. The laminar boundary layer of a rotating body of revolution , 1953 .

[35]  H. Gortler.  A New Series for the Calculation of Steady Laminar Boundary Layer Flows , 1957 .

[36]  K. Pohlhausen,et al.  Zur näherungsweisen Integration der Differentialgleichung der Iaminaren Grenzschicht , 1921 .