Some of the recent advances in the theory of three-dimensional boundary layers are the subject of this paper, which is 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-ordinates 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 (laminar) boundary layers with small cross-flow are then presented. Finally,an outline is given of methods developed for turbulent boundary layers.

Boundary layers in three dimensions

5 An analysis of some performance aspects of various types of aircraft designed to fly over different ranges at different speeds

that has proved most interesting to the theoretical aerodynamicist. Clea rly the former is concerned with the flow over, and the pressures, forces, and moments experienced by, generally shaped streamlined bodies and multiple lifting surfaces (wings, tails, con­ trols) in intimate combination. Until recently he has had to place primary reliance for such informa tion on measurements by wind tunnel and other experimental means. Except in particular cases, he has obtained only a rather piecemeal and preliminary sort of guidance from the produc ts of rational theory, whose focus has been sing le, isolated, planar wings and slender bodies of revolution. Interference was the word chosen to describe situations where flow over one lifting or body element was significantly affected by the presence of an­ other-as if, somehow, this interaction interfered with the purist's more appealing efforts to analyze each aerodynamic entity standing alone. It is no accident that 32 yea rs intervened between the attainment of powered air­ craft flight and the first appearance of even a short , descriptive chapter on flow over the "Airplane as a W hole " (Durand 1935). Many additional years preceded the pub lication of two truly comprehensive survey articles (Law­ rence & Flax 19 54, Fe rrar i 1957). Most of the basic tools of interference or in­ teraction theory, as it exists today, were understood by the latter date. With regard to the complete description of fluid motion past an assemblage of streamlined elements, notable subseque nt progress has been made toward realizing the full potentialities of this theory by means of successive gen­ erations of high-speed data-proces sing equipment. The limited objective of the present authors will be to review and

Wing-Body Aerodynamic Interaction

In this paper, by means of computational fluid dynamics, a significant study has been made on the effects of geometric parameters of wing with capability of flying efficiently and cost-effectively at supersonic condition. Multi-objective optimization has been performed for the aerodynamic shape optimization of the wing configuration. The three-dimensional wing shape defined by four design variables is optimized. For achieving the most desirable aerodynamic efficiency (lift-to-drag ratio), Response Surface Method and Genetic Algorithm is utilized. To ensure the reliability of the solution and validating the numerical evaluation, flow around a delta wing is simulated and results are compared with credible numerical works. Furthermore, the particular design variables, which have serious effects on the objective functions, are found. Wing sweep angle along with aspect ratio has strong effects on the main outputs. Given that the current flow regime is supersonic, counteracting the negative effects of shock waves is one the most important design points. Among the studied parameters, leading edge sweep angle has the greatest impact on the main objectives of this research and it is the primary factor for delaying the formation of shock waves over the wing surface. Lift and drag coefficients, as primary objective functions, have higher sensitivity to changes in aspect ratio. By comparison to best geometry among initial cases, aerodynamic efficiency is increased by approximately 15% as a result of optimization study of this supersonic wing geometry.

R.C. Lock

Papers

Theory of aerodynamic design for swept-winged aircraft at transonic and supersonic speeds