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This handbook is a sequel to an earlier volume entitled "A Theory of Supercritical Wing Sections, with Computer Programs and Examples." Since the completion of the first volume, which we shall refer to as Volume I (cf. [ll), some effort has been made to improve our airfoil design program. A number of more desirable air foils have been designed. In addition several of our wing sections have been tested in wind tunnels. We should like to make this material available here, since it is more convenient to use the design program in conjunction with data for a fairly broad range of examples. Moreover, we have developed new analysis programs that supersede our previous work. Chapter I is devoted to a brief discussion of the mathematics involved in our additions and modifications. There is only a mini mum emphasis on theory, since the representation of important physical phenomena such as boundary layer shock wave interaction and separation is partly empirical. It is our contention, however, that the computer programs provide a better simulation than might have been expected. Chapter II presents numerical results found by our new methods, as well as comparisons with experimental data. Chapter III contains a discussion of the use of the program together with Fortran listings.
The purpose of this book is to survey computational flow research on the design and analysis of supercritical wing sections supported by the National Aeronautics and Space Administration at the Energy Research and Development Administration Mathematics and Computing Laboratory of New York University. The work was performed under NASA Grants NGR 33-016-167 and NGR 33-016-201 and ERDA Contract EY-76-C-02-3077. Computer programs to be listed and described have applications in the study of flight of modern aircraft at high sub sonic speeds. One of the codes generates cascades of shockless tran sonic airfoi~s that are expected to increase significantly the effici ency of compressors and turbines. Good simulation of physically observed flows has been achieved. This work is a sequel to two earlier books [1,2] published by Springer-Verlag under similar titles that we shall refer to as Volumes I and II. New York November 1977 TABLE OF CONTENTS I. INTRODUCTION 1 1. Shockless Airfoils and Supercritical Wing Sections 1 2. Differential Equations of Gas Dynamics 2 II. THE METHOD OF COMPLEX CHARACTERISTICS 5 1. A New Boundary Value Problem 5 2. Topology of the Paths of Integration 8 3. Iterative Scheme for the Map Function 9 III. TRANSONIC AIRFOIL DESIGN CODE 10 1. Isolated Airfoils 10 2. Compressor Cascades 12 3. Turbine Cascades 13 4. Comparison with Experiment 14 IV. TWO-DU1ENSIONAL ANALYSIS CODE 16 1. Wave Drag 16 2. A Fast Solver 19 3. Remarks about Three-Dimensional Flow 24 V. REFERENCES 26 VI.