Linearized Supersonic Flow

Citation

Hayes, Wallace Dean (1947) Linearized Supersonic Flow. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/D7N0-4412. https://resolver.caltech.edu/CaltechETD:etd-04132007-131650

Abstract

This thesis is a presentation of the methods and concepts of the theory of linearized supersonic flow. The fundamental theory which serves as a basis for this investigation is discussed in the first two chapters. Special emphasis is placed upon the study of planar systems. A system of conical coordinates is introduced in which the method of separation of variables is applied. The resultant solutions have the Mach cone as a natural boundary and involve a family of hypergeometric functions related to the Legendre functions. Basic integral relations for planar systems are obtained between the normal velocity component and the component giving the pressure. The behavior of planar systems relative to the planform configuration is discussed and the concept of problems of the first and second kind is introduced. The lift problem is treated with particular reference to the behavior of the leading edge singularity and to the concept of the Kutta condition as applied to a planform in supersonic flow. The nature of drag in linearized supersonic systems is investigated and the separation of the drag into types is discussed. For planar systems the drag may be divided into basic and induced parts. For general systems the basic division may be made into wave drag and vortex drag. Two fundamental reversed flow theorems are obtained which state that the drag of a system is the same as that of the system with the flow reversed in direction. The theory of conical flow as applied to planar systems is developed and the results for a basic thickness distribution and various lifting triangles are presented. The method of the separation of the lateral variable is investigated using Schlomilch series. The flow about bodies of revolution is discussed and the application of the Riemann method to the problem is given.

Thesis Files