THE PROFILE OF SUBSONIC GAS JETS ANALYSED BY THE WIENER-HOPF TECHNIQUE

Abstract

In this thesis, we shall investigate the profile of a subsonic gas jet issuing into a fluid at rest from an infinitely long slit or tube. We assume that the flow is uniform and parallel to the axis of symmetry of the slit or tube at an infinite distance upstream of the mouth of the jet. We also assume that jet mixing does not occur. Our analysis is based on the linearized theory of inviscid flow. The Wiener-Hopf Technique in the style of D. S. Jones (ref. 1) is employed. In Chapter 1, we give an account of linearized theory and the linearized equations of motion for our problem are obtained. In Chapter 2, an account of the Wiener-Hopf Technique is given, together with the results and theorems on Fourier transforms and Theory of Functions, which we shall require in the subsequent analysis. In Chapter 3, the problem of the thesis is analysed for both the plane and axially symmetric jet and solutions in the form of infinite series are obtained. In Chapter 4, numerical values are obtained for the case of the plane subsonic jet and conclusions derived from our analysis is given. In Chapter 5, a very brief review of existing literature on jets in linearized theory is given, together with suggestions of some problems, which may be solved by the Wiener-Hopf Technique, Although the idea of using the Wiener-Hopf Technique for subsonic jets has been suggested by Noble in his book (ref, 2), the analysis or our problem does not appear to have been done before.