THE DEVELOPMENT AT INFINITY OF AXISYMMETRIC FLOW PATTERNS WITH A FREE STREAM MACH NUMBER ONE.
Internal scientific rept.
AEROSPACE RESEARCH LABS OFFICE OF AEROSPACE RESEARCH WRIGHT-PATTERSON AFB OHIO
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A representation for the flow field at infinity in an axisymmetric flow at a free stream Mach number one was originally given by Guderley by means of similarity solutions. Their determination required the solution of ordinary differential equations. Recently, the solutions of these differential equations in the form of polynomials have been given by Mueller, Matschatt and, in a particularly useful form, by Randall. On this basis it is now feasible to derive a representation for the flow field at a large distance for the full potential equation. This work is carried out in the present report. A possible application lies in the determination of initial conditions for Garabedians method of analytic continuations. From computations of this kind, one would obtain accurate examples for axisymmetric flow patterns at a free stream Mach number one. Because of certain idiosyncrasies of this application, which will be explained, the present analysis has been carried out in the hodograph. The report gives the basic mathematic theory and a tabulation of some of the polynomials which are needed for the representation of the flow patterns at infinity. Author
- Fluid Mechanics