A Slender Cone Starting Impulsively

Citation

Jensen, Arnold Axtell (1951) A Slender Cone Starting Impulsively. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/19KD-1M64. https://resolver.caltech.edu/CaltechETD:etd-03102009-074636

Abstract

The problem of a semi-infinite slender cone which starts impulsively from rest so that it suddenly has a constant supersonic velocity is considered. It is treated by using the acoustic wave equation for the air at rest at infinity. The problem is reduced to that of dealing with the radial velocity in two conical variables in space-time. It is shown that there are three fundamental regions from the physical or mathematical standpoint. The boundary conditions and equations for each of these regions are developed so that a numerical solution of the problem may be obtained for a given Mach number and cone angle. From the solution of the radial velocity the potential and thence the pressure on the cone are obtained. An approximation to the pressure far back on the cone where the curvature is small is obtained as an improvement on the piston value for zero curvature. This is done by suppressing variations in the axial direction and solving the resulting equation by Riemann's integration method. An attempt to solve the problem by distributing sources on the axis with resulting difficulties is discussed.

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