Accession Number:

AD0472247

Title:

ON THE NON-LINEAR THEORY OF THIN JETS A PROBLEM IN SINGULAR PERTURBATION,

Descriptive Note:

Corporate Author:

POLYTECHNIC INST OF BROOKLYN NY DEPT OF AEROSPACE ENGINEERING AND APPLIED MEC HANICS

Personal Author(s):

Report Date:

1965-09-01

Pagination or Media Count:

35.0

Abstract:

The injection of a two-dimensional jet into a uniform stream is considered, the fluids being assumed inviscid and incompressible. When the total head of the jet is much larger than that of the uniform flow the motion is characterized by two disparate length scales which are the basis for a singular perturbation procedure. Inner and outer expansions are developed for the jet and the external flow. The basic non-linearity introduced by the pressure condition along the vortex sheet separating the jet from the free stream appears as a non-linear boundary condition for the first order outer solution in the external flow. A trivial solution is avoided by specifying a singularity as an inner boundary condition, and the process later justified by matching. The first order outer solution on the jet yields the usual thin jet approximation which is not uniformly valid except for 90 deg injection. A formal variational principle is given for the non-linear potential problem satisfied by the first order outer solution in the external flow. Author

Subject Categories:

Distribution Statement:

APPROVED FOR PUBLIC RELEASE