Accession Number : AD0465190

Title :   THE POTENTIAL FLOW DUE TO A JET AND A STREAM WITH DIFFERENT TOTAL PRESSURES,

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

Personal Author(s) : Ting, Lu ; Libby, Paul A. ; Ruger, Charles

Report Date : OCT 1964

Pagination or Media Count : 30

Abstract : A simple model of a jet injected into a moving stream with stagnation pressure lower than that of the jet is introduced to demonstrate the fundamental theoretical problems associated with the wing fan. The governing equations for this basic problem are formulated and reduced to a set of non-linear integral differential equations. An iteration scheme for the numerical solution of this problem is outlined. For the limiting case of a large stagnation pressure ratio, the non-linear integral differential equations can be simplified. Nevertheless the problem still has to be solved numerically by iteration methods. For the limiting case of small difference in stagnation pressure, a perturbation procedure is introduced. The basic solution, as expected, should be the classical solution of the free streamline problem with uniform stagnation pressure. The singularity of the perturbation solution near the stagnation point of the main stream is analyzed. The singularity is removed by a modification of the basic solution. The analytical behavior of the perturbation solution at large downstream distances is analyzed so that a class of functions admissible for representation of the perturbation solutions are defined. The problem of obtaining the perturbation solution is then reduced to the solution of simultaneous algebraic equations. (Author)

Descriptors :   (*JET MIXING FLOW, MATHEMATICAL ANALYSIS), STAGNATION POINT, NONLINEAR DIFFERENTIAL EQUATIONS, ITERATIONS, PRESSURE, BOUNDARY VALUE PROBLEMS, PERTURBATION THEORY, CONFORMAL MAPPING, VELOCITY.

Distribution Statement : APPROVED FOR PUBLIC RELEASE