THE POTENTIAL FLOW DUE TO A JET AND A STREAM WITH DIFFERENT TOTAL PRESSURES,
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1964
- Accession Number
- AD0465190
Entities
People
- Charles Ruger
- Lu Ting
- Paul A. Libby
Organizations
- New York University Tandon School of Engineering