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

Tags

DTIC Thesaurus Topics

  • Differential Equations
  • Equations
  • Flow
  • Integrals
  • Iterations
  • Mathematical Analysis
  • Mathematics
  • Perturbations
  • Potential Flow
  • Stagnation Point
  • Stagnation Pressure

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Combustion and Flow Dynamics.