Integral Equation Methods for Two Dimensional Incompressible Flows for Multielement Airfoils.

Abstract

The potential or the stream function of the flow is expressed by potential theoretic methods. Once either of these functions is determined in principle, the velocity along the airfoil profile is determined and the pressure co-efficient can be obtained using Bernoulli's equation. The velocity along the profile either depends upon the solution to an integral equation or is determined as the solution to an integral equation. To insure well conditioned integral equations, the profile elements in the physical plane are transformed (using a Karman Trefftz-like transformation) to an auxiliary near circle plane. In the near circle plane the integrands can be expressed in terms of very smooth functions and consequently the integrals can be evaluated with high accuracy by the trapezoidal rule. Most current methods use panel methods in the numerical evaluation of the integrals. The present method is chosen because it is independent of the number of profile elements. In contrast, procedures based on conformal mapping methods break down completely when the number of profile elements exceeds two. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1977
Accession Number
ADA042984

Entities

People

  • Charles L. Keller

Organizations

  • Flight Dynamics Laboratory

Tags

Communities of Interest

  • Air Platforms
  • C4I
  • Cyber

DTIC Thesaurus Topics

  • Air Force
  • Applied Mathematics
  • Computer Programming
  • Computer Programs
  • Computers
  • Conformal Mapping
  • Coordinate Systems
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Flow
  • Integral Equations
  • Leading Edges
  • Linear Systems
  • Periodic Functions
  • Trailing Edges
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Fluid Mechanics and Fluid Dynamics.