Computer Program for Steady Transonic Flow over Thin Airfoils by Finite Elements
Abstract
A finite element program is described for the analysis of subsonic and transonic flows over thin airfoils by solving the nonlinear transonic potential equation based on small disturbance theory. The present numerical algorithm uses the concept of finite elements in conjunction with the least square method of weighted residuals. Since the governing equation is of the elliptic-hyperbolic type, a 'one-sided assembly technique' was devised and adapted in the supersonic region to restore the directional property of the flow, which was removed by the exclusion of entropy from the transonic potential equation. The finite element discretization results in a system of banded nonlinear algebraic equations, which is solved by direct iterations. The elements presently used include triangles and quadrilaterals with the perturbed potential function and velocity components as nodal unknowns. Boundary conditions of both Dirichlet and Neumann types are therefore imposed conveniently. Secondary unknowns are computed directly without resorting to numerical differentiation. The computer program is separated into two parts: the first part (designated as STRANL-I) generates the necessary mesh information and, if desired, produces a mesh plot and optimal nodal numbering as well; STRANL-II carries out the analysis and displays the pressure coefficients along the chord line on printer plots. Two sample cases of flow over a NACA 64 A006 and a 6% thick circular arc are given.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1975
- Accession Number
- ADB009712
Entities
People
- M. R. Brashears
- S. T. Chan
Organizations
- Lockheed Martin Missiles and Space