Accession Number:

ADB014225

Title:

Finite Element Analysis of Transonic Flows over Thin Airfoils. Volume 2. Program User's Manual

Descriptive Note:

Final rept. Jul 1975-Mar 1976

Corporate Author:

LOCKHEED MISSILES AND SPACE CO INC HUNTSVILLE AL HUNTSVILLE ENGINEERING CENTER

Personal Author(s):

Report Date:

1976-05-01

Pagination or Media Count:

113.0

Abstract:

A finite element program is described for computing steady and unsteady oscillatory and transient transonic flows over thin airfoils by solving directly the unsteady, nonlinear transonic potential equation based on small disturbance theory. The present numerical algorithm is developed using the concept of finite elements in conjunction with the least squares method of weighted residuals applied to both space and time. The basic element presently used is a product of an element in space and an element in time. The former has a cubic expansion inside each element, while the latter is a quadratic Lagrangian element. For each time step, the finite element discretization in both space and time results in a recurrence relationship in the form of a banded system of algebraic equations, which is solved by Gaussian elimination. The embedded shocks are smeared and a matching scheme for computing effectively flow over lifting airfoils is also incorporated in the program. The present computer program is composed of two parts the first part designated as UTRANL-I generates, from a limited number of input cards, the necessary mesh information and, if desired, produces a CALCOMP mesh plot the second part UTRANL-II carries out the analysis and displays the pressure coefficients along the chordline on printer plots. Two sample cases of flow over a NACA 64A 410 and a NACA 64A 006 airfoils are given to demonstrate the applicability and usage of the program. Te solution procedures are found to be quite efficient and accurate, permitting the aerodynamic forces to be calculated to engineering accuracy in less than ten minutes CPU time on a CDC 6600 computer for the most time consuming case among all those studied.

Subject Categories:

  • Aircraft
  • Statistics and Probability
  • Computer Programming and Software
  • Fluid Mechanics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE