Prediction of Aerodynamic Forces on a Circular Cylinder and a Thin Airfoil in a Transonic Airstream by the Finite Element Method.
Abstract
The finite element method was used to solve the nonlinear, small-disturbance, transonic, velocity-potential equation for problems of steady flow over a circular cylinder and over a thin-airfoil in a uniform steady airstream. The governing differential equation is valid for inviscid, irrotational, isenthropic flow of a perfect gas to include weak shocks providing airflow separation does not occur. For compressible subsonic and transonic flows the nonlinear small-disturbance equation was expressed in iterative form as a sequence of linear equations which was solved iteratively until the difference between two successive solutions became arbitrarily small. For analysis purposes the infinite flowfield was replaced by a finite but sufficiently large domain that was discretized with sector elements for the cylinder problem and rectangular elements for the airfoil problem. Three sub-problems were investigated for the circular cylinder. First, three different types of trial functions were investigated to approximate the solution for the velocity potential function for the case of incompressible flow without circulation. The three trial functions were: (1) a trignometric approximation resulting in a non-conforming element, (2) a bilinear polynomial (conforming element) typical of elements used in finite element analysis, and (3) a rational approximation resulting in a new conforming element. Convergence properties of each element were studied as a function of discretization refinement (element size). The second subproblem for the cylinder was to use the two conforming elements to obtain solutions for incompressible flow with circulation. Superposition was used to split the total problem into two elementary component problems.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 05, 1979
- Accession Number
- ADA107201
Entities
People
- James E. Marsh
Organizations
- Air Force Institute of Technology