Prediction of Aerodynamic Forces on a Circular Cylinder and a Thin Airfoil in a Transonic Airstream by the Finite Element Method.
Doctoral thesis 1 Jan 77-20 Apr 79,
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OHIO SCHOOL OF ENGINEERING
Pagination or Media Count:
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, isentropic 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 equations 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. The finite element equtions were obtained from Galerkins Method of Weighted Residuals. Boundary conditions of the Neumann type were imposed along the surface contour of the cylinder and along an approximate boundary in accordance with classical thin-airfoil theory for the airfoil. For both problems Dirichlet conditions were imposed along the farfield boundary from an asymptotic solution which satisfies the actual infinity condition and is valid in the farfield.
- Numerical Mathematics
- Fluid Mechanics