## Electronic Theses and Dissertations

1989

Dissertation

Ph.D.

#### Department

Mathematics and Statistics

Mathematics.

CC BY-NC-ND 4.0

#### Abstract

This dissertation studies steady two-dimensional transonic flows past symmetric airfoils. The flow equations are first transformed into ($\phi$,$\psi$) curvilinear coordinates, where $\psi$(x,y) is the streamfunction and $\phi$(x,y) is arbitrary, and then to von Mises variables (x,$\psi$). Flows over symmetric profile at zero and non-zero angles of attack are formulated in terms of the independent variables (x,$\psi$), providing a rectangular computational domain with Dirichlet boundary conditions. The flow equations in unknowns y(x,$\psi$) and $\rho$(x,$\psi$) are discretized using a finite difference method, producing a system of algebraic equations which is solved by SLOR. The surface pressure coefficient is computed on airfoils at subcritical and supercritical Mach numbers. The present results are in good agreement with available results in the literature. In the (x,$\psi$) system, the airfoil design problem is conveniently formulated as a Newmann boundary value problem and solved numerically to produce the required body shape. The need to solve a sequence of direct problems is eliminated. This dissertation provides simple and fast algorithms for the computation of the flows described above.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1989 .N344. Source: Dissertation Abstracts International, Volume: 50-03, Section: B, page: 0985. Thesis (Ph.D.)--University of Windsor (Canada), 1989.

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