Supersonic Source Flow Past Thin Air Foils

In this thesis the supersonic source flow over a thin sharp- edged airfoil is formulated as a linearized problem. A new potential equation is derived, using a system of spherical coordinates centered at the source; as a simplification only wings symmetrical about the z axis are considered, and of these only the limiting cases of ring- and annular- airfoils are treated. After transforming to characteristic coordinates in the hodograph plane, the potential equation (which has variable coefficients) is shown to be approximated by two classical equations -- one holding for the ring wing and the other applying to the annular wing. The flow over a specific annular wing is computed by en application of the Riemann method to the telegraph equation, which is the appropriate approximation to the governing equation for this case. The linearized potential equation is also solved by the Method of Characteristics, using a numerical equivalent of the Mono, procedure for quasilinear partial differential equations. A complete set of compatibility equations is exhibited, allowing the computation of the perturbation velocity components at any point of the zone of influence of an airfoil set in the supersonic source flow. Two numerical examples are presented, illustrating the application to the computation of the flow over each of a ring- and annular- wing. Finally in an appendix the usually powerful method of separation of variables is shown to be unsuitable as a procedure for solving the potential equation governing the present problem.