Propulsion Nozzle Studies. Volume I. Transonic Flow in an Elliptic Nozzle

The transonic flow field for a converging-diverging propulsion nozzle having an elliptic cross section has been studied. A power series expansion technique is used to obtain the first order approximation to the flow velocity components in terms of the geometric parameters describing the boundaries. Four governing equations for the flow, namely the continuity and irrotationality equations, are put forth and reduced to a convenient first order, nondimensional form. A general series for the radial component of velocity is then assumed along with a coordinate stretching in the axial direction. Corresponding series for the axial and tangential velocity components are then derived to satisfy two of the governing equations. The variable coefficients in the series are then determined such that the remaining governing equations and boundary conditions are satisfied. Constants arising in the solution are related to the boundary geometry. Only the first order solution is obtained herein; however the procedure can be used in a straightforward manner to obtained higher order solutions. Finally, it is shown that the two-dimensional axisymmetric solution is a special case of the three-dimensional solution. (Author) See also VOlume 2, AD-A041 530.