Nonlinear distortion of finite amplitude waves propagating in converging-diverging nozzles

This paper presents an investigation of the nonlinear distortion of a disturbance propagating in a non-uniform steady base flow. The base flow is the steady compressible flow of a gas in a variable area duct. The quasi-one-dimensional continuity and momentum and energy equations for the unsteady disturbance in homentropic flow are solved using the method of characteristics (wave front expansion technique). A closed form solution for the first derivative of wave front in terms is obtained. The solution admits singularity for a compressive disturbance, which is responsible for shock in the flow. The solution is general and applicable in any range of the Mach number of base flow. A special case of the steady gas flow in converging-diverging duct (C-D nozzle), where the flow makes a transition from subsonic to supersonic, is investigated.