Rapid design method and new contours for a class of three dimensional supersonic nozzle of arbitrary exit cross section

The aim of this work is to develop a new and rapid numerical method for designing a new contour of the supersonic nozzle with arbitrary exit cross sections as a class of three dimensional nozzle extracted from the calculation of stationary flow solutions in axisymmetric nozzle. The application is made for nozzle giving a uniform and parallel flow at the exit section. The determination of the points of the axisymmetric nozzle contours in a non-dimensional manner with respect to the arbitrary throat radius is necessary. The exit section of the nozzle must be discretized at several points. The radii of the points of the throat section are determined by equalizing the ratio of the axisymmetric critical sections corresponding to each selected point of the exit section. Each point passes a contour of the nozzle to the throat where their position is determined by the multiplication of the non-dimensional positions of the axisymmetric nozzle point by the throat radius of this contour. A uniform portion is added at the end of each contour to compensate the decrease in its length. Longitudinal discretization of the nozzle is necessary. The flow properties of each point are the same as those of the points of the axisymmetric nozzle. The temperature and the deviation of the flow at each point of any section are determined by their interpolations between two successive points of each contour. The Mach number, the pressure and the density are determined accordingly. The application is made for air at high temperature lower than the dissociation threshold of the molecules.