Using the 2D Method of Characteristics (MOC), the contour of a two dimensional minimum-length nozzle for the expansion of air to a design exit Mach number of 2 is computed and graphed. The problem is extended to include a nozzle with a finite expansion section which is a circular arc with a diameter equal to three throat heights. C++ source codes for the 2 nozzles are included. By inputting the values of gas constant, test section mach number, throat height and level of precision one can design nozzles for different working fluids at different test section mach numbers.
The report was generated as a part of a graduate course on compressible aerodynamics taught that semester by Dr John D Anderson. His book entitled 'Modern Compressible Flow - with Historical perspectives' contain a good chapter on the use of the MOC in designing supersonic nozzle contours (Chapter 11 of the third edition).