On the method of characteristics and its application to the calculations of annular nozzle flowfields

A new, simple and effective approach to deriving the characteristic equations of gas dynamics is proposed. The compatibility equation is derived in vector form, which is valid for any coordinate system. The concepts of this derivation are clearer than previous derivations. A general form of the energy equation which contains the speed of sound directly is obtained. This form, which is valid for either ideal or real gases, is particularly useful for the method of characteristics. Coordinate transformation by algebraic methods is studied in detail. It is found that this method may be the only practical method for solving moving boundary problems, such as the free jet boundary problem. Using the basic concepts of coordinate transformations, all the viscous force terms and the dissipative terms in a curved coordinate system are obtained. Thus, the method of characteristics can be used to solve either real viscous flowfields or flowfields with artificial viscosity for smearing shock waves.