Numerical Solution of Stream Function Equations in Transonic Flows

In order to develop the transonic stream function approach, in this paper one of the momentum equations is employed to form the principal equation of the stream function which does not contain vorticity and entropy terms, and the other one is used to calculate the density directly. Since the density is uniquely determined, the problem that the density is a double-valued function of mass flux in the stream function formulation disappears and the entropy increase across the shock is naturally included. The numerical results for the transonic cascade flow show that the shock obtained from the present method is slightly weaker and is placed farther downstream compared to the irrotational stream function calculation, and is closer to the experimental data. From a standpoint of computation the iterative procedure of this formulation is simple and the alternating use of two momentum equations makes the calculation more effective.