A hybrid numerical procedure for cascade flow analysis

An efficient hybrid difference scheme, based on the second-order time and s patial difference algorithms for solving the time-marching Navier-Stokes eq uations, was developed to simulate turbine cascade flow and heat transfer p roblems. The main feature of the present scheme is that the matrix-valued d issipation terms are incorporated into the time-derivative terms to form a time-dependent discretization scheme. The overall difference scheme consist s of an explicit step in global time steps and an implicit step in each loc al time step. The viscous flux vectors are decomposed to simplify the flow calculation in the explicit step. In order to simplify the programming proc edure and to save computational time, the two-sweep procedure was adopted i n the implicit scheme instead of using traditional matrix operations. The n umerical method proposed in this study comprises of the positive features o f both explicit and implicit algorithms. The method was applied to calculat e the flow around C3X and VKI cascades. The computed results were compared with experimental data as well as with computations solving by other scheme s. It is demonstrated in this article that the computations obtained by usi ng the present scheme show good agreement with both experiments and the com putations obtained with other numerical schemes.