An Implicit Scheme for Cascade Flow and Heat Transfer Analysis

Abstract

A new efficient implicit scheme, based on the second-order time and spatial difference algorithm for solving steady flow by using time-marching Navier–Stokes equations, was developed for predicting turbine cascade flows and heat transfer. The difference scheme comprises an explicit part in the intermediate time-step and an implicit part in the local time-step. The viscous flux vectors are decomposed to simplify the flow calculation in the explicit step. The time difference terms are expressed in terms of the viscous dependent terms that appear in the diffusion terms in the form by adding eigenvalues of viscous flux matrices into the time derivation term. In the presently proposed scheme, the two-sweep procedure is used in the implicit step instead of employing a traditional matrix operation to save the computational time. This method has been used to calculate the flow around C3X and VKI cascades. The computed results were compared with experimental data as well as with other published computations. The comparisons for both surface pressure and heat transfer coefficient showed good agreement with the experiments. [S0889-504X(00)01702-5]