An implicit scheme for cascade flow and heat transfer analysis

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 h eat transfer. The difference scheme comprises an explicit part in the inter mediate time-step and an implicit parr in the local time-step. The viscous flux vectors are decomposed to simplify the flow calculation in the explici t step. The rime difference terms are expressed in terms of the viscous dep endent terms that appear in the diffusion terms in the form by adding eigen values of viscous flux matrices into the time derivation term. In the prese ntly proposed scheme, the two-sweep procedure is used in the implicit step instead of employing a traditional matrix operation to save the computation al rime. This method has been used to calculate the flow around C3X and VKI cascades. The computed results were compared with experimental data as wel l as with other published computations. The comparisons for both surface pr essure and heat transfer coefficient showed good agreement with the experim ents. [S0889-504X(00)01702-5].