An Analysis Method for Multistage Transonic Turbines With Coolant Mass Flow Addition

The subject of this paper is a numerical method for the calculation of the transonic flow field of multistage turbines taking high coolant flow into account. To reduce the processing time, a throughflow method based on the principels of Wu is used for the hub-to-tip calculation. The flow field is obtained by an iterative solution between a three dimensional inviscid hyperbolic time-dependent algorithm with an implicit finite volume method for the blade-to-blade calculations using C-meshes and a single representative meridional S_2m-stream surface. Along the S_2m-plane with respect to non-orthogonal curvilinear coordinates, the stream function equation governing fluid flow is established. The cooling air inflow inside the blade passage forbids the assumption of a constant mass flow along the main stream direction. To consider the change of the aerodynamic and thermodynamic behaviour, a cooling air model was developed and implemented in the algorithm, which allows the mixing of radially arbitrarily distributed cooling air in the trailing edge section of each blade row. The viscous effects and the influence of cooling air mixing are considered by the use of selected loss correlations for profile-, tip leakage, secondary flow and mixing losses in the S_2m-plane in terms of entropy. The method is applied to the four stage high temperature gas turbine Siemens KWU V84.3. The obtained numerical results are in good agreement with the experimental data.