Secondary flows and leakage flows are leading to complex vortex structures in the 3-D flow field of a turbine blading. Aerodynamic losses are the consequence. Reducing the aerodynamic losses related to tip leakage flows by endwall contouring is subject of an actual numerical investigation of the flow field in a 4-stage test turbine with repeating stages. The 3-D flow field for various geometric configurations with endwall contouring is calculated by application of a 3-D Navier-Stokes code. Here, the numerical results of configurations with arc-like and wave-like contours (bumps) at the shaft and the casing with a maximum deviation from the reference contour in the axial gap between stator and rotor are presented. Furthermore, the results are compared to the experimental and numerical data of the test turbine with a reference contour without endwall contouring.
The results show a significant influence of the bumps on the radial velocity distribution in the flow field and the static pressure field. By application of a subtraction method where the reference flow field is subtracted from the flow fields of the bump-configurations, it can be shown that the leakage flows are reduced. A detailed flow analysis shows the presence of a leakage vortex.
For a measure of the flow field inhomogeneity and for reducing the complex 3-D data to 2-D and 1-D values a balance-based averaging method is used. The method is based on a hypothetical equilibration process between two infinitesimal neighbouring control surfaces. During this physically based averaging process, equilibration coefficients can be derived which are a measure for the flow inhomogeneity. It can be shown that arc-like and wave-like endwall contouring has a positive influence on the homogeneity of the flow field. Thus, this effect leads to higher aerodynamic stage efficiencies for repeating stages.
