Discrete Green’s Function Measurements in a Single Passage Turbine Model

The superposition-based Discrete Green’s Function (DGF) technique provides a general representation of convective heat transfer that can capture the numerous flow and thermal complexities of the gas turbine environment and provide benchmark data for the validation of computational codes. The main advantages of the DGF technique are that the measurement apparatus is easier to fabricate than a uniform heat flux or uniform temperature surface, and that the results are applicable to any choice of discretized thermal boundary condition. Once determined for a specific flow condition, the DGF results can be used, for example, with measured surface temperature data to estimate the surface heat flux. In this study, the experimental DGF approach was extended to the suction side blade surface of a single passage model of a turbine cascade. Full-field thermal data were acquired using a steady state, liquid crystal-based imaging technique. The objective was to compute a 10×10 one-dimensional DGF matrix in a realistic turbomachinery geometry. The inverse 1-D DGF matrix, $G−1,$ was calculated and its uncertainties estimated. The DGF-based predictions for the temperature rise and Stanton number distributions on a uniform heat flux surface were found to be in good agreement with experimental data. The G matrix obtained by a direct inversion of $G−1$ provided reasonable heat transfer predictions for standard thermal boundary conditions.