Calculation of the Expansion Through a Cooled Gas Turbine Stage

In recent work by the same authors [Torbidoni, L., and Horlock, J. H., 2005, ASME J. Turbomach, 127, pp. 191–199], a new method for calculating the coolant flow requirements of a high-temperature gas turbine blade was described. It involved consideration of successive chordwise strips of blading; the coolant required in each strip was obtained by detailed study of the heat transfer processes across the wall of the blade and then setting limits on the maximum blade metal temperature. In the present paper, the gas state paths, involving viscous losses, heat transfer, and mixing of the coolant with the mainstream, are determined strip by strip along the whole blade chord for the stator and rotor of the stage and illustrated on an enthalpy-entropy chart. The work output from each rotor strip is obtained together with the losses (entropy creation) through the whole stage. It is then possible to calculate the thermodynamic efficiency for the cooled turbine stage and compare it to that of the uncooled stage. Illustrative calculations are given, a main calculation being based on the mean flow across the blade pitch. But, in a second supplementary calculation, allowance is also made for flow variations across the blade pitch. By comparing these two calculations, it is shown that the mean flow calculation is usually adequate.