A methodology is presented to allow designers to estimate the penalty for turbine efficiency associated with film cooling. The approach is based on the control volume analysis of Hartsel and the entropy-based formulations of Young and Wilcock. The present work extends these techniques to include flow ejected at compound angles and uses three-dimensional computational fluid dynamics (CFD) to provide the mainstream flow properties. The method allows the loss contribution from each hole to be identified separately. The proposed method is applied to an aeroengine high-pressure turbine stage. It is found that, if the efficiency definition includes all irreversibilities, the penalty associated with film cooling would be 8.0%. However, if the pragmatic approach is adopted whereby the unavoidable entropy generated due to the equilibration of coolant and mainstream static temperatures is ignored, the efficiency penalty is 0.7%. Finally, a series of case studies is used to quantify the impact of changes to the local mainstream flow direction and coolant ejection angle on the predicted turbine efficiency. It is shown, quantitatively, that reducing the angle between the directions of the coolant and mainstream flows offers the greatest potential for the designer to improve film-cooled turbine efficiency.

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