Blade Loading and Its Application in the Mean-Line Design of Low Pressure Turbines

In order to minimize the number of iterations to a turbine design, reasonable choices of the key parameters must be made at the preliminary design stage. The choice of blade loading is of particular concern in the low pressure (LP) turbine of civil aero engines, where the use of high-lift blades is widespread. This paper considers how blade loading should be measured, compares the performance of various loss correlations, and explores the impact of blade lift on performance and lapse rates. To these ends, an analytical design study is presented for a repeating-stage, axial-flow LP turbine. It is demonstrated that the long-established Zweifel lift coefficient (Zweifel, 1945, “The Spacing of Turbomachine Blading, Especially with Large Angular Deflection” Brown Boveri Rev., 32(1), pp. 436–444) is flawed because it does not account for the blade camber. As a result the Zweifel coefficient is only meaningful for a fixed set of flow angles and cannot be used as an absolute measure of blade loading. A lift coefficient based on circulation is instead proposed that accounts for the blade curvature and is independent of the flow angles. Various existing profile and secondary loss correlations are examined for their suitability to preliminary design. A largely qualitative comparison demonstrates that the loss correlations based on Ainley and Mathieson (Ainley and Mathieson, 1957, “A Method of Performance Estimation for Axial-Flow Turbines,” ARC Reports and Memoranda No. 2974; Dunham and Came, 1970, “Improvements to the Ainley-Mathieson Method of Turbine Performance Prediction,” Trans. ASME: J. Eng. Gas Turbines Power, July, pp. 252–256; Kacker and Okapuu, 1982, “A Mean Line Performance Method for Axial Flow Turbine Efficiency,” J. Eng. Power, 104, pp. 111–119). are not realistic, while the profile loss model of Coull and Hodson (Coull and Hodson, 2011, “Predicting the Profile Loss of High-Lift Low Pressure Turbines,” J. Turbomach., 134(2), pp. 021002) and the secondary loss model of (Traupel, W, 1977, Thermische Turbomaschinen, Springer-Verlag, Berlin) are arguably the most reasonable. A quantitative comparison with multistage rig data indicates that, together, these methods over-predict lapse rates by around 30%, highlighting the need for improved loss models and a better understanding of the multistage environment. By examining the influence of blade lift across the Smith efficiency chart, the analysis demonstrates that designs with higher flow turning will tend to be less sensitive to increases in blade loading.