A Critical Numerical Review of Loss Correlation Models and Smith Diagram for Modern Low Pressure Turbine Stages

The Smith diagram, originally published in 1965, has been largely exploited as a preliminary design (PD) tool for axial turbines. Currently, it is applied to aeronautical Low Pressure Turbines (LPTs) in order to define basic characteristics during the feasibility study and to compare different configurations. The Smith diagram represents a correlation of stage performance (η) as function of flow coefficient (φ) and loading factor (ψ), but it does not take into account the effects of some important input parameters (single contributions of loss, Reynolds number, Aspect Ratio, Rotor Tip Clearance (RTC)) and does not report some key design outputs (deflections (δ), profile weights and stresses), which have also a direct relation with the configuration position on the Smith diagram. This study employs meanline analyses incorporating two traditional loss correlation models used in the turbine field (Craig and Cox, Kacker and Okapuu) to compare results with the original Smith diagram. The correlation approach allows one to obtain other important multidisciplinary information (primarily aero-mechanical) which was previously absent, which leads to some strategic design achievements. The investigation process is based on a reference two-stage turbine properly set to match specific operating points on the Smith diagram. Several three-dimensional blade geometries have been designed and then detailed 3D CFD analyses have been performed in order to acquire confidence with respect to the meanline results. This research adds additional important information for turbine module design to the Smith chart and allows for a numerical revision of the diagram itself, fine tuning it with data obtained from the analyses of modern blades optimized for high stage performance. Finally numerically-based loss predictors, broadly applicable to LPTs during optimization procedures before detailed CFD analyses, are presented and discussed.