Statistical Evaluation of the Performance Impact of Manufacturing Variations for Steam Turbines

A fast method is presented for evaluating the impact of blade manufacturing variations on the aerodynamic performance of turbomachines. The method consists of two parts. Firstly, an adjoint method is developed to evaluate the aerodynamic sensitivities for multistage turbomachines. This sensitivity information may then be used to perform fast direct Monte Carlo simulations to obtain the statistical distribution of the variations of aerodynamic performances resulting from any given set of manufacturing variations. Secondly, a method is developed to construct reduced-order models for the three-dimensional blades manufacturing variations using the Principal Component Analysis (PCA) method. Monte-Carlo simulations with the adjoint sensitivities can then be applied to the full and individual modes of the blade manufacturing deviations. The proposed method is applied to the last two stages of a low-pressure steam turbine. A total of 29 sets of measured manufacturing deviations of the last-stage rotor blades are used to construct a reduced-order model of the manufacturing variations. The manufacturing variation reduced-order model helps identify origins of the manufacturing deviations connected to the machining processes of the blades. Relations of the statistics of the aerodynamic performance variations such as mean, standard deviation, etc. to the different modes of manufacturing deviations are studied and analyzed.