Performance Impact of Manufacturing Tolerances for a Turbine Blade Using Second Order Sensitivities

Performance changes due to manufacturing variations for a turbine blade are evaluated in the paper using the first order (FO) and second order (SO) sensitivities, which are calculated by a continuous adjoint method. In the case of newly manufactured blades, the geometric variation at each scanning point is assumed to meet a standard normal distribution. In the study, a modelling method taking into account the spatial correlations is employed to quantify the geometric uncertainty, where the contour of manufacturing tolerance is produced by imposing a series of shape functions on the blade. The basis modes of the geometric variations are extracted by principle component analysis. Firstly, the calculations of both FO and SO Sensitivities by solving the Euler adjoint equations are introduced. By regarding a finite number of primary basis modes of the geometric variations as the geometric parameters, the SO sensitivities can be obtained with significantly reduced computation cost. Sensitivity validations and performance evaluations based on sensitivities for each basis mode are then presented, illustrating the dramatic improvements on performance evaluations using the SO sensitivities. Finally, the statistics of performance changes for the turbine blade are evaluated by using the Monte Carlo simulations with respect to two different probability density functions for the input random variables. The results further demonstrate that the nonlinear dependence of the aerodynamic performance on the geometric variations can be captured by using the SO sensitivities.