Vibratory Behavior Prediction of a Mistuned Clustered Stator Vane: Non-Intrusive Stochastic Methods

The role of stator vanes is to straighten the air flow on each stage of axial compressors. They are so subject to dynamically fluctuating high pressure loads. Furthermore, monobloc clustered designs have been developed to facilitate manufacturing process and reduce costs, but they result in loss of cyclic symmetry properties and very low structural damping. This makes it more difficult to predict vibratory behavior, when taking high modal density and extreme sensitivity to mistuning into account, and even more essential to ensure structural strength in the context of fatigue. In most cases, mistuning due to geometrical and material tolerances is unknown. Here, a non-intrusive spectral stochastic method has been developed to predict the vibratory behavior of a clustered stator vane in which the Young modulus of some blades is associated with a random variable representing the mistuning effect. This method is based on a stochastic modal analysis which consists in projecting eigenfrequencies and modes shapes on a polynomial chaos basis. Computation of spectral coefficients is performed through non intrusive ways — making the method applicable to any problem — as Smolyak projection or regression by least square method. These two methods are compared based on criteria of computations costs, accuracy, robustness and convergence. These methods have been tested on a simplified stator vane model - based on a 2D Euler-Bernoulli beams assembly. Regression method provides rather accurate results unlike Smolyak projection whatever the initial configurations of the problem. Computation costs are reasonable but could increase really fast according to polynomial degree and stochastic dimension. Thus, regression method is an accurate, robust and fast enough method to predict the vibratory behavior of a mistuned clustered stator vane.