Numerical Study of Low Engine Order Excitations Due to Manufacturing Variability Part II: An Efficient Approach for Stochastic Studies

Abstract In turbomachinery rows, the geometric variability between the airfoils induces nonuniformity in the flow, which directly translates into low engine order (LEO) excitation and vibration in the adjacent rows. Direct simulations of this phenomenon involve full-row computational fluid dynamics (CFD) analyses, where the exact geometry of each individual blade needs to be properly reproduced. The related computational cost of such simulations is very significant. Since the geometric variability due to the manufacturing scatter is stochastic, valuable information could be derived from Monte Carlo analyses involving randomly generated geometries; nevertheless, this approach would be very resource-intensive. In this paper, we propose a simplified method to determine the flow perturbation generated by this geometric variability. The method is based on studying the underlying properties of the geometric scatter using principal component analysis (PCA) techniques, obtaining a compact description of the variability of the airfoils. The flow perturbation due to a reduced number of reference cases is obtained through direct, large scale simulations. By assuming linearity in the flow perturbations, the solution for a general case of geometric distortion may be obtained very efficiently from these reference cases, which makes Monte Carlo studies to analyze stochastic geometric distortion easily affordable. The capabilities of the method are demonstrated in a test case considering the real geometry scatter from an aircraft turbine. According to the results, the average LEO response due to the random geometry scatter involves significant vibration levels, comparable (in terms of alternating stress) to the response due to the blade-passing excitation.