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Forming the first part of a two-part paper, the methodology of an efficient frequency-domain approach for predicting the forced response of turbomachinery blades is presented. The capability and computational efficiency of the method are demonstrated in Part Two with a three-stage transonic compressor case. Interaction between fluid and structure is dealt with in a loosely coupled manner, based on the assumption of linear aerodynamic damping and negligible frequency shift. The Finite Element (FE) package ANSYS is used to provide the mode shape and natural frequency of a particular mode, which is interpolated onto the CFD mesh. The linearised unsteady Navier-Stokes equations are solved in the frequency domain using a single-passage approach to provide aerodynamic excitation and damping forces. Two methods of obtaining the single degree-of-freedom forced response solution are demonstrated: the Modal Reduction Technique, solving the modal forced response equation in modal space; and a new Energy Method, an alternative method allowing calculations to be performed directly and simply in physical space. Both methods are demonstrated in a preliminary case study of the NASA R67 transonic fan blade with excitation of the 1st torsion mode due to a hypothetical inlet distortion.

This is part two of a two-part paper. Part One describes the methodologies of a blade forced response prediction system. The emphasis of this part is to demonstrate the capability and computational efficiency of the system for predicting blade forced response. Part two firstly presents verification of the multistage time-linearized unsteady flow solver through comparison of predicted blade surface pressure distributions with data measured on a VKI transonic turbine stage. It concludes with presentation of the results of an analysis carried out on the last stage rotor blade of an ALSTOM three-stage transonic test compressor. In the analysis, strain gauge results together with Finite Element (FE) modal analysis identify the resonant crossings. The mode shape of the blade vibration is used in the CFD code to predict the blade aerodynamic damping. The aerodynamic damping is compared with the blade system damping obtained from the strain gauge tests. The variation is shown of aerodynamic and mechanical damping with blade mode shape. The blade unsteady modal forces induced by the upstream stators are derived from the calculated unsteady flows. The blade vibration at three resonant crossings is compared with those given by strain gauge measurements. Good comparisons and high computational efficiency demonstrate that the forced response methodologies described in Part One can be used in the blade design process to tackle blade aeromechanical issues.

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