Analyzing mistuned multi-stage turbomachinery rotors with aerodynamic effects

• A new approach to construct multi-stage ROMs with aerodynamic effects.
• A new classification method for categorizing complex multi-stage modes.
• Many mistuned multi-stage ROMs are created for probabilistic analysis.
• Interaction of damping, mistuning & multi-stage structural coupling is investigated.
• Multi-stage modeling is critical for the analysis of structural and aeroelastic systems.

A great deal of research has been conducted on accurately modeling large cyclic structures such as turbomachinery rotors. Accurate modeling of realistic industrial turbomachinery requires overcoming several challenges. The first is the excessively large size of the finite element models (FEMs) needed, which can contain millions of degrees of freedom per stage of the rotor. The second challenge is the presence of small random variations in the structural properties known as mistuning, which arise from operational wear and/or manufacturing tolerances, and destroy the cyclic symmetry of the FEMs. The third is the complexity of turbomachinery models, which often include multiple stages that often have a mismatched computational grid at the interface between stages. The fourth challenge is associated with modeling the aerodynamic loads on the turbomachinery rotor. Much research has been conducted to overcome the first two challenges. By combining cyclic symmetry analysis and component mode mistuning (CMM), compact single-stage reduced order models (ROMs) can be created to accurately capture the free and forced response of these systems. These highly efficient ROMs can be developed from single sector calculations and can be of the order of the number of sectors in the stage. Recently, the third challenge associated with the complexity of modeling multiple stages has been addressed by the authors. Their method uses cyclic symmetry and CMM to form single-stage ROMs (using only single sector models and single sector calculations), and then combines these single-stage ROMs by projecting the motion along the interface between stages along a set of harmonic shape functions. This method allows for the creation of compact ROMs of multi-stage systems with mistuning using sector only calculations. The fourth challenge has been addressed only for single-stage systems by computing a complex aerodynamic matrix (which contains stiffness and damping terms) using an iterative approach. In this work, some of the effects of the aerodynamics on multi-stage systems are explored. The methodology consists of first creating efficient structural ROMs of a multi-stage rotor using the method previously developed, and then iteratively calculating the complex aerodynamic matrices for each stage. A new way to account for the effects of a shift in frequency due to mistuning on the complex aerodynamic matrix is also proposed. Additionally, a new classification of complex multi-stage aeroelastic modes is introduced. The presented results focus on exploring the influences of the aerodynamics and mistuning on the multi-stage response. A variety of numerical results are analyzed for two stages of an industrial rotor.