The high performance bladed-disks used in today’s turbomachines must meet strict standards in terms of aeroelastic stability and resonant response level. One structural characteristic that can significantly impact on both these area is that of bladed-disk mistuning. To predict the effects of mistuning, computationally efficient methods are necessary to make it feasible, especially in an industrial environment, to perform free vibration and forced response analyses of full assembly finite element models. Due to the size of typical finite element models of industrial bladed-disks, efficient reduction techniques must be used to systematically produce reduced order models. The objective of this paper is to compare two prevalent reduction methods on representative test rotors, including a modern design industrial shrouded bladed-disk, in terms of accuracy (for frequencies and mode shapes), reduction order, computational efficiency, sensitivity to inter-sector elastic coupling, and ability to capture the phenomenon of mode localization. The first reduction technique employs a modal reduction approach with a modal basis consisting of mode shapes of the tuned bladed-disk which can be obtained from a classical cyclic symmetric modal analysis. The second reduction technique is based on a Craig and Bampton substructuring and reduction approach. The results show a perfect agreement between the two reduced order models and the non-reduced finite element model. It is found that the phenomena of mode localization is equally well predicted by the two reduction models. In terms of computational cost, reductions from 1 to 2 orders of magnitude are obtained for the industrial bladed-disk, with the modal reduction method being the most computationally efficient approach.

The paper presents an approach for the modal aeroelastic analysis of three-dimensional turbomachinery bladings with several fluid and structure analyzers. Structure analyzers are three-dimensional solvers for static and dynamic analyses of axisymmetric/cyclic-symmetric blade-shroud-disk-shaft assemblies with/without elastic coupling between blades. Fluid analyzers are two-dimensional/three-dimensional solvers for single/multi-stage steady/unsteady turbomachinery flows. An automatic interfacing procedure for exchanging data at the incompatible fluid-structure boundary and the development of a multi-model interfacing software are discussed. The modal aeroelastic analysis of a first stage shrouded fan is carried out to illustrate the main issues of the paper. In particular, two structural models for the elastic coupling of the part-span shrouds are discussed. The results show the strong dependence of the structure dynamics and aeroelastic analysis on this modelling.

A parametric study on the flutter stability of a turbine cascade as a function of the torsion axis position, the bending direction and the reduced frequency is presented. In this process two different unsteady flow models are used in order to minimize the uncertainties of numerical modeling on the physical conclusions of the study. Comparisons are performed against available experimental data. It was found that the comparison of the global aerodynamic damping between numerical results and experimental data was reasonably good. It was observed that the stability was more sensitive to changes in the mode shape than in the reduced frequency. Comparisons of the local unsteady pressures showed similar tendencies for the numerical models and the experimental data, while discrepancies on the blade suction surface between the models were observed around the trailing edge for the subsonic flow and close to shock location for the transonic flow. The results indicated interesting agreement of the mode shape stability maps with results obtained on a largely different low-pressure turbine blade.

Precise non-linear aeroelastic modeling of shrouded bladed-disc assemblies is generally beyond present capacities and analyses often assume that the behavior of the coupled system remains linear and retains a cyclic symmetrical property. In this paper, several models of shrouded assemblies, in the particular case of fully slipping interfaces, are examined and compared. Considering the cyclic symmetrical property of the structure, only the model where shroud segments can slip and propagation relations are applied in the direction normal to the interface plane, should be used. A reduced model based on a direct discretisation of the whole assembly is presented and validated. The application is based on a first stage shrouded fan. The influence of varying the interface shroud angle is examined in terms of frequency, mode shape and aeroelastic damping.

Two methods are generally used for the aeroelastic analysis of bladed-disc assemblies. The first, often referred to as the energy method, assumes that the fluid does not modify invacuum structural dynamic behavior. On the other hand, the second, based on an eigenvalue approach, considers the feedback effect of the fluid on the structure. In this paper, these methods are compared using different test cases, in order to highlight the limitations of the energy method. Within this comparison, the effect of material modifications on the coupled behavior of the assembly is examined.