Reduced Order Model development for turbine blades modal assessment

Nowadays, gas turbines have become a consolidated reality to obtain mechanical power to be applied in several industrial fields. Actually, in order to obtain it, an exchange of energy between fluid and turbine blades takes place in turbomachines. In this operation, blades deviate fluid direction and, consequently, they endure pressure forces. These forces can change during the time and they depend on the frequency imposed by the rotation speed of the rotor. They also cause time-varying strains and deformations on blades. For these reasons it is not enough to perform only static analysis, because it doesn’t allow to correctly evaluate deformations due to forces and pressures. Actually, for turbine blades design, frequency analysis is fundamental in order to avoid that conditions of resonance fall within the component’s operating range. It can be done through modal analysis of the system, which allows to compute natural frequencies and relative modal shapes. In this thesis a model of gas turbine last stage rotor, provided by Ansaldo Energia S.p.A., will be analysed through this procedure. The Finite Element Method (FEM) will be used in order to discretize the component and the model will be initialized with Ansys Workbench software. Subsequently, that model will be modified to make its reading easier for the software and cyclic symmetry will be applied. This latter property makes the program having the idea that, in a first approximation, turbine blade is composed by N equal sectors. As a consequence, this leads to a reduced computational cost. After that, an input file will be created, which will be imported into Ansys APDL software in order to perform static and modal analysis. Results obtained from FEM analysis are strictly dependent on the number of nodes present in the model. Therefore, an high number of nodes could lead to computations that are too much demanding for the software or to a long analysis time. Furthermore, Finite Element Method is a numerical technique that is used to solve complex structures in an approximate way. Thus, it will be necessary to verify if the results obtained can be considered reliable. Therefore, using Craig-Bampton reduction technique, reduced stiffness matrix K and reduced mass matrix M of the model will be extracted. These will be exported in a file.txt and so they can be read in Matlab. Finally, with another specific procedure, it will be possible to compute natural frequencies of the turbine blade. In this way, natural frequencies calculated by FEM approximation with Ansys and analytically with Matlab can will be compared.