Analysis of Intentional Mistuning on the Aeroelastic Stability of Freestanding Last Stage Blade Rows in Steam Turbines

It is common in the industrial practice of the structural dynamic analysis for a Last Stage Blade (LSB) row to assume that all blades have identical mechanical properties. Nevertheless, the mechanical properties vary from blade to blade due to e.g. manufacturing and assembly tolerances, wear and so forth. These variations influence the vibrational behavior of an LSB row and are known as mistuning. For freestanding LSB rows, the determination of the margin against the onset of unstalled flutter vibrations is of crucial importance. The margin against the onset of unstalled flutter vibration is determined by a stability analysis, i.e. by solving an aeroelastic eigenvalue problem. The aeroelastic stiffness and damping are, in industrial practice, calculated for each vibration mode of the blade row using Computational Fluid Dynamics (CFD) methods. In these calculations, the complex modal work applied from the fluid to the blade row is determined for each vibration mode of interest. The corresponding stiffness and damping can then be derived from this complex modal work. The damping can be derived either as viscous damping (proportional to the velocity) or as structural damping (proportional to the displacement). Both approaches are proposed in the literature and are detailed in terms of an unstalled flutter stability analysis for a freestanding and mistuned LSB row in this paper. Mistuning is modelled using the well-known Fundamental Model of Mistuning (FMM) methodology. Even though both approaches result in approximately equal results w.r.t. the determination of the onset of unstalled flutter vibrations, an explanation is given why the viscous damping approach is, in terms of its physical interpretation from the structural dynamics point of view, superior to the structural damping approach. Mistuning, either natural or intentional, generally increases the margin to the onset of unstalled flutter vibrations. If intentionally mistuning is applied to LSB rows, one question is its interaction with the unavoidable remaining natural mistuning which is random in nature. Even though mistuning is beneficial in terms of the unstalled flutter stability, it has a detrimental effect on forced vibrations because of the amplitude magnification phenomenon which is relevant for start-up and coast-down. Thus, the effect of mistuning on the vibrations of an LSB row needs to be analyzed for both cases, namely unstalled flutter and forced response. A systematic study on the interaction between intentional and natural mistuning is given in this paper for different forms of practical intentional mistuning patterns.