Dynamic Response of Bladed Disks with Uncertain Geometry

Turbomachinery is part of a critical class of mechanical systems essential for many industrial sectors and their operation often relies on bladed disks. In particular, gas turbines have acquired a fundamental role in the fields of aircraft propulsion and power generation thanks to their high efficiency and power-to-weight ratio. However, the operation of these turbomachines presents a few challenges, especially regarding reliability. For heavy-duty gas turbines, the rapid growth of sparse energy sources has led to significant changes in their operation, with one important consequence being an increase in mechanical vibrations. The frequent changes operating regime combined with the high modal density of bladed disks makes resonance crossings very frequent. The resulting stresses can cause fatigue damage to the blades, reducing their service life. For this reason, an accurate prediction of the modal properties and dynamic response is fundamental to ensure the integrity of blades. Their design is a complex process, involving a combination of fluid and structural analyses. Computational Fluid Dynamics (CFD) is used to simulate the flow field, while Finite Element (FE) models are used to obtain the structural response. A coupling between the two analyses is usually required, resulting in high computational costs. An accurate model must also include the effect of uncertainties that may affect the geometry, material properties, or other quantities. Commonly, these are the result of manufacturing or wear and can have a severe impact on the dynamic properties. Bladed disks are periodic structures, and even slight perturbations to individual blade properties can cause a loss of symmetry and mistuning. This phenomenon may result in mode localization and increased vibration amplitudes. Moreover, this phenomenon is generally random in nature, requiring a statistical treatment, which might be impractical on large FE models. Here, we propose a modeling framework that addresses these critical aspects. An efficient reduced-order model (ROM) is implemented to speed up the computations, incorporating the effect of geometric uncertainties and mistuning, and the response is computed using CFD loads applied to the ROM through a highly efficient mapping. This process is validated and applied to an industrial-grade FE model.