The oil and gas, chemical, and process industries employ centrifugal compressors for a wide range of applications. Due to this, the conditions under which centrifugal compressors have to operate vary significantly from case to case. Gas pipeline compressors, for example, may feature discharge pressures well over 100 bar. In other fields of application, like gas injection, which is used to enhance oil recovery, this quantity can reach considerably higher values. Here, discharge pressures over 600 bar and gas densities over 300 kg/m3 are not uncommon. During the last several decades, comprehensive research was conducted on the impact of high-pressure operating conditions on the vibrational behavior of centrifugal compressor wheels. Nowadays, it is well-known that an increase in gas pressure levels leads to a more pronounced interaction between the side cavities and the impeller, which results in a frequency shift of the acoustic and structural modes.
For the safe operation of compressors, it is necessary to predict these coupled natural frequencies accurately. The state-of-the-art approach to achieve this objective is the finite element method. While this technique provides high-quality results, the simulation of acousto-mechanical systems is still a time-consuming process that incurs high computational costs. Therefore, finite element models are, in this case, not suitable for probabilistic studies, sensitivity analyses, and comprehensive simulations of the full operating range of the compressor. In 2013, Magara proposed a simplified model based on an annular plate between two cylindrical cavities to solve this problem. While this method reduces the required computational effort significantly, its use is limited to platelike impellers.
The authors of this paper propose a more generalized method to overcome the challenges mentioned earlier. It uses the uncoupled structural and acoustic modes of the actual impeller and side cavities in a modal superposition to approximate the natural frequencies of the coupled acousto-mechanical system. In this way, the intended design geometries of the impeller and side cavities are considered while maintaining the advantages of Magara's model regarding the computational effort. In a numerical study, Magara's method and the generalized model are applied to different systems of increasing complexity. The investigation starts with a simple annular plate in a cylindrical cavity and ends with an actual compressor impeller. At every complexity level, the results of both approaches are compared to a finite element analysis. Moreover, measurement data of a simplified rotor in a cylindrical cavity are used to validate the numerical models. Finally, this paper concludes with a discussion of the limitations and benefits of all employed numerical methods.