Forced Response Analysis of an Embedded Compressor Rotor Induced by Stator Disturbances and Rotor–Stator Interactions

1. Introduction

Compressor flowfields are inherently unsteady due to the relatively high-speed rotation between rotor blades and stator vanes, which leads to the blades constantly suffering from unsteady external excitation forces, resulting in the forced response of blades [ 1 2 ]. For the embedded rotor blades of a multistage compressor, the most common excitation sources are the wake from the upstream vane row and the potential field from upstream and downstream vane rows [ 3 4 ]. During the compressor operation, the frequencies of excitation forces induced by these disturbances will inevitably coincide with the natural frequencies of rotor blades and resonance may occur, leading to high-cycle fatigue failure. The Campbell diagram can help identify where resonances are likely to occur, but it is almost impossible to avoid all resonant crossings within the operating range of a multistage compressor, thus it is necessary to accurately predict the blade vibration amplitude for each resonance to determine whether the crossings are acceptable [ 5 ].

Many efforts have been made to accurately predict the blade response, including using a fluid-structure-coupled method [ 6 8 ], investigating the influence of the turbulence model [ 9 ], damping [ 6 7 ], boundary condition [ 8 9 ], and mesh densities [ 8 10 ], etc. These studies are helpful but mainly focus on the influence of numerical methods. The multi-row interactions may have a greater influence on the blade response prediction.

In engineering practice, the forced response of an embedded compressor rotor is commonly solved by the decoupled method, where the upstream and downstream stator disturbances are applied as boundary conditions to single-row configurations [ 11 ]. It can be used to accurately and efficiently predict the blade vibration amplitude if the inter-row coupling effects [ 12 13 ], mainly referring to the rotor–stator interactions, can be ignored. However, the use of the decoupled method may lead to inaccurate predictions because the rotor–stator interactions are non-negligible in some cases.

Forced response predictions of a 3.5-stage axial compressor with different computational domains were carried out at Duke University. Besem et al. [ 14 ] focused on the first-stage stators and the second-stage rotors and stators (S1/R2/S2), and performed the predictions with decoupled and coupled configurations. The results showed that using a decoupled method cannot obtain accurate results due to the strong inter-row interactions. A three-row coupled configuration including the downstream stator is necessary when adjacent stators excite the embedded rotor at the same frequency. Li et al. [ 11 ] subsequently performed detailed analyses by investigating five decoupled and coupled cases. The response of the rotor blade including the upstream and downstream stators is 1.73 and 3.13 times larger than that of the decoupled configuration, respectively, indicating that the downstream stator has a more tremendous effect on the rotor blade. Moreover, it was found that the unsteady pressure in the rotor passage of the S1/R2 coupled configuration and R2 decoupled configuration is more or less similar, whereas it differs dramatically between the R2/S2 coupled configuration and the R2 decoupled configuration. Shreyas et al. [ 15 ] suggested that the reflection of the downstream stator has a more significant effect on the response of the rotor blade than that of the upstream stator. Shreyas et al. [ 16 ] then analyzed a four-row case with the downstream R2, a five-row case considering the upstream IGV, and the above three-row case. It was found that the reflection of the downstream R2 was also significant, but not contributed much to the blade response, and thus the three-row case can provide accurate and efficient predictions.

The influence of inter-row interactions on the excitation of blade vibration has also been studied. Schoenenborn and Ashcroft [ 17 ] compared the calculated unsteady pressure of a quasi-3D axial compressor rotor using coupled and decoupled methods. It was found that the IGV-R1-interaction modes can pass through the rotor passage with little attenuation, and concluded that cut-on modes have a huge impact on the unsteady pressure amplitude of the rotor blade. Schoenenborn [ 18 ] showed that the R1-S1-R2 interaction modes can lead to different blade excitations in the circumferential direction. Terstegen et al. [ 9 19 ] investigated the effect of rotor–stator interactions on the rotor blade response of a 2.5-stage axial compressor. They performed detailed and comprehensive azimuthal mode analyses and stress predictions. The results show that the vibrational stress predicted by the decoupled method without considering the rotor–stator interactions was 97% lower than the experimental results. It was concluded that the acoustic modes generated by the interactions between the rotor blades and the downstream stator vanes need special attention.

The above results have shown the importance of rotor–stator interactions for blade response predictions. However, these studies mainly emphasized that the interactions between downstream stator vanes and rotor blades were very important, whereas the upstream stator–rotor interactions seem to be not very significant in comparison. This means that the decoupled method can still be used in some cases. Therefore, the main objective of this paper is to accurately and efficiently predict the response of an embedded compressor rotor induced by stator disturbances and rotor–stator interactions, and to clarify the key factor that determines whether the decoupled method or coupled method should be used. For this purpose, full-annulus unsteady calculations were performed based on the decoupled and coupled methods. The dominant stator disturbances and rotor–stator interactions were identified by analyzing the unsteady static pressure field and total pressure field combined with the spinning mode theory and the acoustic wave equation. Meanwhile, the contribution of rotor–stator interactions to the vibration amplitude of the rotor blade was determined. Furthermore, the formation process of rotor–stator interactions and its influence on the selection of predicted methods were revealed, and the mechanisms of forced response were detailed.