# The Characteristics and Mechanisms of High-Intensity Sound in a High-Speed Multistage Compressor
## 1 Introduction  
Research institutions such as the National Aeronautics and Space Administration (NASA) in the United States and Deutsches Zentrum fur Luft- und Raumfahrt (DLR) in Germany have discovered many structural failures in engine casing components, such as rotor blades and casing, which all result from high-intensity sound [1, 2]. Additionally, the \"Engine Structural Integrity Plan\" presents the notion that the verification of high-intensity sound in aeroengines is difficult because of the simultaneous occurrence of multiple acoustic modes within a closed space. The emergence of multiple modes actually reduces the intensity of every acoustic mode [3]. The establishment of the theoretical model for predicting the occurrence of high-intensity sound in a compressor is rather complicated due to numerous factors including changed duct geometry, the propagation of acoustic waves, load changes, and so on. The simulation of the whole process of pressure disturbance, as well as the coupling calculations in the three-dimensional field for flow, sound and structure are difficult to finish with unsteady methods due to unacceptable computational costs. Therefore, it is necessary to derive a simplified model to study high-intensity sound in multistage compressors [4]. [PERSON] [5] successfully established the first high-intensity sound model based on the plate cascade and experimentally studied acoustic waves and the interaction between shedding vortices and sound. The typical characteristic of \"frequency-locked\" was presented in the experiment. The proposal of [PERSON]'s mode further clarifies that the plate vibration pattern is determined by the interaction between the sound and plate in the duct [6; 7; 8]. [PERSON] made a detailed explanation for the evolution of the shedding vortex of the rectangular plate with a numerical simulation on a two-dimensional cascade model [9]. The key factors affecting high-intensity sound, including slab thickness, the shape of the plate trailing edge, the dimensions of the pipeline, and so on, are ensured, as is the interaction mechanism between plate wake flow and flow-induced high-intensity sound in hard-walled pipelines [10]. [PERSON] completed the recovery of the shedding vortex from the trailing edge of the plate locked in the duct with the assumption that there was little influence on the results from flow velocity changing, and found the phenomenon of the coupling of sound wave frequency and vortex frequency and the interaction between the sound wave and the shedding vortex [11; 12]. For the study of high-intensity sound in real compressors, [PERSON] used a numerical model to capture the interaction of the compressor blades and the acoustic waves during propagation in a multi-stage compressor [1]. [PERSON] then used an experiment base from that model to explore the reason for the occurrence of high-intensity sound [13]. [PERSON] established an excited disk model that could recover the processing of the high-intensity sound of aeroengines and pointed out that the high-intensity sound only occurred in certain combined conditions of the parameters, such as rotor speed, flow velocity, and some other elements [14]. Some investigation into broken components in aeroengines has been implemented [15; 16; 17]. [PERSON]'s study regarding the high-intensity sound in ducts points out the importance of the interaction between acoustic waves and plate wake vortices, which make a foundation for the failure of the components--especially the blades in the compressor of the aeroengine--that arise with high-intensity sound. Structural acoustic resonance is the coupled vibration between the sound and the structure, and is associated with the high-intensity sound in the internal cavity of the structure, and the physical essence of it is the fluid-induced cavity sound. In 1878, [PERSON] conducted an experimental study of the sound of a wire at discrete velocity ranges of wind, which was a precedent study for the wake sounds of turbulent fluid in a flow field.