# Vibroacoustic Optimization Study for the Volute Casing of a Centrifugal Fan
## 1 Introduction  
The centrifugal fan is considered a common turbomachinery that is widely used in the ventilation systems of the ship cabin and other sites, bringing comfortable working and living environments for people. However, the noise and vibrations generated with the fan running troubled researchers; thus, the study of the mechanisms of noise and vibration generation and propagation became more and more important. Most of the current studies on fan noise have dealt with aeroacoustic problems. However, the noise is induced not only by internal turbulent flow, but also by flow-induced structure vibration. In some particular application environments, the fluid should be strictly kept within the fan's systems (e.g., petrochemical compressors and large fans with fan system inlets and outlets are entirely connected to the extended pipe) without any leakage, and the aerodynamic noise-induced unsteady flow of a fan cannot directly spread to the outside. At this moment, the fan casing and the inlet and outlet pipe vibration noise caused by the vibrations of the solute surface are predominant. Therefore, an intensive study of the generation mechanism of the vibrational noise and the noise reduction method is necessary. In fact, the fan noise induced by unsteady flow belongs to fluid-structure coupling noise, and the impeller and volute can be classified as an elastomer; in particular, the volute vibration cannot be neglected in large fans [1]. In addition, the aeroacoustic and vibroacoustic calculations usually require high computational resources; in order to reduce the computational cost and have an accurate response, hybrid methods are applied. With respect to the vibroacoustics of casings, such as the vibrational noise of car body and compressor casings, the hybrid finite-element method/boundary-element method (FEM/BEM) approach and the hybrid finite-element method/statistical energy analysis (FEM/SEA) approach are often used. It could be also appropriate to cite [PERSON] and [PERSON] [2], who have made a comprehensive literature review of both the structural and acoustic modeling methods that are used nowadays to predict the vibroacoustics' performance. They pointed out that lower frequencies, where the tonal resonances are significant, are calculated applying finite element methods (FEM), whereas for higher frequencies, a statistic energy approach can be chosen. Besides, the FEM/BEM method is usually used to perform the free-field sound radiation analysis of open domains. [PERSON] [3,4] carried out a vibroacoustic analysis for the chain cover of a four-stroke four-cylinder diesel engine through an FEM-BEM coupled approach, while [PERSON] [5] described an innovative integrated design verification process, based on the bridging between a new semiempirical jet noise model and a hybrid finite-element method/statistical energy analysis (FEM/SEA) approach for calculating the acceleration produced at the payload and equipment level within the structure, vibrating under the external acoustic forcing field. However, there are few studies on the vibration noise induced by the vibration of the casing in a centrifugal fan. This type of noise is prominent in large-scale fan systems and fans with closed pipelines. At present, research on the vibration noise induced by casing vibration resulting from impeller outlet unsteady flow is usually conducted using simulation methods. A prediction method based on a method of combining boundary element method (BEM) calculations with experimental measurement was proposed by [PERSON] [6]. In this method, the aerodynamic noise is isolated, the volute vibrations induced by the unsteady flow are calculated separately, and the pressure fluctuations required for noise and vibration calculations are obtained experimentally. On this basis, some scholars such as [PERSON] [7], [PERSON] [8,9], and [PERSON] [10] have used the same method to calculate the vibrational sound radiation of a compressor and the T9-19 No.4 industrial centrifugal fan.