Numerical analysis of the flow-induced noise of ventilation wall based on LES and FW-H hybrid method

Qingqing Yu 1 a. School of Mechanical Engineering, Southeast University

No.79 Suyuan Road, Jiangning District, Nanjing City, Jiangsu Province, 211189, P.R China b. Nanjing Research Institute of Electronics Technology

No. 8 Guorui Road, Yuhuatai District, Nanjing City, Jiangsu Province, 210039, P.R China Fei Xue 2 Nanjing Research Institute of Electronics Technology No. 8 Guorui Road, Yuhuatai District, Nanjing City, Jiangsu Province, 210039, P.R China

ABSTRACT As a widely used device in the field of air cooling and heat dissipation of electronic equipment, ventilation walls often have the flow-induced noise problem. This paper presents a numerical study on the flow-induced noise of a ventilation wall based on LES and FW-H hybrid method. Firstly, the pressure fluctuation data on the surfaces of ventilation wall was calculated from a large eddy simulation (LES). Then, taking the fluid pressure fluctuation at the surfaces of the ventilation wall as excitation source, the modal-based vibro-acoustic responses of ventilation wall was obtained by using LMS Virtual.lab. Finally, the structure of ventilation wall was optimized to reduce the flow- induced structural radiation noise. The results show that the flow-induced noise is mainly low- frequency noise. Besides, the peak frequencies of the flow-induced noise ranges from 80Hz to 255Hz, and the peak frequencies are consistent with certain structure mode frequencies. Moreover, the total sound pressure level of the flow-induced noise deceases from 92.5dB to 72.9dB by improving the structure stiffness of ventilation wall. In conclusion, this paper could provide a method for reducing the flow-induced noise of ventilation walls. Keywords: ventilation wall; LES and FW-H hybrid; pressure fluctuation; flow-induced noise; vibro-acoustic response

1. INTRODUCTION

Ventilation wall is a widely used device in the field of air cooling and heat dissipation of electronic equipment. Generally, cool air can be used to dissipate heat for multiple devices through ventilation walls. However, when the airflow passes through the ventilation wall, the thick panels of ventilation is often stimulated to generate structural radiation noise, thus, sometimes, the ventilation wall could be a major noise source.

In the past decades, a large number of studies had been carried out to explore on the principle and prediction of flow-induced noise or aero acoustics. In 1952, Lighthill’s work on acoustic-comparison method opened up the research in the field of aeroacoustics [1]. Later, through the development of Curle, Flowcs Williams and Hawkings, a complete set of aeroacoustics theory has been basically

1 yuqingqing@aliyun.com 2 xuefei8848@163.com

established [2~3]. Recently, based on the above classical aero acoustics principles, more and more scholars pay attention to the problem of flow induced noise in pipelines and cavities, and have carried out extensive experimental research and simulation analysis. In terms of experimental research, Udoetok E.S. et al. carried out a study on the effect of fluid flow inside the pipeline on the natural frequency of the pipeline, and then compared the theoretical results with the experimental results [4]. Bing. K., et al. conducted an experimental analysis on the influencing factors of flow-induced vibration of pipeline elbows [5]. Zhang et al. conducted an experimental study on the noise at the outlet of the elbow, and found that the numerical simulation results are slightly higher than the experimental values [6]. With the rapid development of computing technology, numerical simulation has become a reliable and efficient method to study the flow-induced noise of cavities, chambers, mufflers and pipelines [7~8]. Mao studied a two-part operation of one high head reversible turbine: transient load rejection process and intermittent vane closing conditions, and found that the flow induced noise radiation is consistent with internal fluid characteristics [9]. Ren, et al. carried out a study on the flow-induced noise of deflector jet servo valve based on LES/Lighthill hybrid method, and the result shows that continuous broadband dipole noise with medium- and high-frequency components [10]. Liu, et al. proposed a hybrid method that combined the detached eddy simulation (DES) with Lighthill’s acoustic analogy to simulate flow-induced noise in pipes and found that the noise source is near the opening of the cavity [11]. Han, et al, studied the flow-induced noise generated by natural gas manifolds based on LES and FW-H hybrid method, and a noise experiment was carried out to validate the present numerical model [12]. M. Cianferra carried out an Assessment of methodologies for the solution of the FW-H equation using LES of incompressible single-phase flow around a finite-size square cylinder [13]. Wei et al. used the Flowcs Williams and Hawkings model based on Lighthill’s acoustic analogy to compute the flow-induced noise in high-pressure- reducing valves [14]. Compared with the direct numerical simulation (DNS) and Reynolds-averaged Navier-Stokes (RANS) model, the LES is considered to be the most promising numerical method to study the flow characteristics [15]. Therefore, in this paper, the LES and FW-H hybrid method combining with the vibro-acoustic coupling method is employed to study the flow-induced noise of ventilation wall.

This paper presents a numerical study on the flow-induced noise of a ventilation wall based on LES and FW-H hybrid method. This paper is organized as follows. In Section 2, the geometric model, CFD model and the acoustical model are established. In section 3, the flow-induced noise of the ventilation wall is analyzed. In Section 5, the structure of ventilation wall is optimized to reduce the flow-induced structural radiation noise. Finally, in Section 6, the conclusions are summarized. 2. NUMERICAL MODELS

2.1. Geometric Model The geometric model of the ventilation wall studied in this paper is shown as Figure 1. As seen from Figure 1, there are one inlet and tree outlets, and the ventilation wall is separated into 3 chambers with two clapboards. The thickness of the panels of ventilation wall is 1mm. Besides, the material of the ventilation wall is Aluminum alloy, the tensity is 2700kg/m 3 with Poisson's ratio 0.334.

600

250 250

800

160

Inlet ￠ 110 Outlet

￠ 60 Figure 1: Geometric model of the ventilation wall

2.2. CFD Model As shown in Figure 2, the CFD model of the ventilation wall is its internal space, which is composed of one inlet and three outlets and solid walls. The velocity inlet boundary condition for steady flow velocity (29m/s) is applied to the inlet, the pressure outlet boundary condition for the zero-pressure outlet is applied to the outlets, and the non-slip wall boundary condition is applied to the wall. The Intensity and hydraulic diameter (IHD) method was used to set the turbulence. The max element size is 8mm, and the total number of tetrahedral elements and nodes are about 129 thousand and178 thousand, respectively.

Figure 2: Boundary Conditions of CFD Model

Taking the steady calculation result as the initial flow field of the unsteady calculation, the transient flow field of the T-shaped tee is numerically calculated based on the LES model. Since the calculation step size of the transient flow field needs to be combined with the calculation frequency of the sound field, after fast Fourier transform is performed on a time series, the highest frequency of the analyzable result is 0.5Δt -1 .

Since the frequency range of the sound field analysis in this paper is 20~1000 Hz, the time step is set to 5×10-5s, which can meet the calculation requirements. Through residual analysis and monitoring of indicators such as mass flow at the outlet of the ventilation wall, it is found that after 500 iterations, the transient flow field basically tends to a stable state. At this time, the FW-H acoustic analogy model is opened, and the pulsating pressure sound source on the wall is analyzed. Extract it as the initial data for the later sound field calculation.

2.3. Acoustical Model Figure 3 shows the external acoustic envelope of ventilation wall. Figure 3(a) shows the acoustical convex mesh of the ventilation wall, and Figure 3(b) shows the acoustical boundary condition of the convex mesh. As seem from Figure 3(b), the external surface mesh is set for automatically matched layer property (AML property). Besides, the interior surface mesh is set for acoustic-structure coupling.

AML boundary

Acoustic mapping

mesh

(a) Acoustical convex mesh

(b) Acoustical boundary condition

Figure 3: External acoustic envelope of ventilation wall

Figure 4 shows the structure mesh and the boundary condition settings. Figure 4(a) shows the relationship between the acoustical convex mesh and structure mesh. To calculate the structure radiation noise, mapping processing is required between the structural mesh and the acoustical convex mesh. Figure 4(b) shows the boundary conditions for modal analysis, it can be seen that the fixed boundary conditions are imposed on the edges of ventilation wall, and the simply supported conditions are imposed on the edges of the inlet and outlet pipelines.

Simply Supported

Structure mesh

Fixed Supported

AML boundary

Acoustic mapping

mesh

(b) structure boundary condition (a) structure mesh Figure 4: The structure mesh and its boundary condition settings

Based on the pressure fluctuation data (obtained in transient flow field simulation) on the wall of ventilation wall and the modal simulation data of the ventilation wall, the structural radiation noise can be calculated. In order to better understand the flow-induced noise of the ventilation wall, the ISO power field mesh is defined, as shown in Figure 5. Besides, ISO:19 and IS0:38 are selected as the output field points for monitoring the acoustical responses.

ISO: 38

ISO: 19

Beep rrrongee Bewgeseee Pome

ISO power field mesh

Figure 5: ISO power field mesh 3. RESULTS AND ANALYSIS

3.1. Flow Field Analysis According to the calculation results of steady-state fluid simulation, the total pressure and velocity vectors of the ventilation wall are shown as Figure 6. As seen from Figure 6(a), the total pressure reaches 3550Pa, and pressure decreases gradually from the inlet to the outlets. Besides, it can be found that, seen from Figure 6(b), the maximum velocity insides the ventilation wall is 55.8m/s, which results in the pressure loss and pressure fluctuation at the wall surfaces. Therefore, by optimizing the ventilation wall structure, the velocity fluctuation in the flow field will be reduced, and thereby reducing the structure radiation noise caused by the excitation of the unsteady airflow.

(a) Contours of total pressure (b) Velocity vectors colored by velocity magnitude(m/s) Figure 6: Total pressure and velocity vectors

3.2. Modal Analysis Table 1 shows the modal frequencies of the first 15 orders of ventilation wall. As seen from Table 1, the first order modal frequency is 54.78Hz, which reveals that the structural stiffness of ventilation wall is relatively weak. Besides, for broadband fluid excitation, it is easier to generate low-frequency structural radiation noise. Figure 7 shows the first four mode shapes of the ventilation wall. As seen from Figure 7, it can be found that the main mode forms come from the thick panel vibration, which is the key reason of the flow-induced structural radiation noise.

Table 1: The first 15 orders of modal frequencies Mode Frequency/Hz Mode Frequency/Hz Mode Frequency/Hz 1 54.78 6 102.48 11 121.02 2 77.03 7 105.43 12 138.03 3 81.36 8 107.83 13 139.29 4 82.20 9 114.27 14 140.28 5 86.08 10 121.02 15 143.03

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3.3. Acoustical Analysis Figure 8 shows the modal-based vibration-acoustics responses at the field points of ISO:19 and ISO:38. As seen from Figure 8, it is found that there are four main frequencies, which are 80.50Hz, 140.30Hz, 224.94Hz and 254.92Hz, respectively. Comparing with Table 1, it is found that each peak frequency corresponds to a certain order modal frequency. Besides, the differences in the location and number of outlet pipes lead to differences in the structure radiated noise on both sides from about 600Hz~1000Hz.

86.2dB @140.30Hz

90.94dB @224.94Hz

91.86dB @254.92Hz

87.8dB @81.50Hz

Sound Pressure Levl, dB

Figure 8: The modal-based vibration-acoustics responses at the field points of ISO:19 and ISO:38

4. OPTIMIZATION AND DISCUSSION

According to the mechanism of flow-induced structural radiation noise, the pressure fluctuation generated by the airflow on the wall plays an important role in the excitation. In addition, the modal frequencies of the ventilation wall also make an important contribution to the structural radiation noise. Therefore, there are two ways to reduce the structural radiation noise. Usually, the most effective way is to improve the panel stiffness of the ventilation wall. Figure 9 shows the effect of panel thickness on the flow-induced structural radiation noise. As seen from Figure 9, with the increase of panel thickness, the acoustical response at ISO:19 deceases gradually. Besides, the number of peal frequencies of the acoustical response curves decreases significantly. Therefore, it can be concluded that the flow-induced noise will be effective reduced by simply increase the panel thickness to a certain level.

Sound Pressure Levl, dB

Figure 9: Effect of panel thickness on the flow-induced structural radiation noise

In addition, it does not change the mode forms for ventilation wall by simply increase the panel thickness, and it will therefore bring about a significant increase in weight and cost. Hence, it is required to use other method, ribs for example, to improve the panel stiffness, so that reducing the flow-induced noise. In this paper, four ribs are applied into the large panels of ventilation wall, as shown in Figure 10, and the first order frequency increases from 54.78Hz to 112.10Hz at panel thickness of 1mm. Moreover, by increasing the panel thickness to 1.5mm, the first order frequency reaches 171.69Hz.

Four ribs Figure 10: Structural optimization

Figure 11 shows the comparison among the acoustical responses by using different method to improve the panel stiffness of ventilation wall. As seen from Figure 11, by using four ribs to strengthen panels of ventilation wall, the total sound pressure level decreases from 92.5dB to 82.3dB. Furthermore, by increasing the panel thickness to 1.5mm, the total sound pressure level decreases from 82.3dB to 72.9dB, which significantly reduces the flow-induced structural radiation noise. Therefore, the flow-induced noise can be effectively reduced by improving the panel stiffness of the ventilation wall.

Sound Pressure Levl, dB

Figure 11: Acoustical responses of the ventilation wall by using different methods

5. CONCLUSIONS

This paper presents a numerical study on the flow-induced structural radiation noise of a ventilation wall based on the LES and FW-H hybrid method. Firstly, the interior flow field of the ventilation wall under typical working conditions was calculated, and the pressure fluctuation on the surfaces of the ventilation wall was obtained based on LES method. Secondly, the pressure fluctuation data was Fourier transformed and transferred onto the structural elements to serve as excitation. Thirdly, the

modal-based vibro-acoustic responses was calculated, and the main noise frequencies were found. Finally, the structural optimization was carried out to reduce the flow-induced structural radiation noise. The results show that the flow-induced noise is mainly low-frequency noise that ranges from 20~300Hz. Besides, the peak frequencies ranges from 80Hz to 255Hz, and the peak frequencies are consistent with certain structural mode frequencies. Moreover, by improving the structure of ventilation wall, the total sound pressure level of the flow-induced noise deceases significantly from 92.5dB to 72.9dB. In conclusion, this paper could provide a method for reducing the flow-induced structural radiation noise of ventilation walls.

6. ACKNOWLEDGEMENTS

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The work is supported by the National Key R&D Program (2019YFB 2006404). 7. REFERENCES

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