Development of flow-vibroacoustic coupled numerical methods for prediction of noise radiation due to flow-born vibration of compressor discharge piping system Sangheon Lee 1 School of Mechanical Engineering, Pusan National University 2, Busandaehak-ro 63beon-gil, Geumjeong-gu, Busan, Republic of Korea Cheolung Cheong 2 School of Mechanical Engineering, Pusan National University 2, Busandaehak-ro 63beon-gil, Geumjeong-gu, Busan, Republic of Korea Jinhyung Park 3 Air-Soulution R&D Lab. LG electronics 84, Wanam-ro, Seongsan-gu, Changwon-si, Gyeongsangnam-do, Republic of Korea Jangwoo Lee 4 Air-Soulution R&D Lab. LG electronics 84, Wanam-ro, Seongsan-gu, Changwon-si, Gyeongsangnam-do, Republic of Korea

ABSTRACT The compressor in the air conditioner outdoor unit is the core component that determines noise and cooling or heating performances. For high-efficiency air conditioners, the size and operating speed of the compressor become smaller and faster, respectively. As the operating speed of the compressor increases, flow-born noise makes a more significant contribution to the overall noise of the air conditioner unit than structure-born noise. Especially the compressor piping systems, which can be classified into the discharge and suction ones, are considered one of the dominant noise sources. However, the physical mechanism of noise radiation due to flow-born vibration of these piping systems is so complex that it consists of three steps: flow-born excitation, the vibrational response of the piping system, and noise radiation due to pipe vibration. In this study, flow-vibroacoustic coupled numerical methods are developed to predict noise radiation from the compressor piping system due to refrigerant flow. First, the compressible LES technique is used to predict refrigerant flow accurately. Second, the vibration of the piping system due to surface pressure fluctuation of refrigerant flow is computed using the finite element method. Finally, the acoustic near- and far- fields due to the pipe vibration are calculated using the finite and boundary element methods, respectively. The validity of the proposed method is confirmed by comparing the predicted noise

1 tkdwjdwjd222@pusan.ac.kr 2 ccheong@pusan.ac.kr 3 Jh0311.park@lge.com 4 jonathan.lee@lge.com

spectrum with the measured one. The result reveals that the current numerical methodology can be used as an effective design tool to develop the low-noise compressor piping system. 1. INTRODUCTION

The compressor of air conditioners is a core component that determines their cooling or heating performances. To develop a high-performance and high-efficiency system, the operating speed of the compressor in an outdoor air conditioner unit tends to increase. However, the increment in the operating speed inevitably increases the relative importance of the flow-born noise compared to the traditional structure-born noise. Especially the compressor piping systems, which can be classified into the discharge and suction ones, are considered one of the dominant noise sources. Therefore, it is essential for developing high-performance and low-noise air-conditioner units to develop reliable numerical methods, which can be used as an effective design tool. This study develops flow- vibroacoustic coupled numerical methods to predict noise radiation from the compressor piping system due to refrigerant flow. The physical mechanism of noise radiation due to flow-born vibration of these piping systems is based on three multi-physical phases: flow-born excitation, the vibrational response of the piping system, and noise radiation due to pipe vibration. Therefore, the reliable numerical method must account for these multi-physical aspects.

Berge et al. [1] tried to characterize the flow pattern in the U-curved piping line by using the Dean number defined using pipe curvature, fluid velocity, and pipe diameter. Zhang et al. [2] investigated flow noise in the 90-degree curved pipe using the Large Eddy Simulation and the Ffowcs-Williams Hawking equation and reported that the vorticity on the pipe wall was related to the flow noise. These studies considered only flow fields inside the pipe system without considering its excitation mechanism on the pipe wall. The high-speed walking fluid generates a strong turbulence flow which produces pressure fluctuation on the inner wall surface of the pipe. The fluctuating pressure field can be classified into incompressible and compressible ones. The former associated with the vortex structure in the turbulent flow fields directly excites the pipe wall at the flow convection speed. The latter, i.e., the acoustic pressure field produced by flow noise sources such as turbulent flow, excites the pipe wall at the sound speed. Ku et al. [3] decomposed the pressure fluctuation field of the critical nozzle flow into the incompressible and compressible ones by using the wavenumber-frequency transform and showed that the compressible pressure field made more contribution in a high- frequency range. However, this study did not associate the identified incompressible and compressible pressure fields with the vibro-acoustical feature of the relevant structure system. Maurerlehner et al. [4] conducted an experimental investigation on the flow-induced vibration and noise and reported that the pipe inner-wall pressure fluctuations depend on turbulence flow and acoustic resonance. In addition, the noise radiation due to the flow-born pipe vibration was shown to be closely related to the vibration modes of the pipe wall structure. Therefore, it is critical for the accurate prediction of noise radiation from the piping system due to flow disturbances to couple the flow field excitation with the vibrational characteristics of the related system.

The numerical methods developed in this study consist of three sequential methods. First, the compressible LES technique is used to predict refrigerant flow accurately. Second, the vibration of the piping system due to surface pressure fluctuation of refrigerant flow is computed using the finite element method. Finally, the acoustic near- and far-fields due to the pipe vibration are calculated using the finite element and boundary element methods. The validity of the proposed method is confirmed by comparing the predicted noise spectrum with the measured one. 2. NUMERICAL METHOD

In this section, the three numerical methods which are sequentially used for the prediction of noise radiation from the compressor-discharging piping system due to refrigerant flow are described in detail.

2.1. Computation Fluid Dynamic (CFD) The compressible Large Eddy Simulation (LES) technique is employed to compute the incompressible and compressible parts of internal refrigerant flow through the compressor’s discharging piping line with high resolution. The governing equations can be written in the form,

∂𝜌

∂t + ∂

(𝜌𝑢 𝑖 ̅ ) = 0 (1)

∂x 𝑗

− ∂𝑃̅

∂(𝜌𝑢 𝑖 ̅ )

∂t + ∂(𝜌𝑢 𝑖 ̅𝑢 𝑗 ̅)

= ∂𝜎 𝑖𝑗

− ∂τ 𝑖𝑗

(2)

∂x 𝑗

∂x 𝑖

∂x 𝑖

∂x 𝑙

∂(𝜌ℎ 𝑠 ̅̅̅) ∂t + ∂(𝜌𝑢 𝑖 ̅ℎ 𝑠 ̅̅̅) ∂x 𝑗

− ∂𝑃̅

∂t −𝑢 𝑗 ̅ ∂𝑃̅

(𝜆 ∂𝑇̅

− ∂

) = − ∂

[𝜌(ℎ 𝑠 𝑢 𝑖 ̅̅̅̅̅̅ −ℎ 𝑠 ̅̅̅𝑢 𝑖 ̅)] (3)

𝑥 𝑖

∂x 𝑖

∂x j

∂x 𝑗

The Smagorinski Lilly model is used as the subgrid model, which is written in the form,

2 |𝑆|, where |𝑆| = √2𝑆 𝑖𝑗 ̅̅̅̅ 𝑆 𝑖𝑗 ̅̅̅̅ (4)

μ 𝑡 = 𝜌𝐿 0

𝜕𝑥 𝑗 ̅ + 𝜕𝑢 𝑗 ̅

𝑆 𝑖𝑗 ̅̅̅̅ = 1

2 (𝜕𝑢 𝑖 ̅

𝜕𝑥 𝑖 ̅ ) (5)

Table 1 lists the pressure-velocity coupling method and the spatial schemes to discretize the governing equations.

Table 1: Solution method setting

Setting Value

Pressure-velocity coupling Simple C

Pressure discretization 2 nd order upwind

Momentum discretization 2 nd order upwind

Energy discretization 2 nd order upwind

The R410A is used as the working refrigerant fluid in the compressor piping system. Due to high pressure and temperature, the density is modeled using a real gas model rather than an ideal gas one. The Aungier Redlich Kwong model is adopted as the real gas model, which is written as

P = 𝑅 𝑠 𝑇

𝑣−𝑏 ̃ − 𝑎(𝑇) 𝑣 2 + 𝑏 0 𝑣

(6)

where

𝑛

a(T) = 𝑎 0 ( 𝑇 𝑐

(7)

𝑇 )

2 𝑇 𝑐

2

𝑎 0 = 0.42747 𝑅 𝑠

(8)

𝑃 𝑐

𝑛= 0.4989 + 1.1735𝜔+ 0.4754𝜔 2 (9)

𝑏 ̃ = 𝑏 0 −𝑐 0 (10)

𝑏 0 = 0.08664 𝑅 𝑠 𝑇 𝑐

(11)

𝑃 𝑐

𝑐 0 = 𝑅 𝑠 𝑇 𝑐 𝑃 𝑐 + 𝑎 0

(12)

(𝑣 𝑐 2 + 𝑏 0 𝑣 𝑐 ) ⁄

The letter 𝑅 𝑠 is the gas constant, and P, T, and 𝑣 denote pressure, temperature, and specific volume, respectively. The subscript c indicates the value at the critical point. The letter 𝜔 is the acentric number. Since the vapor properties are dominantly affected by the temperature, they are modeled using the fourth-order polynomial equations of temperature. Figure 1 shows the target compressor and its piping systems with a crossectional view of typical pipe flow meshes. As shown in Figure 1a, the whole compressor piping system can be divided into the discharging and suction lines. The discharging piping system consists of various pipe components such as U-curved, 90-degree curved, and straight pipelines. In addition to these pipelines, there are specific-purpose components such as silencer and four-way valve. The compressor can be operated in two modes: heating and cooling modes. In this study, the only heating mode is considered. Figure 1b shows the discharge piping system through which the refrigerant fluid flows in the heating model. Figure 1c shows the cross-sectional view of pipe with flow meshes. The sixteen prism layers are used to resolve the boundary layer flow in the pipe with sufficient resolution, and the y+ value is kept less than one on the entire pipe inner-wall surface.

(a) (b) (c) Figure 1: Geometries of target compressor and piping systems with cross-sectional view of flow meshes: (a) entire system, (b) discharge pipeline at heating mode, and (c) computational meshes on cross-section of pipe The pressure and temperature are specified as the inlet boundary conditions. The mass flow rate is set as the outlet boundary condition.

2.2. Vibro-acoustic numerical methods

The Finite Element (FE) method is employed for the numerical simulation of the vibration of the target piping structure. The transient modal analysis is carried out to compute the dynamic response of the discharge piping system in the time domain. The governing equation is written as

[M]{𝑥̈(𝑡)} + [𝐾]{𝑥(𝑡)} = {𝐹(𝑡)} (13)

In Modal transient analysis, the coordinate of response vector {x(t)} is replaced with modal coordinate, which is defined as

{𝑥(𝑡)} = [∅]{ξ(t)} (14)

The vector [∅] denotes an eigenvector. Substituting Eq. (14) into Eq. (13) and pre-multiplying the resultant equation with the transpose matrix of the eigenvector lead to

[∅] 𝑇 [M][∅]{ξ ̈ (𝑡)} + [∅] 𝑇 [K][∅]{ξ(𝑡)} = [∅] 𝑇 {𝐹(𝑡)} (15)

The resultant matrix in Eq. (15) forms a diagonal matrix. By solving Eq. (15), the modal coordinate response ξ(𝑡) can be found. The substitution of ξ(𝑡) into Eq. (14) results in the total response.

The right-hand term of Eq. (13) represents the pressure load term, which can be obtained from the surface pressure predicted using the LES. The time interval is set to be 5e-5 sec. and the total time- lapse for the simulation span from 0 sec. to 0.02 sec..

Figure 2 shows the computational domain for the vibration analysis. In Fig. 2a, the orange-colored part denotes the pipeline through which the refrigerant fluid flows. The fluctuating pressure fields obtained from the LES are applied as the excitation source on the inner wall surface of the pipeline. Although the excitation force is applied only on the heat-mode discharge pipeline, the entire piping systems are included for the vibration computation because these are connected all together and thus possible sources for vibration-induced noise. Figure 2b shows the detailed components constituting the piping system included in the vibrational computation. The points marked with a red dot denote the fixed boundary points.

(a) (b) Figure 2: Piping system considered for vibration computation: (a) Entire piping system and discharge pipeline (oranrge-color) for heating mode and (b) components included in vibration computation and boundary points (red-dot) on which fixed boundary condition is applied

Acoustic analysis of noise radiation from the pipe vibration is conducted using the velocity data on the external wall of the pipe obtained from the vibration simulation as the acoustic source. The acoustic computation was carried out in the frequency domain by using the direct method of FE. The governing equation can be written in the form,

ae * Fixed { foursway vale] [Heating duct . a {cooling duct 1 [Discharge duct] Cintake duct ]

[M 𝑎 ]{𝑝̈(𝑡)} + [𝐵 𝑎 ]{𝑝̇(𝑡)} + [𝐾 𝑎 ]{𝑝(𝑡)} = {𝑃(𝑡)} (16)

where the matrices [M 𝑎 ] , [𝐵 𝑎 ] and [K 𝑎 ] are the compressibility matrix, impedance matrix, and mobility matrix, respectively. In the direct method, Eq. (16) is solved using the inverse matrix as follows

−1 {𝑃(𝑡)} (17)

{𝑝(𝑡)} = [−𝜔 2 [M 𝑎 ] + 𝑖𝜔[𝐵 𝑎 ] + [𝐾 𝑎 ]]

The righthand term of Eq. (16) represents the source pressure which is obtained from the surface velocity by using the following relation,

𝑃(𝑡) = 𝑍 0 𝑣 𝑤𝑎𝑙𝑙 (𝑡) = 𝜌 0 𝑐 0 𝑣 𝑤𝑎𝑙𝑙 (𝑡) (18)

where the letter 𝑍 0 denotes the acoustic impedance that is the multiplication of density and wave speed. For air, the density is 1.23 kg/ m 3 and the wave speed is 340m/s. The 𝑣 𝑤𝑎𝑙𝑙 is the surface velocity response of the piping system to the input surface pressure fluctuations due to refrigerant flow. All of these numerical methods are realized using the commercial software SIMCENTER 3D. The frequency resolution is set to be 40Hz, and the frequency range is from 0 to 10,000Hz. As the acoustic analysis is conducted in the frequency domain, the vibration analysis results obtained from the time-domain method are transformed into the frequency domain using the Fast Fourier.

Figure 3 shows the computational domain of acoustic analysis. The acoustic mesh surrounds the structure mesh. The velocity node dataset of structure mesh is transformed into the acoustic source in the form of acoustic pressure through the interface between structure mesh and acoustic mesh. Figure 3a shows the FE mesh for the computation of near-field acoustic field. In this domain, the acoustic pressure is computed. The non-reflecting boundary condition is applied to the external meshes. The acoustic pressure and particle velocity on the surface are used to calculate the far-field sound pressure on the microphone mesh, as shown in Figure 3b.

(a) (b) Figure 3: Computation domains of acoustic simulations for (a) near-field sound pressure and (b) far- field sound pressure. 3. RESULTS

Figure 4 compares the predicted sound pressure spectral levels with the measured ones. Although the experiment was carried out for the entire outdoor unit of the air conditioner, and thus the measured spectrum includes other noise sources, there is reasonable agreement between the two results

on_noR

Figure 4: Comparison of predicted sound pressure spectrum with measured ones in one-third octave band levels

Figure 5 compares the snap-shot of the vibration of the discharge piping system in the low- and high-frequency range. The high vibration magnitude occurs on the U-curved pipeline directly connected to the compressor outlet in the frequency range below 1,000 Hz, while it occurs on the four-way valve in the frequency range higher than 3,000 Hz. Figure 6 compares the iso-contours of sound pressure in the near field in the low- and high-frequency ranges. A similar feature can be found in the sound pressure field. The U-shaped and compressor outlet pipelines are the dominant sound source in the low-frequency range, and the four-way valve dominantly contributes to the high- frequency sound pressure field.

(a) (b) Figure 5: Comparison of vibrational features according to frequency range: (a) below 1,000Hz and (b) above 3,000Hz

(a) (b) Figure 5: Iso-contours of acoustic pressure produced by pipeline vibration in frequency range (a) below 1,000Hz and (b) above 3,000Hz

4. CONCLUSION

In this study, the flow-vibroacoustic coupled numerical methodology was developed to predict the sound pressure radiation from the compressor discharge piping system due to internal refrigerant flow in the outdoor air-conditioner unit. The developed numerical methods consisted of three sequential steps which could account for three physical aspects: flow-born excitation, the vibrational response of the piping system, and noise radiation due to pipe vibration. First, the compressible LES technique was utilized to predict both incompressible and compressible refrigerant flow fields responsible for so-called FIV and AIV, respectively. Second, the vibration of the piping system due to surface pressure fluctuation of refrigerant flow was computed using the finite element method. Finally, the acoustic near- and far-fields due to the pipe vibration were calculated using the finite element and boundary element methods. The validity of the proposed method was confirmed by comparing the predicted noise spectrum with the measured one. The coupled analysis between the pipe vibration and the corresponding acoustic pressure fields showed that the primary noise generation mechanism is related to the U-pipe line at low frequency and the four-way valve at high frequency. This illustrative analysis revealed that the current methods could be used as a design tool to develop a low- noise pipe system for the outdoor air-conditioner unit. 5. ACKNOWLEDGEMENTS

This research was supported by the National Research Foundation of Korea(NRF) gran funded by the Korea government(MSIT)(No. 2020R1F1A1066701) 6. REFERENCE

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