Aerodynamic noise due to complex internal flow through cordless vac- uum cleaner and suction tower station Kwongi Lee 1 , Cheolung Cheong 1,* School of Mechanical Engineering, Pusan National University Busan 46241, Republic of Korea Kyeonghun Park 2 , Jinman Jang 2 LG Electronics Changwon-si 51554, Republic of Korea

ABSTRACT Although the demands and sales of cordless vacuum cleaners are on the rise in the global home appliance markets, some consumers are still complaining of the inconvenience such as short battery life and frequent emptying of a dust box. To resolve such inconvenience, a suction sta- tion tower that can automatically charge the battery and empty the dust box has been developed and is now on the market. However, aerodynamic noise generated when the station tower sucks dust in the vacuum cleaner causes another inconvenience. The purpose of this study is to iden- tify the major aerodynamic noise sources in the complex internal flow passage which forms when the station tower is connected to a wireless vacuum cleaner and to develop a low-noise design based on the identified noise sources. First, the entire flow path through the cordless vacuum cleaner and the station tower was simulated using the unsteady compressible Reynolds- Averaged Navier-Stokes equations. Then, the main aerodynamic noise sources were identified using the vortex sound sources. From these results, the flow region through the head nozzle throat of the cordless vacuum cleaner was identified as one of the most significant aerodynamic noise sources. Based on the identified noise source mechanism, two new throat designs named Model A and B were proposed, and their validity was investigated using a high-resolution Large Eddy Simulation technique. It was found that the strength of the vortex sound source of pipe flow through Model B was much less than the others. This result well matched the predicted and measured sound pressure levels according to the different shapes of the head nozzle throats.

1. INTRODUCTION

The vacuum cleaner is a device that uses a high-pressure fan to create a partial vacuum to suck dust and dirt from the floor, sofas, and other upholstery. Cordless vacuum cleaners are battery-pow- ered and provide better portability and convenience compared to corded vacuum cleaners. In recent years, the share of cordless vacuum cleaners in the global home appliance markets is rising due to these merits. However, the most frequently claimed issue by the customers in using the cordless vac- uum cleaner is the need to change the battery and empty the dust box. To resolve this problem, a suction station tower, which can automatically charge the battery and empty the dust of the cordless vacuum cleaner, has been developed. Nevertheless, these conveniences are provided at the cost of

1 dlrnjsrl93@pusan.ac.kr(K.L.); ccheong@pusan.ac.kr(C.C.)

2 Kyeonghun.park@lge.com(K.P.); jinman.jang@lge.com(J.J.)

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additional aerodynamic noise generated by airflow through the complex internal flow passage of a suction station tower and a cordless vacuum cleaner. The purpose of the current study is to identify the major aerodynamic noise sources in the complex internal flow and to develop a low-noise design based on the identified noise source.

The previous studies about vacuum cleaners have been carried out in terms of flow and noise performances. Brungart et al. [1] experimentally showed that the reshaped fan-housing and the use of an uneven fan blade arrangement were effective in the reduction of noise. Kale et al. [2] experi- mentally designed the vacuum cleaner by adopting the absorptive muffler to reduce noise and im- prove efficiency. Jafar et al. [3] experimentally reduced the broadband noise by changing the material of the filter in the vacuum cleaner. Son et al. [4] numerically and experimentally designed the fan- motor unit of the vacuum cleaner by optimizing the selected design parameters through the applica- tion of the Plackett-Burman design technique. Kim et al. [5] proposed high-performance and low- noise designs of impeller blades for the cordless vacuum cleaner by utilizing the virtual fan perfor- mance tester in a combination with the surface response method. However, most of the previous studies focused on the fan noise which is known as one of the most contributing noise sources in vacuum cleaners. The flow passage of the suction station tower and the vacuum cleaner consists of various pipe components such as nozzle, filter, and fan which can be potentially important aerody- namics noise sources. Therefore, the most contributing noise sources need to be identified in the current study.

Lighthill [6-7] firstly defined the aerodynamic noise sources by deriving the wave equation from the Navier-Stokes equations. Howe [8] rewrote the Lighthill’s sound source in terms of vortex sound source. Lee et al. [9] used the vortex sound source to identify aerodynamic sound sources causing a whistling sound of the narrow gap of automobile side mirror and successfully found the generation mechanism of the whistle sound. Kim et al. [10] also quantified the reduction of internal aerodynamic noise due to the use of perforated plates in a high-pressure valve flow by utilizing the vortex sound source. In this study, the vortex sound source is used to quantify the aerodynamic sound sources in the complex internal pipe flow.

First, the entire flow path of the station tower connected to a cordless vacuum cleaner is simulated by solving the unsteady compressible Reynolds-Averaged Navier-Stokes equation numerically. The main aerodynamic noise sources are identified using the vortex sound sources. Based on these results, the flow region of the head nozzle throat located at the inlet of the cordless vacuum cleaner is ranked as one of the most significant aerodynamic noise sources. Through the identified noise source mech- anism, new nozzle throat designs are proposed, and its validity is confirmed by comparing the results obtained from high-resolution Large Eddy Simulation with that of the original design. It is shown that the strength of the vortex sound source in the new head nozzle throat was much less than the original one. Finally, the validity of the new nozzle throat design was confirmed by comparing the sound pressure spectrum measured for the new vacuum cleaner with the proposed design of nozzle with that of the original one.

2. GOVERNING EQUATIONS AND COMPUTATIONAL METHODS

The three-dimensional unsteady compressible Reynolds-Averaged Navier-Stokes equations were numerically solved to predict the entire flow field through the flow passage of the vacuum cleaner and the station tower. The relative contribution of aerodynamic noise sources was assessed by using the vortex sound sources obtained from the flow field. Then, the Large Eddy Simulation (LES) tech- nique was used to calculate the aerodynamic sound and sound sources of the selected source regions with higher resolution in time and space. The radiated sound pressure was predicted applying the

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Ffowcs-Williams and Hawkings integral equation over the selected surface. The vortex sound source was again calculated to compare the aerodynamic sound sources between the different models. All numerical methods were realized using the commercial software ANSYS Fluent (V19.1).

2.1. Reynolds-Averaged Navier-Stokes Equations

The three-dimensional unsteady compressible Reynolds-Averaged Navier-Stokes (RANS) equa- tions can be written in the form:

where 𝜎 𝑖𝑗 is the stress tensor defined as

+ 𝜕𝑢 𝑗

𝜎 𝑖𝑗 = ቈ𝜇 ቆ 𝜕𝑢 𝑖

ቇ቉− 2

3 𝜇 𝜕𝑢 𝑘

𝛿 𝑖𝑗 . (4)

𝜕𝑥 𝑗

𝜕𝑥 𝑖

𝜕𝑥 𝑘

Equations (1) to (3) were numerically solved by using the finite volume method. The k- 𝜔 Shear Stress Transport (SST) model was used as the closure model.

2.2. Large Eddy Simulation

The three-dimensional unsteady compressible Large Eddy Simulation (LES) technique with Wall- Adapting Local Eddy-Viscosity (WALE) sub-grid model can be written in the form below:

where 𝜏 𝑖𝑗 is the sub-grid-scale stress tensor. Equations (5) and (7) were numerically solved byusing the finite volume method.

2.3. Ffowcs-Williams and Hawkings equation

The Ffowcs-Williams and Hawkings (FW-H) equation was used to predict the sound pressure level and can be written in the form:

When predicting the flow field with a low Mach number, the contributions of quadrupole sound sources, which is the third term of the right-hand side of Eq. (8), can be negligible. In the present study, only the monopole and dipole sound sources were considered for the prediction of radiated aerodynamic noise.

2.4. Vortex Sound Source

Lighthill [6-7] derived the exact formula defining aerodynamic sound sources in a turbulent flow, transforming the set of continuity and Navier-Stokes equations into an inhomogeneous wave equa- tion. In this wave equation, the inhomogeneous term plays the role of a sound source:

2 ∇ 2 ቇሺ𝜌−𝜌 0 ሻ= 𝜕 2 𝑇 𝑖𝑗

ቆ 𝜕 2

, (9)

𝜕𝑡 2 −𝑐 0

𝜕𝑥 𝑖 𝜕𝑥 𝑗

where 𝑇 𝑖𝑗 is Lighthill’s tensor:

2 ሺ𝜌−𝜌 0 ሻ൯𝛿 𝑖𝑗 + 𝜎 𝑖𝑗 . (10)

𝑇 𝑖𝑗 = 𝜌𝑣 𝑖 𝑣 𝑗 + ൫ሺ𝑝−𝑝 0 ሻ−𝑐 0

With the conditions of inviscid flow, high Reynolds number, and adiabaticity, the aerodynamic sound source is approximated by:

~𝜌 0 𝑑𝑖𝑣ሺ𝜔ሬሬԦ × 𝑢ሬԦሻ+ 𝜌 0 ∇ 2 ൬ 1

𝜕 2 𝑇 𝑖𝑗 𝜕𝑥 𝑖 𝜕𝑥 𝑗

2 𝑢 2 ൰ (11)

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After Lighthill’s equation was derived, Howe [8] reformulated it using the total enthalpy B defined by:

𝐵≡න𝑑ℎ+ 1

2 𝑣 2 , (12)

where the enthalpy h is given by:

𝑑ℎ= 𝜌 −1 𝑑𝑝+ 𝑇𝑑𝑆. (13)

For homentropic flow with dS = 0, B is approximated by:

𝐵 ~ 𝑝

𝜌 + 1

2 𝑣 2 , (14)

which is considered the independent acoustic variable. For compressible, homentropic turbulent flow with low Mach number, Lighthill’s equation is well approximated by:

∂ 2

ቆ 1

∂t 2 −∇ 2 ቇB ~ 𝑑𝑖𝑣 ሺ 𝜔ሬሬԦ × 𝑢ሬԦ ሻ . (15)

c 0 2

This means that the sound in terms of B is generated by the motion of vortices. The righthand term of Eq., 𝑑𝑖𝑣ሺ𝜔ሬሬԦ × 𝑢ሬԦሻ , is defined as the vortex sound source in this study. 3. TARGET CORDLESS VACUUM CLEANER WITH SUCTION STATION TOWER

3.1. Entire Flow Path

Figure 1a shows the entire computational domain for the simulation of the entire flow field includ- ing internal flow passing through the cordless vacuum cleaner and suction station tower. Fig 1b details the internal flow passage with the two inflows of the cordless vacuum cleaner and the one outflow of the suction station tower. Figure 1c shows the fan-motor unit in the suction station tower driving the entire flow field. The flow simulation was carried out by using three-dimensional unsteady compress- ible RANS solvers. The rotating frequency of the fan-motor is 570 Hz and the blade passing frequency is 5130Hz. The time step size is set 1/(570Hz ∙ 360) second, which is equal to the time taken for the fan to rotate by 1 degree. The maximum grid length of the internal flow region, which starts from the inlets of the cordless vacuum cleaner and ends at the outlet of the suction station tower, is 3.5mm, which is determined to resolve the one wavelength of the blade passing frequency with the minimum of 19 grid points. The entire region is created using the polyhedral type of grids. The total number of nodes and cells is about 105 million and 22 million, respectively.

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ss tl t

l

l

l t l

l t l

(a) (b)

(c) (d) Figure 1: Computational domains and related geometries: (a) dimensions and boundary conditions

of entire computational domain; (b) flow paths through vacuum cleaner and suction station tower;

(c) fan-motor; and (d) detailed grids.

3.2. Local Flow Path

After the flow simulation result of the entire flow path, the more resolved simulations were carried out for the selected main aerodynamic source regions, which is the head nozzle throat of the vacuum cleaner as shown in Figure 2a. Except for the head nozzle throat region, other complex internal flow regions of the cordless vacuum cleaner and suction station tower were removed. The aim of the sim- ulation of the selected local flow path is to capture detailed aerodynamic sound sources by using the compressible LES technique with high-resolution grids. For this reason, the internal flow region con- sists of high-resolution grids with a maximum of 1mm grid space, as shown in Fig. 2b. The integration surface denoted in Fig. 2 was used for the computation of the FW-H equation. The tetrahedral meshes were used. The prismatic meshes are used to capture the accurate boundary layer ensuring that 𝑦 + is smaller than 1. The number of grids used was about 95 million.

l it il tl t

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t g ti s

t l

(a) (b) Figure 2: Computational domain for selected local flow region: (a) detailed flow path with bound-

ary condition applied; (b) grids on sectional plane. 4. RESULTS AND DISCUSSIONS

4.1. Numerical Results of Entire Flow Path System

Figure 3-a, -b and -c shows the iso-contours of flow velocity, turbulent kinetic energy, and the vortex sound source obtained from the predicted flow field of the entire flow path. It can be seen that the most intense velocity and turbulent kinetic energy fields form in the flow of the fan-motor of the suction station tower. However, in Fig. 3c, the intense aerodynamic sources which are assessed by using the vortex sound source can be identified in the inlet flow through the head nozzle throat of the vacuum cleaner as well as the fan motor flow. To quantify the relative contribution of aerodynamic noise sources, the vortex sound source level is used, which is obtained by integrating the vortex sound sources over the specified volume regions. As shown in Figure 4, the total nine integration regions are determined, and the vortex sound source levels are calculated and compared between these re- gions. Table 1 listed the calculated vortex sound source level for each region. It is found that the most significant aerodynamic noise sources occur in the head nozzle throat of the cordless vacuum cleaner except for the fan-motor. From this result, the inlet head nozzle throat is selected for further study to reduce the noise of the system.

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Velocity 100 5 80 25 °o

ee

i butte

(a) (b) (c) Figure 3: Instantaneous internal flow fields of entire flow path system: (a) flow velocity; (b) turbu-

lent kinetic energy; and (c) vortex sound source

“Turutent Kinet Energy i as

t L l

vss dV 0s 05 A

(a) (b) Figure 4: Comparison of aerodynamic sound sources: (a) selected regions: ; (b) spectrum of vortex

sound source levels Table 1: Comparison of overall vortex sound source Levels between selected r egions

Integration Overall

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region vortex sound source levels

1 X

2 X – 6.5

3 X – 29.8

4 X – 42.2

5 X – 127.5

6 X – 29.5

7 X – 28.3

8 X – 38.0

9 X – 1.0

4.2. Numerical Results of Head Nozzle Throat

Based on the analysis result for the vortex sound sources, two additional models of the head nozzle throat were designed, which are named Model A and Model B. The more high-resolution numerical simulations were carried out using the LES technique for the three head nozzle throats. Figure 5 compares the predicted flow fields in terms of the flow velocity and the vortex sound source fluctua- tion between the three models. The geometry of the original model can be characterized by the right angle at the entrance and the bent crinkled tube at the throat, which cause a shear layer as shown in Fig. 5a. It can be found from Fig. 5d that the strong vortex sound sources are generated along with the shear layer. To reduce the identified noise generation mechanism, Model A is devised by modi- fying the inlet shape of the original one. However, the shear layer at the bent crinkled tube was still observed. The Model B is created by removing the right-angle geometry and the bent shape. Figures 5-c and -f show the smooth velocity distribution and the decreased vortex sound source fluctuation in Model B.

(a) (b) (c)

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(d) (e) (f) Figure 5: Instantaneous flow fields of local flow path system: (a-c) flow velocity; (d-f) vortex sound

source fluctuation normalized by cell volume.

4.3. Comparison with Experimental Results

The sound pressure spectrums radiated from the inlet nozzle throats are predicted using the FW- H equation. Figure 6a shows the location of observation points which is the same at the measured points. Figure 7b compares the predicted sound pressure spectrums with the measured ones. Because the experiments were carried out for a full set product, the measured results include all the aerody- namic noise sources of the vacuum cleaner and the suction tower. Therefore, the trend in the measured and predicted data according to the inlet nozzle throat models needs to be checked. Overall, there is good agreement in terms of the trend between the two group results. The sound pressure spectral levels of Model B are lower than those of the original model and Model A. To quantitatively confirm the trend according to the inlet shapes, the overall sound pressure levels (OASPLs) are compared in Table 2. It can be found that there is the same trend between the measured and predicted results: the OASPL of the Model B is the lowest and that of the Model A is the highest.

Finally, Figure 7 compares the predicted spectral levels of the vortex sound source with the meas- ured sound pressure spectrum. There is again good agreement in terms of the trend according to the different inlet models between the two group results: the vortex sound source level of the Model B is the lowest among the three models.

(a) (b)

Figure 6: Comparison of sound pressure spectrum between numerical and experimental results: (a)

locations of observation points; (b) sound pressure spectral levels according to inlet shapes Table 2: Comparison of overall sound pressure levels predicted and measured for different inlet noz- zle shapes

OASPL

Original Model A Model B

Exp Num Exp Num Exp Num

[dBA]

66.9 55.0 67.5 59.3 65.1 53.9

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Figure 7: Comparison of measured sound pressure level and calculated vortex sound source level. 5. CONCLUSIONS

In this study, systematic numerical methodology was proposed to identify and reduce the aerody- namic sound sources of complex internal flow through the cordless vacuum cleaner and the suction station tower which consisted of many potential aerodynamic noise source components such as noz- zle, crinkled tube, bent pipe, filters, perforated plate and fan-motors. First, the entire flow field was simulated using the unsteady compressible RANS equations. Then, the vortex sound source was used to identify and rank the significant aerodynamic sound sources. The head inlet nozzle throat was identified as the most contributing noise source region. The two modified models were proposed to reduce the identified aerodynamic noise sources. Finally, the high-resolution LES was used to char- acterize the head inlet flow between different models. The strength of vortex sound source was com- pared between the original and proposed models. It is found that the aerodynamic noise source level of the Model B is the lowest. This result well matched the predicted and measured sound pressure levels according to the different shapes of the head nozzle throats.

6. ACKNOWLEDGEMENTS

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2020R1F1A066701). 7. REFERENCES

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