# Experimental Analysis of the Discharge Valve Movement of the Oil-Free Linear Compressor in the Refrigeration System

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## Abstract

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## 1. Introduction

_{v}is the effective mass of the reed valve, x

_{v}is the displacement of the reed valve, c

_{v}is the damping coefficient, t is the time in a cycle, k

_{v}is the spring stiffness of the reed valve, and F

_{p}is the pressure difference acting on the reed valve.

_{v}, which affects the motion of reed valve, is directly related to the viscosity of the working fluid. Therefore, the viscosity of the refrigerant is also different from that of the nitrogen. This is also a difference between the present work and the work by Liu et al. [21]. It can be seen that the motion of the reed valve in a vapor compression refrigeration cycle driven by a linear compressor is still rare.

## 2. Experimental Apparatus

#### 2.1. The Linear Compressor

#### 2.2. The Discharge Valve Structure

#### 2.3. The Test Setup

#### 2.4. The Data Acquisition System

## 3. Results and Discussion

#### 3.1. The Movements of the Discharge Valve under Different Discharge Pressures

#### 3.2. The Movements of the Discharge Valve under Different Frequencies

#### 3.3. The Movements of the Discharge Valve under Different Strokes and Different Clearance Lengths

#### 3.4. The Discharge Valve Movements with the p-t Diagram inside the Cylinder and Piston Motion

## 4. Conclusions

- By observing the time-domain curves of the discharge valve displacement, the dynamic behavior is visually understood. The discharge valve flutters due to the change in the form of pressure in the cylinder, which changes from static pressure to dynamic pressure. The delayed opening of the valve is caused by the valve inertia. Additional displacement fluctuations are present, which is due to the unevenness of the valve plate surface between the valve and the valve seat.
- With the decrease in the discharge pressure, the valve flutters increase due to the pressure fluctuations in the cylinder, the mean displacement of the valve increases due to the high static pressure difference between the cylinder and the discharge chamber, and the duration of the discharge increases due to the low speed of the valve.
- With the increase in the operation frequency, the duration of the discharge decreases, but the mean displacement of the valve increases due to the higher static pressure in the cylinder for the higher frequency. The oscillation period of the valve movement is almost identical under different operation frequencies; this is because the parameters of the discharge valve do not change.
- For a high stroke and a low clearance length, the duration of the discharge increases due to the increase in the volume efficiency and the increase in the duration of the discharge for a cycle, and the valve flutters increase due to the pressure fluctuations in the cylinder.
- In terms of the relationship between the valve movements, piston movements, and cylinder pressure, the delayed closing of the valve is little affected by the piston stroke, while the delayed opening of the valve is evidently affected at a low stroke (7 mm) due to the low pressure difference between the cylinder and the discharge chamber, and the delayed opening of the valve is more evident with the increase in the operating frequency. The delayed closing of the valve occurs at a high frequency (75 Hz).

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- She, X.H.; Cong, L.; Nie, B.J.; Leng, G.H.; Peng, H.; Chen, Y.; Zhang, X.S.; Wen, T.; Yang, H.X.; Luo, Y.M. Energy-efficient and -economic technologies for air conditioning with vapor compression refrigeration: A comprehensive review. Appl. Energy
**2018**, 232, 157–186. [Google Scholar] [CrossRef] - Liang, K. A review of linear compressors for refrigeration. Int. J. Refrig.
**2017**, 84, 253–273. [Google Scholar] [CrossRef] - Lee, H.; Ki, S.H.; Jung, S.S.; Rhee, W.H. The innovative green technology for refrigerators development of innovative linear compressor. In International Compressor Engineering Conference; Purdue University: West Lafayette, IN, USA, 2008; p. 1867. [Google Scholar]
- Kim, J.K.; Kim, J.B. Modulation characteristics of a linear compressor for evaporating and condensing temperature variations for household refrigerators. Int. J. Refrig.
**2014**, 40, 370–379. [Google Scholar] [CrossRef] - Liang, K.; Stone, R.; Dadd, M.; Bailey, P. A novel linear electromagnetic-drive oil-free refrigeration compressor using R134a. Int. J. Refrig.
**2014**, 40, 450–459. [Google Scholar] [CrossRef] - Zou, H.M.; Li, X.; Tang, M.S.; Tian, C.Q.; Chen, X. Performance analysis of linear compressor using R290 for commercial refrigerator. Int. J. Refrig.
**2020**, 109, 55–63. [Google Scholar] [CrossRef] - Jomde, A.; Anderson, A.; Bhojwani, V.; Kedia, S.; Jangale, N.; Kolas, K.; Khedkar, P. Modeling and measurement of a moving coil oil-free linear compressor performance for refrigeration application using R134a. Int. J. Refrig.
**2018**, 88, 182–194. [Google Scholar] [CrossRef] - Sun, J.; Jianguo Li, J.G.; Liu, Y.L.; Huang, Z.J.; Cai, J.H. A Novel Oil-Free Dual Piston Compressor Driven by a Moving Coil Linear Motor with Capacity Regulation Using R134a. Sustainability
**2021**, 13, 5029. [Google Scholar] [CrossRef] - Bradshaw, C.R.; Groll, E.A.; Garimell, S.V. Sensitivity analysis of a comprehensive model for a miniature-scale linear compressor for electronics cooling. Int. J. Refrig.
**2013**, 36, 1998–2006. [Google Scholar] [CrossRef][Green Version] - Dainez, P.S.; Oliveira, J.; Nied, A.; Cavalca MS, M. A linear resonant compressor model based on a new linearization method of the gas pressure force. Int. J. Refrig.
**2014**, 48, 201–209. [Google Scholar] [CrossRef] - Li, C.Z.; Zou, H.M.; Cai, J.H.; Jiang, Y.Y.; Guo, C.H. Dynamic behavior analysis of a moving coil-free linear compressor in refrigeration system. Int. J. Refrig.
**2022**, 133, 235–246. [Google Scholar] [CrossRef] - Choe, G.S.; Kim, K.J. Analysis of nonlinear dynamics in a linear compressor. JSME Int. J. Ser. C–Mech. Syst. Mach. Elem. Manuf.
**2000**, 43, 545–552. [Google Scholar] [CrossRef][Green Version] - Ribas, F.A.; Deschamps, C.J.; Fagotti, F. Thermal analysis of reciprocating compressors—A critical review. In Proceedings of the International Compressor Engineering Conference, West Lafayette, IN, USA, 17–20 July 2008. [Google Scholar]
- Woo, S.; O’Neal, D.L.; Pecht, M. Reliability design of a reciprocating compressor suction reed valve in a common refrigerator subjected to repetitive pressure loads. Eng. Fail. Anal.
**2010**, 17, 979–991. [Google Scholar] [CrossRef] - Park, S.J.; Hwang, I.S.; Wonsik, O. A study on cycle performance variation of a linear compressor considering valve behavior. J. Mech. Sci. Technol.
**2017**, 31, 4481–4488. [Google Scholar] [CrossRef] - Hwang, I.S.; Park, S.J.; Wonsik, O. Linear compressor discharge valve behavior using a rigid body valve model and a FSI valve model. Int. J. Refrig.
**2017**, 82, 509–519. [Google Scholar] [CrossRef] - Choi, Y.; Lee, J.; Jeong, W. Dynamic behavior of valve system in linear compressor based on fluid-structure interaction. J. Mech. Sci. Technol.
**2010**, 24, 1371–1377. [Google Scholar] [CrossRef] - Liang, K.; Stone, C.; Davies, G.; Dadd, M.; Bailey, P. Modelling and measurement of a moving magnet linear compressor performance. Energy
**2014**, 66, 487–495. [Google Scholar] [CrossRef] - Jomde, A.; Bhojwani, V.; Kedia, S. Modeling and Simulation performance of reed valve in linear compressor. Hyberabad Mater. Today Proc.
**2017**, 4, 7228–7233. [Google Scholar] [CrossRef] - Reed, J.; Dadd, M.; Bailey, P.; Petach, M.; Raa, J. Development of a valved linear compressor for a satellite borne J–T cryocooler. Cryogenics
**2005**, 45, 496–500. [Google Scholar] [CrossRef] - Liu, Y.L.; Sun, J.; Xun, Y.Q.; Huang, Z.J.; Cai, J.H.; Li, C.Z. Experimental investigation of the discharge valve dynamics in an oil-free linear compressor for Joule-Thomson throttling refrigerator. Appl. Therm. Eng.
**2022**, 209, 118288. [Google Scholar] [CrossRef] - Liang, K.; Dadd, M.W.; Bailey, P.B. Clearance seal compressors with linear motor drives. Part Ⅰ: Background and system analysis. Proc. Inst. Mech. Eng. Part A J. Power Energy
**2013**, 227, 242–251. [Google Scholar] [CrossRef] - Zheng, H.; Tian, G.; Zhao, Y.; Jin, C.; Ju, F.; Wang, C. Experimental study of R290 replacement R134a in cold storage air conditioning system. Case Stud. Therm. Eng.
**2022**, 36, 102203. [Google Scholar] [CrossRef] - ANSI/AHAM HRF-1-2007; Energy, Performance and Capacity of Household Refrigerators, Refrigerator-Freezers and Freezers. The Association of Home Appliance Manufacturers: Washington, DC, USA, 2007. Available online: https://webstore.ansi.org/standards/aham/ansiahamhrf2007 (accessed on 5 October 2007).
- Ma, Y.; He, Z.; Peng, X.; Xing, Z. Experimental investigation of the discharge valve dynamics in a reciprocating compressor for trans-critical CO
_{2}refrigeration cycle. Appl. Therm. Eng.**2012**, 32, 13–21. [Google Scholar] [CrossRef] - Wang, Y.; Feng, J.; Zhang, B.; Peng, X. Modeling the valve dynamics in a reciprocating compressor based on two-dimensional computational fluid dynamic numerical simulation. Proc. Inst. Mech. Eng. Part E J. Process Mech. Eng.
**2013**, 227, 295–308. [Google Scholar] [CrossRef] - Tao, W.; Guo, Y.; He, Z.L.; Peng, X.Y. Investigation on delayed closure of suction valve in the refrigerator compressor by FSI modeling. Int. J. Refrig.
**2018**, 91, 111–121. [Google Scholar] [CrossRef]

**Figure 10.**The relationship between the valve displacement, cylinder pressure, and the piston motion at different strokes (valve displacement also called valve lift). (

**a**) Stroke = 7 mm. (

**b**) Stroke = 8 mm. (

**c**) Stroke = 9 mm.

**Figure 11.**The relationship between the valve displacement, cylinder pressure, and piston motion under different frequencies. (

**a**) Frequency = 35 Hz. (

**b**) Frequency = 50 Hz. (

**c**) Frequency = 62.5 Hz. (

**d**) Frequency = 75 Hz.

Items (Unit) | Value |
---|---|

Total mass of moving part (kg) | 0.313 |

Resistance of motor coil (Ω) | 2.62 |

Motor constant (N/A) | 28.5 |

Inductance of motor coil (mH) | 3 |

Cylinder diameter (mm) | 19 |

Maximum stroke (mm) | 9 |

Flux density in gas gap (T) | 0.8 |

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**MDPI and ACS Style**

Li, C.; Sun, J.; Zou, H.; Cai, J.; Zhu, T. Experimental Analysis of the Discharge Valve Movement of the Oil-Free Linear Compressor in the Refrigeration System. *Sustainability* **2023**, *15*, 5853.
https://doi.org/10.3390/su15075853

**AMA Style**

Li C, Sun J, Zou H, Cai J, Zhu T. Experimental Analysis of the Discharge Valve Movement of the Oil-Free Linear Compressor in the Refrigeration System. *Sustainability*. 2023; 15(7):5853.
https://doi.org/10.3390/su15075853

**Chicago/Turabian Style**

Li, Chengzhan, Jian Sun, Huiming Zou, Jinghui Cai, and Tingting Zhu. 2023. "Experimental Analysis of the Discharge Valve Movement of the Oil-Free Linear Compressor in the Refrigeration System" *Sustainability* 15, no. 7: 5853.
https://doi.org/10.3390/su15075853