# Investigation on the Mass Flow Rate of a Refrigerator Compressor Based on the p–V Diagram

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## Abstract

**:**

## 1. Introduction

_{2}compressor and presented the flow losses related to the suction and discharge valves in the diagram. Their research clearly showed that the suction power loss was lower than the discharge flow loss since the amplitude of the pressure loss in the discharge process was much larger than that in the suction process.

## 2. Experimental Setup

#### 2.1. Test Compressor

^{−1}.

#### 2.2. Data Acquisition System

## 3. Method to Calculate the Refrigerant Mass Flow Rate

#### 3.1. Validation of Adiabatic Process Hypothesis in the Expansion Phase and Compression Phase

#### 3.2. Calculation Method

_{c}is the cylinder volume at the corresponding time, and p is the refrigerant pressure in the cylinder. The ratio C

_{p}/C

_{v}is usually considered equal to the adiabatic exponent. Moreover, the density ρ of refrigerant in the cylinder is a function of p and C

_{p}/C

_{v}. The physical property data for R600a are derived from NIST PEFPROP [16].

_{p}/C

_{v}is determined by the corresponding temperature and p. However, the measurement of the instantaneous refrigerant temperature in the cylinder is a difficult problem. In this paper, due to the expansion phase and compression phase being close to the adiabatic process, the adiabatic exponent is approximately equal to the polytropic exponent obtained from the log(p)–log(V/Vmax) diagram [12]. In addition, p and V

_{c}could be measured directly by experiment.

## 4. Results and Discussion

#### 4.1. Verification of Mass Flow Calculation Method

#### 4.2. Effect of Suction Pressure on the Compressor Performance

_{theo}is cylinder volume of the refrigerator compressor without clearance volume, and ρ

_{Inlet}is the refrigerant density at the suction conditions.

#### 4.2.1. Effect of Suction Pressure on the Volumetric Efficiency

#### 4.2.2. Effect of Suction Pressure on Suction Flow Loss

## 5. Conclusions

- With the compression and expansion phase approximating the adiabatic process being experimentally verified, a calculation method for the mass flow rate of a compressor is proposed, based on the experimental p–V diagram.
- The accuracy of the calculation method for the mass flow rate of a compressor is directly verified by a mass flow meter. Furthermore, the error of the calculation method is less than 3.13%, which can replace the mass flow meter for most application situations.
- Based on the calculation method, the influence of suction pressure on compressor performance is investigated. Under a constant pressure ratio, the higher suction pressure leads to a higher volumetric efficiency and less suction loss.
- As the measuring equipment is expensive and the calculation method is complex, the proposed method at present is mainly suitable for scientific research. In the future, the authors will focus on reducing the complexity of the method, and based on this method, the mass flow meter of compressor will be manufactured.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

Cp | Specific heat at constant pressure |

Cv | Specific heat at constant volume |

m | Refrigerator mass in the cylinder |

p | Pressure |

V_{c} | The volume of cylinder |

V_{theo} | Theoretical volume of the compressor |

ρ | Refrigerant density |

Subscripts | |

com | Compression phase |

exp | Expansion phase |

Inlet | Suction states |

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**Figure 4.**Comparison of theoretical adiabatic pressure variations and experimental data in a p–V diagram.

Parameters | Value |
---|---|

Crank Radius | 10 mm |

Connecting Rod Length | 40.5 mm |

Cylinder Diameter | 31 mm |

Rated Speed | 2950 r·min^{−1} |

Relative Clearance Volume | 2.35% |

Compression Phase | Expansion Phase | ||||
---|---|---|---|---|---|

Experimental Pressure (MPa) | Adiabatic Line (MPa) | Error (%) | Experimental Pressure (MPa) | Adiabatic Line (MPa) | Error (%) |

0.088 | 0.086 | 1.86 | 0.529 | 0.504 | 4.64 |

0.089 | 0.088 | 1.04 | 0.473 | 0.483 | −2.16 |

0.090 | 0.090 | 0.24 | 0.457 | 0.467 | −2.12 |

0.091 | 0.092 | −1.73 | 0.449 | 0.450 | −0.23 |

0.094 | 0.095 | −1.20 | 0.440 | 0.432 | 1.81 |

0.097 | 0.098 | −1.06 | 0.425 | 0.413 | 2.86 |

0.099 | 0.101 | −2.10 | 0.390 | 0.384 | 1.53 |

0.103 | 0.105 | −1.68 | 0.357 | 0.366 | −2.31 |

0.109 | 0.109 | −0.81 | 0.294 | 0.303 | −3.17 |

0.114 | 0.114 | 0.00 | 0.292 | 0.287 | 1.50 |

0.117 | 0.120 | −1.72 | 0.268 | 0.264 | 1.51 |

0.126 | 0.125 | 0.54 | 0.246 | 0.250 | −1.68 |

0.130 | 0.132 | −1.45 | 0.230 | 0.236 | −2.59 |

0.137 | 0.140 | −1.63 | 0.206 | 0.212 | −2.91 |

0.148 | 0.148 | −0.14 | 0.202 | 0.200 | 0.71 |

0.154 | 0.158 | −2.50 | 0.195 | 0.190 | 2.65 |

0.166 | 0.168 | −1.53 | 0.172 | 0.170 | 0.66 |

0.178 | 0.181 | −1.60 | 0.159 | 0.162 | −1.35 |

0.190 | 0.194 | −2.01 | 0.151 | 0.153 | −1.41 |

0.205 | 0.210 | −2.37 | 0.148 | 0.146 | 1.33 |

0.223 | 0.228 | −1.92 | 0.145 | 0.139 | 4.70 |

0.242 | 0.248 | −2.72 | 0.121 | 0.120 | 0.86 |

0.268 | 0.272 | −1.31 | 0.111 | 0.111 | −0.16 |

0.296 | 0.299 | −1.15 | 0.106 | 0.106 | 0.24 |

0.325 | 0.331 | −1.74 | 0.094 | 0.091 | 3.97 |

0.363 | 0.368 | −1.34 | 0.081 | 0.081 | −0.05 |

0.412 | 0.412 | 0.09 | 0.075 | 0.078 | −3.75 |

0.461 | 0.463 | −0.53 | 0.068 | 0.066 | 2.77 |

0.531 | 0.525 | 1.17 | 0.061 | 0.063 | −2.97 |

Suction Pressure (MPa) | Suction Temperature (℃) | Discharge Pressure (MPa) | Flow Rate | Error (%) | |
---|---|---|---|---|---|

By the p–V Diagram (kg·h ^{−1}) | By Flow Meter (kg·h ^{−1}) | ||||

0.11 | −5.60 | 0.59 | 6.09 | 5.99 | 1.64 |

0.12 | −2.50 | 0.75 | 6.91 | 6.72 | 2.75 |

0.10 | −0.80 | 0.66 | 5.17 | 5.03 | 2.71 |

0.11 | 2.80 | 0.64 | 5.45 | 5.38 | 1.28 |

0.08 | 6.40 | 0.60 | 3.51 | 3.40 | 3.13 |

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**MDPI and ACS Style**

He, Z.; Li, D.; Ji, L.; Wang, X.; Wang, T.
Investigation on the Mass Flow Rate of a Refrigerator Compressor Based on the p–V Diagram. *Appl. Sci.* **2020**, *10*, 6650.
https://doi.org/10.3390/app10196650

**AMA Style**

He Z, Li D, Ji L, Wang X, Wang T.
Investigation on the Mass Flow Rate of a Refrigerator Compressor Based on the p–V Diagram. *Applied Sciences*. 2020; 10(19):6650.
https://doi.org/10.3390/app10196650

**Chicago/Turabian Style**

He, Zhilong, Dantong Li, Lantian Ji, Xiaolin Wang, and Tao Wang.
2020. "Investigation on the Mass Flow Rate of a Refrigerator Compressor Based on the p–V Diagram" *Applied Sciences* 10, no. 19: 6650.
https://doi.org/10.3390/app10196650