# Analysis of 3D Transient Flow in a High-Speed Scroll Refrigeration Compressor

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Geometric Model of Scroll Compressor

#### 2.2. Mesh Generation

#### 2.3. Computational Model

_{i}is the grid velocity which is independent on the rotation of the orbiting scroll. The motion of the orbiting scroll is defined by the user. In Equation (2), Γ is the diffusivity, A is the surface enclosing CV, and S is the source or sink in CV.

^{−4}.

#### 2.4. Grid Independence Check

_{in}is the volume of the inlet chamber; n is rotational speed; v

_{in}is inlet specific volume; M

_{act}is the actual mass flow. When calculating the volumetric efficiency of the simulation, the M

_{act}can be obtained statistically from the simulation results.

## 3. Results and Discussion

#### 3.1. Experimental Validation

_{act}) of R134a in order to obtain volumetric efficiency. M

_{act}was calculated as shown in Equation (4).

_{heat}is the heating power of the electric heater; H

_{in}and H

_{out}are the inlet and outlet enthalpy of the calorimeter, respectively.

#### 3.2. Effect of High Speed on the Pressure Field

_{θ}is the pressure in the compressor chamber when the crank angle is θ, P

_{s}is the suction pressor, vs. is the volume of suction chamber, V

_{θ}is the volume of the compressor chamber when the crank angle is θ, and n is the adiabatic index, which was 1.2 in this equation, and 1.2 was the arithmetic average of the adiabatic index at the inlet and outlet of the compressor.

#### 3.3. Effect of High Speed on Tangential Leakage

#### 3.4. Effect of High Speed on Radial Leakage

## 4. Conclusions

- At high-speed conditions, there were greater pressure fluctuations in compression chambers due to the faster solid boundary motion at higher speeds. Additionally, the compression process index decreased with the increase in the rotational speed, indicating that the heat transfer of the working gas decreases. In the discharge process, there are much larger pressure fluctuations and over-compression. Therefore, when the compressor is running at a high rotational speed, the discharge valve could be opened appropriately in advance.
- The maximum axial leakage velocity was larger than the maximum radial leakage velocity. The maximum tangential leakage velocity was 159.75 m/s at 3000 rpm, 162.85 m/s at 6000 m/s, and 164.33 m/s at 9000 rpm. The maximum radial leakage velocity was 145.77 m/s at 3000 rpm, 147.99 m/s at 6000 m/s, and 150.50 m/s at 9000 rpm.
- The axial clearances were where the radial leakage was mainly observed. However, there was also a slight leakage between a pair of symmetrical chambers, where gas flowed into the axial clearance from the symmetrical chambers on both sides and leaked along the direction of the scroll rolling. At the ending point of radial clearance, the gas in the low-pressure chamber flowed into the high-pressure chamber.
- The maximum tangential and radial leakage velocity showed a sinusoidal trend with the increase in the crank angle. With the increase in the rotational speed, the crank angle of the maximum tangential and radial leakage increased and the position was closer to the starting part of the scroll. Hence, the axial and radial seal at the starting part of the scroll is very important in high-speed scroll compressors.
- The relationship between radial leakage and speed is not a simple proportional relation, so it is extremely necessary to study the leakage characteristics under different operating conditions, especially under high-speed conditions.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 9.**Comparison of the pressure change profiles with the crank angle between the theoretical adiabatic process and 3D transient simulation.

**Figure 14.**Velocity distribution on a cross-section of the top axial clearance domain (z = 0.005 mm).

**Figure 15.**Velocity distribution on a cross-section of the bottom axial clearance domain (z = 20.015 mm).

Parameter | Symbol | Unit | Value |
---|---|---|---|

Basic circle radius | a | mm | 2.580 |

Eccentric distance | e | mm | 3.989 |

The thickness of scroll vane | t | mm | 4.107 |

Height of scroll vane | h | mm | 20.00 |

Axial clearance | ac | μm | 10 |

Radial clearance | rc | μm | 10 |

The radius of the connect arc | r_{i} | mm | 5.586 |

The radius of the correction arc | r_{o} | mm | 1.588 |

Number of circles | n | 2.92 |

Simulation Method | Operating Conditions | ||
---|---|---|---|

Software | Ansys-CFX, TwinMesh | Working fluid | R134a |

Turbulent model | SST | Inlet temperature | 288.15 K |

Advection scheme | High resolution | Inlet pressure | 349.96 KPa |

Transient scheme | Second-order backward Euler | Outlet pressure | 1681.8 KPa |

Transient inner loop coefficients | 10 | Rotational speed | 3000; 6000; 9000 rpm |

Convergence control | RMS < 10^{−4} | Direction of rotation | Clockwise |

Case | Number of Layers in XY-Plane | Number of Layers in Z-Axis Direction | Number of Grids of All Domains | Volumetric Efficiency/% |
---|---|---|---|---|

1 | 9 | 44 | 1,105,810 | 94.009% |

2 | 13 | 48 | 1,715,337 | 95.121% |

3 | 15 | 50 | 2,010,369 | 95.046% |

4 | 17 | 50 | 2,217,478 | 94.976% |

Device | Range | Accuracy |
---|---|---|

Pressure sensor | 0–3 MPa | 0.5% FS |

Temperature sensor | −200–500 °C | 0.2% |

Electric heater | 0–20 kW | 1% |

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**MDPI and ACS Style**

Li, X.; Wu, W.; Zhang, J.; Guo, C.; Ke, F.; Jiang, F. Analysis of 3D Transient Flow in a High-Speed Scroll Refrigeration Compressor. *Energies* **2023**, *16*, 3089.
https://doi.org/10.3390/en16073089

**AMA Style**

Li X, Wu W, Zhang J, Guo C, Ke F, Jiang F. Analysis of 3D Transient Flow in a High-Speed Scroll Refrigeration Compressor. *Energies*. 2023; 16(7):3089.
https://doi.org/10.3390/en16073089

**Chicago/Turabian Style**

Li, Xiaoran, Weifeng Wu, Jing Zhang, Chengqiang Guo, Feng Ke, and Fuqiang Jiang. 2023. "Analysis of 3D Transient Flow in a High-Speed Scroll Refrigeration Compressor" *Energies* 16, no. 7: 3089.
https://doi.org/10.3390/en16073089