# Numerical Investigation of Compression and Expansion Process of Twin-Screw Machine Using R-134a

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## Abstract

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## 1. Introduction

^{−3}·min

^{−1}. You et al. [4] discovered that the geometrical parameters of a rotor, such as the lobe combination, length-to-diameter ratio, and wrap angle, have a noticeable effect on the compressor performance. A lobe combination of 5/6 contributed to the highest overall performance, although it may lead to female rotor deflection if operated in high-pressure conditions. In addition, the peak isentropic efficiency was observed at a wrap angle of 325° for all the lobe combinations. Furthermore, the optimization of the profile design and advancement of the rotor manufacturing can increase the competitiveness of the screw compressors [5]. For this oil-injected compressor, an increase in the rotational speed decreased the flow leakage and increased the volumetric efficiency. In addition, the volumetric efficiency was influenced by the injected oil temperature and injection angle. Lee et al. [6] found that the compressor efficiency increased with the injection temperature until an optimum oil temperature was reached.

## 2. Geometric Modeling and Meshing

## 3. Simulation Settings

#### 3.1. Governing Equations and Boundary Conditions

#### 3.2. Meshing of the Fluid Domains

#### 3.3. Grid Independence Verification

## 4. Simulation Results

#### 4.1. Twin-Screw Compressor

^{−1}. High velocities were primarily observed at the interface and hosing gaps. The leakage flow from the housing clearance was plotted, and it was primarily caused by the pressure difference in the axial direction. According to this figure, the leaking flow near the suction port was not strong. The high-velocity leakage flow was observed near the discharge port because of the increased pressure difference. This leakage flow could lead to backflow problems when the discharge pressure is less than the outlet pressure boundary condition and an increase in the required power input occurs.

^{−1}, as shown in Figure 11. Regarding the outlet mass flow rate, an increase in the pressure ratio did not cause undercompression even though a larger leakage flow was experienced, which also resulted in a lower volumetric efficiency of 69.7%. A power input that was approximately 15% higher was required for the high-pressure-ratio case. However, the effect of the pressure ratio on the isentropic efficiency was not substantial.

#### 4.2. Twin-Screw Expander

^{−1}and 0.24 kg·s

^{−1}, respectively. The difference was primarily caused by the leakage flow and backflow.

^{−1}, were found within the front and interlobe gaps. The leakage flow through the blow hole can also be observed, and this was mainly caused by the pressure difference between the high- and low-pressure working chambers in the axial direction. The leakage flow through the blow hole was a jet of fluid ejected from the high-pressure chamber to the low-pressure side. This leakage flow and the underexpanded conditions had a detrimental effect on the efficiency of the screw expander. The volumetric and isentropic efficiencies were 69.2% and 42.5%, respectively.

## 5. Conclusions

- The wrap angle influenced the distribution of the sealing lines and altered the leakage flow, which affected the delivery rate and volumetric efficiency by up to 2%.
- The leakage flow could be determined from the predicted flow distribution, and the highest velocity was above 100 m·s
^{−1}during the compression process as a result of the small gap clearance. - The isentropic efficiency was not sensitive to the change in the wrap angle, and the difference was within 1%.
- An increase in the pressure ratio led to a decrease in the mass flow rate and volumetric efficiency because of the higher leakage flow rate. However, its influence on the isentropic efficiency was also unnoticeable.
- This screw expander was operated in underexpanded conditions, and the pressure contours demonstrated a minimum pressure level below the outlet pressure. Higher volumetric and isentropic efficiencies could be achieved if the expander was operated at a ratio that was close to the built-in expansion ratio.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

${C}_{p}$ | Specific heat capacity |

K | Thermal conductivity |

P | Pressure |

R | Gas constant |

${S}_{T}$ | Internal heat source and the viscous dissipation term |

T | Temperature |

u, v, w | Velocity |

μ | Viscosity |

ρ | Density |

τ | Component of the viscous stress |

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

Lobe combination | 5/6 |

Rotor length (mm) | 167 |

Inlet angle (°) | 280.52 |

Outlet angle (°) | 60.48 |

Male rotor head diameter (mm) | 138.54 |

Female rotor head diameter (mm) | 109.86 |

Center distance (mm) | 98 |

Wrap angle (male rotor) (°) | 280, 290, 300 |

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

Compressor (R134a) | Wrap angle (degree) | 280, 290, 300 |

Inlet pressure (bar) | 2.55 | |

Inlet temperature (K) | 288.47 | |

Discharge pressure (bar) | 8.05, 10.24 | |

Discharge temperature (K) | 328.98, 337.45 | |

Rotational speed (rpm) | 3600 | |

Expander (R134a) | Inlet pressure (bar) | 3 |

Inlet temperature (K) | 350.15 | |

Discharge pressure (bar) | 1 | |

Discharge temperature (K) | 311.03 | |

Rotational speed (rpm) | 3600 |

Wrap Angle | Flow Rate (kg·s^{−1}) | Power (kW) | Volumetric Efficiency (%) | Isentropic Efficiency (%) |
---|---|---|---|---|

280° | 0.742 | 35.6 | 74.5 | 54.6 |

290° | 0.732 | 35.2 | 73.85 | 54.5 |

300° | 0.719 | 34.83 | 72.9 | 54.1 |

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**MDPI and ACS Style**

Tsao, C.-C.; Lin, W.-K.; Lai, K.-Y.; Yavuzkurt, S.; Liu, Y.-H.
Numerical Investigation of Compression and Expansion Process of Twin-Screw Machine Using R-134a. *Energies* **2023**, *16*, 3599.
https://doi.org/10.3390/en16083599

**AMA Style**

Tsao C-C, Lin W-K, Lai K-Y, Yavuzkurt S, Liu Y-H.
Numerical Investigation of Compression and Expansion Process of Twin-Screw Machine Using R-134a. *Energies*. 2023; 16(8):3599.
https://doi.org/10.3390/en16083599

**Chicago/Turabian Style**

Tsao, Chia-Cheng, Wen-Kai Lin, Kai-Yuan Lai, Savas Yavuzkurt, and Yao-Hsien Liu.
2023. "Numerical Investigation of Compression and Expansion Process of Twin-Screw Machine Using R-134a" *Energies* 16, no. 8: 3599.
https://doi.org/10.3390/en16083599