# Exergy Analysis of a Subcritical Refrigeration Cycle with an Improved Impulse Turbo Expander

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}) or hydrofluorocarbons (HFCs), are often thermodynamically less efficient compared with the conventional HCFC-based systems. In this situation, the issue of energy-savings in refrigeration-related applications has been of growing widespread concern over the past decades.

_{2}cycle can increase the COP and exergy efficiency by 33% and 30%, respectively. The two values become lower when HCFCs/HFCs are used as refrigerants, but the gain is still interesting to enhance the overall efficiency of the system, especially for large capacity systems, where it is not only evaluated in a relative value but also in an absolute value. In recent years, various expander concepts and prototypes have been investigated and developed for the transcritical CO

_{2}refrigeration cycles as well as subcritical refrigeration systems with traditional HCFCs/HFCs as refrigerants, e.g., piston [2,3], rolling/swing piston [4–7], vane [8–10], scroll [11–13], and screw [14,15], which have demonstrated the viability of this approach.

_{2}expander-economizer hybrid cycle and reported a 5–8% and a 60% increase in COP over the expander cycle and the basic cycle, respectively.

_{2}as the refrigerant. However, the expander exhibited low efficiency.

## 2. The Improved Impulse Turbo Expander and the Corresponding Cycle

- (1)
- A liquid accumulator is provided in the lower part of the housing to collect the liquid working fluid which is fed to the evaporator through outlet 1 arranged at the bottom of the accumulator. Thus if the volume of the accumulator is appropriately determined, the liquid working fluid can remain at a constant level in the accumulator so as not to get in touch with the disk of the expander.
- (2)
- Another outlet (outlet 2), through which the saturated flash vapor is discharged, is provided at the upper part of the housing and communicates with the room inside the housing.

_{1}denotes the disk friction coefficient, k

_{2}is an empiric coefficient taking into account the influence of the rotor geometrical shape, H is the blade height. ρ is the fluid density.

## 3. Thermodynamic Modeling

- (1)
- There are no pressure losses in pipes and heat exchangers.
- (2)
- The small difference among the intermediate pressure, the discharge pressure of the low-stage compressor and the suction pressure of the high-stage compressor is negligible.
- (3)
- The vapor stream and the liquid stream exiting the ITE are assumed to be saturated.
- (4)
- The exiting working fluid of the evaporator is saturated vapor.
- (5)
- The ITE and the compressor are treated adiabatically.
- (6)
- The numerical simulation modeling of the cycle is based on one unit of the working fluid at the inlet of the ITE.
- (7)
- (8)
- The vapor and liquid separation efficiencies in the turbine and the economizer are negligible.

#### 3.1. Energy Analysis

#### 3.2. Exergy Analysis

_{Q}can also be calculated by:

## 4. Results and Discussion

_{int}to p

_{gm}. Thus it can be stated as:

_{gm}. The COP value of the improved ITE cycle is higher than that of the conventional ITE cycle around the optimum intermediate pressure. Nevertheless, the improper selection of intermediate pressure may make the COP of the improved ITE cycle shift to lower values compared with the conventional ITE cycle.

_{opt}for the improved ITE cycle. Figure 9 shows PR

_{opt}versus the evaporator temperature under different condenser temperatures for the improved ITE cycle. It is observed from Figure 8 that the value of PR

_{opt}drops rapidly with the increase of the ITE efficiency. But the effects of the evaporator temperature and the condenser temperature seem to be relatively negligible compared with that of the ITE efficiency. A correlation for PR

_{opt}(R

^{2}= 99.961%) in terms of the ITE efficiency based on a square polynomial fit of the simulated results is obtained:

## 5. Conclusions

- An increase of 20% in the isentropic efficiency can be attained for the improved ITE compared with the conventional ITE owing to the reduction of the friction loss of the rotor.
- Unlike the typical two-stage compression refrigeration cycles, the optimum intermediate pressure for the improved ITE cycle shows a deviation from the square root of the condenser pressure times the evaporator pressure. This deviation mainly depends on the ITE efficiency, and a correlation of the optimum intermediate pressure for the improved ITE cycle is developed.
- As the ITE efficiency increases, the corresponding COPs of the conventional ITE cycle and the improved ITE cycle increase. The improved ITE cycle outperforms the conventional one.
- The improved ITE cycle improves the COP and the exergy efficiency by 1.4%–6.1% over the conventional ITE cycle, 4.6%–8.3% over the economizer cycle and 7.2%–21.6% over the base cycle.
- The total exergy loss in the improved ITE cycle is lower than that in the other three cycles. This reduction is mainly due to the decrease in the expansion process.

## Acknowledgments

Nomenclature | |
---|---|

COP | coefficient of performance in cooling condition |

Ex | exergy (kJ/kg) |

h | enthalpy (kJ/kg) |

H | height (m) |

I | specific irreversibility (kJ/kg) |

m | mass flow rate (kg/s) |

N | friction power loss (kW) |

p | pressure (MPa) |

PR | pressure ratio |

q | specific heat transfer rate (kJ/kg) |

Q_{0} | refrigeration capacity (kW) |

R | radius (m) |

s | specific entropy (kJ/kg K) |

t | temperature (°C) |

T | temperature (K) |

w | specific power (kJ/kg) |

x | vapor quality |

ω | angular velocity (rad/s) |

ρ | density (kg/m ^{3}) |

η | efficiency |

Subscripts | |
---|---|

0 | reference environment |

c | compressor |

con | condenser |

e | evaporator |

gm | geometric mean |

int | intermediate |

opt | optimal |

r | refrigerated object |

rot | rotor |

s | isentropic process |

t | turbo |

tot | total |

v | throttle valve |

## Author Contributions

## Conflicts of Interest

## References and Notes

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**Figure 9.**PR

_{opt}versus evaporator temperature under different condenser temperatures for the improved ITE cycle.

**Figure 11.**COP of investigated cycles versus evaporator temperature under different condenser temperatures.

**Figure 12.**Exergy efficiencies of the investigated cycles versus evaporating temperature at different condenser temperatures.

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**MDPI and ACS Style**

Zhang, Z.; Tian, L.
Exergy Analysis of a Subcritical Refrigeration Cycle with an Improved Impulse Turbo Expander. *Entropy* **2014**, *16*, 4392-4407.
https://doi.org/10.3390/e16084392

**AMA Style**

Zhang Z, Tian L.
Exergy Analysis of a Subcritical Refrigeration Cycle with an Improved Impulse Turbo Expander. *Entropy*. 2014; 16(8):4392-4407.
https://doi.org/10.3390/e16084392

**Chicago/Turabian Style**

Zhang, Zhenying, and Lili Tian.
2014. "Exergy Analysis of a Subcritical Refrigeration Cycle with an Improved Impulse Turbo Expander" *Entropy* 16, no. 8: 4392-4407.
https://doi.org/10.3390/e16084392