# Comparison of the Net Work Output between Stirling and Ericsson Cycles

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Model

#### 2.1. Stirling Cycle

#### 2.2. Ericsson Cycle

## 3. Results and Discussion

#### 3.1. Comparison with Equivalent Mass and Temperature Limits

#### Fixed Pressure and Volume Limits

#### 3.2. Comparison with Equivalent Mass and Pressure or Volume Ratios

#### 3.2.1. Equivalent Pressure Ratios

#### 3.2.2. Equivalent Volume Ratios

#### 3.3. Comparison with Equivalent Temperature Limits and Pressure or Volume Ratios

#### 3.3.1. Equivalent Pressure Ratio and Fixed Maximum Volume

#### 3.3.2. Equivalent Volume Ratio and Fixed Maximum Pressure

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

W | Work (kJ) |

P | Pressure (kPa) |

V | Volume (m${}^{3}$) |

T | Temperature (K) |

m | Mass of the working fluid (kg) |

R | Ideal gas constant (kJ/kg·K) |

## Subscripts

max | Maximum |

min | Minimum |

H | High |

L | Low |

S | Stirling |

E | Ericsson |

## References

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**Figure 3.**(

**a**) Pressure ratio relationship and (

**b**) volume ratio relationship between Stirling and Ericsson cycles, where the solid lines indicate equal net work output for equivalent mass and temperature limits.

**Figure 4.**P-V diagrams of Stirling and Ericsson cycles for fixed mass and temperature limits with (

**a**) fixed maximum pressure and volume and (

**b**) fixed minimum pressure and volume.

**Figure 5.**(

**a**) High temperature relationship between Stirling and Ericsson cycles for fixed pressure ratios and ${T}_{L}=25{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$C, with solid lines denoting equal net work output; and (

**b**) P-V diagrams of Stirling and Ericsson cycles for fixed mass, pressure limits and low temperature for equal net work output.

**Figure 6.**(

**a**) High temperature relationship between Stirling and Ericsson cycles for fixed volume ratios and ${T}_{L}=25{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$C, with solid lines denoting equal net work output; (

**b**) P-V diagrams of Stirling and Ericsson cycles for fixed mass, volume limits and low temperature for equal net work output.

**Figure 7.**(

**a**) Relationship between pressure and temperature ratio for equal net work output and P-V diagram of Stirling and Ericsson cycles for fixed temperature and pressure limits and maximum volume for equal net work output (inset); (

**b**) non-dimensional net work as a function of pressure ratio and temperature ratio (inset).

**Figure 8.**(

**a**) Relationship between volume and temperature ratio for equal net work output and P-V diagram of Stirling and Ericsson cycles for fixed temperature and volume limits and maximum pressure for equal net work output (inset); (

**b**) non-dimensional net work as a function of volume ratio and temperature ratio (inset).

**Table 1.**Parameters for a small-scale engine (referring to Figure 4).

Operating Parameters | Case (i) | Case (ii) |
---|---|---|

Working fluid | air | air |

m (kg) | 0.00003 | 0.00003 |

${T}_{H}$ (${}^{\circ}$C) | 500 | 500 |

${T}_{L}$ (${}^{\circ}$C) | 25 | 25 |

${P}_{\mathrm{max}}$ (kPa) | 1013.3 | − |

${V}_{\mathrm{max}}$ (m${}^{3}$) | 6.28 × 10${}^{-5}$ | − |

${P}_{\mathrm{min}}$ (kPa) | − | 101.33 |

${V}_{\mathrm{min}}$ (m${}^{3}$) | − | 6.28 × 10${}^{-6}$ |

Operating Parameters | Case (i) | Case (ii) |
---|---|---|

Working fluid | air | air |

m (kg) | 0.00003 | 0.00003 |

${T}_{L}$ (${}^{\circ}$C) | 25 | 25 |

${T}_{H,S}$ (${}^{\circ}$C) | 500 | − |

${T}_{H,E}$ (${}^{\circ}$C) | − | 500 |

${P}_{\mathrm{max}}$ (kPa) | 1013.3 | − |

${P}_{\mathrm{min}}$ (kPa) | 101.33 | − |

${V}_{\mathrm{max}}$ (m${}^{3}$) | − | 3.14 × 10${}^{-5}$ |

${V}_{\mathrm{min}}$ (m${}^{3}$) | − | 3.14 × 10${}^{-6}$ |

Operating Parameters | Case (i) | Case (ii) |
---|---|---|

Working fluid | air | air |

${T}_{H}$ (${}^{\circ}$C) | 500 | 500 |

${T}_{L}$ (${}^{\circ}$C) | 25 | 25 |

${P}_{\mathrm{min}}$ (kPa) | 101.33 | − |

${V}_{\mathrm{max}}$ (m${}^{3}$) | 2.51 × 10${}^{-5}$ | − |

${V}_{\mathrm{min}}$ (m${}^{3}$) | − | 4.71 × 10${}^{-6}$ |

${P}_{\mathrm{max}}$ (kPa) | − | 1013.3 |

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**MDPI and ACS Style**

Costa, R.F.; MacDonald, B.D.
Comparison of the Net Work Output between Stirling and Ericsson Cycles. *Energies* **2018**, *11*, 670.
https://doi.org/10.3390/en11030670

**AMA Style**

Costa RF, MacDonald BD.
Comparison of the Net Work Output between Stirling and Ericsson Cycles. *Energies*. 2018; 11(3):670.
https://doi.org/10.3390/en11030670

**Chicago/Turabian Style**

Costa, Rui F., and Brendan D. MacDonald.
2018. "Comparison of the Net Work Output between Stirling and Ericsson Cycles" *Energies* 11, no. 3: 670.
https://doi.org/10.3390/en11030670