# General-Purpose and Scalable Internal-Combustion Engine Model for Energy-Efficiency Studies

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## Abstract

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## 1. Introduction

## 2. Engine Power and Specific Fuel Consumption

## 3. Calculation Method Comparison, Calibration, and Validation Using Real Engine Results

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Example of a typical engine’s full-load power, torque, and specific fuel consumption curves according to engine manufacturer’s brochure [25].

**Figure 5.**Results obtained from AGCO Power 49 engine model. (

**a**) Specific fuel consumption (g/kWh) map calculated by the model. (

**b**) Percentage differences between calculated and measured values of ${b}_{e}$.

**Figure 7.**Results obtained from SCANIA DC 09 engine model. (

**a**) Specific fuel consumption (g/kWh) map calculated by model. (

**b**) Percentage differences between calculated and measured values of ${b}_{e}$.

**Figure 8.**Results obtained from Iveco 8460 engine model. (

**a**) Specific fuel consumption (g/kWh) map calculated by model. (

**b**) Percentage differences between calculated and measured values of ${b}_{e}$.

**Table 1.**Original structure of calculation method and submodels in Section 2.5 (Mechanical systems) of [26]. Bolded submodels are used in this study.

Torque Generation | Thermodynamic Efficiencies |
---|---|

Willans approximation | Engine speed (Table 2, Equation (1)) |

Extended Willans | Air-Fuel ratio |

ETH-Friction model (Equation (3)) | Injection timing (Equation (2)) |

Compression ratio | |

Burnt gas fraction/EGR |

**Table 2.**Typical indicated efficiency values of diesel engines as a function of speed [26].

Engine Speed | Indicated Efficiency of Diesel Engine |
---|---|

100 rad/s | 0.43 |

300 rad/s | 0.46 |

600 rad/s | 0.41 |

Measured Value | Instruments |
---|---|

Torque and power | Horiba WT-300 Eddy-Current dynamometer |

Fuel consumption | Coriolis-based system by Emerson |

Pressure and temperature | NI PXI and NI Labview-based data acquisition |

Manufacturer | AGCOPower | SCANIA | IVECO |
---|---|---|---|

Type | 49 | D9 84 A | 8460.48 |

Bore/Stroke | 108/134 mm | 130/140 mm | 112/130 mm |

Cylinder number | 4 | 5 | 6 |

Working type | 4-stroke | 4-stroke | 4-stroke |

Rated power | 148 kW | 202 kW | 224 kW |

Purpose | Agricultural | Industrial | Truck |

Parameter | Initial Value | AGCO Power | SCANIA | IVECO |
---|---|---|---|---|

${k}_{\theta}$ | 0.0004 | 0.0004 | 0.0004 | 0.0004 |

$\theta -{\theta}_{0}$ | 0 | 0 | 0.015n − 18.00 | −0.0028n + 11.11 |

${k}_{1}$ (kPa) | 144 | 144 | 120 | 160 |

${k}_{2}$ | 0.50 | 0.50 | 0.50 | 0.50 |

${k}_{3}$ (s${}^{2}$/m${}^{2}$) | 0.0011 | 0.0011 | 0.0016 | 0.0011 |

${k}_{4}$ (m) | 0.075 | 0.075 | 0.075 | 0.075 |

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**MDPI and ACS Style**

Laurén, M.; Goswami, G.; Tupitsina, A.; Jaiswal, S.; Lindh, T.; Sopanen, J.
General-Purpose and Scalable Internal-Combustion Engine Model for Energy-Efficiency Studies. *Machines* **2022**, *10*, 26.
https://doi.org/10.3390/machines10010026

**AMA Style**

Laurén M, Goswami G, Tupitsina A, Jaiswal S, Lindh T, Sopanen J.
General-Purpose and Scalable Internal-Combustion Engine Model for Energy-Efficiency Studies. *Machines*. 2022; 10(1):26.
https://doi.org/10.3390/machines10010026

**Chicago/Turabian Style**

Laurén, Mika, Giota Goswami, Anna Tupitsina, Suraj Jaiswal, Tuomo Lindh, and Jussi Sopanen.
2022. "General-Purpose and Scalable Internal-Combustion Engine Model for Energy-Efficiency Studies" *Machines* 10, no. 1: 26.
https://doi.org/10.3390/machines10010026