# Numerical Methodology for Determining the Energy Losses in Auxiliary Systems and Friction Processes Applied to Low Displacement Diesel Engines

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## Abstract

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## 1. Introduction

_{2}emissions [6,7]. This percentage tends to increase due to the globalized growth of economic activities [8]. In order to minimize the environmental impact, international organizations and governments have agreed to set strict levels of emission control for ICE [9]. In order to reduce ICE emissions, the implementation of different post-treatment systems has been investigated, among which it is possible to highlight particle filters, selective catalytic reduction, and the catalytic converter [10,11,12]. However, the structure of the engines used for electricity generation limits the use of systems such as catalytic converters and exhaust gas recirculation [5]. Additionally, the installation of these systems causes high back pressures in the engine exhaust system. Therefore, greater pumping work is required, which produces an increase in fuel consumption [13,14]. As a result, it is necessary to implement alternative strategies to reduce the emissions of ICEs for electric power generation.

## 2. Energy Loss Models for Auxiliary Systems

#### 2.1. Fuel Injection System

#### 2.2. Lubrication System

#### 2.3. Cooling System

## 3. Energy Loss Models for Friction Processes

#### 3.1. Energy Losses in the Valve Train

#### 3.2. Energy Losses in the Piston

- The inner diameter of the ring is considered rigid, so radial inertial forces are ignored.
- Flow processes are considered isothermal.
- The radial and tangential friction forces are calculated based on the Stribeck function.
- The Reynolds equation is used to determine the damping force.
- The flow of gas pressures is considered stationary.

#### 3.3. Energy Losses in Bearings

## 4. Numerical Methodology

^{®}software. Figure 4 describes the diagram for the development of the experimental and numerical methodology.

## 5. Experimental Methodology

## 6. Results and Discussions

#### 6.1. Experimental Validation

#### 6.2. Analysis of Energy Losses in the Engine

#### 6.3. Analysis of Energy Loss Distributions

#### 6.4. Lubrication Film Analysis

#### 6.4.1. Piston

#### 6.4.2. Valve Train

#### 6.4.3. Bearings

#### 6.5. Friction Force Analysis

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

$E$ | Energy losses |

$\dot{V}$ | Volumetric flow of fuel |

${P}_{cr}$ | Common rail pressure |

$\dot{m}$ | Mass flow |

$\Delta P$ | Pressure drop |

$D$ | Diameter |

$L$ | Length |

$f$ | Friction factor |

$g$ | Gravity |

$r$ | Roughness |

$N$ | Rotational speed |

$k$ | Fan factor |

${V}_{s}$ | Supply voltage |

$I$ | Electric current |

${F}_{cf,v}$ | Contact friction between the follower and the cam |

${F}_{ac,v}$ | Asperity contact force between the follower and the cam |

${F}_{vf,v}$ | Viscous friction force between the follower and the cam |

${c}_{p}$ | Coefficient of the shear strength |

${l}_{c}$ | Load carried by the asperities |

${A}_{a}$ | Asperity area |

${\tau}_{ss}$ | Eyring shear stress |

${r}_{s}$ | Composite surface roughness parameter |

${r}_{a}$ | Asperities radius of curvature |

${\rho}_{a}$ | Asperity density |

${E}_{e}$ | Effective elastic modulus |

${H}_{c}$ | Hertzian contact area |

${r}_{e}$ | Equivalent radius of curvature |

${w}_{cam}$ | Cam width |

${F}_{n,v}$ | Force normal |

${\vartheta}_{foll}$ | Poisson ratio of the follower |

${\vartheta}_{cam}$ | Poisson ratio of the cam |

${E}_{foll}$ | Young module of the follower and cam |

${E}_{cam}$ | Young module of the cam |

${F}_{2}$ | Statistical function |

${s}_{p}$ | Separation parameter |

$h$ | Thickness of the lubrication film |

${c}_{pv}$ | Pressure viscosity coefficient |

${r}_{cc}$ | Combined radius of curvature |

${v}_{e}$ | Entrainment velocity |

${v}_{c}$ | Contact velocity |

${n}_{ind}$ | Number of intake valves |

${n}_{exh}$ | Number of exhaust valves |

$v$ | Piston velocity |

$p$ | Lubrication film pressure |

${F}_{fr,p}$ | Frictional force produced between the ring face and the cylinder liner |

${F}_{fr,s}$ | Asperity friction force between the ring face and the cylinder liner |

${F}_{fr,v}$ | Viscous friction force between the ring face and the cylinder liner |

$Z$ | Piezoelectric viscosity |

${S}_{o}$ | Thermo-viscosity indice |

${\beta}_{o}$ | Thermo-viscosity coefficients |

${\alpha}_{o}$ | Atmospheric piezo-viscosity |

${c}_{fr}$ | Metal-metal friction coefficient |

${P}_{c}$ | Asperity contact pressure |

${r}_{c}$ | Radius of curvature of asperities |

${\rho}_{s}$ | Asperity density of the surface |

${\sigma}_{c}$ | Surface roughness of the cylinder liner |

${\sigma}_{p}$ | Surface roughness of the piston ring |

${F}_{5/2}$ | Gaussian roughness distribution |

$\omega $ | Angular speed |

${D}_{b}$ | Bearing length |

${L}_{b}$ | Bearing length |

${c}_{jb}$ | Clearance between journal and bearing |

${v}_{b}$ | Speed of the bearing centre displacement |

${e}_{r}$ | Eccentricity ratio |

${e}_{b}$ | Eccentricity between the bearing centre and journal |

${F}_{load,b}$ | Instantaneous load applied to the bearing |

${c}_{rc}$ | Radial clearance |

Greek Letters | |

$\eta $ | Efficiency |

$\mu $ | Dynamic viscosity |

$\rho $ | Density |

Subscripts | |

$f$ | Fuel injection system |

$lub$ | Oil pump |

$o$ | Atmospheric conditions |

$c$ | Cooling system |

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**Figure 5.**Engine operating modes, A: 4 Nm-3400 rpm, B: 4 Nm-3600 rpm, C: 4 Nm-3800 rpm, D: 6 Nm-3400 rpm, E: 4 Nm-3600 rpm, F: 6 Nm-3800 rpm, G: 8 Nm-3400 rpm, H: 8 Nm-3600 rpm, I: 8 Nm-3800 rpm.

**Figure 6.**Engine test bench. 1. Data acquisition (DAQ), 2. Crank angle encoder, 3. Dynamometer, 4. Resistive bench, 5. Engine, 6. Median variables DAQ, 7. Diesel tank, 8. Fuel inlet valve, 9. Fuel filter, 10. Injection pump, 11. Airflow meter.

**Figure 7.**Energy losses by auxiliary systems and friction processes were obtained experimentally and modeled.

Engine | SOKAN |
---|---|

Model | SK-MDF300 |

Compression ratio | 20:1 |

Number of cylinders | 1 |

Fuel injection system | Direct injection |

Cylinder stroke/bore [mm] | 63/78 |

Intake system | Naturally Aspirated |

Volume [cc] | 300 |

Cycle | 4 Strokes |

SAE15W-40 | |
---|---|

Density at 20 °C | 0.864 g/cm^{3} (DIN 51757) |

Pourpoint | −33 °C (ISO 3016) |

Viscosity at 40 °C | 91.76 mm^{2}/s |

Flashpoint | 224 °C (DIN ISO 2592) |

Lower explosion limit | 0.6 vol% |

Upper explosion limit | 6.5 vol% |

Properties | Units | Diesel | Hydroxy Gas |
---|---|---|---|

Density | kg/m^{3} | 0.827 | 0.084 |

Kinematic viscosity | cSt | 3.2 | - |

Flash point | °C | 74 | - |

Calorific value | MJ/kg | 41 | 115 |

Parameter | Instrument | Manufacturer | Range | Accuracy |
---|---|---|---|---|

Angle | Crankshaft angle | Beck Arnley 180-0420 | 5–9999 RPM | 0.03% |

Cylinder pressure | Piezoelectric transducer | KISTLER type 7063-A | 0–250 bar | < ±0.5% |

Airflow | Air mass sensor | BOSCH OE-22680 7J600 | 0–125 g/s | 1% |

Fuel measuring | Gravimetric meter | OHAUS-PA313 | 0–310 g | 1.5% |

Temperature | Temperature sensor | Type K | −200–1370 °C | 0.1% |

Pressure | Pressure sensor | KISTLER Type 4067-E | 0–200 bar | 1% |

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**MDPI and ACS Style**

Abril, S.O.; Piero Rojas, J.; Flórez, E.N.
Numerical Methodology for Determining the Energy Losses in Auxiliary Systems and Friction Processes Applied to Low Displacement Diesel Engines. *Lubricants* **2020**, *8*, 103.
https://doi.org/10.3390/lubricants8120103

**AMA Style**

Abril SO, Piero Rojas J, Flórez EN.
Numerical Methodology for Determining the Energy Losses in Auxiliary Systems and Friction Processes Applied to Low Displacement Diesel Engines. *Lubricants*. 2020; 8(12):103.
https://doi.org/10.3390/lubricants8120103

**Chicago/Turabian Style**

Abril, Sofia Orjuela, Jhan Piero Rojas, and Eder Norberto Flórez.
2020. "Numerical Methodology for Determining the Energy Losses in Auxiliary Systems and Friction Processes Applied to Low Displacement Diesel Engines" *Lubricants* 8, no. 12: 103.
https://doi.org/10.3390/lubricants8120103