# Study of the Kinematics and Dynamics of the Ring Pack of a Diesel Engine by Means of the Construction of CFD Model in Conjunction with Mathematical Models

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## Abstract

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## 1. Introduction

_{2}[5,6]. The friction losses present in the piston assembly can represent approximately 50% of the total friction losses in ICEs [7]. Much of this percentage of losses is located in the piston ring package [8]. Therefore, it is necessary to achieve a better compression of the complex processes related to the interaction between the piston rings and the cylinder liner, which influence friction, wear, sealing capacity, consumption of lubricating oil, among other factors. This is of utmost importance to achieve an increase in performance and a reduction in fuel consumption [9]. Another problem present in piston rings is leakage loss in the combustion chamber. Studies estimate that the leakage losses are equivalent to a loss of 0.5% of the total energy input of the fuel [10]. On the other hand, Turnbull et al. [11] noted that leakage losses are six times higher compared to energy losses associated with friction processes. Despite the importance of this type of energy loss, there are few quantitative analyzes available in the literature that evaluate the impact of leaks on engine performance. Bolander et al. [12] experimentally and theoretically investigated the lubrication conditions and losses associated with friction between the piston ring and the cylinder liner. Avan et al. [13] studied through the development of experimental tests the thickness of the lubrication film. Zavos et al. [14] investigated by means of numerical simulation and experimental tests the deformations of the ring in a single-cylinder engine as a consequence of the friction between the compression ring and the cylinder liner.

## 2. Test Bench Engine

## 3. Auxiliary Mathematical Models

#### 3.1. Piston Kinematics

#### 3.2. Lubrication Oil Properties

#### 3.3. Contact Friction Model

#### 3.4. Blow-By Model

#### 3.5. Tribological Model

## 4. CFD Procedure

## 5. Results and Discussion

#### 5.1. Analysis of Movement of Piston Rings

#### 5.2. Pressure Conditions Analysis

#### 5.3. Leakage Flow Analysis

#### 5.4. Analysis of Power Loss in the Piston Rings

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Nomenclature | |

${l}_{c}$ | Length of the crankshaft |

${l}_{r}$ | Length of the connecting rod |

${v}_{p}$ | Piston velocity |

${a}_{p}$ | Piston acceleration |

${c}_{th}$ | Coefficient of thermal expansion |

$Z$ | Lubricant piezo-viscosity index |

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

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

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

${f}_{c}$ | Contact friction force |

${f}_{v}$ | Viscous friction force |

${f}_{a}$ | Asperity friction force |

$\tau $ | Viscous shear stress of the lubricating oil |

$A$ | Apparent contact area |

${A}_{e}$ | Real contact area between ring and liner |

$h$ | Lubricant film thickness |

${W}_{l}$ | Asperity contact load |

${F}_{2\left(\lambda \right)}$ | Statistical function |

${c}_{d}$ | Coefficient of discharge |

${T}_{u}$ | Orifice upstream temperature |

${A}_{r}$ | Ring end-gap area |

$R$ | Gas constant |

${f}_{m}$ | Compressibility factor |

${P}_{u}$ | Upstream pressure |

${P}_{d}$ | Downstream pressure |

${r}_{s}$ | Ratio of specific heats |

$h$ | Thickness of the lubrication film |

$p$ | Pressure between the ring surface and the cylinder liner |

Greek Letters | |

${\tau}_{o}\text{}$ | Limiting Eyring shear stress |

$\kappa $ | Average radius of curvature of asperities |

$\xi $ | Density of asperity peaks per unit area |

$\sigma $ | Surface roughness |

$\lambda $ | Stribeck lubricant film ratio |

$\mu $ | Dynamic viscosity of the lubricating oil |

$\beta $ | Angle between the connecting rod and the piston displacement axis |

${\omega}_{c}$ | Angular velocity of the crankshaft |

${\omega}_{rel}$ | Relative angular velocity of the movement between connecting rod and piston |

${\alpha}_{rel}$ | Relative acceleration of the movement between connecting rod and piston |

$\rho $ | Density of the lubricating oil |

$\zeta $ | Coefficient of asperity shear strength |

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Model | Reference 4JJ1 |
---|---|

Manufacturer | ISUZU |

Engine type | 4 cylinders |

Bore | 95.4 mm |

Stroke | 104.9 mm |

Compression ratio | 17.5:1 |

Injection system | Direct injection |

Displaced volume | 2999 cc |

Cycle | 4 Strokes |

Properties | Unit | SAE 10W40 |
---|---|---|

Kinematic viscosity (40 °C) | m^{2}/s | $91.057\times {10}^{-6}$ |

Density (40 °C) | kg/m^{3} | 866 |

Flash point | °C | 230 |

Dynamic viscosity (40 °C) | m^{2}/s | $105.10\times {10}^{-6}$ |

Pressure—viscosity coefficient | m^{2}/N | $1\times {10}^{-8}$ |

Crankshaft Angle (°) | Pressure (bar) | |||
---|---|---|---|---|

First Land | Second Land | Third Land | Crankcase | |

0 | 2.43 | 1.40 | 1.53 | 0.08 |

45 | 1.94 | 1.25 | 1.23 | 0.11 |

90 | 1.57 | 1.28 | 1.14 | 0.09 |

135 | 1.68 | 1.40 | 1.15 | 0.10 |

180 | 1.55 | 1.44 | 1.18 | 0.07 |

225 | 2.03 | 1.40 | 1.24 | 0.08 |

270 | 2.88 | 1.77 | 1.35 | 0.09 |

315 | 7.74 | 2.46 | 1.31 | 0.13 |

360 | 44.02 | 6.72 | 1.73 | 0.15 |

405 | 22.82 | 8.43 | 3.51 | 0.16 |

450 | 4.43 | 5.05 | 2.19 | 0.11 |

495 | 3.08 | 3.20 | 1.86 | 0.14 |

540 | 1.49 | 1.90 | 1.46 | 0.07 |

585 | 1.85 | 1.38 | 1.44 | 0.08 |

630 | 1.84 | 1.23 | 1.35 | 0.10 |

675 | 2.08 | 1.36 | 1.30 | 0.07 |

720 | 1.95 | 1.50 | 1.33 | 0.09 |

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**MDPI and ACS Style**

Orozco Lozano, W.; Fonseca-Vigoya, M.D.S.; Pabón-León, J.
Study of the Kinematics and Dynamics of the Ring Pack of a Diesel Engine by Means of the Construction of CFD Model in Conjunction with Mathematical Models. *Lubricants* **2021**, *9*, 116.
https://doi.org/10.3390/lubricants9120116

**AMA Style**

Orozco Lozano W, Fonseca-Vigoya MDS, Pabón-León J.
Study of the Kinematics and Dynamics of the Ring Pack of a Diesel Engine by Means of the Construction of CFD Model in Conjunction with Mathematical Models. *Lubricants*. 2021; 9(12):116.
https://doi.org/10.3390/lubricants9120116

**Chicago/Turabian Style**

Orozco Lozano, Wilman, Marlen Del Socorro Fonseca-Vigoya, and Jhon Pabón-León.
2021. "Study of the Kinematics and Dynamics of the Ring Pack of a Diesel Engine by Means of the Construction of CFD Model in Conjunction with Mathematical Models" *Lubricants* 9, no. 12: 116.
https://doi.org/10.3390/lubricants9120116