# A Comprehensive Numerical Study of a Wedge-Shaped Textured Convergent Oil Film Gap

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## Abstract

**:**

## 1. Introduction

- Melting/vaporization (for example, electric discharge machining);
- Ablation (for example, laser surface texturing);
- Forced material removal (for example, micro-grinding);
- Dissolution (for example, chemical etching);
- Solidification (for example, micro-casting);
- Material addition (for example, chemical vapor deposition).

- Increase the hydrodynamic pressure;
- Supply the surfaces with additional lubricant;
- Store lubricant;
- Trap wear particles;
- Reduce the real contact area.

## 2. Simulation Model

#### 2.1. Mathematical Formulation of a Multiphase Flow

#### 2.2. Comparison of Different Simulation Models

#### 2.3. Simulation Methodology for Wedge-Shaped Textured Surfaces

## 3. Results

#### 3.1. Analysis of Variation Parameters Depending on PER

#### 3.2. Pressure and Velocity Field Analysis

## 4. Discussion

## 5. Conclusions

- The performance of a wedge-shaped texture is strongly influenced by the geometry parameters. An increasing texture length $l$ improves the tribological behavior and the maximal PER can be achieved with an open texture at the inlet. This means that the texture increases the area of the face where the fluid advects.
- Depending on the dimensions of the oil film gap, a relative texture width $b/{b}_{0}$ of $85\%$ to $87\%$ leads to the best performance.
- With increasing dimensions of the oil film gap, the optimum texture angle $\alpha $ decreases. The best performance can be achieved if the oil film gap at the inlet side has an absolute height of about $52-55\mathsf{\mu}\mathrm{m}$, more or less independent of the geometry of the oil film gap.
- A relative start position of the texture ${x}_{start}/{l}_{0}$, referring to the length of the oil film gap ${l}_{0},$ between $6.7\%$ and $10\%$ enhances the performance in the best way.
- The texture increases the fluid velocity perpendicular to the movement direction, leading to an increasing volume flow perpendicular to the movement direction.
- The texture also induces additional pressure.
- Textures that are only located in the area of maximal pressure deteriorate the tribological performance.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**Boundary conditions for velocity $\overrightarrow{u}$, pressure $p$ and liquid volume fraction ${\alpha}_{l}$ of simulation model, as well as lifting force ${\overrightarrow{F}}_{lift}$ and drag force ${\overrightarrow{F}}_{drag}$ (unscaled).

**Figure 6.**Overview of all simulations of geometry I for (

**a**) ${x}_{start}=0.1\mathrm{mm}$, (

**b**) ${x}_{start}=0.2\mathrm{mm}$, (

**c**) ${x}_{start}=0.3\mathrm{mm}$, (

**d**) ${x}_{start}=0.4\mathrm{mm}$, (

**e**) ${x}_{start}=0.5\mathrm{mm}$, (

**f**) ${x}_{start}=0.6\mathrm{mm}$, (

**g**) ${x}_{start}=0.7\mathrm{mm}$ and (

**h**) ${x}_{start}=0.8\mathrm{mm}$.

**Figure 7.**Overview of all simulations of geometry II for (

**a**) x

_{start}= 0.2 mm, (

**b**) x

_{start}= 0.4 mm, (

**c**) x

_{start}= 0.6 mm and (

**d**) x

_{start}= 0.8 mm.

**Figure 8.**Overview of all simulations of geometry III for (

**a**) ${x}_{start}=0.1\mathrm{mm}$, (

**b**) ${x}_{start}=0.3\mathrm{mm}$, (

**c**) ${x}_{start}=0.5\mathrm{mm}$ and (

**d**) ${x}_{start}=0.7\mathrm{mm}$.

**Figure 9.**Performance enhancement ratio (PER) for geometry I as a function of texture (

**a**) length $l$, (

**b**) width $b$, (

**c**) angle $\alpha $ and (

**d**) start position ${x}_{start}$.

**Figure 10.**Performance enhancement ratio PER for geometry II as a function of texture (

**a**) length $l$, (

**b**) width $b$, (

**c**) angle $\alpha $ and (

**d**) start position ${x}_{start}$.

**Figure 11.**Performance enhancement ratio PER for geometry III as a function of texture (

**a**) length $l$, (

**b**) width $b$, (

**c**) angle $\alpha $ and (

**d**) start position ${x}_{start}$.

**Figure 12.**Pressure distribution and volume flow of geometry I (

**a**) untextured and (

**b**) textured ($l=1.8\mathrm{mm},b=1.7\mathrm{mm},\alpha =1.2\xb0,{x}_{start}=0.2\mathrm{mm})$.

**Figure 13.**Pressure distribution and volume flow of geometry II (

**a**) untextured and (

**b**) textured ($l=2.8\mathrm{mm},b=2.6\mathrm{mm},\alpha =0.75\xb0,{x}_{start}=0.2\mathrm{mm})$.

**Figure 14.**Pressure distribution and volume flow of geometry III (

**a**) untextured and (

**b**) textured ($l=3.7\mathrm{mm},b=3.4\mathrm{mm},\alpha =0.6\xb0,{x}_{start}=0.3\mathrm{mm})$.

**Figure 15.**Velocity field of geometry I (

**a**) untextured and (

**b**) textured ($l=1.8\mathrm{mm},b=1.7\mathrm{mm},\alpha =1.2\xb0,{x}_{start}=0.2\mathrm{mm})$.

**Figure 16.**Velocity field of geometry II (

**a**) untextured and (

**b**) textured ($l=2.8\mathrm{mm},b=2.6\mathrm{mm},\alpha =0.8\xb0,{x}_{start}=0.2\mathrm{mm})$.

**Figure 17.**Velocity field of geometry III (

**a**) untextured and (

**b**) textured ($l=3.7\mathrm{mm},b=3.4\mathrm{mm},\alpha =0.6\xb0,{x}_{start}=0.3\mathrm{mm})$.

Designation | ${\mathit{l}}_{0}\left[\mathbf{mm}\right]$ | ${\mathit{b}}_{0}\left[\mathbf{mm}\right]$ | ${\mathit{\alpha}}_{0}\left[\mathbf{\xb0}\right]$ | ${\mathit{h}}_{0}\left[\mathsf{\mu}\mathbf{m}\right]$ |
---|---|---|---|---|

Geometry I | 2 | 2 | 0.15 | 15 |

Geometry II | 3 | 3 | 0.15 | 15 |

Geometry III | 4 | 4 | 0.15 | 15 |

Parameters | |
---|---|

Density oil liquid ${\rho}_{l}$ | 857 $\mathrm{kg}/{\mathrm{m}}^{3}$ |

Density oil vapor ${\rho}_{v}$ | 0.13 $\mathrm{kg}/{\mathrm{m}}^{3}$ |

Dynamic viscosity liquid ${\eta}_{l}$ | 22.4 $\mathrm{mPas}$ |

Dynamic viscosity vapor ${\eta}_{v}$ | 2 × 10^{−2} $\mathrm{mPas}$ |

Condensation coefficient ${C}_{C}$ | 33.3 |

Vaporization coefficient ${C}_{v}$ | 1.55 × 10^{−3} |

Vapor pressure ${p}_{v}$ | 165 $\mathrm{Pa}$ |

Input velocity ${U}_{\infty}$ | 10 $\mathrm{m}/\mathrm{s}$ |

Reference time ${t}_{\infty}$ | ${l}_{0}/{U}_{\infty}$ |

$\mathit{P}\mathit{E}\mathit{R}\left[-\right]$ | $\mathit{P}\mathit{E}{\mathit{R}}_{\mathit{l}\mathit{i}\mathit{f}\mathit{t}}=$ $\frac{\left|\left.{\overrightarrow{\mathit{F}}}_{\mathit{l}\mathit{i}\mathit{f}\mathit{t},\mathit{t}\mathit{e}\mathit{x}\mathit{t}\mathit{u}\mathit{r}\mathit{e}\mathit{d}}\right|\right.}{\left|\left.{\overrightarrow{\mathit{F}}}_{\mathit{l}\mathit{i}\mathit{f}\mathit{t},\mathit{u}\mathit{n}\mathit{t}\mathit{e}\mathit{x}\mathit{t}\mathit{u}\mathit{r}\mathit{e}\mathit{d}}\right|\right.}$$\left[-\right]$ | $\mathit{P}\mathit{E}{\mathit{R}}_{\mathit{d}\mathit{r}\mathit{a}\mathit{g}}=$ $\frac{\left|\left.{\overrightarrow{\mathit{F}}}_{\mathit{d}\mathit{r}\mathit{a}\mathit{g},\mathit{t}\mathit{e}\mathit{x}\mathit{u}\mathit{r}\mathit{e}\mathit{d}}\right|\right.}{\left|\left.{\overrightarrow{\mathit{F}}}_{\mathit{d}\mathit{r}\mathit{a}\mathit{g},\mathit{u}\mathit{n}\mathit{t}\mathit{e}\mathit{x}\mathit{t}\mathit{u}\mathit{r}\mathit{e}\mathit{d}}\right|\right.}$$\left[-\right]$ | |
---|---|---|---|

Geometry I | 2.65 | 2.18 | 0.82 |

Geometry II | 1.99 | 1.64 | 0.82 |

Geometry III | 1.67 | 1.43 | 0.87 |

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## Share and Cite

**MDPI and ACS Style**

Scharf, R.; Maier, M.; Pusterhofer, M.; Grün, F.
A Comprehensive Numerical Study of a Wedge-Shaped Textured Convergent Oil Film Gap. *Lubricants* **2024**, *12*, 121.
https://doi.org/10.3390/lubricants12040121

**AMA Style**

Scharf R, Maier M, Pusterhofer M, Grün F.
A Comprehensive Numerical Study of a Wedge-Shaped Textured Convergent Oil Film Gap. *Lubricants*. 2024; 12(4):121.
https://doi.org/10.3390/lubricants12040121

**Chicago/Turabian Style**

Scharf, Raphael, Michael Maier, Michael Pusterhofer, and Florian Grün.
2024. "A Comprehensive Numerical Study of a Wedge-Shaped Textured Convergent Oil Film Gap" *Lubricants* 12, no. 4: 121.
https://doi.org/10.3390/lubricants12040121