# Computational Fluid Dynamics Modeling of Top-Down Digital Light Processing Additive Manufacturing

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## Abstract

**:**

## 1. Introduction

## 2. Model Description

#### 2.1. Governing Equations

#### 2.2. Numerical Model

#### 2.3. Post-Processing

## 3. Results and Discussion

#### 3.1. Fluid Viscosity

#### 3.2. Traveling Speed

#### 3.3. Travelling Speed Ratio

_{up}and S

_{down}are the upward and downward traveling speeds, respectively. The effects of travelling speed ratio (0.75 ≤ $\mathrm{T}\mathrm{S}\mathrm{R}$ ≤ 1.25) on the settling time using the parameters of case 2 are presented in Figure 7. According to Figure 7, by increasing the TSR from 0.75 to 1.25, the settling times are observed to decrease. The decrease in settling times is observed to be higher when the TSR is increased from 0.75 to 1, as compared to 1 to 1.25. The results reveal that the upward speed of the part must always be more than or equal to its downward speed. Since there is only a marginal variation between the settling times at TSR = 1 and TSR = 1.25, using the same upward and downward speeds is a reasonably good choice. Furthermore, it is observed that the variation in settling times with TSR is very small compared to the variation with resin viscosity and travelling speed. Therefore, it is inferred that TSR is an insignificant parameter in the context of the settling time.

#### 3.4. Print Layer Thickness

#### 3.5. Travel Distance

## 4. Conclusions

- By increasing the fluid viscosity from 0.05 to 1 Pa.s, the fluid interface will need more time for reaching a stable state. According to the plotted working curves, stabilizing the fluid interface requires approximately 16.5 s when applying the reference parameters.
- Considering the optimization results, for case 4 with the fluid viscosity of 1 Pa.s, a maximum stability time of 51 $\mathrm{s}$ was achieved.
- A diminishing trend was found for the stability time by augmentation of the traveling speed from 1 to 2 mm/s, remarkably. Moreover, the maximum stability time of almost 51 s was obtained for thickness deviation of 2 µm and the traveling speed of 1 mm/s.
- A smaller stability time of the fluid interface was obtained by increasing the travelling speed ratio from 0.75 to 1.25. In addition, the minimum and maximum stability times for the travelling speed ratio parameter considering thickness deviation of 2.5 µm were obtained at roughly 15 s and 17 s, respectively.
- A stable situation was obtained for the fluid interface in a shorter time considering high printed layer thickness values.
- According to the results of the travel distance parameter, the minimum and maximum stability times at thickness deviation of 3 µm were achieved at approximately 10.5 s and 19.5 s, respectively.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Symbols | |

${e}_{t}$ | The thickness of the layer at time $t$ |

${e}_{n}$ | Nominal thickness of the layer |

${u}_{i}$ | The velocity component in the $i$-direction |

$p$ | Local pressure |

${g}_{i}$ | Gravitational body forces per mass unit in the $i$-direction |

$t$ | Time |

${t}_{m}$ | Traveling time |

${t}_{f}$ | Finishing time |

${t}_{s}$ | Stability time |

${x}_{i}$ | Spatial coordinates |

$x,y,z$ | Coordinates |

Greek symbols | |

${\delta}_{i}$ | Distance of the fluid interface from the surface of the build part |

$\u2206{e}_{t}$ | Thickness deviation |

$\u2206{e}_{t}^{\mathrm{*}}$ | Particular thickness deviation |

$\mu $ | Fluid viscosity |

Abbreviations | |

AM | Additive manufacturing |

CFD | Computational fluid dynamics |

DLP | Digital light processing |

DMD | Digital micromirror device |

2D | Two-dimensional |

3D | Three-dimensional |

FDM | Fused deposition modeling |

GMRES | Generalized minimum residual |

LCD | Liquid crystal display |

SLA | Stereolithography |

TD | Travelling distance |

TS | Traveling speed |

TSR | Traveling speed ratio |

UV | Ultraviolet |

VOF | Volume of fluid |

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**Figure 3.**The schematic of post-processing calculation: (

**a**) at ${t}_{m}\le t\le {t}_{s}$, (

**b**) at $t\to \infty $.

**Figure 4.**Contours of the fraction of fluid at four time steps and different fluid viscosity ($\mathrm{T}\mathrm{S}=1.5\mathrm{m}\mathrm{m}/\mathrm{s},\mathrm{T}\mathrm{S}\mathrm{R}=1,\mathrm{T}\mathrm{D}=6\mathrm{m}\mathrm{m}$).

Quantity | Unit | Mesh 1 | Mesh 2 | Mesh 3 |
---|---|---|---|---|

Number of cells | - | 33,108 | 68,580 | 104,091 |

Maximum cell size (in X/Z direction) | $\mathsf{\mu}\mathrm{m}$ | 31.8/49 | 20.8/37.6 | 17.30/30.50 |

Minimum cell size (in X/Z direction) | $\mathsf{\mu}\mathrm{m}$ | 30.1/13.6 | 20.8/7.5 | 16.66/5.99 |

Maximum ratio of adjacent cell size ratio (in X/Z direction) | - | 1.02/1.22 | 1/1.23 | 1/1.20 |

Maximum aspect ratio (X:Z ratio) | - | 2.33 | 2.77 | 2.88 |

Case Numbers | $\mathbf{Density}\phantom{\rule{0ex}{0ex}}(\mathbf{k}\mathbf{g}/{\mathbf{m}}^{3})$ | $\mathbf{Viscosity}\phantom{\rule{0ex}{0ex}}(\mathbf{P}\mathbf{a}.\mathbf{s})$ | $\mathbf{Travelling}\mathbf{Speed}\phantom{\rule{0ex}{0ex}}(\mathbf{m}\mathbf{m}/\mathbf{s})$ | Travelling Speed Ratio (-) | $\mathbf{Layer}\mathbf{Thickness}\phantom{\rule{0ex}{0ex}}\left(\mathsf{\mu}\mathbf{m}\right)$ | $\mathbf{Travel}\mathbf{Distance}\phantom{\rule{0ex}{0ex}}\left(\mathbf{m}\mathbf{m}\right)$ |
---|---|---|---|---|---|---|

Case 1 | 1100 | 0.05 | 1.5 | 1 | 50 | 6 |

Case 2 | 0.1 | 1.5 | 1 | 50 | 6 | |

Case 3 | 0.5 | 1.5 | 1 | 50 | 6 | |

Case 4 | 1 | 1.5 | 1 | 50 | 6 | |

Case 5 | 0.1 | 1 | 1 | 50 | 6 | |

Case 6 | 0.1 | 2 | 1 | 50 | 6 | |

Case 7 | 0.1 | 1.5 | 0.75 | 50 | 6 | |

Case 8 | 0.1 | 1.5 | 1.25 | 50 | 6 | |

Case 9 | 0.1 | 1.5 | 1 | 30 | 6 | |

Case 10 | 0.1 | 1.5 | 1 | 70 | 6 | |

Case 11 | 0.1 | 1.5 | 1 | 100 | 6 | |

Case 12 | 0.1 | 1.5 | 1 | 50 | 3 | |

Case 13 | 0.1 | 1.5 | 1 | 50 | 9 |

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## Share and Cite

**MDPI and ACS Style**

Moghadasi, H.; Mollah, M.T.; Marla, D.; Saffari, H.; Spangenberg, J.
Computational Fluid Dynamics Modeling of Top-Down Digital Light Processing Additive Manufacturing. *Polymers* **2023**, *15*, 2459.
https://doi.org/10.3390/polym15112459

**AMA Style**

Moghadasi H, Mollah MT, Marla D, Saffari H, Spangenberg J.
Computational Fluid Dynamics Modeling of Top-Down Digital Light Processing Additive Manufacturing. *Polymers*. 2023; 15(11):2459.
https://doi.org/10.3390/polym15112459

**Chicago/Turabian Style**

Moghadasi, Hesam, Md Tusher Mollah, Deepak Marla, Hamid Saffari, and Jon Spangenberg.
2023. "Computational Fluid Dynamics Modeling of Top-Down Digital Light Processing Additive Manufacturing" *Polymers* 15, no. 11: 2459.
https://doi.org/10.3390/polym15112459