# Numerical Simulation of Two-Phase Flow in Liquid Composite Moulding Using VOF-Based Implicit Time-Stepping Scheme

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## Abstract

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## 1. Introduction

## 2. Numerical Simulation Approach

#### 2.1. Volume of Fluid (VOF)

#### 2.2. Time-Stepping Scheme

#### 2.3. Darcy’s Law for a Transient Flow

## 3. Results and Discussion

#### 3.1. Two-Dimensional Rectangular Mould for Regular Shapes

#### 3.2. Three-Dimensional Curved Mould for Complex Shapes

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**A schematic diagram illustrating mould-filling process parameters, saturation and unsaturation regions, and filling front advancement with uniform permeability.

**Figure 3.**Geometry and boundary conditions used in the numerical simulation, including flow-front tracking points.

**Figure 4.**Numerical rectilinear/channel flow saturation throughout a porous medium with $50\%$ aggregate porosity $\left({\varphi}_{o}\right)$ at a constant injection pressure for different time-step sizes: 5 s, 25 s, and 50 s. (

**a**) 5 s, (

**b**) 25 s, and (

**c**) 50 s.

**Figure 6.**A VARTM experimental setup used for a curved or L-shaped composite components [27].

**Figure 7.**A schematic diagram of (

**a**) curvature and straight regions of the L-shaped composite part, (

**b**) 1-ply fibre preform with 1.46 mm thickness, and (

**c**) 6-ply fibre preform with a 4.84 mm thickness.

**Figure 8.**Numerical flow-front predictions vs. experimental observations for a complex shape with single and multiple plies.

**Figure 9.**Three-dimensional numerical mould-filling process of a curved-type (L-shaped) composite component. (

**a**) 1-ply (

**b**) 6-ply.

**Table 1.**Selection of numerical contributions that evaluated simulation tools for flow-front modelling.

References | Fabric Architecture | Injection Method | Flow Modelling | Computational Approach |
---|---|---|---|---|

Tan et al. [3] | Bi-axial | Unidirectional | Dual-scale | FE/CV-PoreFlow |

Simacek et al. [13] | UD | Unidirectional | Dual-scale | FE/CV-LIMS |

Oliveira et al. [14] | Fibre mats | Unidirectional | − | Darcy-based PAM-RTM |

Grossing et al. [15] | UD/Triaxial NCF | Radial | Dual-scale | FVM-VOF OpenFoam |

Sas et al. [16] | UD | Unidirectional | − | FEM-LSM COMSOL |

Wei et al. [22] | Fibre mats | Unidirectional | − | FVM-VOF Moldex3D |

Medium Porosity [%] | Time-Stepping Size [s] | CPU [s] | Real Time [s] |
---|---|---|---|

40 | 5 | 19.75 | 481 |

25 | 5.44 | 89 | |

50 | 2.97 | 57 | |

50 | 5 | 14.67 | 319 |

25 | 3.76 | 67 | |

50 | 2.2 | 40 | |

60 | 5 | 8.14 | 148 |

25 | 2.26 | 42 | |

50 | 1.55 | 26 |

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**MDPI and ACS Style**

Alotaibi, H.; Abeykoon, C.; Soutis, C.; Jabbari, M.
Numerical Simulation of Two-Phase Flow in Liquid Composite Moulding Using VOF-Based Implicit Time-Stepping Scheme. *J. Compos. Sci.* **2022**, *6*, 330.
https://doi.org/10.3390/jcs6110330

**AMA Style**

Alotaibi H, Abeykoon C, Soutis C, Jabbari M.
Numerical Simulation of Two-Phase Flow in Liquid Composite Moulding Using VOF-Based Implicit Time-Stepping Scheme. *Journal of Composites Science*. 2022; 6(11):330.
https://doi.org/10.3390/jcs6110330

**Chicago/Turabian Style**

Alotaibi, Hatim, Chamil Abeykoon, Constantinos Soutis, and Masoud Jabbari.
2022. "Numerical Simulation of Two-Phase Flow in Liquid Composite Moulding Using VOF-Based Implicit Time-Stepping Scheme" *Journal of Composites Science* 6, no. 11: 330.
https://doi.org/10.3390/jcs6110330