# Sensor Fusion for Simultaneous Estimation of In-Plane Permeability and Porosity of Fiber Reinforcement in Resin Transfer Molding

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Setup

## 3. Methodologies

#### 3.1. Capacitance Sensing for Porosity Measurement

_{1}and V

_{2}are the corresponding volume ratios. The medium in Region 1 is a mixture of fibers and resin. Therefore,

#### 3.2. Darcy’s Law for Permeability Measurement

^{2}, the value of permeability ($K$) can be obtained from the slope.

#### 3.3. Numerical Simulation

#### 3.3.1. Equipment Modeling and Mesh Generation

#### 3.3.2. Process Simulation

**K**of the porous preform should be known,

_{ij}(i, j = x, y, or z) are the components of the permeability tensor, ${K}_{11}$, ${K}_{22}$, and ${K}_{33}$ are the principal permeability,$l$

_{ij}are the directional cosines of the local coordinates, and

_{11}dominates the resin flow behavior. Therefore, we set ${K}_{11}={K}_{22}={K}_{33}=K$ for simplicity.

## 4. Experimental Results

#### 4.1. Experiments on Nine-Layer Fiber Preforms

_{0}= 1 atm, into the fitting result of (22), the permeability was estimated as $K=1.85\times {10}^{-10}{\mathrm{m}}^{2}$. Such results were consistent with our previous results achieved using another measurement system [13].

#### 4.2. Experiments on Seven-Layer Fiber Preforms

^{−10}m

^{2}.

#### 4.3. Verifications with Simulations

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 9.**Flow visualization of RTM using a nine-layer fiber preform: images captured at the 50th, 150th, 250th, 350th, 450th, and 550th second.

**Figure 11.**Relationship between flow front displacement and capacitance in the first RTM experiment using a nine-layer fiber preform.

**Figure 13.**Relationship between flow front displacement and capacitance in the second RTM experiment using a nine-layer fiber preform.

**Figure 14.**Flow visualization of RTM using a seven-layer fiber preform: images captured at the 50th, 100th, 150th, 200th, 250th, and 300th second.

**Figure 16.**Relationship between flow front displacement and capacitance in the first RTM experiment using a seven-layer fiber preform.

**Figure 18.**Relationship between flow front displacement and capacitance in the second RTM experiment using a seven-layer fiber preform.

**Figure 19.**Comparison between experimental and simulated flow front positions in the case study of nine-layer fiber preform.

**Figure 20.**Snapshot of flow front positions at the 50th second in the case study of nine-layer fiber preform.

**Figure 21.**Snapshot of flow front positions at the 450th second in the case study of nine-layer fiber preform.

**Figure 22.**Comparison between experimental and simulated flow front positions in the case study of seven-layer fiber preform.

**Figure 23.**Snapshot of flow front positions at the 250th second in the case study of seven-layer fiber preform.

Parameters | Porosity | Permeability (m^{2}) |
---|---|---|

Measured values from experiment 1 | 0.758 | 1.85 × 10^{−10} |

Measured values from experiment 2 | 0.767 | 2.07 × 10^{−10} |

Average values used in numerical simulation | 0.763 | 1.96 × 10^{−10} |

Parameters | Porosity | Permeability (m^{2}) |
---|---|---|

Measured values from experiment 1 | 0.754 | 4.26 × 10^{−10} |

Measured values from experiment 2 | 0.718 | 2.9 × 10^{−10} |

Average values used in numerical simulation | 0.736 | 3.58 × 10^{−10} |

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**MDPI and ACS Style**

Qi, W.; Chiu, T.-H.; Kao, Y.-K.; Yao, Y.; Chen, Y.-H.; Yang, H.; Wang, C.-C.; Hsu, C.-H.; Chang, R.-Y. Sensor Fusion for Simultaneous Estimation of In-Plane Permeability and Porosity of Fiber Reinforcement in Resin Transfer Molding. *Polymers* **2022**, *14*, 2652.
https://doi.org/10.3390/polym14132652

**AMA Style**

Qi W, Chiu T-H, Kao Y-K, Yao Y, Chen Y-H, Yang H, Wang C-C, Hsu C-H, Chang R-Y. Sensor Fusion for Simultaneous Estimation of In-Plane Permeability and Porosity of Fiber Reinforcement in Resin Transfer Molding. *Polymers*. 2022; 14(13):2652.
https://doi.org/10.3390/polym14132652

**Chicago/Turabian Style**

Qi, Wei, Tzu-Heng Chiu, Yi-Kai Kao, Yuan Yao, Yu-Ho Chen, Hsun Yang, Chen-Chieh Wang, Chia-Hsiang Hsu, and Rong-Yeu Chang. 2022. "Sensor Fusion for Simultaneous Estimation of In-Plane Permeability and Porosity of Fiber Reinforcement in Resin Transfer Molding" *Polymers* 14, no. 13: 2652.
https://doi.org/10.3390/polym14132652