# Simulating Mold Filling in Compression Resin Transfer Molding (CRTM) Using a Three-Dimensional Finite-Volume Formulation

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## Abstract

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## 1. Introduction

^{®}. To include the CRTM simulation method in this open-source framework enables to flexibly embed the simulations in a virtual process chain for CoFRP manufacturing, like developed by Kärger et al. [16].

## 2. Basic Fluid Mechanic Equations for Mold Filling Simulations

^{®}by ESI Group.

**S**is also known as the Darcy-Forchheimer term containing the Darcy term $\frac{\mu}{\mathbf{K}}$ and the Forchheimer term $\frac{1}{2}\rho \left|\mathbf{v}\right|F$ with the fluid density $\rho $ and the inertial resistance coefficient F. For small fluid velocities and high permeabilities all terms in Equation (5) except the pressure gradient $\nabla p$ and the Darcy term can be neglected, which again leads to the Darcy equation. The Navier-Stokes-equations can be numerically solved by the finite-volume (FV) method. This method uses the integral form of the differential equations in a control volume ${V}_{p}$ and the Gauss’ theorem to alter the volume integrals of the spatial derivatives to surface integrals of the element faces, which in total leads to several volume and surface integrals that have to be evaluated. The main source about the implementation of the FV method in OpenFOAM is the work of Jasak [19], where all equations are derived in detail. The discretisation of Equation (4) using Gauss’ theorem and assuming linearity yields

## 3. Finite-Volume CRTM Mold Filling Simulation Method and Implementation to OpenFOAM

#### 3.1. Treatment of the Mesh Deformation during the Compression Step

#### 3.2. Modeling of the Fluid Velocity

## 4. Verification of the CRTM Mold Filling Simulation Method

^{®}by ESI Group.

#### 4.1. Simulation Model and Parameters

^{®}only allows a two-dimensional CRTM simulation containing triangular elements. To compare the results to the finite-volume simulations, the triangular element size is chosen to have the same mean edge length in flow direction as the hexahedrons in the finite-volume simulation.

#### 4.1.1. Material Parameters

^{TM}, type: PX35UD0300) were carried out by process-oriented experiments using a unidirectional permeability test setup. In the experiments, the fibrous preform with a previously defined fiber volume fraction is placed in a rectangular plate mold made of stainless steel and a linear injection with constant pressure is performed. The advancement of the flow front is tracked with several pressure sensors that are integrated in flow direction into the mold. Details of the permeability measurements are explained in [25]. The results for the fiber-parallel and fiber-perpendicular permeabilities of a unidirectional carbon fiber preform at a fiber volume fraction of ${\phi}_{exp}=0.5$ are ${K}_{\perp ,exp}=6.40\times {10}^{-12}$ m${}^{2}$ and ${K}_{\parallel ,exp}=2.72\times {10}^{-11}$ m${}^{2}$, respectively. By applying these values to Equations (18) and (19) and assuming a hexagonal fiber arrangement with ${\phi}_{max}=90.69\%$, the values of A and B can be calculated, which allows for evaluating permeabilites for different fiber volume fractions. The resulting dependency of the permeability on fiber volume fraction and fiber orientation is shown in Figure 3. It should be stated here that this approach is not always valid for fibrous preforms because it is based on micro-scale assumptions; however, it is chosen to show the influence of an increasing fiber volume fraction on the permeability and thus on the resulting cavity pressure. It facilitates the calculation of the analytic solution of a one-dimensional Compression-RTM mold filling.

#### 4.1.2. Boundary Conditions

^{3}/s is applied. The injection time is 10 s which leads to a half filled cavity after the injection step. Second, a constant pressure of $3\times {10}^{5}$ Pa is set at the inlet until the cavity is half filled. In the compression step, the compression velocity is set to ${v}_{comp}=0.1$ mm/s so that the cavity is fully filled with a final height of ${h}_{t=20\phantom{\rule{0.166667em}{0ex}}s}=2$ mm and a final fiber volume fraction of ${\phi}_{t=20\phantom{\rule{0.166667em}{0ex}}s}=0.5$.

#### 4.2. Analytic Solution

#### 4.3. Simulation Results

#### 4.3.1. Results for Injection-RTM Boundary Conditions

^{®}and the analytic solution. The graphs show a linear increase of the injection pressure and all three graphs are indistinguishable.

#### 4.3.2. Results for Compression-RTM Boundary Conditions

^{®}.

## 5. Application Examples of CRTM Mold Filling Simulations

#### 5.1. Application 1: Complex Geometry

#### 5.2. Application 2: Sandwich Part

## 6. Summary and Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A. Analytic Solution of 1D Compression RTM

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**Figure 3.**Permeability after Gebart, using the measured values ${K}_{\parallel ,exp}=2.72\times {10}^{-11}$ m${}^{2}$ and ${K}_{\perp ,exp}=6.40\times {10}^{-12}$ m${}^{2}$ at ${\phi}_{exp}=0.5$.

**Figure 4.**Pressure distribution in x-direction in the plate at the end of the injection step with a filling up to $0.1$ m.

**Figure 6.**Pressure increase for a constant inlet pressure of $3\times {10}^{5}$ Pa. The analytic solutions are compared to the numerical solution using OpenFOAM at four different locations.

**Figure 7.**Pressure distribution in the x-direction in the plate at the end of the compression step with a filling up to $0.2$ m.

**Figure 8.**Pressure increase at the inlet (set to a wall boundary condition) while Compression-RTM boundary conditions are applied.

**Figure 9.**Simulation model of the complex part with the location of inlet, outlet and three pressure sensors.

**Figure 12.**Cavity pressure development for sensors ${p}_{1}$, ${p}_{2}$ and ${p}_{3}$ of the complex part.

**Figure 13.**Simulation model of the sandwich part with the main flow direction and the location of two pressure sensors.

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**MDPI and ACS Style**

Seuffert, J.; Kärger, L.; Henning, F. Simulating Mold Filling in Compression Resin Transfer Molding (CRTM) Using a Three-Dimensional Finite-Volume Formulation. *J. Compos. Sci.* **2018**, *2*, 23.
https://doi.org/10.3390/jcs2020023

**AMA Style**

Seuffert J, Kärger L, Henning F. Simulating Mold Filling in Compression Resin Transfer Molding (CRTM) Using a Three-Dimensional Finite-Volume Formulation. *Journal of Composites Science*. 2018; 2(2):23.
https://doi.org/10.3390/jcs2020023

**Chicago/Turabian Style**

Seuffert, Julian, Luise Kärger, and Frank Henning. 2018. "Simulating Mold Filling in Compression Resin Transfer Molding (CRTM) Using a Three-Dimensional Finite-Volume Formulation" *Journal of Composites Science* 2, no. 2: 23.
https://doi.org/10.3390/jcs2020023