# Numerical modeling of vacuum-assisted resin transfer molding using multilayer approach

Raounak Loudad, Abdelghani Saouab, Pierre Beauchene, Romain Agogue, Bertrand Desjoyeaux

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Raounak Loudad, Abdelghani Saouab, Pierre Beauchene, Romain Agogue, Bertrand Desjoyeaux. Numerical modeling of vacuum-assisted resin transfer molding using multilayer approach. Journal of Composite Materials, 2017, 51 (24), pp.3441-3452. 10.1177/0021998316687145. hal-01558436

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# Numerical modeling of vacuum-assisted resin transfer molding using multilayer approach

Raounak Loudad<fnref n="1" />, Abdelghani Saouab<fnref n="1" />, Pierre Beauchene<fnref n="2" />, Romain Agogue<fnref n="2" /> and Bertrand Desjoyeaux<fnref n="3" />

## Abstract

Vacuum-assisted resin transfer molding (VARTM) is a very suitable solution for composite manufacturing industry. It allows the manufacturing of large and complex shape parts at low costs. However, the simulation of this process is complicated due to myriad physical phenomena involved, specifically the strong coupling between the resin flow and the preform compressibility, i.e. hydro-mechanical coupling. Moreover, the use of the distribution medium involves two types of flow: Planar flow and through-the-thickness flow. These flows cannot be considered together by a 2D model. On the other hand, 3D models require an important amount of computation time. This article presents a VARTM modeling approach that takes into account the hydro-mechanical coupling and the coexistence of planar and transverse flows. The proposed modeling approach allows the simulation of the infusion process in the case of multilayer preform with different materials and orientations, including the distribution medium. This model is validated experimentally based on several infusions.

## Keywords

Polymer-matrix composites, finite element analysis, vacuum-assisted resin transfer molding, process simulation, permeability

## Introduction

Vacuum-assisted resin transfer molding (VARTM) is a closed mold process that allows the manufacturing of high-performance composite parts. It is also known as vacuum infusion (VI),<fnref n="1" /> vacuum bag resin transfer molding (VBRTM),<fnref n="2" /> resin injection under flexible tooling (RIFT),<fnref n="3" /> Seemann composites resin infusion molding process (SCRIMP™)⁴ and liquid resin infusion (LRI).⁵ This process consists in placing the preform fabric between a half rigid mold and a vacuum bag. Then, a vacuum is generated inside the mold, making the vacuum bag compact to the preform and the resin infuses into the preform. This solution is very cost efficient, particularly for large parts with complex shapes. However, its understanding is still very limited. In fact, the flexibility of the vacuum bag makes the part thickness vary depending on the resin pressure. The variation in the part thickness, and thereby in its fiber volume fraction, results in changes in the preform permeability, and varies the resin pressure. This mutual influence,

between the resin flow and the preform deformation, is called the hydro-mechanical (HM) coupling.

In order to ensure the mold filling in the case of large parts, a distribution medium (DM) of very high permeability is placed between the vacuum bag and the preform. The use of the DM accelerates the preform impregnation by adding the filling through the thickness direction, also called transverse flow.

The modeling of the infusion process has been widely studied in the literature. Several analytical

<footnote n="1">¹Laboratoire Ondes et Milieux Complexes, Normandie Université, France</footnote>

<footnote n="2">²Département Matériaux et Systèmes Composites, Office National d'Etudes et de Recherches Aérospatiales (ONERA), France</footnote>

<footnote n="3">³SAFRAN Nacelles, France</footnote>

<footnote>**Corresponding author:**
Abdelghani Saouab, Laboratoire Ondes et Milieux Complexes, UMR CNRS 6294, LABEX EMC3, Normandie Université, 53, rue de Prony, CS 80540, 76058 Le Havre Cedex, France.
Email: abdelghani.saouab@univ-lehavre.fr</footnote>
and numerical methods have been developed for this purpose.

The analytical methods have been used to study the infusion in simple unidirectional cases. These studies are divided into two categories: on one hand, the study of HM coupling in infusion process without the use of the DM,⁶⁻⁸ and on the other hand, the study of flow front kinetics in infusion processes using the DM by simplifying the HM coupling model.⁹⁻¹²

Several numerical approaches have been used to study infusion processes. Many authors have developed models based on finite difference method.¹³,¹⁴ Kessels et al.¹⁵ have modeled RIFT process in 2.5D using finite volume method. Gantois et al.¹⁶ have developed a modeling approach based on boundary element method. Rouhi et al.¹⁷,¹⁸ proposed a dual-scale HM coupling of the infusion process. Sirtautas et al.¹⁹ developed a mesoscopic model for draping and infusion simulation. Poorzeinolabedin et al.²⁰ modeled RIFT process using 2.5D PAMRTM code without considering the HM coupling.

Celle et al.⁵ and Dereims et al.²¹ have proposed a non-isothermal finite element model of infusion in which the flow is governed by Stokes law in the DM and by Darcy law in the preform. These models are based on a mixed formulation using P1 + P1 elements and Arbitrary Lagrangian Eulerian (ALE) formulation.

Control volume finite element method (CVFEM) has been widely used in the literature to simulate RTM and infusion processes. Kang et al.² have developed a diphasic CVFEM model of resin infusion in 3D, which allows to simulate the creation of dry zones. Dong²² has proposed an adaptation of the 3D CVFEM modeling called “Equivalent medium method”. This adaptation consists in increasing the thickness of the DM so as to mesh the structure conveniently.

In order to reduce the computation time of 3D modeling, some authors (Calado and Advani,²³ Chen et al.²⁴ and Yoon and Dolan²⁵) have modeled the resin flow in 2D by using an equivalent permeability that takes into account the flow front shape. These models have been validated by comparing 3D models results. Simancek and Advani²⁶ proposed to homogenize the DM and the preform permeability and introduced a correcting factor so as to have the same front advance. Han et al.⁴ and Kang and Lee²⁷ have modeled SCRIMP using a hybrid 2.5D-3D CVFEM model.

In sum, since the infused parts have usually shell-like shapes, it is suitable to model them in 2D. However, the coexistence of the planar flow and the transverse flow, involved by the DM, makes the flow happen in 3D. This leads to the modeling dimensions dilemma between simplified 2D modeling and time consuming 3D modeling. In the case of 2D modeling, the transverse flow cannot be considered and the superposed

layers with different materials and orientations are homogenized into one.²³⁻²⁶ Whereas in 3D modeling, a fine mesh is required to guarantee convenient shape factor elements, since the part thickness is very small comparing to the other directions²⁴,²²,²⁸ which increases the computational time.

Another alternative has been introduced by Young²⁹ who has developed a two-layer model, one modeling the DM and the other the preform. This model was validated analytically based on simplifying assumptions such as considering constant permeability or equal constant porosity in both layers.

In this paper, we propose a model of mold filling by VARTM that takes into account the HM coupling with both planar and transverse flows. This model is based on a multilayer approach that is less time consuming than 3D modeling.

## Governing equations: HM coupling

The fluid flow through deformable fibrous media has been studied by many authors.⁹⁻¹²,³⁰ In this study, we use the model proposed by Kempner and Hahn.³¹ This model is based on Darcy equation³² and the mass conservation equation in a deformable elementary representative volume (ERV). The combination of these equations leads to the following governing equation of the resin pressure P

$$ \nabla \left( \frac{-K_{ij}}{\mu} \nabla P \right) = \frac{1}{V_f} \frac{\partial V_f}{\partial t} + \frac{1}{V_f} u_s \frac{\partial V_f}{\partial t} \quad (1) $$

where $V_f$ is fiber volume fraction, $K_{ij}$ the medium permeability, $\mu$ the viscosity, and $u_s$ the solid velocity.

The second term in the right hand equation is negligible because the fiber velocity is negligible comparing to fluid velocity.⁶ The governing equation of the pressure is then simplified

$$ \nabla \left( \frac{-K_{ij}}{\mu} \nabla P \right) = \frac{1}{V_f} \frac{\partial V_f}{\partial t} \quad (2) $$

The force equilibrium in the porous medium leads to the relationship between the resin pressure P and the preform compressibility $\sigma$. This relationship is given by the theorem of Terzaghi³³

$$ \sigma = P_{atm} - P \quad (3) $$

where $P_{atm}$ is the atmospheric pressure.

The flow modeling requires the behavior laws of the fibrous medium in terms of permeability and compressibility. These physical quantities evolve during the infusion. In fact, the fiber volume fraction $V_f$ is
expressed in terms of compressibility

$$V_f = F_c(\sigma) \qquad (4)$$

whereas the permeability varies as a function of the fiber volume fraction

$$K_{ij} = F_p(V_f) \qquad (5)$$

The HM coupling represents the relationship between the fluid flow and the fibrous medium deformation. This coupling is modeled by the equation system (2) to (5) combined with the boundary conditions which are the imposed pressures at the injection and vent gates.

## Numerical resolution scheme

The HM equation system is solved numerically using the CVFEM.34 This method, based on the Eulerian approach, uses a fixed mesh which saves the remeshing computation time. In fact, instead of moving the meshed domain after each time step, this domain evolves by changing the filling factor of the control volumes using the volume of fluid (VOF) method (Figure 1(a)). However, although this method is fast, it does not ensure the accurate application of the boundary conditions at the flow front. Actually, the flow front position is estimated by interpolation between nodes, whereas the boundary conditions are

applied on the nodes. To address this problem, a mesh refining method at the flow front region called floating imaginary nodes and elements (FINE)34 is used in this study. This method consists in dividing the partially filled elements into completely filled and empty sub-elements.

In order to model the infusion of stack of different materials and orientations, we model the HM coupling in each layer with a surface mesh that includes a degree of freedom on the thickness. The transverse flow is modeled by 1D elements that link the surface mesh as shown in Figure 1(b).

As in the conventional CVFEM, the mass balance is rigorously respected within the control volume by integrating fluxes on the control volume borders. To do so, the divergent theorem is applied on the pressure governing equation (2)

$$\int_{CS} \left( \frac{-\bar{\bar{K}}}{\mu} \nabla P \right) \cdot \bar{n} \, dS = \int_{CV} \frac{1}{V_f} \frac{\partial V_f}{\partial P} \frac{\partial P}{\partial t} dV \qquad (6)$$

Using the linear interpolation of the elements, the pressure gradient can be expressed in terms of nodal pressures and the nodes coordinates.34 The source term is integrated on the control volume and expressed in terms of the present nodal pressure, the nodal pressure at the previous time step and the time step which corresponds to an implicit scheme.

<figure><img src="image_2.png" /><figcaption>**Figure 1.** Control volume finite element method (CVFEM) computation field in (a) the conventional 2D approach and in (b) the multilayer approach.</figcaption></figure>
And finally, the system matrix is constructed and resolved after applying the boundary conditions.

In the multilayer modeling approach, the system global matrix contains less than half of the non-null coefficients of the system global matrix in the 3D modeling. Moreover, 3D modeling generates an error due to the homogenization of properties, such as the porosity, in the nodes shared by two layers, which requires special treatment in the flow front or mesh refinement. All these considerations makes the computation time in the multilayer approach less important than in 3D modeling.

## Experimental characterization

In order to validate experimentally the proposed model of VARTM, we characterized experimentally the compressibility and the permeability behavior laws for both reinforcement material and DM. These behavior laws were used to simulate the experimental infusions that we performed using these materials.

### Compressibility

*Preform.* Before the beginning of each infusion, we subjected the infused stack to three pre-compaction cycles in order to increase the fiber volume fraction of the preform. These cycles were performed under the flexible bag using the vacuum. Figure 2 shows the total thickness evolution over time in the case of plate infusion described in “Experimental infusion recording” section.

This total thickness of four reinforcement layer and DM is measured on a point located at 29 cm from the injection line.

The preform has a viscoelastic behavior and a plastic behavior related to the nesting of the layers. Also, this behavior depends on whether the preform is dry or wet. In this study, we modeled the compressibility behavior law with a nonlinear elastic model. Hence, in order to

characterize the closest behavior law to the preform compressibility during the infusion, we performed the same protocol of compressibility using the universal testing machine. Figure 3 presents the experimental thickness and compressibility versus time applied on a sample of four layers of the reinforcement used in this study.

From Figure 3, we notice the existence of plastic strain caused by the layers nesting. Relaxation phenomena are also observed from the asymptotic evolution of the thickness while the compressibility remains constant. In addition, when the thickness is expressed in terms of compressibility, we notice hysteresis behavior from the difference between loading and unloading curves. These relaxation behavior and hysteresis behavior prove that the preform has a viscoelastic behavior. Moreover, the compressibility behavior differs depending on whether the preform is dry or wet.

After the pre-compaction cycles, the compressibility is measured during the unloading of the sample as during the infusion, where the preform compressibility decreases as a result of the increase of the fluid pressure. This measured compressibility is assumed to be representative of the fabric behavior during infusion, although the preform is unloaded with the different velocities depending on the distance from the injection.

This compressibility is modeled by Grimsley model³⁵ expressed in equation (7)

$$H = \frac{A\sigma + B}{C\sigma + 1} \qquad (7)$$

where $A = 7.12 \times 10^{-7} \text{ m} \cdot \text{Pa}^{-1}$; $B = 3.03 \text{ mm}$; $C = 3.77 \times 10^{-4} \text{ Pa}^{-1}$ and $H$ the thickness of the four layers sample. The relationship between the preform thickness $H$ and its fiber volume fraction $V_f$ is given by the following equation³⁵

$$H \cdot V_f = H_{ini} \cdot V_{fini} \qquad (8)$$

<figure><img src="image_3.png" /><figcaption>**Figure 2.** The evolution of the infused stack thickness at 29 cm from the injection line during pre-compaction cycles and infusion-plate infusion case.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>**Figure 3.** Four layers preform compressibility and thickness following the infusion protocol.</figcaption></figure>
where $H_{ini}$ and $V_{fin}$ are, respectively, the initial preform thickness and initial fiber volume fraction. The Grimsley model is very suitable to infusion process because, unlike power model, it can fit low compressibility values accurately. Figure 4(a) shows that this model fits perfectly the experimental data in the infusion application field of compressibility.

<figure><img src="image_5.png" /><figcaption>**Figure 4.** Experimental compressibility behavior law of four layers preform (a) and the distribution medium (b).</figcaption></figure>

**Distribution medium.** The DM compressibility has also been measured during the unloading. It is modeled by a power model with high accuracy as shown in Figure 4(b).

## Permeability

The permeability is measured by applying air flow rates through the sample and extracting the pressure at several positions. This experiment is repeated for many fiber volume fractions in the compressibility application field. The use of air to measure the permeability has been widely used in the literature,³⁶⁻⁴⁰ and it requires vigilance to not exceed the limit air velocity so as the Reynolds number condition for laminar flow stays respected. Scholz et al.³⁶ has proposed a correcting factor related to air compressibility. In our measures this factor is always close to one.

**Planar permeability.** The planar permeability bench contains four pressure sensors at the horizontal and vertical directions and three on the diagonal direction as shown in Figure 5(a). The air flows from the central injection point to the vent located at the borders.

For a specific fiber volume fraction value, the experimental pressure field is measured. Then, from this

<figure><img src="image_6.png" /><figcaption>**Figure 5.** Experimental device (a) planar permeability bench, (b) transverse permeability bench, and (c) infusion recording device (front tracking and DIC).</figcaption></figure>
pressure field and the applied air flow rate at the injection point, a reverse analysis using COMSOL™ allows the identification of the planar permeability tensor coefficients, which are the permeability in both principal directions and the orientation angle.⁴¹

Figure 6 presents the preform planar permeability in the principal directions $K_1$ and $K_2$ versus the fiber volume fraction. These behavior laws are modeled by a power model.

Due to its low thickness of the DM and its high permeability, the planar permeability of the DM is highly influenced by the border effects. In this study, a constant value has been identified for the DM planar permeability in the flow direction by a reverse analysis on the infusions performed experimentally

$$K_{DM1} = 1.610^{-9}m^2$$

*Transverse permeability.* The transverse permeability is identified by injecting air through the thickness direction of the sample using the bench shown in Figure 5(b). In this bench, a pressure sensor is placed at the injection side, and the vent at the atmospheric pressure is located at the other side of the sample.

The transverse permeability $K_3$ is deduced from the injection relative pressure, the sample's thickness, the air flow rate and its viscosity using Darcy law. The preform transverse permeability versus the fiber volume fraction experimental curve is given in Figure 6. This behavior law is modeled by a power law with reasonable accuracy.

The DM transverse permeability is very high in comparison with the preform one. Hence, its influence on the flow is negligible as shown in equation (9)¹²

$$\frac{h_d + h_p}{k_T^t} = \frac{h_d}{k_d^t} + \frac{h_p}{k_p^t} \approx \frac{h_p}{k_p^t} \qquad (9)$$

where $h_p$ and $h_d$ mean the thickness of the preform and the DM, $k_p^t$ and $k_d^t$ are respectively their transverse permeability and $k_T^t$ their equivalent transverse permeability.

<figure><img src="image_7.png" /><figcaption>Figure 6. Preform permeability in the principal directions.</figcaption></figure>

In this study, we took a DM transverse permeability value of $10^{-6} m^2$ so as to neglect its influence.

## Experimental infusion recording

In order to validate the proposed model experimentally, two infusions were recorded and simulated. The recorded experimental data are the DM and the total thickness of the stack constituted of the preform and the DM and the flow front positions in the preform.

The thickness of the stack is measured by digital image correlation (DIC).⁴² This method consists in filming the vacuum bag from two different angles of view and deducing the distribution of its height. The flow front is tracked on both sides of the mold using two cameras positioned over and below the infusion bench as illustrated in Figure 5(c).

## Experimental validations

### First case: Plate infusion

*First case data.* This infusion case is performed using a silicone oil of 1 Pa.s viscosity. The infused stack is composed of four layers of the characterized preform and the characterized DM. The length of these layers is 50 cm and the injection pressure is $0.96 \ 10^5$ Pa, as the oil free surface was 30 cm under the mold (Figure 7(a)).

This infusion was simulated using the mesh presented in Figure 7(b). The upper surface mesh models the DM and the lower surface mesh models the four-layer preform.

### Results comparison

**Thickness.** Figure 8 presents the experimental and numerical thickness of the infused stack at the mold

<figure><img src="image_8.png" /><figcaption>Figure 7. Plate infusion case study: (a) case data, (b) numerical mesh and (c) numerical velocity vectors during infusion.</figcaption></figure>
filling time, with the x-axis representing the position in the infused plate. The experimental results are limited to 318 mm, which is the DIC camera field of vision. Increasing fluctuations in the experimental thickness

according to the position are observed in Figure 8. These fluctuations are due to the collapse of the vacuum bag into the DM under the difference between the fluid and external pressure. Hence, the numerical thickness corresponds to the maxima of these corrugations. Figure 8 shows a reasonable match between these results.

**Flow front kinetics.** The recorded pictures of the flow front are processed by ImageJ.⁴³ As shown in Figure 9, the flow front position in the DM can be easily identified thanks to the discontinuity between the wet and dry region. On the other hand, an unsaturated region exists in the preform between the saturated region and the dry region. This is caused mainly by the double scale porosity of the preform. Thus, one flow front position in the DM is tracked whereas both saturated and unsaturated flow front positions were recorded in the preform.

Since the numerical model does not consider the double scale porosity, only one numerical flow front is modeled in the preform. Figure 10(a) shows the numerical and experimental flow front kinetics on both sides of the mold. Again, the experimental results are limited to the field of vision of the cameras.

Figure 10(a) shows that the numerical front position in the DM side is close to the experimental results. This is due mainly to the fact that the DM permeability has been determined by reverse analysis. On the preform side, the numerical front agrees more with the experimental unsaturated front than the saturated one.

<figure><img src="image_9.png" /><figcaption>**Figure 8.** Total thickness distribution at the mold filling in the plate infusion case.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Figure 9.** Processed images of the infusion on both sides.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**Figure 10.** Numerical and experimental flow front kinetics in the plate infusion case using the measurable preform transverse permeability (a) and a lower one (b).</figcaption></figure>
This is because of the measured transverse permeability of the preform that is closer to the macropores permeability than to the micropores permeability.⁴⁴ In fact, since these pores are in a parallel configuration regarding through-the-thickness flow, the average

permeability is an arithmetic average that is dominated by the higher permeability,⁴⁵ in this case the macropores permeability.

If we use a lower transverse permeability of the preform, the gap between the flow front position in

<figure><img src="image_12.png" /><figcaption>**Figure 11.** Sensitivity analysis of the flow front kinetics on the planar permeability of the DM (a) and the preform (b) in the case of plate infusion.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**Figure 12.** Ply drop case study: (a) case data, (b) ply drop shape by DIC and (c) ply drop shape by simulation.</figcaption></figure>
the DM and the preform increases. Figure 10(b) presents the numerical flow front kinetics using a modified preform transverse permeability with a correcting factor of 0.1

$$K_{3\text{modified}} = 2.74 \times 10^{-15} V_f^{-9.4}$$

Whereas the measured permeability was (Figure 10(b))

$$K_{3\text{measured}} = 2.74 \times 10^{-14} V_f^{-9.4}$$

Figure 11(a) presents the numerical flow front kinetics in three cases where the DM planar permeability is slightly modified.

<figure><img src="image_14.png" /><figcaption>Figure 13. Total thickness distribution at the mold filling in the ply drop infusion case.</figcaption></figure>

Figure 11(b) presents the numerical flow front kinetics in three cases where the preform planar permeability is considerably modified. From this sensitivity study, we notice that the infusion is highly sensitive to the DM planar permeability and lowly sensitive to the preform planar permeability. This could be explained by the fact that the DM and the preform are parallel to the flow (Figure 7(c)), which means that the flow is dominated by the higher permeability.⁴⁵ The transverse permeability of the preform has an important influence on the gap between the flow front positions in the DM and the preform.

### Second case: Ply drop infusion

**Second case data.** We study, in this case, an infusion of a ply drop from 7 to 4 plies of the characterized preform. As in the previous case, the infusion is performed using the silicone oil of 1 Pa.s viscosity and the injection pressure is also equal to 0.96 x 10⁵ Pa. The data of this studied case are given in Figure 12(a).

### Results comparing

**Thickness.** Figure 12(b) presents the thickness distribution of the infused stack measured experimentally by DIC. These values were measured at the mold

<figure><img src="image_15.png" /><figcaption>Figure 14. Numerical and experimental flow front kinetics in the ply drop infusion case using the measurable preform transverse permeability (a) and a lower one (b).</figcaption></figure>
filling time. The DM corrugation can be noted in this
figure, which explains the variability of the experimen-
tal data in Figure 13.

In Figure 13, values covering one corrugation pitch
were extracted. A reasonable match is observed
between the experimental and the numerical results.
The maximal difference between the numerical curve
and the experimental fluctuations peaks is about
0.1 mm, which represents an error of 3%.

**Flow front kinetics.** The numerical and experimen-
tal flow front kinetics on the DM side are given in
Figure 14(a). In this figure, a good match is observed
between the numerical and experimental results until
200 mm, which is the end of the plate area of four
preform layers and DM. Then, in the DM, the experi-
mental flow front becomes faster than the numerical
one until 290 mm, after that, the experimental and the
numerical flow fronts evolve with a similar velocity and
a constant gap of 26 mm.

As in the previous case, we performed a simulation
using a modified transverse permeability of the preform
with a correction factor of 0.1 and we obtained numer-
ical flow front kinetics closer to the experimental results
(Figure 14(b)).

Again, this leads us to think that the measured trans-
verse permeability using air flow, which represents the
saturated permeability, is higher than the unsaturated
permeability that we have during the infusion. In fact,
the measured permeability is dominated by the perme-
ability of the macropores because the micropores and
the macropores are parallel to the flow during the meas-
ure.⁴⁵ Whereas during the infusion, the macropores are
filled in first place, and then the micropores are filled.
During the filling of the micropores, the micropores
and the macropores are in series. Hence the transverse
permeability in this case is dominated by the lower per-
meability,⁴⁵ i.e. the transverse permeability of the tows.

Conclusion

In this article, we presented a numerical modeling of the
infusion process in the case multilayer preform. The pro-
posed model takes into account the HM coupling and
the flow through the thickness direction. This model,
based on the proposed multilayer approach, saves a sig-
nificant amount of computation time compared to 3D
modeling.

The developed model is validated experimentally using
measured behavior laws and gives satisfying results.

The sensitivity study carried out on the permeability
values shows that the DM planar permeability plays the
most preponderant role in determining the flow front

velocity. Whereas the transverse permeability of the
preform determines the gap between the flow front pos-
itions in the DM and in the preform. This transverse
permeability was measured using a saturated flow,
which makes it equivalent to macropores permeability.
Hence, it does not correspond to the transverse filling
where the macropores are filled in first place and then
the micropores, making the filling of these pores in
series. The flow in this case is controlled by micropores
permeability. Based on this conclusion, dual scale por-
osity of the preform must be considered for a more
accurate transverse permeability.

Acknowledgment

The collaboration with SAFRAN Nacelles is gratefully
acknowledged.

**Declaration of Conflicting Interests**

The author(s) declared no potential conflicts of interest with
respect to the research, authorship, and/or publication of this
article.

Funding

The author(s) disclosed receipt of the following financial sup-
port for the research, authorship, and/or publication of this
article: the PRC Composites, French research project funded
by DGAC (French Civil Aviation Authority), involving
SAFRAN Group, ONERA (French Aeronautics and Space
Research Center) and CNRS (National Center for Scientific
Research).

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