Numerical Simulation of Air Entrapment During Resin Transfer

Molding

C. DeValve and R. Pitchumani*

Advanced Materials and Technologies Laboratory

Department of Mechanical Engineering

Virginia Polytechnic Institute and State University

Blacksburg, Virginia 24061-0238

*Author for correspondence; pitchu@vt.edu • Phone: +1 540 231 1776 • Fax: +1 540 231 9100

ABSTRACT

A critical issue in resin transfer molding (RTM) processes is air entrapment within the fiber

preform during the mold filling stage, leading to undesirable material characteristics such as

discontinuous properties and potential failure zones. An accurate prediction of local air

entrapment locations during mold filling is an essential step toward determining processing

conditions that lead to void-free filling. This study presents a numerical simulation of the

infiltrating dual-scale resin flow through the fiber preform combined with the capillary effects

within each fiber bundle applied to a commercially available plain weave fiber preform geometry.

Air entrapment locations within the fiber preform and the resulting void quantity are predicted

using the outcome of the numerical simulations. The numerical simulation results are used to

understand the effects of the preform fiber bundle volume fraction and resin injection rate towards

minimizing void entrapment and wasted resin during RTM processes.

1. INTRODUCTION

Composite materials fabricated through resin transfer molding (RTM) and similar methods often

exhibit defects from entrapped air within the fiber preform as a result of the resin infiltration

process. These void locations are detrimental to the overall integrity of the composite material,

resulting in potential failure zones and discontinuous material properties. The selection of the

fiber weave preform geometry and material, the resin type, and the mold complexity all affect the

resin flow field as it infiltrates the fiber bundles during the mold-filling stage of RTM processes.

In addition, the processing parameters imposed on the system, such as injection flow rates in

RTM or vacuum pressure levels in vacuum assisted resin transfer molding (VARTM), have a

significant effect on the mold filling process and, in turn, affect the final location and relative size

of the entrapped air voids within the resulting cured composite material.

The flow through the fibrous preform is fundamentally governed by the preform permeability of

the fiber bundles, which are modeled as porous media. Permeability is a measure of the resistance

offered to the flow by the porous structure of the preform. The majority of RTM methods utilize

some type of preform fabric composed of woven bundles of fiber tows, where these bundles can

be idealized as arrangements of aligned rigid cylindrical fibers. Several studies are reported in the

literature on relating the fiber bundle volume fraction to the transverse and longitudinal

permeability of these fiber bundles for idealized rectangular and triangular packing arrangements

of the individual fibers tows within the fiber bundle [e.g. 1,2]. Drummond and Tahir [3]

developed an analytical solution for this problem using a sum of solutions for the Stokes equation

with balanced singularities inside each unit cell of the flow field. A full review of experiments

and theoretical predictions outlining permeability values for low Reynolds number flow through

fibrous porous media was conducted by Jackson and James [4]. Also important to the resin

infiltration into the fiber bundles is the capillary pressure at the resin flow front, which becomes

increasingly significant at the relatively high fiber bundle volume fractions generally found in

RTM preform fabrics [5]. The capillary force cause the resin to be drawn into the fiber preform

independent of external processing parameters, and is fundamentally a function of the fiber

bundle volume fraction, the individual fiber radius, and the surface tension and wetting angle of

the infiltrating resin [6].

The formation of entrapped air locations is primarily the result of the dual-scale nature of the resin

infiltration, consisting of flow through the macroscale channels around the fiber bundles

combined simultaneously with flow through the microscale pores within the fiber bundles around

the individual fibers [7]. The difference between the infiltrating resin flow fronts in these two

flow regimes causes uneven filling of the fibrous preform, and as a result the surrounding air

initially within the mold may become entrapped within the preform as the resin migrates through

and around the fiber bundles. To model the resulting void entrapment in RTM and similar

processes, several techniques have been explored in the literature. Parnas [8] presented a

simplified model of void formation using Darcy's law combined with an ideal gas expression for

tracking the air entrapped in a fiber bundle where the resin was considered to permeate radially

inward through the fiber bundle cross-section. Foley and Gillespie [9] built upon on the model

proposed by Parnas [8] and studied the effects of individual fiber diameter and fiber bundle count

on the resulting size of the entrapped air void within the fiber bundle. Spaid and Phelan [10] used

the lattice Boltzmann method to simulate flow through square-packed fiber tows and showed that

the numerical simulations closely matched similar experimental results. A control volume

approach to air entrapment prediction was investigated by Jinlian and Xueming [11] and applied

to two dimensional unit cell cross-sections of geometrically simplified multi-layer woven fabrics,

where the resulting simulations were able to predict void locations in the low permeability regions

of the fiber architecture.

In this study, a numerical model is developed for resin permeation through a preform geometry

comprised of stacked layers of a commercially available plain weave fabric. Resin is forced

through the preform according to a specified inlet plane resin velocity and allowed to permeate

the considered geometry while also accounting for the capillary forces at the resin-air interface. In

addition, the effects of nesting of fiber bundles between adjacent layers of fabric are included in

the model geometry. Simulations are performed at various values of the inlet plane resin velocity

and fiber bundle volume fraction in order to explore their individual effects on the location and

relative size of air entrapment within the preform architecture. Based on the numerical simulation

results, the effects of the processing and the preform parameters on void content and resin

wastage are elucidated. Section 2 of the paper describes the model formulation, the results of the

study are presented and discussed in Section 3, and conclusions are drawn from the simulation

results in Section 4.

2. NUMERICAL MODEL

The geometry considered in the current study consists of a unit cell with multiple nested layers of

plain weave fabric, illustrated in Figure 1. Figure 1a shows two layers of fabric simply stacked in

an “un-nested” configuration, which is presented to contrast the nested configuration of two fabric

layers shown in Figure 1b, as considered in the modeling. The fabric geometry chosen for

Figure 1. The fiber preform architecture shown with (a) two layers of "un-nested" plain weave

preform, and (b) two layers of nested plain weave preform

the study is that of a commercially available WR10/3010 plain weave fabric from Owens Corning

with its associated fiber radius, fiber bundle dimensions, and inter-bundle spacing. The weave of

the fiber bundle is considered to be a sinusoidal function and the cross section of each bundle is

defined to be approximately lenticular in shape. In actuality, each fiber bundle consists of

numerous individual fiber tows, which is modeled by describing the fiber bundle as a porous

medium with a permeability defined as a function of the fiber bundle volume fraction and the

individual fiber tow radius, considering the fiber arrangement within the bundle to be triangular

packing. The preform geometry described above is studied by defining thin slices of the stacked

fabric layers in the direction of fluid flow, as illustrated in Figure 2, and simulating the resin

permeation through three such two-dimensional planes: (1) at the middle of the unit cell (Fig. 2a),

(2) at a quarter of the width of the unit cell (Fig. 2b), and (3) at the edge of the unit cell (Fig. 2c).

It can be observed from the unit cell in Figure 1 that the three-dimensional fiber architecture is

anti-symmetric about the middle plane defined in Figure 2a, which implies that the quarter width

(edge) slice is inverted at the quarter width (edge) on the other side of the middle plane. However,

in a two-dimensional modeling, the flow is identical through these inverted configurations and as

a result, the simulations on one half of the unit cell are representative of the flow through the

entire domain. A permeability tensor is defined along the curvature of the fiber bundle based on

projecting the longitudinal and transverse permeability values of the idealized aligned rigid fiber

bundles onto the local axis of the woven fiber bundle throughout the unit cell. The resin properties

were chosen to be those of Shell EPON Resin 828 with Shell Epicure 3274 catalyst.

The governing mathematical equations describing the resin flow through the macroscale inter-

bundle regions and through porous fiber bundles are the conservation of mass and momentum

along with the equation associated with the volume of fluid (VOF) method [12] used to track and

Figure 2. Cross sectional slices of the (a) middle, (b) quarter-width, and (c) edge planes of the

plain weave architecture presented in Fig. 1. The dark gray color indicates the fiber bundles and

the light gray color indicates the air initially surrounding the fiber preform.

advance the resin/air interface during the filling process. In the VOF method, the volume fraction

of the resin in a computational cell, �, is governed by:

���� � � · ���� � 0 (1)

where � is the time, and � is the velocity vector. The continuity equation is given by:

���� � � · ���� � 0 (2)

where � is the density of the fluid. Conservation of momentum is enforced through the Navier-

Stokes equation combined with two source terms, one describing the flow through the porous

fiber bundle and the other imposing the capillary body force at the resin-air interface, written as

��� ���� � � · ����� � ��p � � · ����� � ����� � F��� � F��� (3)

where p is the pressure, � is the viscosity of the respective fluid, F��� is the porous media source

term, and F��� is the capillary source term. The source term corresponding to the flow through the

porous fiber bundle was expressed using Darcy's Law as

F��� � �µ�κ���u (4)

where �κ� is the permeability tensor of the porous media. The permeability values were calculated

using the relationships with the fiber bundle volume fraction shown graphically in Figure 3,

Figure 3. Relationships between the dimensionless longitudinal [13] and transverse [14]

permeability and the fiber bundle volume fraction, for triangular packing of individual fibers

within the fiber bundle.

which presents the permeability normalized by the square of the individual fiber radius, r�. The

longitudinal permeability values in Figure 3 are based on an analytical permeability model

presented in [13] and the transverse permeability values were taken from [14].

By definition, the capillary forces are present only at the resin-air interface within the flow field

of the geometry. However, Brackbill et al. [15] have developed a continuum method for modeling

surface tension effects across the interface of two adjacent fluids. By using the divergence

theorem, the capillary effects at the resin-air interface can be converted to a body force and

expressed as a source term in the momentum equation [16], written as

F��� � 2!K�#��# (5)

where ! is the surface tension of the resin-air interface, K is the curvature of the resin-air

interface, and �# is the local volume fraction of the resin. In the VOF model, the volume fraction

variable is defined as 0 for purely resin and 1 for purely air. The interface of these two phases is a

thin region where the volume fraction varies between 0 and 1, and a value of 0.5 is chosen to

represent the approximate transition between phases. Therefore, it is evident that the gradient of

the volume fraction term in equation (5) will be non-zero only along this thin region at the

interface, satisfying the physical presence of the capillary forces only at the resin-air interface.

Within the idealized fiber bundle of straight aligned rigid fibers, the capillary force occurs in two

principal directions, causing the resin to wick radially inward perpendicular to the fibers as well

as longitudinally through the fibers. In the first case, the capillary pressure forcing the resin

radially into the fiber bundle (perpendicular to the fiber tows) can be expressed according to [9] as

P���,� � 1π' !cos�+ � x�

r� -. π

2√3v� � cos �x�3π4�π4

dx (6)

where + is the wetting angle of the resin, r� is the radius of the individual fiber tow, and v� is the

volume fraction of the fiber bundle. The integral here is necessary to average the pressure as the

capillary width changes according to perpendicular flow between two adjacent cylindrical fibers.

In the case of flow longitudinal to the aligned rigid fibers the capillary width is constant as the

resin is wicked along the channels, and consequently the capillary pressure is constant as well and

is written according to [6] as

P���,6 � 2!v�cos �+�r��1 � v�� (7)

Following the foregoing approach, the capillary pressure values can be calculate at the resin-air

interface in the two principle resin infiltration directions. In turn, interface curvature values can be

determined according to

P��� � !K (8)

and implemented into the source term of equation (5).

Equations (1)–(8) provide a complete description of the resin flow through the preform and are

solved to investigate the air fraction evolution through the plain weave preform architecture

described in Figure 2. The fluid density and dynamic viscosity of the resin were taken to be 1.22

g/cm2 and 0.7 Pa·s, respectively, while the resin-air interface was described with a surface tension

of 0.065 N/m and a contact angle of 30 degrees. . . In addition, the individual fiber tows within

the fiber bundle were considered to be 10 µm in diameter. A constant and uniform resin velocity

was imposed as the boundary condition at the inlet plane of the unit cell geometry and a constant

pressure of zero was enforced at the outlet plane. The top and bottom faces of the unit cell were

defined as periodic boundaries based on the geometry of the two-dimensional fiber arrangements

as seen in Figure 2a–2c. It must be mentioned that the domain considered for the modeling, as

shown in Figures 2a–2c, consists of a full repeating unit cell and a quarter unit cell length

upstream and a quarter unit cell downstream. This extended unit cell geometry allows the initially

uniform resin flow front to migrate naturally through and around the fiber bundles before entering

the complete unit cell of study (which is the focus of the results presented in Section 3), thereby

better approximating the actual resin flow through the preform geometry. The domain geometry

and the model formulation were implemented in and solved using the commercial ANSYS

Fluent™ software.

3. RESULTS

Parametric studies were conducted on investigating the effects of the fiber volume fraction in the

bundles, 78, and the resin inlet velocity, �9:;<=, on the resulting void fraction evolution with time

in each of the three planar slices identified in Figure 2. Four different fiber bundle volume

fractions of 0.5, 0.6, 0.7 and 0.8 as well as four different inlet plane resin velocities of 0.25, 0.50,

1.00, and 2.00 cm/s were studied in each of the three planes, for a total of 48 parametric runs. In

each run, the flow progression with time and the corresponding overall void fraction with time

were recorded. The results of these parametric runs are presented and analyzed in this Section.

Figure 4 presents snapshots of the resin infiltrating the edge plane (Fig. 2c) of the plain weave

fiber architecture with a fiber bundle volume fraction of 0.8 and an inlet plane resin velocity of

2.00 cm/s at various times throughout the mold filling process. The resin is injected uniformly at

the left plane of the unit cell as shown in Figure 2c and allowed to permeate through the entire

geometry. It can be observed from Figure 4a, t = 0.05 s, that the resin first follows the path of

least resistance through the macroscale channels in between the fiber bundles. Also notice the

periodic nature of the resin flow enforced on the top and bottom faces of the unit cell. In Figure

4b, t = 1 s, it is evident that the resin flow front has now reached the exit plane of the unit cell for

the macroscale channels, and the resin is beginning to permeate into the fiber bundles. In Figure

4c, t = 10 s, the resin has permeated well into the fiber bundles and has entrapped significant

pockets of air within the cross-running fiber bundles as well as the longitudinally running fiber

bundles. Figure 4d, t = 20 s, presents a pictorial description of the entrapped air pockets within the

fiber bundles after a long time from the start of infiltration as the void content becomes nearly

steady over time.

Several observations can be made regarding the void formation in each of the fiber bundles

included in the present simulation: It is evident that the voids in the first cross-running bundles

(seen as two quarter bundle sections at the left edge of the frame in Fig. 4d) are larger than the

voids in the center cross-running bundle (the full bundle cross section in Fig. 4d), which are both

greater than the voids in the third cross-running fiber bundles (seen as two quarter bundle sections

at the right edge of the frame in Fig. 4d). This suggests that as the resin moves from left to right

Figure 4. Snapshots of the resin (gray area) infiltrating through the edge two-dimensional plane

(Fig. 2c), for a fiber bundle volume fraction of 0.8 and an inlet plane resin velocity of 2.00 cm/s at

t = (a) 0.05 s, (b) 1 s, (c) 10 s, and (d) 20 s.

through adjacent unit cells downstream from the present geometry, the amount of air entrapped in

the cross-running fiber bundles will decrease. It can also be seen that the void remaining in the

center cross-running fiber bundle is larger in diameter than that of the void remaining in the

longitudinal fiber bundle. In general, the qualitative observations from the results of the edge

plane presented in Figure 4 can be similarly found in the results of the middle plane geometry

with the same fiber bundle volume fraction of 0.8 and inlet plane resin velocity of 2.00 cm/s,

which are omitted for brevity. Furthermore, the trends observed in the numerical simulations for

the additional parametric combinations of the edge plane and middle plane cases were similar to

those presented in Figures 4, with the principal difference being the final volume of the entrapped

void as the system approaches its steady state.

Figure 5 presents snapshots of the resin infiltrating the plane at the quarter-width of the unit cell

(Fig. 2b) of a plain weave fiber architecture with a fiber bundle volume fraction of 0.8 and an inlet

plane resin velocity of 2.00 cm/s at various times throughout the mold filling process. The

snapshots in Figure 5 correspond to equivalent time instants as shown in Figure 4, as well as the

same flow conditions and the same fiber bundle volume fraction as in Figure 4 to facilitate

comparison between the flow fields of the edge plane with the plane at the quarter-width. In

Figure 5a, t = 0.05 s, the resin again follows the path of least resistance and rapidly fills the

macroscale channels within the unit cell. The resin flow front reaches the macroscale channels

exit planes while simultaneously permeating a significant distance into the fiber bundles within

the preform geometry in Figure 5b, t = 1 s. A comparison between Figures 5b and 4b illustrates

Figure 5. Snapshots of the resin (gray area) infiltrating through the two-dimensional plane at the

quarter-width (Fig. 2b) of the unit cell, for a fiber bundle volume fraction of 0.8 and an inlet plane

resin velocity of 2.00 cm/s at t = (a) 0.05 s, (b) 1 s, (c) 10 s, and (d) 20 s.

that the resin has permeated much further into the fiber bundles in the plane at the quarter-width

than along the edge plane for the same geometry and inlet flow rate and at the same instant in

time. This trend becomes even more apparent in Figures 5c and 5d as the resin continues to

permeate into the fiber bundles in the plane at the quarter-width more rapidly than the

corresponding cases in Figures 4c and 4d, until reaching a nearly steady air void content a t = 20 s

(Fig. 5d). Note that in Figure 5d the resin has almost completely saturated the longitudinal fiber

bundles, leaving nearly no entrapped air in these regions. However, there are significant amounts

of air entrapped in the cross running fiber bundles, where the largest void formation occurs in the

fiber bundle in the center of the unit cell geometry in Figure 5d. In general, the same trends were

observed in the numerical simulations for the other parametric combinations for the flow along

the plane at the quarter-width of the unit cell, except that the air entrapment was seen to reduce

significantly at the low fiber bundle volume fraction and a high inlet plane resin velocity.

In order to quantitatively compare the void fraction evolution with time, the air entrapped within

the unit cell, 7>9#, was tracked over time for the various fiber bundle volume fractions and resin

velocities studied for the middle plane (Fig. 2a), the edge plane (Fig. 2c), and the plane at the

quarter width (Fig. 2b), presented in Figures 6 and 7, respectively. Figure 6 presents the void

content along the edge plane over time, where it is evident that initially the void content within

the unit cell decreases rapidly at all four inlet resin velocity values (Figs. 6a–6d and Figs. 7a–7d)

corresponding to the quick infiltration of the macroscale channels within the unit cell geometry.

However, after the initially quick decrease in void content, the entrapped air amount within the

unit cell begins to level out, appearing to then asymptotically approach zero, as the resin

continues to infiltrate the fiber bundles. Eventually, the void fraction reaches a near steady-state

condition as the air entrapment amount becomes approximately constant with time. From Figures

Figure 6. Percentage of air remaining in the unit cell of the edge two-dimensional plane for a inlet

plane resin velocity of (a) 0.25 cm/s, (b) 0.50 cm/s, (c) 1.00 cm/s, and (d) 2.00 cm/s

6 and 7 it is also seen that the initial decrease in the void content within the unit cell is more rapid

as the fiber bundle volume fraction increases for fixed inlet plane resin velocity values. The

sharper initial decrease in the void fraction for the fiber bundle volume fraction of 0.8 can be

explained by the fact that there is relatively less air within the entire unit cell before resin

infiltration, resulting in a sharper transition between primarily macroscale channel infiltration and

microscale pore infiltration. Conversely, in the case where the fiber bundle volume fraction is

equal to 0.5 the air entrapment trend is more gradual over time because of the faster resin

infiltration into the microscale pores of the unit cell as a result of the lower permeability of the

fiber bundle, and as a consequence the transition from predominantly macroscale channel

infiltration to microscale pore infiltration is less distinct.

An examination of the trends in the curves from Figures 6a–6d reveal that the variation with fiber

volume fraction gets progressively less as the inlet plane resin velocity is increased. This can be

explained by the fact that as the flow velocity increases, the resin pressure increases

correspondingly so as to maintain the flow velocity, causing faster infiltration of the preform and

a consequent rapid decrease in the void content. The increase in the pressure is more pronounced

for the higher fiber bundle volume fractions, which causes a reduction in the void content with

increasing fiber bundle 78 as seen throughout in Figure 6. It is seen from the result in Figure 6

that, in general, the flow characteristics and resulting void content in the two different planes

considered are nearly the same for the parametric combinations considered.

Figure 7 compares the results of the flow simulations along the middle, quarter-width, and edge

planes for the extreme parameter limits of the fiber bundle volume fraction (0.5 and 0.8) and the

inlet plane resin velocity (0.25 and 2.00). As previously mentioned, the air entrapment evolution

Figure 7. Percentage of air remaining in the unit cell of the middle, quarter-width, and edge two-

dimensional planes at the extreme parameter limits of (a) 0.5 fiber bundle 78 and 0.25 cm/s, (b)

0.5 78 and 2.00 cm/s, (c) 0.8 78 and 0.25 cm/s, and (d) 0.8 78 and 2.00 cm/s

is similar within the middle and edge planes, which is reflected in the results presented in Figures

7a–7d. On the other hand, the results of the quarter plane simulations exhibit significant

differences from the middle and edge plane simulations. It is evident that, in general, the air

entrapment in the plane at the quarter-width of the unit cell decreases much more rapidly than

either the middle or edge plane cases. This trend is most evident at a fiber bundle volume fraction

of 0.5 and an inlet resin velocity of 2.00 cm/s (Fig. 7b), where the air entrapment is quickly

reduced to approximately zero. However, in the case of a fiber bundle volume fraction of 0.8 and

an inlet resin velocity of 0.25 cm/s (Fig. 7c), the results of the three different planes are

approximately equivalent. In general, the faster evacuation of the air in the quarter-width plane

case can be explained by considering that the geometry in this case offers less overall macroscale

volume to the resin flow than in the edge or middle plane cases, therefore forcing the resin to

permeate into the fiber bundles more rapidly in the plane at the quarter-width of the unit cell. The

results of the simulations on the plane at the quarter-width suggest the existence of a spatial

variation of the void content in the three-dimensional volume.

Figure 8 presents the predicted maximum and average values of the near steady-state void

content, 7>9#? , within the unit cell, corresponding to the tails of the curves in Figures 6 and 7 for

the different fiber bundle volume fractions and the middle, quarter-width, and edge planes of the

plane weave architecture. The maximum steady-state void content is calculated from the edge

plane results, which represents the case in which the highest air entrapment amounts were

observed and therefore represents a worse-case scenario in terms of void formation. The average

steady-state void content values were calculated from a volume average of the void content in the

three different planes at their respective steady-state conditions and is representative of the void

content measurement that would be reported experimentally. The maximum steady-state void

content values, 7>9#? , of the cases studied all fall between the range of approximately four to seven

Figure 8. Void content within the unit cell of the middle and edge two-dimensional plane at

various inlet plane resin velocities and fiber bundle volume fraction values

percent of the entire unit cell volume while the average steady-state void content values all fall

within the range of approximately two to six percent. It is observed from the data in Figure 8 that

the maximum void content is highest at the low inlet plane resin velocities and low fiber bundle

volume fractions and progressively decreases as the fiber bundle volume fraction and the inlet

plane resin velocity are increased. This trend can be explained by a combination of factors. First,

the capillary forces at the resin-air interface increase as the fiber bundle volume fraction

increases, which would cause the resin to permeate into the fiber bundle more rapidly. In addition,

a higher fiber bundle volume fraction indicates that there is less initial air within the fiber bundle

to be pushed out (or potentially entrapped), resulting in a lower final void content. Also, as

discussed earlier, a higher inlet plane resin velocity will result in higher pressures which, in turn,

forces the resin to permeate further into the fiber bundles, thereby reducing the overall void

content in the unit cell. The average void content for each of the fiber bundle volume fraction

values are all only slightly less than the maximum void content values at the low inlet plane resin

velocity, suggesting a high degree of spatial uniformity of the void content in the preform.

However, the average void content decreases from the maximum drastically as the inlet plane

resin velocity is increased for each of the fiber bundle volume fractions, pointing a greater spatial

nonuniformity in the void content in the case of processing at high speeds. It is also seen that at

the high inlet velocities, the average void content increases with increasing fiber bundle volume

fraction, opposite to the trend noted in the maximum void content.

While void content decreases with increasing fiber bundle volume fraction and with inlet flow

rate, it is equally important to consider the amount of excess resin needed to achieve the steady-

state void fractions reported. In an ideal mold fill, the time scales of the macroscale and

microscale flows will be equal such that the macroscale voids and the microscale voids within the

fiber bundles will be filled simultaneously. However, in an actual fill, the resin races across the

Figure 9. Excess resin wasted during infiltration of the middle and edge two-dimensional plane at

various inlet plane resin velocities and fiber bundle volume fraction values

unit cell along the macroscale channels, and the resin flow needs to be continued until the

microscale voids are filled (to their final extent). The volume of the “excess resin” that needs to

be flowed, denoted as @<A, is a measure of the resin wastage, which needs to be minimized. Figure

9 presents the variation of the excess resin as a function of the resin inlet velocity for the different

fiber bundle volume fractions and considering the volume averaged flow through the three

different planes of the unit cell. It is evident from Figure 9 that there is the least amount of excess

wasted resin at low fiber bundle volume fractions and the low inlet plane resin velocities—the

conditions that correspond to the highest maximum void content in Figure 8. On the other hand,

for the high fiber bundle volume fractions and the high inlet plane resin velocities—that resulted

in the lowest maximum void content in Figure 8—a large volume of excess wasted resin is noted

due to the resin flowing quickly through the macroscale channels and exiting the unit cell rapidly,

while the small microscale pores continue to be filled. In addition, at relatively higher fiber

bundle volume fractions the bundle permeability is very low, causing the resin to be forced

through the macroscale channels within the unit cell at even greater average velocity than

situations with the same inlet plane resin velocity specification at lower fiber bundle volume

fractions.

In conjunction, Figures 8 and 9 provide an example of using the current numerical simulation

results as a decision making tool regarding mold filling processing parameters. that the results

suggest that void content may be minimized in the final products, but at the cost of wasted resin.

The numerical simulation provides for arriving at designs that trade off between the two

competing effects.

4. CONCLUSIONS

A numerical model was presented to investigate dual scale resin flow through a nested plane

weave preform architecture, considering capillary effects within each individual fiber bundle. The

results of the numerical simulations were used to both illustrate and quantitatively predict the air

entrapment locations within the fiber preform along with the resulting size of the void. The final

void entrapment volumes were compared across different fiber bundle volume fractions and inlet

plane resin velocities. The void content was observed to decrease with increasing fiber bundle

volume fraction and resin velocity. However, it was found that conditions that led to lower void

content also corresponded to a higher volume of excess resin needed to complete the fill. The

numerical simulations serve as a guide to designing processing conditions to balance final void

content with wasted resin during mold fill in RTM.

5. ACKNOWLEDGEMENTS

This research is funded in part by the National Science Foundation through Grant No. CBET-

0934008, and the U.S. Department of Education through a GAANN fellowship to Caleb DeValve

as part of Award No. P200A060289. Their support is gratefully acknowledged.

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