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493Polymers & Polymer Composites, Vol. 10, No. 7, 2002

A Study on Resin Flow through a Multi-layered Preform in Resin Transfer Molding

*To whom correspondence should be addressed.

INTRODUCTION

Resin transfer molding (RTM) is an efficient andfrequently used process for producing fiber reinforcedpolymer composite products which have smallstructures of simple shape or large structures withcomplex shape. In resin transfer molding, mold fillingis governed by the flow of resin through the preformwhich is considered as an anisotropic porous media.The resin flow is usually described by Darcy’s lawand the permeability tensor must be obtained forfilling analysis1-26.

u

KP= − ∇

µ(1)

where u is the velocity vector of resin, µ is theNewtonian viscosity of the fluid, ∇ P is pressuregradient, and K is the permeability tensor of theporous medium.

A preform basically consists of a number of the layersof fiber mats. These layers may be composed ofdifferent materials and each layer has different in-plane permeability. In particular, a preform hasmultiple layers composed of different kinds of fibersand the difference of in-plane permeability betweendifferent layers may be large. Therefore it is necessaryto evaluate the effective average permeability.

One of the simplest averaging schemes is the weightedaveraging scheme.2,3,4

K

Hh Kij

lijl

l

n

==∑1

1

(2)

A Study on Resin Flow through a Multi-layered Preform in ResinTransfer Molding

D. G. Seong, K Chung, T. J. Kang and J. R. Youn*School of Materials Science and Engineering, Seoul National University, San 56-1, Shinlim-Dong,

Gwanak-Gu, Seoul, Korea

Received: 2 January 2002 Accepted: 1 March 2002

SUMMARY

In resin transfer molding, mold filling is governed by the flow of resin through a preformwhich is considered as an anisotropic porous media. The resin flow is usually describedby Darcy’s law and the permeability tensor must be obtained for filling analysis. Whenthe preform is composed of more than two layers with different in-plane permeability,effective average permeability should be determined for the flow analysis in the mold.The most frequently used averaging scheme is the weighted averaging scheme, but it doesnot account for the transverse flow between adjacent layers. A new averaging scheme issuggested to predict the effective average permeability of the multi-layered preform,which accounts for the transverse flow effect. When the flow in the mold is unsaturated,the effective average permeability is predicted by using the predicted mold filling timeand transverse permeability. The new scheme is verified by measuring the effectivepermeability of the multi-layered preforms which consist of glass fiber random mats,carbon fiber woven fabrics, aramid fiber woven fabrics. Fluid flow through the preformcomposed of more than two layers with different in-plane permeability shows differentflow fronts between layers. The difference in the flow front advancement is observedwith a digital camcorder. The predicted flow front is compared with the experimentalresults and shows a good agreement. It is expected that the effective average permeabilitycan be used for modeling the resin flow through the multi-layered preform.

494 Polymers & Polymer Composites, Vol. 10, No. 7, 2002

D. G. Seong, K Chung, T. J. Kang and J. R. Youn

where Kij is the averaged in-plane permeability

tensor, Kijl is the in-plane permeability tensor for

each layer, H is total preform thickness, hl is individuallayer thickness, and n is the total number of layers.Several researchers have shown that for relativelythin preforms with moderately varying permeabilities,this scheme provides an estimate of the effectivepermeability within 10% to 15% error of theexperimental value.2 But this scheme does not accountfor transverse flow in thickness direction.3,5 Theweighted average scheme implies that flow across thepreform layers is instantaneous such that a plug flowprofile be achieved through the thickness directionduring the mold filling process.6 For multi-layeredpreform, the transverse flow effect cannot be neglected.Especially, when the preform is relatively thick andthe difference of the in-plane permeabilities betweenadjacent layers is large, the transverse flow effect ismore significant. When the in-plane permeabilitiesare not the same, a non-uniform flow front developsthrough the thickness of the preform due to transverseflow, which has been verified experimentally.7,8 Inpractice, the transverse flow across preform layerstakes place in a region near the flow front and is astrong function of both the in-plane permeabilities ofthe adjacent layers and their transverse permeability.6

In order to account for transverse permeability effect,numerical simulation of three dimensional flow isnecessary. In a three dimensional problem, theadditional material property required is the transversepermeability for each element of the preform. It isdifficult to measure the property because of thelimited length in the transverse direction and limitedavailability of the compression characteristics ofpreforms.7,9 Hence, averaging of the properties in thethickness direction has been accepted generally asthe error made in the measurement of transversepermeability may be of the same order as the errormade in the estimation of an average permeability.Moreover, three dimensional flow simulation of theRTM process is highly inefficient and time consumingas the computational time increases by one order ofmagnitude with each additional degree of freedom. Itmay also be unnecessary because the transverse flowin the third direction in most cases may be limitedonly near the flow front region. A new averagepermeability is needed as a averaging scheme whichaccounts for the transverse flow near the flow frontregion and enables us to eliminate one dimension butto capture the effect of a non-uniform stackingsequence. Thus there is a need to develop a generalscheme to calculate an effective permeability for a

preform with multiple layers, accounting for thetransverse flow between layers,.6 So far severalresearchers2,6,7 have suggested models and someexperimental data to account for the transverse floweffect in the multi-layered preforms.

Calado and Advani6 suggested an averaging scheme,the transverse flow scheme, that included thetransverse flow effect by considering the flow frontlength of each layer. They verified the averagingscheme by comparing the results with the numericalsimulations.

Mogavero and Advani2 evaluated experimentally theresin flow through the multi-layered preforms ofmoderate-to-high thicknesses that possessed largedifferences in the in-plane permeabilities of eachlayers. They compared their experimental resultswith the weighted average permeabilities.

Luce et al.7 measured experimentally the unsaturatedand saturated permeabilities of multi-layered preformsconstructed from the random mat and 3-D weavematerials. They also compared the experimental datawith the weighted average permeability.

In this study, a new averaging scheme is suggested topredict the effective permeability of the multi-layeredpreform, the effective average permeability, whichaccounts for the transverse flow effect by includingtransverse permeability directly. The effective averagepermeability is also measured experimentally formulti-layered preforms which are composed of glassfiber random mat, carbon fiber woven fabric, andaramid fiber woven fabric. By comparing the effectiveaverage permeability with the experimental result,the new averaging scheme is verified to be moreaccurate than the weighted average scheme that doesnot consider the transverse flow.

The advancement of the flow front for the multi-layered preform is evaluated by a digital camcorder.The difference of the flow fronts is also calculated inthe course of calculating the effective averagepermeability, and compared with the experimentalresult obtained from the image of the digital camcorder.

THEORY

A simplified two dimensional cross-sectionalgeometry of the multi-layered perform is shown inFigure 1. Based on this two dimensional geometry, a



new scheme predicting the effective averagepermeability is developed.

From Darcy’s law, the flow front length, l, is given asfollows.6,9,11-26

l

ut

KPt

P Kl

t= = − ∇ =ε εµ εµ

0 (3)

l

P Kt= 0

εµ(4)

where ε is porosity of perform, t is time, P is pressure,and Po is inlet pressure.

It is assumed that the transverse permeability has afinite value and pressure in the mold has a linearprofile.

∆l l l

P t K K= − = −

2 1

0 2

2

1

1µ ε ε(5)

v

KPT= − ∇

µ(6)

P x P

Pl

x Pxli

i i

( ) = − = −

0

00 1 (7)

where KT is transverse permeability, K1 is in-planepermeability of the 1st layer, K2 is in-planepermeability of the 2nd layer, ε1 and ε2 are porositiesof the 1st and 2nd layers, ν is velocity of flow in thetransverse direction, Pi is pressure in the i-th layer, liis distance of the flow front in the i-th layer, and x isthe coordinate.

If K1 < K2, the transverse flow occurs from the 2ndlayer to the 1st layer.

P x P

xl2 0

2

1( ) = −

(8)

P x

P l ll

l l2 2

0 2 1

2

1 2

2=( ) = −+ (9)

∇ =− −

+

−= −

+P

P l ll

hh h

P l ll h h

0 2 1

2

21 2

0 1 2

2 1 2

2

2 2

( )( )

(10)

Figure 1 Two dimensional cross-sectional geometry of the multi-layered preform used for the study



v

K P l ll h h

K Ph h

KK

T T= − −+

=+

−

µ µεε

0 1 2

2 1 2

0

1 2

2 1

1 2

1( )

( ) ( )(11)

Assuming unit width, volume flow rates are expressed as follows.

Q u h

P K hl

P Kt

h1 1 10 1 1

1

1 0 11= = =

µε

µ(12)

Q u h

P K hl

P Kt

h2 2 20 2 2

2

2 0 22= = =

µε

µ(13)

Q v l l

P K th h

KK

K K

T

T

= −

=

+

−

−

( )

( )

2 1

0

32

1 2

2 1

1 2

2

2

1

1

1µ

εε ε ε

(14)

where Q1 is volumetric flow rate in x direction through the 1st layer, Q2 is volumetric flow rate in x directionthrough the 2nd layer, and QT is volumetric flow rate in the transverse direction.

When the flow reaches the steady state, the following relations must be satisfied.

Q Q Q QT T2 1− = + (15)

Pt

K h K h

P K th h

KK

K KT

02 2 2 1 1 1

0

32

1 2

2 1

1 2

2

2

1

1

2 1

µε ε

µεε ε ε

−( )=

+

−

−

( )

(16)

From the above relationship, transverse permeability can be obtained.

Kh h K h K h

P

K

K K tT =+ −( )

−( )µ ε ε ε ε

ε ε

( )1 2 2 2 2 1 1 1

0

1 2 2

1 2 2 1

221

(17)

If the time interval from ξ to tf - ξ is considered, the time averaged transverse permeability is expressed as follows.

Kt

K dt

h h K h K h

P

K

K K

tt

T

f

T

t

f

f

f

=−

=+ −( )

−( )−

−

−

∫12

2 21 2 2 2 2 1 1 1

0

1 2 2

1 2 2 1

2

ξµ ε ε ε ε

ε ε

ξξ

ξ

ξ

( ) ln( ) (18)



where tf is filling time and ξ is a dummy variable for time.

If it is assumed that ξ = 1, the time averaged permeability becomes

Kh h K h K h

P

K

K K

ttT

f

f

=+ −( )

−( )−

−

µ ε ε ε ε

ε ε

( ) ln( )1 2 2 2 2 1 1 1

0

1 2 2

1 2 2 1

221

2(19)

In order to determine the effective average permeability and the flow front difference between the two performlayers, it is assumed that transverse flow starts at time t.

The volume of fluid transported in each layer at time t, Vi(t) is given by the following equation.

V t Q t t

P K thi i

i ii( ) ( )= = ε

µ0 (20)

If the transverse flow is neglected, the volume of fluid transported in each layer at time (t + τ) is given by thefollowing equations.

V t

P K th1

1 0 11'( )

( )+ = +τ ε τµ

(21)

V t

P K th2

2 0 22'( )

( )+ = +τ ε τµ

(22)

The volume of fluid transferred in the transverse direction is derived as follows.

V t v l l

P Kh h

KK

K KtT

T( ) ( )( )

+ = − =

+

−

−

τ τ

µεε ε ε

τ2 10

32

1 2

2 1

1 2

2

2

1

1

1 (23)

By considering the transverse flow from the 2nd layer to the 1st layer, the volume of fluid flow in each layer isobtained as follows.

V t V t V t

P K th

P Kh h

KK

K Kt

T

T

1 1

1 0 11

0

32

1 2

2 1

1 2

2

2

1

1

1

( ) '( ) ( )

( )( )

+ = + + +

= + +

+

−

−

τ τ τ

ε τµ µ

εε ε ε

τ(24)

V t V t V t

P K th

P Kh h

KK

K Kt

T

T

2 2

2 0 22

0

32

1 2

2 1

1 2

2

2

1

1

1

( ) '( ) ( )

( )( )

+ = + − +

= + −

+

−

−

τ τ τ

ε τµ µ

εε ε ε

τ(25)

Therefore, the distance of the flow front considering transverse flow is readily calculated.

L

Vhii

i i

=ε

(26)



where Li is the distance of flow front in the i-th layer considering transverse flow.

LVh

P K t P Kh h h

KK

K KtT

11

1 1

0 1

1

0

32

1 1 1 2

2 1

1 2

2

2

1

1

1

=

= + +

+

−

−

ε

τε µ µ ε

εε ε ε

τ( )( )

(27)

LVh

P K t P Kh h h

KK

K KtT

22

2 2

0 2

2

0

32

2 2 1 2

2 1

1 2

2

2

1

1

1

=

= + −

+

−

−

ε

τε µ µ ε

εε ε ε

τ( )( )

(28)

Difference between the two flow fronts at time (t + τ) becomes

L L

P t K K

P Kh h

KK

K Kh h

t

t

T

2 1

0 2

2

1

1

0

32

1 2

2 1

1 2

2

2

1

1 1 1 2 2

11 1

−

= + −

−

+

−

−

−

+( )

( )

( )

τ

τµ ε ε

µεε ε ε ε ε

τ

(29)

The average flow front difference is obtained by integrating the flow front difference with respect to time andaveraging by the filling time.

( ) ( )

( )L L

t t tL L d dt

f f

t tt

t

ff

2 1 2 100

1 1− =−

−+

−

∫∫ ττ

= −

−

−

+

−

−

−

23

83

2 2

215

11 1

0 2

2

1

1

0

32

1 2

2 1

1 2

2

2

1

1 1 1 2 2

32

ln

( )

P K K

P Kh h

KK

K Kh h

tTf

µ ε ε

µεε ε ε ε ε

(30)

At filling time, tf, the time intervals are as follows.

t tt t

f

f

+ == = −

ττ1 1, (31)

The distance of the flow front in the 1st layer at the filling time is given by substituting equation (31) into equation (27).

LP K t P K

h h hKK

K Kt

L

tf T

ff10 1

1

0

32

1 1 1 2

2 1

1 2

2

2

1

1

1 1= +

+

−

−

−( )

=ε µ µ ε

εε ε ε( ) (32)



By defining A and B’s shown below, the equation (32)is expressed by the equation (35).

A

P Kh h h

KK

K KT=

+

−

−

0

32

1 1 1 2

2 1

1 2

2

2

1

1

1µ ε

εε ε ε( )

(33)

B

P K= 0 1

1ε µ(34)

At Bt A Lf f+ − − =12 0 (35)

The filling time is predicted by using the aboveequation.

t

B B A ALAf = − + + +

2 22

4 42

(36)

As a result, the effective average permeability, Keff,can be determined by using the average flow frontvelocity.

ULt

K PLf

eff= =εµ

0 (37)

K

LP

B B A ALAeff = − + + +

−

µ ε 2

0

2 22

4 42

(38)

EXPERIMENTAL

Materials

Three kinds of fiber preforms were used in this study,which were glass fiber random mats, carbon fiberwoven fabrics, and aramid fiber woven fabrics.Permeability is a strong function of porosity. In order tospecify the porosity, volume fraction of the fiber preformshould be determined. Volume fraction of fiber preformwas calculated through the following equation.

Vf

m

f

* = ρρ

(39)

where V*f is volume fraction of fiber perform, ρf is

density of fiber, ρm is density of mat. Density andvolume fraction of each fiber preform are representedin Table 1.

Silicone oil (dimethyl siloxane polymer, DC 200F/100CS, from Dow Corning) was used as the injectionfluid. It can be assumed that the silicone oil showsNewtonian behavior so that the Darcy’s law can beapplied. Its viscosity is 9.7 x 10-2 Pa·s.

Experimental Apparatus

RTM apparatus was designed and built for measuringpermeability and observing mold filling pattern. It ispresented schematically in Figure 2. Compressednitrogen (N2) gas was used for injecting resin into themold. Transparent mold was made of acrylic resin(PMMA), which enabled us to observe the resin flowduring mold filling. For recording of the fluid motionin the mold, a digital camcorder was used in order tovisualize flow pattern10. Two pressure transducerswere located in the mold to measure the pressuredifference. To prevent the leakage of the resin fromthe mold, O-rings were installed between the top andbottom molds, and several bolts, nuts, and C-clampswere used for tightening the gap between the top andbottom parts of the mold. The size of mold cavity was400 x 100 x 10 mm3 as shown in Figure 3.

Single Layered Preform

The in-plane permeabilities of three fiber preforms,glass fiber random mats, carbon fiber woven fabrics,and aramid fiber woven fabrics, were measured.Volume fraction of each preform was determinedexperimentally. Each experiment was performedunder the constant inlet pressure which was appliedby using compressed nitrogen and was in the rangefrom 0.25 MPa to 0.26 MPa. Pressure gradient wascalculated from two values measured at the twodifferent pressure transducers. Volumetric flow ratewas calculated from measuring both volume of fluidand time. The measured average flow rate was in therange from 1.79 m3/s to 6.28 m3/s. From these data,the in-plane permeability of each single layered fiberpreform was calculated by Darcy’s law. Advancementof the flow front through each perform was alsoobserved by using a digital camcorder.

tnereffidfonoitcarfemulovdnaytisneD1elbaTstnemirepxerofdesusmroferpdereyalelgnis

mroferprebiF ρf mc/g( 3) ρm mc/g( 3) V*f

)seilp8(ssalG 5.2 594.0 891.0

)seilp41(nobraC 8.1 073.0 602.0

)seilp8(dimarA 4.1 024.0 003.0



Multi-layered Preform

Multi-layered preforms were prepared by combiningtwo preforms out of the three different fiber performs.Three kinds of multi-layered preforms were possible.They were combinations of glass (4 plies) / carbon(7 plies), glass (4 plies) / aramid (4 plies), or aramid(4 plies) / carbon (7 plies). Physical properties of themulti-layered performs are given in Table 2.

The same silicone oil that was used in the experimentof single layered preform was selected as the fluid forthe experiment. Permeability was measured at thetime when the mold was saturated with the resin. The

Figure 2 Schematic diagram of the experimental setup for the study of resin transfer molding

suoiravfonoitcarfemulovdnaytisneD2elbaTstnemirepxerofdesusmroferpdereyal-itlum

mroferprebiF ρf mc/g( 3) ρm mc/g( 3) V*f

nobraC/ssalG 51.2 5234.0 102.0

dimarA/ssalG 59.1 5754.0 532.0

nobraC/dimarA 06.1 0352.0 851.0

overall method to determine the permeability ofmulti-layered preform was the same as that of singlelayered preform. Experiments were performed atconstant inlet pressure. Applied pressure in each



experiment was in the range from 0.19 MPa to 0.28MPa and average flow rate was varied from 2.22 m3/s to 5.04 m3/s.

Because the permeability of each layer in multi-layered preform was different, the flow front positionof each layer was different. Flow front advancedfaster in the layer with higher permeability than inthe layer with lower permeability. Difference betweentwo flow fronts was observed through the transparentside wall of the mold by using a digital camcorder.Variation of the flow front difference was observedwith respect to time. Because flow front boundary isnot exactly vertical, the exact flow front position was

determined by the midpoint at each flow front. Acommercial image analysis software, Image Pro 4.1(Media Cybernetics®) was used to determine theexact position of the flow front.8 These measuredvalues were compared with the theoretically predictedvalues.

RESULTS AND DISCUSSION

Single Layered Preform

Volume of fluid transported through the perform wasmeasured with the exact elapsed time. Two pressurevalues were measured at two locations where the

Figure 3 Structure of the mold used in the experiment



pressure transducers were inserted in the mold.According to the Kozeny-Carman equation,permeability increases with increasing porosity.11

K

k L LR

e

f=−

14 10

2

2 3

2( / ) ( )ε

ε(40)

where Rf is radius of the fibers, ε is porosity, Le is lengthof actual flow path, L is length of porous medium, andk0 is shape factor determined by the structure ofporous medium. Permeability and porosity of eachfiber perform were measured and plotted in Figure 4.As shown in Figure 4, carbon fiber preform has thehigher permeability than aramid fiber preform becauseof the higher porosity. But glass fiber preform has alower permeability than carbon fiber preform in spiteof higher porosity because the structure of each fiberpreform is different. In other words, the carbon andaramid fiber preforms are woven fabrics, and the glassfiber preform is a random mat. The shape factor, k0, islarger for the random mat than for the woven fabric inKozeny-Carman equation, i.e., flow channel is presentin the woven fabric perform. Therefore, carbon fiberpreform has the higher permeability than glass fiberpreform in spite of the lower porosity. The sameinterpretation will be possible for permeability of themulti-layered performs.

Flow front advancement in the glass fiber preform isshown in Figure 5. Edge effects were observed, which

are caused by the poor fitting of the preform at thewall of the cavity.

Multi-layered Preform

The same procedure was repeated to determine theeffective permeability of multi-layered preform.Measured effective permeabilities of the multi-layeredpreforms are listed in Table 3 and correspondingweighted average permeabilities and effective averagepermeabilities are also given. The measured effectivepermeabilities of the multi-layered performs are alsoplotted in Figure 6. The weighted average permeabilityand effective average permeability of the multi-layeredperform are compared with the measured permeabilityin Figure 7 and Figure 8. It is shown that the effectiveaverage permeability is closer to the experimentalresult than the weighted average permeability. Effectsof the in-plane permeability ratio in the multi-layeredperform on errors of the weighted average permeabilityand the effective average permeability are shown inFigure 9. As expected, the effective averagepermeability has smaller error because it considerstransverse flow between two adjacent layers. Thetime averaged transverse permeabilities calculatedby the equation (19) are 1.26 x 10-11 (glass/carbon),2.13 x 10-11 (glass/aramid), and 1.69 x 10-11 m2

(aramid/carbon). These values are lower than the in-plane permeabilities by about two orders of themagnitude. Especially, when the difference of in-plane permeabilities between two layers is large, the

Figure 4 Permeability of the single layered preform with respect to the porosity



ehthtiwytilibaemrepderusaemyllatnemirepxeehtfonosirapmoC3elbaTytilibaemrepegarevaevitceffeehtdnaytilibaemrepegarevadethgiew

mroferPytilibaemreP

nobraC/ssalG dimarA/ssalG nobraC/dimarA

K AW m( 2) 01x1029.1 9- 01x1284.1 9- 01x0216.1 9-

K ffe m( 2) 01x9268.1 9- 01x4922.1 9- 01x9288.1 9-

K PXE m( 2) 01x2838.1 9- 01x6153.1 9- 01x1889.1 9-

K AW K,ytilibaemrepegarevadethgiewsi ffe Kdna,ytilibaemrepegarevaevitceffesi PXE

ytilibaemrepderusaemyllatnemirepxesi

Figure 5 Advancement of the resin flow front in glass preform

Figure 6 Permeability of the multi-layered preform with respect to the porosity



Figure 8 Predicted values of the effective average permeability in comparison with the experimental result

Figure 7 Predicted values of the weighted average permeability in comparison with the experimental result

transverse fluid flow affects the effective permeabilitymore significantly. Therefore, the weighted averagingscheme which ignores the transverse flow effectcauses a large error when the difference of in-planepermeabilities between two layers is large. In glass/

carbon preform in which the difference of in-planepermeabilities is not large, the weighted averagepermeability is relatively close to experimental result.However, in aramid/carbon preform in which thedifference of in-plane permeabilities is large, the



Figure 9 Effect of the in-plane permeability ratio on the error

weighted averaging scheme produces a large error,about 19%. On the other hand, the effective averagescheme produces small errors in the two cases. Butboth schemes produce large errors in glass/aramidpreform, which may be caused by the experimentalerror. In the experimental measurement of glass/aramid preform, the layer of aramid woven fabric wasdeformed slightly during resin filling. The deformationof the aramid fabric is regarded as the reason for theexperimental errors in determining the effectivepermeability.

The fact that the capillary effect was not consideredin the unsaturated flow would be another source oferror. It is known that permeability obtained from theunsaturated flow measurement is larger by 2-4% thanone from the saturated flow measurement.12 It is dueto the effect of capillary pressure in fiber tows. In thisstudy, all the permeabilities were measured in thecase of saturated flow.

Using the effective average scheme, variations of flowfront distances are presented in Figure 10 and thedifference in flow fronts between perform layers areplotted in Figure 11. In terms of these data, theadvancement of flow front in each layer is representedin Figure 12. In all cases, velocity of the flow frontslows down as flow front progresses because thepressure gradient under the constant inlet pressure

becomes small as flow front progresses. The differenceof the flow front increased steeply at initial stage butthe increasing rate became smaller, which means thatthe flow reaches steady state as flow front progresses.

The calculated flow front distance of carbon fiberlayer in glass/carbon preform was compared with theexperimental results within the distance of 16.55 ~23.45 cm from the gate as shown in Figure 13. Imagesprocessed by the image processing tool is also shownin Figure 14. As shown in these results, the flowpattern observed in the experiment was less stablethan the predicted one. As the captured image of themoving flow front in the glass fiber layer was not clearenough to identify, the exact flow front advancementin the glass fiber layer in glass/carbon preform wasobtained after image processing.

CONCLUSIONS

Permeabilities of three kinds of single layered preformsare measured in the saturated flow and permeabilitiesof three kinds of multi-layered preform are alsomeasured in the same way. A new effectivepermeability considering transverse flow betweentwo different layers is proposed and compared withthe weighted average permeability and theexperimentally measured result. The effective averagepermeability is much closer to the experimentally



Figure 11 Calculated difference of the flow front between two layers in different multi-layered preforms

Figure 10 Position of the flow front predicted as a function of time in different multi-layered preforms. (a) glass/carbon preform, (b) glass/aramid preform, (c) aramid/carbon preform



Figure 13 Comparison of the calculated flow front distance with the experimental result in glass/carbon preform

Figure 12 Advancement of the flow front through different performs. (a) glass/carbon preform, (b) glass/aramidpreform, (c) aramid/carbon preform



measured permeability than the weighted averagedpermeability that does not consider the transverseflow. The advancement of flow front in multi-layeredpreform is investigated theoretically and visualizedby a digital camcorder. An image processing methodis used for determining the exact position of flowfront. The effective average permeability has a goodagreement with the experimental results and can beused for modeling of the resin flow through the multi-layered preform in resin transfer molding.

ACKNOWLEDGEMENTS

This study was partially supported by the Ministry ofScience and Technology through the NationalResearch Laboratory and by the Korea Science andEngineering Foundation through the AppliedRheology Center (ARC). The authors are grateful forthe support.

REFERENCES

1. Greenkorn R. A., “Flow Phenomena in PorousMedia”, Marcel Dekker, New York (1983)

2. Mogovero J. and Advani S. G., PolymerComposites, 18 (1997) 649

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Figure 14 Advancement of the resin flow front in glass/carbon perform



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