Numerical simulation and experimental investigation for design of a carbon fiber tow pneumatic spreading system

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Numerical simulation and experimental investigation

for design of a carbon ﬁber tow pneumatic spreading system

Jen-Chung Chen, Chuen-Guang Chao

*

Department of Materials Science and Engineering, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 30050, Taiwan, ROC Received 15 October 2004; accepted 5 May 2005

Available online 5 July 2005

Abstract

The work successfully designs a high efficient carbon fiber pneumatic spreading system. The internal flow field of the fiber pneu-matic spreader was first simulated by solving Reynolds-averaged Naiver–Stokes equations, and the characteristics of the flow pat-tern in the spreader under various operation conditions were analyzed in terms of the mass flow rate and the velocity distributions. Comparisons of numerical results with measured velocity and pressure distributions were made to determine the accuracy of the employed method. A good agreement was found in both qualitative and quantitative analysis. A new variable, spreading evenness, was defined to specify the dispersing extent of fibers in a carbon fiber tow during the fiber pneumatic spreading process. By the spreading evenness, a quantitative comparison of a spread carbon fiber tow can be made and the optimum condition can be easily obtained at fiber spreading experiments. The dispersing mechanism of a carbon fiber tow was comprehensive by the computational modeling and the spreading experiment. The performance of the fiber tow pneumatic spreader system was better than prior studies, and the use of numerical analysis combined with the fiber spreading experiment was useful for the development of the fiber pneu-matic spreading system.

Keywords: Carbon ﬁbers; Modeling; Transport properties

1. Introduction

In recent years, metal-coated carbon ﬁber has been considered a promising material widely used as electrical contact devices, power semi-conductor devices, EMI (electromagnetic impulse) shielding, electrical brush and sink etc., owing to its high electrical conductivity, thermal conductivity, excellent wear resistance and high speciﬁc strength[1–6]. Above all, the importance of EMI shielding relates to the high demand of todayÕs society on the reliability of electronics and the rapid growth

of radio frequency radiation source. Therefore, metal-coated carbon fibers have great potential application as structural and functional materials in the future. The primary concern, however, relates to the difficulty of coating metal uniformly on continuous carbon fiber tows, and the chemical reaction at the interface between carbon fibers and metal.

A very thin and uniform coating over a fiber surface can promote the characteristics of carbon fiber compos-ites; therefore, many methods have been proposed for the preparation of metallic deposition to improve and enhance the surface state of carbon fibers. However, the variation in the thickness of the coating on a carbon fiber tow has been observed. The variation between fibers on the inside of each bundle and those on the out-side, however, is up to 20–90%[2,4,7–12]. The thickness of the layer on the monofilaments in the center of the www.elsevier.com/locate/carbon

* _{Corresponding author. Tel.: +886 35 712121x55309; fax: +886 35} 724727.

E-mail addresses: chen8864338@yahoo.com.tw, u8518807@cc.

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fiber tow is considerably less than that of the layer deposited on the monofilaments at the outer of the tow. The results demonstrate that the EMI shielding capability of the fibers decreased as the coating thick-ness reduced, but the strength of the fibers decreased with increasing coating thickness[1,4,13–16]. Therefore, significant difference of the mechanical behaviors and the physical properties yielded between the inner and outer fibers of a tow. The outer fibers in a tow are well activated during surface treatment, but the inner fibers in the tow are barely activated. The excess of compact carbon filaments is responsible for the non-uniform acti-vation and the non-uniformity of the subsequent coating in a carbon fiber tow[11,12]. It may not be possible to get an identical thin film and coat less than 0.2 lm thin layer on each fiber in a carbon fiber tow[2,8,17,18]. The change in the film thickness is as a function of the dis-tance from the axis of the fiber tow and as the relative concentration of the chemicals as a function of the difference from the axis of the fiber tow for different positions in the reactor and for different deposition con-ditions. Deposition onto the central fibers is difficult; reactants are prevented from approaching the inner fi-bers. Thus, if the fibers are separated uniformly, it is advantageous for the improvement of fiber coatings

[15,19,20].

Process and apparatus were developed for pneumati-cally spreading carbon filaments from a tow bundle to produce a sheet or a ribbon in which the filaments were separated and maintained in parallel [21–24]. The car-bon fiber tow is comprised of thousands of filaments and the filaments are interacted with air in the pneu-matic spreader. Baucom and Marchello were the first to attempt to design a pneumatic spreader [21]. They

modeled a single fiber suspended in air under both a pressure drop and tow tension, and derived a formula-tion from orifice equaformula-tion to predict the spread angle of a carbon fiber tow in the spreader. Comparisons of the experimental data for a 12k tow (containing 12,000 filaments) with the single fiber prediction indicated that the results were not satisfactory because there is a large deviation in the spread degree between the experiment and the model. They concluded the flow field is too com-plex in the spreader to know the interaction between the airflow and fibers, for the model derived from Bernoul-lisÕ ideal assumptions cannot calculate and present the overall status of airflow. Also, the model of the single fi-ber prediction cannot describe the internal flow field of the spreader. Newell et al. and Kawabe et al. focused their research on the design and processing factors of an effective pneumatic spreading system, respectively

[22,23]. They qualitatively examined the spreading char-acteristics of the carbon fiber tow in the spreader under various conditions; however, the discussion of the inter-action between the flow fluid and the carbon fiber tow was unclear and incomplete because the flow field in the spreader remained unknown. Klett et al. employed a pressurized air-comb to separate the tow bundle be-fore a coating process[24]. Also, they qualitatively illu-minated the uniform spreading of a fiber tow exposed individual filaments by the air-comb for subsequent coating, but neither the procedures of tow spreading in the air-comb nor the spreading degree of the fiber tow were discussed. Accordingly, the spreading degree for a carbon fiber tow was considered in a very limited sense in the cited works, only a few which considered the evenness of a spread tow. When the fiber tow cannot be uniformly spread, some of the fibers pile up tightly. Nomenclature

A cross-sectional area c1, c2and cl empirical coeﬃcient

E empirical coeﬃcient k turbulent kinetic energy

p pressure

Q ﬂux

t time

u0_iu0_j Reynolds stress tensor

u0_i; u0_j, ﬂuctuation parts of the velocity uj velocity

u average velocity u+ scaled velocity

U, V, W velocity components VF ﬁber transported velocity

UT total axial velocity

X, Y, Z Cartesian coordinates y+ dimensionless distance

Greek symbols

e turbulent dissipation rate ls turbulent viscosity

k Von Karman constant n, f, g curvilinear coordinate m molecular kinematic viscosity mT eddy viscosity

q density

rk turbulent Prandtl number for k

re turbulent Prandtl number for e

s shear stress ~

sij Reynolds stress tensor u general variable Mathematical operators

, _{del operation}

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Without effective spreading, the effects of fiber bridging may become severe[23].

The critical part of the spreading process is the design of the fiber spreader itself. None of the cited investiga-tions explored the effect of the airflow by the spreader design, and none of them qualitatively and quantita-tively analyzed the internal flow patterns of the fiber spreader in detail. A highly chaotic or turbulent flow field would bring about the variation in air velocity and airflow agitation in the spreader. Agitation can entangle fibers, making fiber spreading difficult and damaging the fibers. The characteristics of the internal flow field in the pneumatic spreader will be given by the design. This present work aims to establish a three-dimensional (3-D) model of the spreader by apply-ing a computational fluid dynamics (CFD) method com-bined with far-field treatment to study the internal flow field of the spreader. The CFD method was also imple-mented to visualize velocity fields, pressure and stream-lines distribution, and thus elucidates the spreading mechanism of the new design spreader to optimize the design factors. The fiber pneumatic spreader is used to estimate experimentally the effect of air velocity on a carbon fiber tow. The goal is to develop an effective pneumatic fiber spreading system that can uniformly spread the fiber tow for post treatment, such as surface treatment or surface coating. The spreading process of a carbon fiber tow is recorded photographically. More-over, a method of measurement is constructed to evalu-ate the distribution of the spread carbon fiber tow.

2. Computational techniques

The computational fluid dynamics methodology using the Reynolds-averaged Navier–Stokes (RANS) equations with no-slip boundary conditions was adopted to investigate the internal flow field of the pneu-matic spreader. Finite difference approximations were employed to solve the transport equations with a body-fitted grid system. The incompressible and isother-mal Reynolds-averaged Navier–Stokes equations are: ouj oxj ¼ 0 oui ot þ ouiuj oxi þ1 q op oxj þ o oxj ðu0 iu0jÞ o oxj m oui oxj þouj oxi ¼ 0; i; j¼ 1; 2; 3;

where uj is the velocity; p is the pressure; q is the

con-stant density; m is the molecular kinematic viscosity; u0_i; u0_j are the ﬂuctuation parts of the velocity uiand uj,

and u0

iu0j is the Reynolds stress tensor, which can be

modeled by the eddy viscosity hypothesis:

u0 iu0j¼ ~sij¼ 1 q^sij ¼2 3dijk 2 3lsr uidijþ lsðruiþ ðruiÞ T Þ. Here, k¼1 2u

2 _{is the turbulent kinetic energy, and l} sis

the turbulent viscosity. This has to be prescribed by a turbulent model.

The turbulent model can be described by a generic ke model as[25]: qok otþ qr ðuikÞ ¼ r ððm þ rkmTÞrkÞ þ ~sijr ui qe qoe otþ r ðuieÞ ¼ r ððm þ remTÞreÞ þ c1e=k~sijr ui c2q e2 k; where rk¼ k2 ðc2 c1Þ ffiffiffiffiffipcl

kðVon Karman constantÞ ¼ 0.4187 The eddy viscosity is calculated from: mT¼ clq

k2 e ;

where rkand reare the turbulent Prandtl number for k

and e, respectively, and the c1, c2and clare the empirical

coeﬃcient [26]; the set of model constants employed is summarized inTable 1.

3. Boundary conditions

As shown inFig. 1(a), the geometry of the 3-D sprea-der model was defined first in a physical space (x, y, z). It was symmetrical in the vertical plane (x–y plane), so only half of the geometry was simulated to reduce the computer time. In most work of simulation, the bound-ary conditions at inlets were used to setting to be a uni-form velocity that was quoted from measured data, or used ambient pressure for an internal flow field. In the present study, the inlet velocity was unknown, and mak-ing measurements in the case of sudden contraction was difficult. Therefore, the fluid flow is characterized in the far field. Thus, the computational domain was extended along the x-, y- and z-direction as depicted inFig. 1(b). The multi-block approach was used to maximize com-putational efficiency and save memory[27,28]. The multi-Table 1

Model constants employed in the computation

c1 c2 cl rk re

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block grid divided the solution domain into subdomains, and each subdomain has its associated subgrid or block. In multi-block grids, data are transferred from one block to another using a generalization of the periodic bound-ary conditions. The blocks were built on each side of the spreader model. Therefore, the boundary condition at the outer surface of each block could be specified by the atmospheric pressure (101,300 Pa), and the flow field was computed from the external flow field to the internal flow field. The grid is structured and orthogonal curvilin-ear. The number of nodes and elements in the fluid domain were 137,800 and 129,600 respectively. Grid con-vergence was examined to ensure that the resolution of

this mesh was adequate. Doubling the number of nodes changed the solution by less than 0.01%.

The boundary conditions were as follows: (1) Symmetry plane V ¼ W ¼ 0; oU ox ¼ 0; o/ ox ¼ 0; where / = k, e and p.

(2) Pressure boundaries: The computational domains were extended in the mathematical grid, to enable pres-sure boundaries to be created on the surfaces of the blocks, as shown in Fig. 1(b). For the surfaces were Fig. 1. (a) A three-dimensional mathematical model of the pneumatic spreader, (b) a perspective of a far-ﬁeld treatment by multi-block technique (U, V and W are the velocity components).

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sufficiently far downstream, fixed values of all variables could be specified at the pressure boundaries.

p¼ 101; 300 ðPaÞ ðatmospheric conditionÞ; U ¼ V ¼ W ¼ 0 ðfree streamÞ:

(3) Outlet: Static pressure was introduced at the out-let to model the outflow boundary. Various static pres-sures were used in the computation to elucidate the flow field in the 3-D spreader model. They were 101,200 (pressure drop = 100 Pa), 101,250 (pressure drop = 50 Pa) and 101,270 Pa (pressure drop = 30 Pa) respectively. This approach was useful for predicting the experimental conditions, and comparing velocities computed from various pressure data and other measurements.

(4) Walls: The boundary wall was fixed and a no-slip condition was imposed on all velocity components. Many variables varied rapidly in the near wall regions of the flow and, instead of using extremely fine grids in these regions, their behavior was specified with wall functions[25].

Discretization was carried out using the ﬁnite volume method. The governing equations were integrated over the control volume and reduced to algebraic equations, which followed conservation laws. In order to avoid pressure–velocity decoupling problems, arising from the fact that pressure and velocity were calculated in the same location, the convection ﬂux through each cell

face was calculated using the modiﬁcation proposed by Rhie and Chow [29], extended here for a multi-block grid. The SIMPLE algorithm was used as a pressure-correction method [30], to derive the pressure equation from the continuity equation. In this work, since the transient evolution was not of interest, the time step was optimized for fast convergence; acceleration tech-niques like false time step were applied [26]. Therefore, a typical simulation of the 3-D model on the base mesh required 300 MB of memory, and consumed a total CPU time of 7.237· 104s. The program was executed on a vector computer, the CRAYJ916 super computer, with eight 100 MHz processors and 1 GB of main sys-tem RAM.

4. Experimental 4.1. Experimental setup

Experiments were conducted using the setup sche-matically presented in Fig. 2. The main elements were comprised in sequence of: the tow feed spool, the tension control device, the pneumatic tow spreader, the vacuum pump and the take-up spool. The fibers from the carbon fiber tow that contained 12,000 filaments were passed through a fiber guide into a first friction roller. The first roller was synchronized with the second friction roller at

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a constant speed. Both two rollers were controlled by a variable speed driver. Hence, the fibers between these two rollers, which were subsequently spread in the pneu-matic spreader, remained under low tension that was maintained by the tension control device. For the air-flow rate in the pneumatic spreader, the vacuum pump sucked air, and gave a stable control of flow rate that was measured by a multiple tube flow meter and a pre-cision pressure controller. After the fibers spread and left the second roller, the fibers were taken up by a take-up system.

The pneumatic spreader was formed by PAN (poly-acrylonitrile) pieces, which were transparent, allowing the spreading procedure of carbon fibers to be photo-graphed. It was fixed by two steel plates to prevent vibration during spreading the fibers. The fiber entrance, 2, had a half-width of 2.5 mm. The fiber exit, inlet-1, had a final fiber spread half-width of 25 mm. The clapboard contained nine slots are parallel to the sym-metry plane, as shown inFig. 1. Each slot is 5 mm wide and 10 mm apart; the first slot is behind the inlet-1 50 mm long.

According to the simulation results, the pneumatic spreader would be modified, and spreading experiments would be undertaken to test the applicability of the 3-D mathematical model. First, the downstream pressures and velocities near the outlet were measured by preci-sion pressure controller and digital micromanometer, under various flow rates without carbon fiber tow, and the velocities would be compared with the calculated data to confirm the accuracy. Spreading experiments of a fiber tow were executed at various fiber transporting rates and airflow rates. Photography techniques were used to record the processes of fibers separated. The photographs were taken from the top view. Five Nikon FM2 cameras were used and each was fitted with a 52 mm lens. The single-frame photographs were taken with shutter speeds of 1/15 to 1/60 s, so that the images showed how fibers was spread and moved in the pneu-matic spreader.

4.2. Image process

This study more effectively determines the spreading degree of a carbon fiber tow than other investigations, but the evenness for a spread fiber tow is more impor-tant than the spreading degree. If the fiber tow were not uniformly separated, some of the fibers would be tightly piled up. Therefore, the spreading evenness for a carbon fiber tow in the spreading process should be considered first. A carbon fiber tow was spread in 50 mm wide. The LECO 2001 Image Processing System was used to evaluate the evenness of the spread fiber tow. Firstly, the image (50 mm· 50 mm, width · length) of the spread fiber tow was captured by using a CCD, and an image was taken at intervals of 50 mm. The, area

fractions of five consecutive images of the fiber tow at a specified area (50· 50 mm2

) were calculated using the image processing system at a setting gray level. The spreading evenness was determined by the average value of the ﬁve area fractions.

Spreading evenness¼XXi=5;

where Xi (%) is the area fraction of the spread ﬁbers, i = 1–5.

5. Results and discussion

5.1. Analysis of the simulated ﬂow pattern in the pneumatic spreader

Fig. 3 illustrates the streamlines, which were plotted at the central plane (y = 2.5 mm) of the pneumatic spreader. There were three of circulation (2–4) and one low-pressure zone (1) in the spreader. The simulation yielded the following results:

(a) The air was sucked into and entered the spreader, and it was accelerated due to sudden contraction at inlet-1 and inlet-2. Accordingly, the circulation zone was formed by ﬂuid viscosity and drag. (b) The airﬂow entered inlet-1, and passed through the

nine slots on the clapboard; therefore, two circula-tion zones were presented behind the clapboard. (c) Additionally, a narrow low-pressure zone formed

near the clapboard because the airflow passed through the separation location S; hence airflow separation generated. Air could not enter this zone near the clapboard, so it was thin and did not flow; thus, the pressure dropped. However, the area of the low-pressure zone declined as the air flux decreased.

In this moment, the main interest was the flow field between the symmetry plane and the clapboard owing to the fiber tow was spread in this region.

It was shown that the varieties of flow velocity appeared at inlet-1, inlet-2 and slots from the color level, since the cross-sectional area decreased. The velocity of airflow differed only a little between inlet-1 and inlet-2. That Q = qVA is well known, where Q is the flux or mass flow rate; q is the fluid density; V is the fluid veloc-ity, and A is the cross-sectional area of the inlet. The flux at inlet-1 was 10 times greater than that at inleat-2, and the slots on the clapboard were close to inleat-1. The air-flow varied mainly near inlet-1, so this investigation on the discussion concentrated in the region between in-let-1 and the slots.

Fig. 4(a) demonstrates a complete view of the

W-velocity (lateral velocity) contour, which reveals a high lateral velocity at the slots. A close-up view of

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the W-velocity contour in the vicinity of the slots was shown inFig. 4(b). The distribution of the lateral veloc-ity W was reducing with the distance Z approaching symmetry plane; similarly, the more air flowed into the inner location, the more velocity W increased. Above all, the much variation in the velocity W existed behind the slots. Compared axial velocity U with the lateral velocity W in the fiber spread region, the U-velocity is much larger than W-velocity. To test the accuracy of the numerical simulation, the physical model was con-structed according to the numerical parameters, and a series of experimental measurements were made, the downstream pressures and velocities near the outlet were measured by a precision pressure controller and digital micromanometer, under various flow rates without carbon fiber tow, and the velocities were compared with the calculated data as revealed inFig. 5. The computa-tional data were in good agreement with the measured data. Similar trends were observed at the static pressure, 101,250 (pressure drop 50 Pa) and 101,200 Pa (pressure drop = 100 Pa).

The air flux was related to the fluid velocity and pres-sure in the spreader, and it was controlled by the flow meter.Fig. 6indicates these measured values. The mean mass flow rate increased linearly with the axial velocity and was proportional to the mean static pressure. Simi-larly, the computational results exhibit the same trends as the measured results. The converged solution was cal-culated from upstream to downstream; moreover, the upstream computational results had the same order in

numerical error as the downstream. The simulated and measured data were both qualitatively and quantita-tively similar; further, the 3-D computational results can be helpful for designing a pneumatic spreader. Although considering no fiber addition might not be precise enough to lead to an understanding of the inter-action of fiber and airflow, the results gave us insight and led to the realization of the 3-D flow field. There-fore, the flow field can qualitatively understand before the fiber spreading experiment executed.

5.2. Eﬀect of the air velocity

Fig. 7 demonstrates spreading experiments of a car-bon ﬁber tow. The ﬁber tow was hardly to be spread by air drag owing to the small air velocity, under the condition VF= 7 m/min and Q < 60 L/min, where VF

is the fiber transporting velocity and Q is the flux. There-fore, it kept the original size about 5 mm. Fig. 8shows the results of the spreading experiment combined with the simulated flow field represented by streamlines. Car-bon fiber tow was spread over a width of approximately 20 mm at the fiber exit under the constant fiber trans-porting velocity (VF= 7 m/min), but flux Q was

increased to 70 L/min, as revealed in Fig. 8 (left). As mentioned above, when air was sucked into the sprea-der, the main variations in the air velocity occurred near inlet-1 because of a sudden contraction in the cross-sectional area and an acceleration of airﬂow. Further-more, the inlet-1 was more than 10 times the ﬂux of Fig. 3. A complete view of streamlines at the central plane (y = 2.5 mm) under the pressure drop 50 Pa for the nine slots designed pneumatic spreader.

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the inlet-2, as the area of inlet-2 was reduced during the fiber tow passed. Hence, the fiber tow was fluffed and separated at fiber exit (i.e. inlet-1) by airflow. Subse-quently, carbon fibers progressively moved to lateral side until 20 mm wide, while the fiber tension was balanced with the drag force. FromFig. 3, it was readily comprehensive that the uniform flow existed in the

range between the inlet-1 and slot-1 and the main flow velocity was axial velocity (U-velocity). The airflow was accelerated to a maximum axial velocity at the fiber exit. Transverse flow was produced downstream, for the airflow turned toward the clapboard. Hence, the lateral velocity W increased with decreasing the axial velocity, approaching the maximum near the inner slots. The Fig. 4. W-velocity (lateral velocity) contour under the pressure drop 50 Pa: (a) a complete view and (b) a close-up view.

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axial velocity was 3.21 m/s and the lateral velocity near inner slots was 0.7 m/s, as shown inFig. 8(right).

While flux Q was increased to 90 L/min, it was seen that the fiber tow was easily spread, and most fibers shifted toward the clapboard and concentrated at the clapboard. As demonstrated inFig. 9, the carbon fiber tow was spread over a width of 50 mm. During the spreading process, the separated fibers were gradually extended to the clapboard by the large axial velocity of approximately 5 m/s. However, the distribution of the lateral velocity increased abruptly near the clap-board, since the airflow turned toward the slots. Thus, as air flowed into the inner location, axial velocity de-creased sharply. The lateral velocity W rose to 1.5 m/s at the inner slots, as indicated inFig. 4. The air

cross-flow provided a drag force to the carbon fibers. Finally, the fibers were dragged toward the clapboards, and the same width was maintained as the fiber exit. Similar spreading results were obtained under other conditions, with the same spreading procedures. The continuous fi-ber spreading procedures are summarized as the follow-ing three main steps:

(1) The fiber tow was initially spread out and fluffed at the fiber exit by the axial airflow.

(2) Fibers gradually moved toward lateral side, and the lateral velocity would inﬂuence the ﬁber movement.

(3) As the ﬁbers moved closer to the clapboard, the transverse velocity increased; hence, the ﬁbers were dragged toward the clapboard.

The proposed spreading procedures were more de-tailed and differed significantly from the procedures pro-posed by previous investigators. Baucom and Kawabe et al. argued that applying transverse airflow to carbon fibers results in tow spread across the pneumatic sprea-der. They neglected the preliminary opening in the fiber tow was conducted by axial airflow. Fig. 10 illustrates the width of the unspread and spread fiber tow under different test conditions. To study the spreading even-ness of the carbon fiber tow by the pneumatic spreading system, the area fraction of the fiber tow in areas of 50· 50 (mm2) was calculated by the above-mentioned method and the evenness of the spread fiber tow was thus obtained. The spreading evenness in Figs. 7, 8

and9was 10%, 36.3% and 38.2%, respectively. The dif-ference of the evenness can be realized by previous discussion.

5.3. Eﬀect of the ﬁber transporting velocity

The spreading evenness increased with the air flux at a given fiber transporting velocity, but it decreased as the air flux increased beyond 80 L/min, because the lat-eral velocity was large as revealed inFig. 10. Favorable spreading evenness was obtained under a certain condi-tion, and similar trends were observed at other fiber transporting velocities. The fiber transporting velocity caused a difference between values of the spreading evenness at small air fluxes, such as Q = 70 L/min. As the transporting velocity increased, the spreading even-ness was improved at a constant mass flow rate. How-ever, the spread fiber tow at VF= 7 m/min and

Q = 80 L/min yielded the evenness of 62.3(%). This is because the fibers separated were conducted by axial velocity; in addition, there was a short interaction time between airflow and fibers with high fiber transporting velocity. Therefore, the transverse-flow applied to the carbon fibers was limited; the values of the evenness dif-fered a little at Q = 90 L/min for the three fiber trans-50 40 30 20 10 0 -10 -20 -30 -40 -50 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 Speed (m/s)

The width of the outlet (mm)

Pressure drop= 30pa Pressure drop= 50pa

Calculated data Experimental data Calculated data Experimental data Calculated data Experimental data Pressure drop= 100 pa

Fig. 5. Comparison of computational and measured speed at outlet under diﬀerent conditions.

0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0

Pressure drop (Pa)

Mass flow rate (lit./min) Experimental results

measured data curve fitting

Fig. 6. The relations of the experimentally measured mean mass ﬂow rate Q and pressure drops at outlet.

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porting velocities. The higher lateral velocity droved car-bon ﬁbers rapidly toward the clapboard; consequently, more ﬁbers were dragged toward the clapboard, reduc-ing the evenness.

A carbon fiber tow will be hardly spread out during the spreading experiment, even though the air flux was raised to 90 L/min, if the fiber tow was static or at a

low ﬁber transporting velocity VF< 1.5 m/min. Thus,

the fiber transporting velocity provided the frequency of fiber movement reducing the friction among each fi-ber, which made fibers easily separated. Moreover, it also supplied a relative velocity with respect to the air-flow. In other words, the preliminary opening in a car-bon fiber tow was conducted by the total axial velocity Fig. 8. Photograph of the spreading experiment on a carbon fiber tow combined with the streamlines of the flow field under VF= 7 m/min and Q = 70 L/min.

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UT. UT= U (VF), where U is the axial velocity; VFis

the ﬁber transporting velocity, and minus sign expresses the opposite direction to the axial velocity. When the lateral velocity was small at Q = 70 L/min, the ﬁbers

were spread out by the axial velocity. The higher ﬁber transporting velocity (VF= 7 m/min) results in a good

spreading evenness. At this case, the UT was 3.34 m/s

at VF= 7 m/min. The ﬁber transporting velocity would

influence the fiber separation as the air velocity smaller enough. However, the effect of the transporting velocity could be neglected at high air velocity, but no investiga-tor has considered this effect. Newell and Kawabe em-ployed a very large air flux of 720 L/min and the higher air velocity of 50 m/s, respectively, in the fiber spreading process. Notably, the spreading evenness can be used easily to compare quantitatively the spread fiber tows under various test conditions.

5.4. Eﬀect of modifying the number of slots

The fiber spreading efficiency was obviously pro-moted, but the spreading evenness was still unsatisfied. The lateral velocity was an important parameter at the spreading experiments, as discussed above, and the evenness was almost constrained by air drag, which results from lateral airflow. The coverage of the lateral velocity was broad in the pneumatic spreader with nine slots. When the air flux was increased, the lateral veloc-ity was distributed from the first slot to the ninth slot. The lateral velocity was higher at the inner location; Fig. 9. Photograph of the spreading experiment on a fiber for combined with the velocity-vector representation of the flow field under VF= 7 m/min and Q = 90 L/min.

0 20 40 60 80 100

Mass flow rate Q (L/min) 0 20 40 60 80 100 Spreading evenness (%) V = 1 m/min V = 3 m/min V = 5 m/min V = 7 m/min F F F F

Fig. 10. The relations of the fiber spreading evenness and the mass flow rates under different fiber-transporting velocities.

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therefore, the drag force would be sufficiently large to apply to the carbon fibers. Meanwhile, increase the air flux, and the axial velocity is also promoted. Hence, the spreading evenness cannot be improved further be-cause the axial and lateral velocities are large. It was well known that the flux is constrained by the cross-sectional area, and fluid velocity is inversely proportioned to the

cross-sectional area. Form the half of the geometry, as shown in Fig. 1(a), the cross-sectional area are 250 mm2 at inlet-1 and 25 mm2at inlet-2, respectively. The total cross-sectional area on the clapboards is 450 mm2at the spreader with nine slots open. However, if the slots were reduced, the cross-sectional area on the clapboard was smaller than that at inlets. Similarly, the

Fig. 11. A complete view of streamlines at the central plan (y = 2.5 mm) under (a) pressure drop 50 Pa and (b) pressure drop 70 Pa, between far-ﬁeld pressure boundary and outlet pressure boundary.

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airﬂow would be accelerated at inlet-1 and a given slot; above all, the lateral velocity could be increased and concentrated in front of the slot. The total axial velocity UT can be controlled by adjusting the axial velocity

combined with the ﬁber transporting velocity. There-fore, eight slots were sealed in the spreader, leaving only the ﬁrst one opened.

Fig. 11shows the simulated flow pattern, it was ob-served that the air was sucked into the spreader and the airflow quickly passed through the first slot to the outlet as the air flux increased. The lower velocity was existed at fiber exit because the flux was constrained by the slot 1. Also, it was found that the flow pattern was significantly different from the spreader with nine slots open at the same boundary condition (as Fig. 3). The variation in the velocity was not obvious at inlet-1 nearby, but the coverage of lateral velocity was more concentrated between the symmetry plane and the clap-board. The air velocity at inlet-2 was much lower than that at the spreader with nine slots open under the same condition, as illustrated inFig. 11(a). Disturbance and agitation can be avoided at a low air velocity. While the pressure drop was increased at the boundary condi-tion, the physical phenomena were more significant as presented inFig. 11(b).

Compared with the above experiment at inlet-1 near-by under the same conditions, it is shown inFig. 12that the U-velocity component increased with increasing the pressure drop, and the increasing rate was larger at the spreader with nine slots open than that with one slot open. Simultaneously, the axial velocity at the spreader with one slot open was smaller than that with nine slots open under the same pressure drop of 50 Pa, even

though the pressure drop increased to 70 Pa; however, the U-velocity was still smaller than that at nine slots open. The results are attributed to the limited flux in the one slot. By the results, it was known that the air velocity will be easily controlled at fiber spreading exper-iment. Furthermore, when we examined the distribution of the axial velocity U from symmetry plane to the clapboard in front of slots, and compared one slot open with nine slots open under the same condition, as revealed inFig. 13(a). Each curve represented the veloc-ity variation of each slot from symmetry plane. The re-sults present that U-velocity component decreased as the air flowed into the inner location at the spreader with nine slots open. The main reason was the airflow turned direction and the fluid friction as shown in previous paragraphs. There was a negative U-velocity around slot 9; this was because airflow came from inlet-2. The fluid velocity at one slot open was much lower than that at

0 5 10 15 20 25 30 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

The fluid velocity U (m/s)

The width of the inlet-1 (mm) 9 slots open Pressure drop = 30 Pa Pressure drop = 50 Pa Pressure drop = 100 Pa 1 slot open Pressure drop = 50 Pa Pressure drop = 70 Pa

Fig. 12. Comparison of calculated U-velocity components from symmetry plane (width at 0 mm) to the clapboard (width at 25 mm) at the inlet-1, between the spreader with nine slots open and one slot open. 0.0 5.0 10.0 15.0 20.0 25.0 -1.0 0.0 1.0 2.0 3.0 4.0 5.0

The fluid velocity U (m/s)

The fluid velocity W (m/s)

The width from symmetry plane to clapboard (mm)

The width from symmetry plane to clapboard (mm) 9 slots open slot-1 slot-5 slot-9 1 slot open slot-1 0.0 5.0 10.0 15.0 20.0 25.0 -6.0 -5.0 -4.0 -3.0 -2.0 -1.0 0.0 9 slots open slot-1 slot-5 slot-9 1 slot open slot-1 a b

Fig. 13. Comparison of calculated velocity components from symme-try plane (width at 0 mm) to the clapboard (width at 25 mm) in front of slots under the pressure drop = 50 Pa, between the spreader with nine slots open and one slot open (a) velocity U and (b) velocity W.

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nine slots open. But it abruptly increased with the dis-tance approaching clapboard from 0.65 m/s to 1.1 m/s. The U-velocity abruptly increased owing to a sudden contraction and an acceleration of airﬂow at one slot open.

For the cross-sectional areas were reduced to 50 mm2 on the clapboards in the spreader with one slot open, the flux would be constrained by slot-1. Initially, the fluid was also accelerated at inlet-1 as the airflow entered the spreader; however, the fluid was accelerated once again at slot-1 due to the sudden contraction. The lateral velocity W exhibited a significant difference between one slot open and nine slots open, as demonstrated in Fig. 13(b). The distribution of the W-velocity component was increasing with the distance approaching the clap-board at slots 1, 5 and 9 with nine slots open because the airflow turn toward. The more air flowed into the in-ner position, the more velocity W increased. However, a large increase in lateral velocity W was found at one slot open, and the distribution of the velocity W was larger than that at nine slots open.

Hence, the high-speed transverse flow provided higher air drag to the carbon fiber tow. In the fiber spreading experiment, the fiber tow was transported into the sprea-der at a high fiber transporting velocity and fibers were separated and moved lateral side by a given total axial velocity UT. Subsequently, the fibers were dragged to

lat-eral side by the transverse flow. Consequently, the even-ness in a carbon fiber tow was increased, and the fibers

spread out smoothly. The calculated evenness reached 83% at VF= 5 m/min and Q = 105 L/min, as shown in

Fig. 14(a). While the flux Q was increased to 125 L/ min, the fibers were dragged to clapboard, owing to the increase in the lateral velocity W. It can be seen that the partial spread fiber extend to the inner of the spreader about the location of the ninth slot, as illustrated inFig. 14(b). Modifying the number of slots increased the spreading evenness; the flow field of the pneumatic sprea-der varied significantly and the velocity and pressure dis-tributions differed from those of the spreader with nine slots.

To identify the non-uniform coating in a carbon fiber tow can be overcome by the pneumatic spreading pro-cess; two groups of spread and unspread carbon fiber tow coated with nickel by physical vapor deposition (PVD) and electroless plating were compared. The re-sults showed that a uniform Ni coating could be ob-tained on each fiber in the spread carbon fiber tow, and the thickness of the Ni film could be coated on car-bon fiber tow less than 0.2 lm. Similar results were also obtained in aluminum coated carbon fibers by PVD[31].

6. Conclusion

The internal flow field of the pneumatic spreader was first simulated by numerical investigation, and the work successfully developed a new and efficient fiber Fig. 14. Photographs of fibers spread experiment under VF= 5 m/min and (a) Q = 105 L/min and (b) Q = 125 L/min.

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pneumatic spreading system. The spreading process of a carbon ﬁber tow was ﬁrst visualized by the photographic technique. The performance is better than that at previ-ous studies. The main results and of this investigation are summarized as follows:

1. By the three-dimensional mathematical model of the fiber pneumatic spreader, the simulated flow patterns are helpful to analyze the variation of airflow and to understand the internal flow field of the spreader at different conditions.

2. The spreading evenness is first used and discussed in spread carbon fiber tow, and it is more useful than spreading degree in elucidating the spreading process of the fiber tow. The newly defined variable, spread-ing evenness, facilitates a quantitative comparison among the spread fiber tow under various test condi-tions, and the optimum conditions for the spreading process can thus be obtained.

3. The pneumatic spreading system outperforms sys-tems described elsewhere, and a carbon fiber tow can be uniformly and efficiently spread out. The opti-mum conditions for fiber spreading are VF= 7 m/min

and Q = 80 L/min, for the nine slot pneumatic sprea-der, with a evenness of spread of 62.3(%).

4. The spreading evenness of a carbon fiber tow was constrained by the large air velocity; therefore, when eight slots in the spreader were sealed, the evenness of the fiber tow reached 83%, differing considerably from that in the flow field of the spreader with nine slots.

5. The ﬁber spreading procedures are proposed in detail by computational ﬂuid modeling and experiment, and they can help in understanding the spreading process and the design of a pneumatic spreader.

Acknowledgement

The supports from National Science Council of the Republic of China and National Center of High Perfor-mance Computing are greatly appreciated.

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