Abstract In this study, a thermal-gradient chemical vapor infiltration (TG-CVI) process was numerically studied in order to enhance the deposition uniformity within the preform. The computational fluid dynamics technique was used to solve the governing equations for heat transfer and gas flow during the TG-CVI process for two- and three-dimensional (2-D and 3-D) models. The temperature profiles in the 2-D and 3-D models showed good agreement with each other and with the experimental results. The densification process was investigated in a 2-D axisymmetric model. Computation results showed the distribution of the SiC deposition rate within the preform. The results also showed that using two-zone heater gave better deposition uniformity.

1. 25
Numerical study on heat transfer and densification for SiC
composites during thermal gradient chemical vapour
infiltration process
Zaher Ramadan1
and Ik-Tae Im2,♠
1
Department of Mechanical Design Engineering, Graduate School, Chonbuk National University, Jeonju 54896, Korea
2
Department of Mechanical Design Engineering, College of Engineering, and Design Center for Eco-Friend Machine Parts, Chonbuk
National University, Jeonju 54896, Korea
Received 14 January 2017
Accepted 24 September 2017
♠
Corresponding Author
E-mail: itim@jbnu.ac.kr
Tel: +82-63-270-4761
Open Access
pISSN: 1976-4251
eISSN: 2233-4998
CarbonLettersVol.25,25-32 (2018)
Original Articles
Article Info
Copyright © Korean Carbon Society
http://carbonlett.org
Abstract
In this study, a thermal-gradient chemical vapor infiltration (TG-CVI) process was numeri-
cally studied in order to enhance the deposition uniformity within the preform. The compu-
tational fluid dynamics technique was used to solve the governing equations for heat transfer
and gas flow during the TG-CVI process for two- and three-dimensional (2-D and 3-D)
models. The temperature profiles in the 2-D and 3-D models showed good agreement with
each other and with the experimental results. The densification process was investigated in
a 2-D axisymmetric model. Computation results showed the distribution of the SiC deposi-
tion rate within the preform. The results also showed that using two-zone heater gave better
deposition uniformity.
Keywords: SiC composites, porous media, thermal gradient chemical vapor infiltration,
computational fluid dynamics
1. Introduction
Chemical vapor infiltration (CVI) is one of the most common ways to fabricate ceramic
matrix composites without damaging the fibers and has the advantage of making near-net-
shape products. Numerous types of fiber-reinforced ceramic composites can be fabricated by
the CVI process [1,2]. CVI is a process derived from chemical vapor deposition (CVD) [3]
that is widely used for the deposition of thin films. The method involves placing a substrate
in a surrounding of reactive gases or precursors, and the thermally activated reaction yields a
solid deposit [4]. The main difference between CVD and CVI is the nature of the substrate;
for CVI, a porous medium substrate is used that can be infiltrated by the precursor gases. A
variety of techniques can be applied for infiltration that are classified according to whether
they utilize diffusion in isothermal CVI reactors or forced flow for transport of gaseous spe-
cies, and whether thermal gradients are imposed.
The earliest type of CVI, still in use today, the isothermal CVI (I-CVI) is the most widely
used technique for fabrication of ceramic composites. I-CVI has been widely applied to
commercial process [5-10]. The key feature of this approach is that both temperature and
pressure are kept constant during the infiltration process. It has been found that I-CVI in-
volves completion between gas diffusion and reaction [11-13]. Moderate temperature and
low pressure are used to prevent premature pore plugging. To preserve the material quality
under such condition, a very long infiltration time and additional energy are required. In
order to overcome this limitation of the I-CVI process, a variety of modifications have been
developed by application of thermal gradient and/or forced gas flow to fibrous preform [14-
17]. In the forced CVI (F-CVI) process, the reactant gas is forced to flow through the pre-
form by inducing a pressure gradient from one surface to the opposite surface of the preform.
DOI: http://dx.doi.org/
DOI:10.5714/CL.2018.25.025
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Gold functionalized-graphene oxide-reinforced acrylonitrile butadiene rubber nanocomposites for piezoresistive
and piezoelectric applications
BismarkMensah,DineshKumar,Gi-BbeumLee,JoohyeWon,KailashChandraGuptaandChangwoonNah
Preparationandcapacitancepropertiesofgraphenebasedcompositeelectrodescontainingvariousinorganicmetaloxides
Jeonghyun Kim, Sang Chul Byun, Sungwook Chung and Seok Kim
KCS Korean Carbon Society
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pISSN: 1976-4251
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VOL. 25 January 31 2018

2. Carbon Letters Vol. 25, 25-32 (2018)
DOI: http://dx.doi.org/10.5714/CL.2018.25.025 26
to create a thermal gradient in the preform, a hollow cylindrical
heater is embedded in the center of the reactor. The heater is
electrically heated to maintain a constant temperature of 1323
K. Subsequently, reactant gases are supplied from the bottom of
the reactor and the introduced gases are distributed uniformly
around the preform throughout 16 holes. The developed model
for this study is based on the geometry of the prototype designed
for the experiment. Fig. 1b and c show the 3-D and 2-D axisym-
metric models, respectively, used in this study.
The following important assumptions were employed in the
numerical simulation to reduce the computational complexity.
● The gas follows the ideal gas law.
● The gas flow in the reactor is laminar. The range of Reynolds
number (Re) that is typically observed for CVD and CVI
systems is generally much smaller than the turbulent
threshold value of ~2,300 for flow in a pipe [3,25].
● Heat transfer is a steady-state phenomenon.
Based on these assumptions, the governing equations in-
cluded mass, momentum, energy, and species conservation
equations. The conjugate heat transfer was solved for the en-
tire reactor including conduction, convection, and radiation.
The discrete ordinate method developed by Fiveland [26]
However, it has been reported that some densification gradient
and pore closure due to gradual decrement of reactant gas con-
centration between the inlet and outlet were found. In order to
overcome this problem, a temperature gradient was introduced
into the process of F-CVI to enhance the quality and to shorten
the processing time. This process is so-called thermal gradient
CVI (TG-CVI) process. Golecki et al. [18] have implemented a
“rapid densification” process based on isobaric conditions and
the creation of hot side and cold side on the preform. TG-CVI
has also been considered with in situ heat production, like mi-
crowave heating [19,20] or radio-frequency induction heating
[21,22], with the idea of creating a hot deposition zone at the
preform center.
In the TG-CVI process for producing a carbon/silicon carbide
(C/SiC) composite, a cylinder-shaped preform is placed in the
center of a reactor. During the process, vapor precursor gases,
such as methyltrichlorosilane (CH3SiCl3, abbreviated as MTS),
diffuse through the preform from the cold side and deposit a
layer of solid SiC near the hot surface, filling the inter-fiber void.
As the deposition progress continues the spaces between the fi-
bers become smaller and the depositing moves from the inside
to the outside of the preform. Thus, the external surface of the
preform will remain unsealed until the end of the process. It is
very important because blocking precursor gases due to surface
sealing is the main drawback of the simple isothermal CVI pro-
cess. However, due to the prevention from early closure of the
preform surface, TG-CVI method allows better densification of
the ceramic matrix [23].
One of the main drawbacks of the CVI process is the long
manufacturing time [24]. In densification, it is desirable to mini-
mize the processing time, which is subjected to the constraints
of the required degree of densification. In addition, uniformity
is particularly critical in the infiltration process. This process in-
cludes complex physiochemical phenomena such as transport of
momentum, energy and mass in free media, and porous medium,
as well as changes of pore structure in the preform due to the
deposition. Moreover, the CVI process depends on the tempera-
ture, reactor pressure, gas flux, structure, and geometry of the
preform and reactor. These conflicting goals of reducing manu-
facturing time while maintaining deposition uniformity can be
achieved by careful selection of the processing conditions.
In the present work, we used the computational fluid dy-
namics technique to describe the heat and mass transfer ef-
fects on densification during the TG-CVI process. The flow
behavior, temperature distribution, and concentration profiles
in the TG-CVI reactor were predicted by using two-dimen-
sional (2-D) and three-dimensional (3-D) models. Based on
the results from these models, the densification process was
simulated using a 2-D model in order to provide better pro-
cess parameters.
2. Analysis
2.1. Problem description
The thermal-gradient CVI apparatus considered in this study
is shown in detail in Fig. 1. A hollow cylindrical preform is in-
stalled in the center of the reactor as shown in Fig. 1a. In order
Fig. 1. Schematic diagram of TG-CVI reactor. (a) Configuration, (b) 3-D
model, (c) 2-D model.

3. Heat transfer and densification for SiC composites
27 http://carbonlett.org
2.2. Modeling of densification
The densification within the preform was predicted in a 2-D
axisymmetric model. MTS and hydrogen were used as a precur-
sor and a carrier gas, respectively. The flow rates of the precur-
sor gas and the carrier gas were 3960 mL min–1
and 960 mL
min–1
, respectively. As the temperature of the gasses reached
close to the reaction temperature, MTS pyrolysis occurs in the
deposition zone. The SiC deposition is a very complex process
and the overall chemical reaction is as follow:
(1)
The reaction rate constant was computed based on the Reuge-
Vignoles Model [10],
(2)
where R=8314 J/(kmol-K) is the universal gas constant and T
is the temperature in Kelvin. The evolution of the porous struc-
ture due to SiC deposition was described using the quasi-steady
state approach because the characteristic time of pore struc-
ture change was much longer than the time for mass transport
through the porous media. Therefore, the overall simulation for
was used to model the radiation heat transfer. The flow of
the multicomponent gas mixture was considered in the free
gas region and in the porous medium in the preform. Navier-
Stokes equations were used to solve the flow in the gas region
and the Darcy-Brinkman-Forchheimer flow model was used
to describe flow in the porous preform. The fibrous preform
was considered as a porous medium. The effective thermal
conductivity, permeability, diffusion coefficients, and viscos-
ity of the vapor in the pore region were computed from local
values of porosity, vapor composition, pressure, and tempera-
ture [27]. Details of the governing equations can be found in
the literatures [10,28,29].
The pressure in the reactor was 2666.5 Pa (20 torr) and the
heater temperature was 1323 K. The hydrogen flow rate at the
inlet was 3960 mL min–1
. The 2-D model of the reactor was con-
sidered axisymmetric despite the non-axisymmetric configura-
tion of the heater holes. In order to overcome this non-axisym-
metric state, the holes on the heater were also treated as parts of
the heater, having fluid properties.
An example of a computational mesh for the 3-D model is
shown in Fig. 2. Two different grid systems were created to
check the independence of the results to the size of the mesh
cells. The first grid system shown in Fig. 2a has a fine grid di-
vided by a total of 1,891,615 cells and the second grid system
has a coarse grid, as shown in Fig. 2b, which is divided by a
total of 779,173 cells. Comparison between computational and
experimental results of temperatures showed a reasonable agree-
ment as shown in Fig. 3. Three thermocouples were used in the
experiment and placed in specific positions to show the tem-
perature gradient along the preform length and thickness. The
numerical computation results from both grids agree but show
a lower temperature at the external surface of the preform, T3,
than the measured value. This is because the densification pro-
cess was not considered in the computations. The densification
increases the thermal conductivity of the preform and thus the
temperature T3 is expected to be high in the experimental result.
The less dense grid shown in Fig. 2b was used in all simulations
in order to reduce computing time.
Fig. 2. Two different grid systems used in the grid dependency test. (a)
Dense grid with 1,891,615 cells and (b) coarse grid with 779,173 cells.
Fig. 3. Comparison between the computed temperature using two
different grid systems and the measured temperature. (a) Thermocouples
positions on the preform and (b) temperatures profiles.
Table 1. Characteristics and properties of the preform
Characteristic Value
Bundle diameter (mm) 0.8
Fiber diameter (μm) 7.0
No. of fibers in the bundle 12 000
Porosity 0.7
Permeability (m2
) 3.98×10–8
Specific surface (m–1
) 1.33×103
Average diameter of pores (mm) 2.02

4. Carbon Letters Vol. 25, 25-32 (2018)
DOI: http://dx.doi.org/10.5714/CL.2018.25.025 28
tor is higher than in the region near the inlets.
It is important to predict the temperature distribution
within the preform and to improve the densification rate and
uniformity. Fig. 5 presents the temperature profiles along
the preform height plotted for three positions at the preform
thickness: the inner surface, the middle of the preform thick-
ness, and the outer surface. It can be concluded from Fig. 5
that the temperature along the height is almost constant and
no significant drop occurs. The temperature from the 3-D
simulation at the middle and outer surfaces of the preform
is lower than that from the 2-D simulation. Convective heat
transfer due to cold inlet gas may be captured better in the
3-D model than in the 2-D model. The temperatures from the
2-D and 3-D simulations at the inner surface of the preform
are almost the same because of the fixed heater tempera-
ture. Fig. 6 shows the temperature profiles along the preform
thickness. The profiles are plotted at the middle of the height
the densification process was divided by a series of steady-state
problems describing the growth of SiC at a certain moment. De-
tails about modeling in the densification process including the
governing equations can be found in the literature [30,31]. Table
1 shows the properties of the preform considered in this study.
3. Results and Discussion
3.1. Temperature distribution and flow pattern
Fig. 4 shows the temperature distribution in a vertical cross
section of the reactor. In the inlet, the cold gas enters the reac-
tor and is heated. A relatively clear gradient in temperature is
observed in the reactor and the preform, especially in the radial
direction. The highest temperature is in the heater and the tem-
perature decreases almost linearly toward the reactor wall. It can
also be observed that the temperature in the top part of the reac-
Fig. 4. Temperature distribution in a vertical cross section of the reac-
tor. (a) 3-D simulation result and (b) 2-D simulation result.
Fig. 5. Temperature profiles along the preform height at the inner sur-
face, the middle of the preform (in thickness), and the outer surface for
the 2-D and 3-D models.
Fig. 6. Temperature profiles along the preform thickness at the middle
of the preform height for 2-D and 3-D models.
Fig. 7. Comparison of temperatures from simulations and measure-
ment.

5. Heat transfer and densification for SiC composites
29 http://carbonlett.org
it further decreases because of the porous medium resistance to
the flow. This resistance leads to the formation of an almost uni-
form radially-oriented flow through the preform. The gas flow
remains slow until it infiltrates the preform. The gas then enters
the reactor centre and the velocity starts to increase. The highest
magnitude of velocity is around 11 m s–1
at the outlet. Some vor-
tex or flow circulation in the top of the reactor near the brick can
also be observed. Obviously, this is because the brick prevents
gas from passing through it, producing a stagnation zone in the
top of the reactor.
The flow pattern from the 2-D simulation is similar to that
shown in Fig. 9. It can be seen that in the centre of the rector,
the velocity is high and the greatest magnitude is at the outlet.
The velocity vectors and flown pattern shown in Fig. 9 is almost
the same as those shown in Fig. 8. The length of the vectors in
Fig. 9b was made to be uniform in order to show flow pattern
clearly so the length of vectors in this figure does not represent
the velocity magnitude.
3.2. Densification process
A number of parameters describe the progress of the den-
sification process within the preform and are therefore re-
lated to the properties of the preform material. Temperature
and species mass fraction are examples of these parameters,
which are distributed in space within the preform and vary
in time.
Fig. 10 shows the temperature distribution in the preform
during the process. The overall preform temperature increases
of the preform. A temperature drop is observed along the
preform thickness, which is desired for the TG-CVI process.
This temperature drop produces a good deposition without
blocking the gas flow directing the densification process from
inside to outside of the preform. Once again, 3-D simulation
gives a lower temperature profile than that of 2-D simulation.
This is because the fluid parts in the heater in the 2-D model
were given the same temperature of the heater, which might
be higher than the gases flowing through in a real situation.
The temperatures obtained from the 2-D and 3-D simulations
are compared with the measured values in Fig. 7. Three thermo-
couples were placed at specific positions relevant to the pilot
reactor, which was made for process optimization. The three
positions were selected in order to show the temperature gradi-
ent along the preform length and thickness. The computed and
measured data are in good agreement, as shown in Fig. 7. The
temperature from 3-D calculation is lower than that of the 2-D
calculation, as discussed in the previous paragraph.
The gas velocity field in the reactor is presented in Fig. 8.
Fig. 8a shows the distribution of the velocity magnitude in the
entire reactor and Fig. 8b presents the flow pattern described by
arrows having the same length at a cross section of the reactor.
We set the length of all the velocity vectors to be the same in
order to show the flow fields clearly in Fig. 8b. The magnitude
of the vectors is expressed in colors, as shown on the right side
bar. It can be seen that the gas velocity in the inlet is low, and
Fig. 8. Flow pattern in the reactor. (a) Distribution of the velocity mag-
nitude and (b) flow pattern in a cross section.
Fig. 9. Flow fields from 2-D model. (a) Distribution of the velocity mag-
nitude and (b) flow pattern at a cross section.
Fig. 10. Distribution of temperature in the preform during the densifi-
cation process at a heater temperature of 1323 K.

6. Carbon Letters Vol. 25, 25-32 (2018)
DOI: http://dx.doi.org/10.5714/CL.2018.25.025 30
the low temperature, as shown in Fig. 10. It is expected that it is
difficult to fill the bottom part of the preform because of the inlet
air (gas) with low temperature.
3.3. Design improvement
In order to improve the deposition uniformity in the preform,
the heater is divided into two zones and different temperatures
are given to each zone. The temperature of the lower part of the
heater, depicted as T* in Fig. 14, is increased from 1323 K to
1353 K, 1373 K, and 1393 K, as shown in Fig. 14a-d, respec-
tively, while the upper part of the heater is maintained at 1323 K.
The use of this two-zone heater is expected to improve the po-
rosity distribution because it is possible to give additional heat
to the lower part of the heater.
Analyses results show that using two-zone heating is effec-
tive, as shown in Fig. 14. The temperature difference (ΔT) be-
tween the maximum temperature and the minimum temperature
within the preform at the end of the process showed that increas-
ing T* by 50 K decreases the temperature difference ΔT within
the preform. Other T* suggestions did not result in a success-
ful decrease in ΔT. No significant decrease in ΔT was observed
when increasing T* from 1323 K to 1353 K, as shown in Fig.
14b. By increasing the temperature from 1323 K to 1393 K, the
lower edge of the preform becomes hotter than the top edge and
the temperature difference within the preform increases again.
The second suggestion (T*=1373 K) shown in Fig. 14c gives the
smallest temperature difference within the preform.
Fig. 15 shows a comparison of the distribution of porosity within
the preform between the original heater and the two-zone heater. It
gradually as the time step increases. It can be seen that the tem-
perature in the bottom part of the preform is the lowest. This
drop in temperature is due to the gas flow within this region.
Obviously, the gas moves in the easiest path with the least resis-
tance, which is near the heater’s slots in this case and fresh inlet
air is continuously introduced to this region. Thus, the preform
temperature at the bottom area is the lowest throughout the pro-
cess. Figs. 11 and 12 plot the distributions of the MTS and HCl
mass fractions, respectively, within the preform at two different
times. The minimum concentration of MTS, and correspond-
ingly, the maximum concentration of HCl, is observed in the top
and adjacent to the heater region of the preform where the tem-
perature is the highest. Obviously, the disappearance of MTS
and the generation of HCl is the result of chemical reaction [1].
Fig. 13 shows the evolution of the structure of the preform
porous medium as a result of matrix material deposition. The
figure shows the distributions of porosity at different moments
during the process. The red color in the figure corresponds to the
value of initial porosity. As the densification process develops
from the inner surface of the preform toward the outer surface,
the porosity decreases according to the deposition. Deposition
takes place in the radial direction in the early stage of the pro-
cess, where t=200 h. However, the porosity at the bottom of the
preform still remains at a high value until t=400 h because of
Fig. 11. Distribution of MTS mass fraction within the preform at a
heater temperature of 1323 K.
Fig. 12. Distribution of HCl mass fraction within the preform at a heater
temperature of 1323 K.
Fig. 13. Distribution of porosity within the preform at the heater tem-
perature of 1323 K.

7. Heat transfer and densification for SiC composites
31 http://carbonlett.org
4. Conclusions
In this study, 2-D and 3-D models for analysis of a TG-CVI
process of C/SiC composites were developed and applied to the
pilot reactor. The commercial computational fluid dynamics
software package CFD-ACE+ was used to investigate the heat
and gas flow during the process in both the 2-D and 3-D models.
The densification behavior of the C/SiC composites was inves-
tigated in a 2-D model. The analyses results of heat transfer,
gas flow, and densification can be summarized as follows. First,
the temperature distribution profiles showed good agreement
between the 2-D and 3-D models. In addition, the measured
temperature using thermocouples at three reference points were
compared with computed temperatures in both the 2-D and 3-D
models. The comparison showed a relatively good agreement
between the computed and measured temperatures. Second, the
temperature along the preform height was almost constant and
no significant drop was observed. On the other hand, a signifi-
cant drop in temperature along the preform thickness direction
was observed. This drop forms a gradient in temperature which
is favorable in the TG-CVI process. Third, the flow profiles in
the 2-D and 3-D models showed good agreement. The resistance
of porous medium preform leads to the formation of a uniform
radially-oriented flow through the preform. And fourth, in order
to improve the deposition uniformity in the preform, a two-zone
heater was proposed and the temperature of the lower part of
the heater was increased to different values. Increasing the tem-
perature by 50 K was the most effective method for ensuring the
uniformity of the SiC deposition rate.
Conflict of Interest
No potential conflict of interest relevant to this article was
reported.
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