numerical modeling of the air permeability of knitted...
TRANSCRIPT
1804
ISSN 1229-9197 (print version)
ISSN 1875-0052 (electronic version)
Fibers and Polymers 2017, Vol.18, No.9, 1804-1809
Numerical Modeling of the Air Permeability of Knitted Fabric Using
Computational Fluid Dynamics (CFD) Method
Seyedeh Sarah Hosseini Dehkordi1, Mohammad Ghane
1, Sayyed Behzad Abdellahi
1*, and
Milad Babadi Soultanzadeh2
1Department of Textile Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran2Department of Mechanical Engineering, Islamic Azad University, Khomeini Shahr Branch, 8418148499, Iran
(Received March 14, 2017; Revised June 12, 2017; Accepted July 18, 2017)
Abstract: In this study computational fluid dynamics (CFD) method was applied to simulate air permeability of knittedfabrics with rib and interlock structures. For this purpose, two types of knitted fabrics with rib 1×1 and interlock structureswere produced with three different loop densities. Air permeability test was carried out on all samples. A unit cell of eachsample was created using CATIA software by Vassiliadis model which considers the real shape of knit loop in threedimensions space. CFD analysis was then executed on all samples by Fluent software. Two turbulent models, k-ε and k-ω,were used for CFD analysis. The numerical results showed good agreement with the experimental results. It can be concludedthat CFD model is an efficient model to predict air permeability of knitted fabric by using unit cell of knitted fabric structure.Using this procedure can reduce the operation size and consequently the solution time is considerably reduced.
Keywords: Knitted fabrics, Air permeability, Numerical modeling, Computational fluid dynamics (CFD), Knit loopgeometry
Introduction
Fabric comfort is the one of the most important
characteristics which depends on various factors such as air
permeability, heat transfer, water vapor permeability and etc.
[1]. Air permeability is an important property of clothing
that is defined as the rate of volume flow air pass
perpendicularly through an unit of fabric area at some
pressure gradient over a time unit [2]. In this way, extensive
studies have been carried out to predict and compute fabric
air permeability. Hagen-Poiseuille formula together with
Darcy law were applied by Kulichenko and Langenhove to
predict air permeability of woven fabrics by a theoretical
model [3]. Zupin et al. investigated construction parameters
of fabric to calculate porosity of woven fabrics [4]. Xu and
Fang used the Hagen-Poiseuille formula to establish the
equation expressing the relationship between permeability
of interyarn interstices and fabric structures [5]. Havalova
studied influence of plain woven fabric structure on air
permeability and discussed the possibility of the prediction
of fabric air permeability [6]. A theoretical model was
developed to predict air permeability of plain knitted fabric
by Ogulata and Mavruz [7]. On the other study, Afzal et al.
analyzed and modeled the effect of knitting parameters on
the air permeability of cotton/polyester double layer interlock
knitted fabrics. The model predicted air permeability of
knitted fabrics and predicted values had good agreement
with experimental data [8]. Karaguzel calculated values of
pore size and pore volume for plain knitted fabrics. The pore
sizes were measured by image analysis and fluid extrusion
procedures [9].
On the other hand, computational fluid dynamic (CFD)
modeling can be an effective tool to predict and model fabric
air permeability. Consequently, the number of researches
who use CFD for fabric air permeability modeling is
increasing recently. Reif et al. investigated modeling and
CFD simulation of woven fabrics. They used three dimensional
(3D) geometry of yarn to CFD model of air permeability
woven fabric [10]. 3D simulation of air permeability of
single layer woven fabric by CFD tool was applied by
Angelova et al. [11]. On the other study, Kyosov et al.
investigated numerical modeling of the air permeability of
two layer woven fabric by CFD model. The model and
experimental results obtained acceptable agreement [12].
Wang et al. used a unit cell geometry of plain woven fabric
for modelling pressure drop of monofilament-woven fabrics.
They designed filaments elliptical cross-sections and used
CFD method to model pressure drop. The results showed
that the discharge coefficient decreased by increasing the
aspect ratio of the filaments cross-section [13].
There is limited number of studies that illustrate how to
use CFD technique to model and simulate knitted fabrics air
permeability. Cimilli et al. used CFD model to determine
natural convective heat transfer coefficient for plain knitted
fabric. 3D geometry of plain knitted fabric loop was created
by CATIA software and Fluent software was employed to
CFD analysis [14]. Mullings et al. developed a geometric
model of a knitted metal filter and coupled geometry model
outputs to a novel CFD model for fibrous filters. The CFD
results showed increased capture efficiency and pressure
drop compared to fibrous filter theory [15]. Mezarcioz et al.
employed Fluent software for CFD modeling of plain
knitted fabric. They assumed porosity of knitted fabric as
some circular spaces and air move through these spaces. The*Corresponding author: [email protected]
DOI 10.1007/s12221-017-7238-0
Numerical Modeling of Air Permeability of Knitted Fabric Fibers and Polymers 2017, Vol.18, No.9 1805
CFD and experimental results were compared and were
compatible together [16].
As it stands, in most studies plain knitted fabric were
modeled and rib or interlock knitted fabrics have not been
modeled by CFD technique. Supposedly, simplification for
modeling knitted fabric loop also led to increase error in
CFD modeling. In this study, we tried to develop a novel
approach to simulate rib and interlock knitted fabrics based
on 3D geometry of knit loop and CFD. Loop geometry was
created by equations of loop curve in CATIA software and
CFD modeling was performed by using Fluent software.
Experimental
Cotton/polyester yarn (30 denier count and 0.22 mm
diameter) was used to produce knitted fabrics. All fabrics
were manufactured by Mayer & Cie® double jersey circular
knitting machine.
The fabrics were made with rib and interlock pattern.
Table 1 shows structural and physical properties of knitted
samples. The knitted samples were conditioned for 48 hours
in atmospheric conditions of 20±2 oC temperature and
65±2 % relative humidity before structural properties were
measured and air permeability test was performed.
Geometry of loops plays an important role in size rope and
air permeability of fabric. The microscopic pictures of
knitted samples are shown in Figure 1.
Air permeability test was performed by Shirley Air
Permeability tester according to ASTM D737-96 standard
[17]. The test area for air permeability was 78.5 mm2. The
pressure difference between two sides of the fabric was set at
constant value of 100 Pa. Ten measurements were performed
for each sample.
Numerical Modeling
Equations for Loop of Weft Knitted Fabric
Vassiliadis model was used to create 3D geometry of
knitted fabric loop [18]. This is a three dimensional model of
a loop with high compatibility to the actual shape of the loop
in fabric structure. A loop was made from four same parts in
this model and equations were used for a quarter of the loop.
Geometrical parameters of the looped structure including
wales spacing, courses spacing, and yarn diameter must be
predetermined while the other essential characteristics of
knitted fabric could be achieved from the main features.
Figure 2 illustrates the Vasiliadis proposed geometrical
structure of a knit loop.
Based on Figure 2, a quarter of a loop consists three
sections; ƩM (from the side view), MK (from the front view)
and KA (from the top view). Therefore, curve equation
needs to be defined for these three sections. The section ƩM
is considered as an elliptic arc in 3D space that can be
represented as a circle with radius of (r+D/2) in the YZ
plane and a straight line in XY plane. D is the diameter of
yarn and r can be calculated as follow:
(1)
where c is courses spacing and t is a parameter that is related
r cD
2----–
t
2---–⎝ ⎠
⎛ ⎞2 D
2----
t
2---+⎝ ⎠
⎛ ⎞2
–⎩ ⎭⎨ ⎬⎧ ⎫
/ 2D( )=
Table 1. Structural properties of knitted samples
Sample
codePattern
Wale per
cm
Course per
cm
Thickness
(mm)
Weight
(g/m2)
R-1 rib 1×1 9 11 0.56 130.82
R-2 rib 1×1 9 13 0.58 134.61
R-3 rib 1×1 9 14 0.63 151.23
I-1 Interlock 9 11 0.7 278.04
I-2 Interlock 11 16 0.79 246.70
I-3 Interlock 11 18 0.81 264.14
Figure 1. Microscopic pictures of knitted fabrics; (a) Sample R-1, (b) Sample R-2, (c) Sample R-3, (d) Sample I-1, (e) Sample I-2, and
(f) Sample I-3.
1806 Fibers and Polymers 2017, Vol.18, No.9 Seyedeh Sarah Hosseini Dehkordi et al.
to loop curvature ( ). The next section (MK) is
also considered as an elliptic arc in 3D. It is allocated as an
arc of the mentioned circle in the YZ plane and a quarter of
an ellipse of minor and major radius and b = R
in the XY plane. R can be calculated by the following equation:
(2)
Thus, the coordinates of the sections ƩM and MK are
derived from the following equations:
Part ƩM ( ):
(3)
(4)
Part MK ( ):
(5)
(6)
Considering Figure 2(a), the section KA is calculated as
circular equations that could be allocated to this section as
following:
Part KA ( ):
(7)
(8)
where
(9)
(10)
(11)
In equation (7)-(9), w is wales spacing.
Creating Geometry of Weft Knit Loop
To create 3D geometry of weft knit loop in first step, all
equations in previous sections were rewritten in MATLAB
software. Then, the point’s coordinates on central axis of the
loop path were entered in CATIA software. By using yarn
diameter and loop path, a quarter of loop was drawn in
CATIA. The cross section of yarn was assumed to have a
circular shape. Regarding loop symmetry, one complete loop
can be created by symmetry tool in CATIA. A knit loop is
shown in Figure 3.
Figure 4 illustrates schematic structural characteristics of
1×1 rib and interlock knitted fabric.
Considering Figure 4, in rib structure, the location of each
knit loop in a wale is reverse of lateral loop and in interlock
fabric there are two rows of knit loops whose locations in
each row are opposite. The design of a knitted fabric
structure is shown in Figure 5.
0 t c 2D–≤ ≤
a D/2 h+=
Rc
2---
t
2---
D
2----––=
0 y c/2< <
x y( )D
c----y–=
z y( ) r D/2+( )2 y2
– rD
2----+⎝ ⎠
⎛ ⎞–=
c
2--- y
c
2---< < R+
x y( ) h a 1y c/2–
b---------------⎝ ⎠⎛ ⎞
2
––=
z y( ) r D/2+( )2 y2
– rD
2----+⎝ ⎠
⎛ ⎞–=
c/2 R+ x w/4< <
z x( ) OZ A2
x OX–( )2––=
y x( ) r D/2+( )2 z r D/2+ +( )2–=
OX w/4=
OZx2 OX–( )2 x1 OX–( )2 z2
2z12
–+–
2z2 2z1–------------------------------------------------------------------------=
A x1 OX–( )2 z1 OZ+( )2+=
Figure 2. Geometrical model of the knit loop; (a) top view, (b) front view, and (c) side view [18].
Figure 3. A knit loop for sample R-1.
Figure 4. Schematic structural of knitted fabric; (I) Rib 1×1 and
(II) Interlock [19].
Numerical Modeling of Air Permeability of Knitted Fabric Fibers and Polymers 2017, Vol.18, No.9 1807
As it is shown in Figure 5, a cell containing two courses
and two wales were designed. In order to develop CFD
modeling, a unit cell from each sample was separated and
input to CFD software. For rib and interlock structures a unit
cell contains two and four cross-overs, respectively. A Unit
cell for rib and interlock structures is shown in Figure 6.
CFD Analysis
For CFD analysis, ANSYS 15.1 package was used that
included Fluent software for CFD analysis. The sample was
immersed in a pipe-like domain, 4 mm after the domain inlet
and 9 mm before the domain outlet, so as to assure the total
flow formation after the sample. Sample structures were
meshed by Tet element. Mesh generated details and a meshed
sample are shown in Table 2 and Figure 7, respectively.
Using a unit cell of model caused to reduce time resolution
because of small dimensions of the model. Two different
turbulent models were used to CFD analysis: k-ε and k-ω
from the group of the Eddy Viscosity Models (EVMs). The
k-ε turbulence model adds two extra transport equations to
the RANS equations for the kinetic energy k and its
dissipation rate ε. The k-ω turbulence model is also a two-
equation model, in which an equation for the specific
dissipation ω is included instead of the dissipation ε of the
kinetic energy k. Pressure difference between two faces of
fabric was set to 100 Pa (according to experiment).
Results and Discussion
The output of air permeability tester machine is the flow
rate of the air for the fabric (Q). The value of air permeability
(R) is calculated according to the follow equation (12):
(12)
where At is the tested fabric area. In fact, air permeability
refers to air velocity passes through the fabric. The
simulation results for the velocity field for all samples are
shown in Figure 8.
As shown in Figure 8, airflow moved from inlet (left of
Figure 8) to outlet (right of Figure 8) due to pressure
difference between two sides of the sample.
As the air flow touches the fabric, it deviates its pass
toward the pore locations in order to pass through the fabric.
This causes the increase of the air flow velocity. After
passing the fabric, the air flow tends to retain its direct pass.
This phenomenon is well illustrated in Figure 8.
Increasing the loop density causes the decrease of pore
size in the sample and consequently decreases the air
permeability. On the other hand, because of two layers of
structural interlock in comparison to the rib structure, the
RQ
At
----=
Figure 5. Fabric structure designed in CATIA software; (a) Sample
R-1, (b) Sample R-2, (c) Sample R-3, (d) Sample I-1, (e) Sample
I-2, and (f) Sample I-3.
Figure 6. Fabrics unit cell; (I) Rib 1×1 and (II) Interlock.
Table 2. Details of the meshing of the samples
Sample
code
Element
type
Number of
elements
Number of
nods
R-1 Tet 58831 13085
R-2 Tet 52261 11588
R-3 Tet 49609 11086
I-1 Tet 91289 20128
I-2 Tet 73944 16499
I-3 Tet 65769 14639
Figure 7. Computational mesh for sample R-1.
1808 Fibers and Polymers 2017, Vol.18, No.9 Seyedeh Sarah Hosseini Dehkordi et al.
value of air permeability is less for the sample with interlock
structure than the one with rib structure (for example sample
R-1 with I-1). The valuations between numerical and
experimental results are summarized in Table 3.
It can be seen that there is a high agreement between
numerical and experimental results. According to Table 3,
the results for k-ε model shows less error value in comparison
to k-ω.
Using the actual structural parameters of the knitted fabric
leads to obtain acceptable simulation geometry. Thus, the
CFD can be applied more precisely in prediction of fabric air
permeability.
Existence of two rows in interlock fabric leads to a
decrease of porosity in fabric structures. In fact, loops
overlap is one of the important reasons to reduce the fabric
porosity in interlock structure.
One the other hand, according to Unal et al. study [20] air
permeability of knitted fabrics has significant negative
correlation with yarn hairiness. Increasing yarn hairiness
leads to increase friction between fibers and airflow and
decreas air permeability. In this study, yarn was assumed as
yarn without any hairiness which can be one of the reasons
for having difference between experimental and numerical
results.
Conclusion
In this article air permeability test for knitted fabrics with
rib and interlock structures was simulated by CFD technique.
Based on the results obtained in this study, increase of loop
density of knitted fabric led to decrease of air permeability.
On the other hand, knitted fabric with interlock structure
contained less air permeability in comparison with knitted
fabric with rib structure in the same loop density. In this
study, CFD method was verified and applied successfully for
predicting and investigating the air permeability of knitted
fabrics with rib and interlock structures. Using unit cell for
knitted fabric created by 3D geometry of knit loop, the
solving time was reduced as well as improving the CFD
results.
Acknowledgement
The authors would like to express their sincere thanks to
the deputy of research of Isfahan University of Technology
for the financial support.
Figure 8. Velocity counters for all samples; (a) Sample R-1, (b)
Sample R-2, (c) Sample R-3, (d) Sample I-1, (e) Sample I-2, and
(f) Sample I-3.
Table 3. Numerical and experimental results
Sample
code
Experimental air
permeability
results (ml/s·cm2)
Experimental
results (m/s)
Numerical air permeability
results (ml/s·cm2)Numerical results (m/s) Error (%)
k-ε k-ω k-ε k-ω k-ε k-ω
R-1 364 4.636 376.012 378.56 4.793 4.825 3.3 4.0
R-2 321 4.089 343.47 341.54 3.802 3.824 7.0 6.4
R-3 290 3.694 297.25 299.28 3.790 3.815 2.5 3.2
I-1 275 3.237 285.175 283.8 3.117 3.131 3.7 3.2
I-2 156 2.276 165.51 166.29 2.416 2.427 6.1 6.6
I-3 140 1.863 148.26 148.54 1.973 1.977 5.9 6.1
Numerical Modeling of Air Permeability of Knitted Fabric Fibers and Polymers 2017, Vol.18, No.9 1809
References
1. A. Das, V. Kothari, and A. Sadachar, Fiber. Polym., 8, 116(2007).
2. G. Bedek, F. Salaün, Z. Martinkovska, E. Devaux, and D.Dupont, Appl. Ergon., 42, 792 (2011).
3. A. Kulichenko and L. V. Langenhove, J. Text. Inst., 83, 127(1992).
4. Ž. Zupin, A. Hladnik, and K. Dimitrovski, Text. Res. J., 82,117 (2012).
5. G. Xu and F. Wang, J. Ind. Text., 34, 243 (2005).6. M. Havlová, Fibres & Text. Eas. Euro., 21, 98 (2013).7. R. T. Oğulata and S. Mavruz, Fibres & Text. Eas. Euro.,
18, 82 (2010).8. A. Afzal, T. Hussain, M. H. Malik, A. Rasheed, S. Ahmad,
A. Basit, and A. Nazir, Fiber. Polym., 15, 1539 (2014).9. B. Karaguzel, MS Thesis, Notrth Carolina State University,
USA, 2004.10. S. Rief, E. Glatt, E. Laourine, D. Aibibu, C. Cherif, and A.
Wiegmann, AUTEX Res. J., 11, 78 (2011).11. R. Angelova, P. Stankov, I. Simova, and I. Aragon, Open
Engineering, 1, 430 (2011).12. M. Kyosov, R. A. Angelova, and P. Stankov, Text. Res. J.,
82, 2067 (2016).13. Q. Wang, B. Maze, H. V. Tafreshi, and B. Pourdeyhimi,
Chem. Eng. Sci., 62, 4817 (2007).14. S. D. Cimilli, E. Deniz, C. Candan, and B. Nergis, Fibres
& Text. Eas. Euro., 20, 90 (2012).15. B. J. Mullins, A. Kinga, and R. D. Braddock, “19th
International Congress on Modelling and Simulation”,Perth, Australia, 2011.
16. S. Mezarciöz, S. Mezarciöz, and R. T. Oğulata, J. Text.
App/Tekstil ve Konfeksiyon, 24 (2014).17. ASTM D737-96, American Society for Testing and
Materials, 2004.18. S. G. Vassiliadis, A. E. Kallivretaki, and C. G. Provatidis,
Indi. J. Fib. Text. Res., 32, 62 (2007).19. D. J. Spencer, “Knitting Technology: A Comprehensive
Handbook and Practical Guide”, CRC Press, 2001.20. P. G. Unal, M. E. Üreyen, and D. Mecit, Fiber. Polym., 13,
87 (2012).