Numerical Modeling of the Air Permeability of Knitted...

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].


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


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