Major project report

CFD analyses of an air-jet loom
i
CFD ANALYSES OF AN AIR-JET LOOM
by
Ágnes Livia BODOR
/GG1E60/
Submitted to the
Department of Fluid Mechanics of the
Budapest University of Technology and Economics
in partial fulfillment of the requirements for the degree of
Master of Science in Mechanical Engineering Modelling
May, 2011
Project Report
Major Project /BMEGEÁTMWD1/
Supervisor:
Gergely KRISTÓF, PhD associate professor
Evaluation Team Members, advisors:
Jenő Miklós SUDA, PhD assistant professor
Viktor SZENTE, PhD research assistant
Department of Fluid Mechanics
Faculty of Mechanical Engineering
Budapest University of Technology and Economics

ASSIGNMENT
MSc MAJOR PROJECT (BMEGEÁTMWD1)
Title: CFD analyses of an air-jet loom
Author’s name (code): Ágnes Livia BODOR (GG1E60)
Curriculum : MSc in Mechanical Engineering Modelling / Fluid Mechanics
Supervisor’s name, title: Gergely KRISTÓF, PhD associate professor
Affiliation: Department of Fluid Mechanics / BME
Assistant supervisor’s name, title: -
Affiliation:
Description / tasks of the project: 1/ To design and to build an experimental device for aerodynamic
testing of a single air-jet loom sub-nozzle and for measuring drag force
acting on the thread. The reed can be replaced with a properly shaped
plate in the experiments (cross-flow can be neglected).
2/ To measure velocity profiles of the air flow for various supply
pressures. To measure the drag force in every experimental case.
3/ To build the 3D geometrical model of the test section in ANSYS
simulation system. To mesh the computational domain with 3 different
spatial resolution.
4/ To compute the flow field for cases of different supply pressure by
taking into account the compressibility effect. To compute the drag
force acting on the thread by means of the air velocity distribution.
5/ To compare simulation results with experimental data.
6/ To assess the effect of periodic boundary condition on the flow
pattern for a given supply pressure.
7/ To document the experimental and the CFD analyses according to
formal requirements of Major Projects.
Handed out / Deadline: 7th
of February 2011. / 13th
of May 2011.
Budapest, 7th
of February 2011.
……………………………….
Head of Department
Received by: The undersigned declares that all prerequisite subjects of the Major Project have been
fully accomplished. Otherwise, the present assignment for the Final Project is to be
considered invalid. Signed in Budapest, on the 7th
of February 2011.
……………………………….
Student

i
DECLARATION
Full Name (as in ID): Ágnes Livia BODOR
Neptun Code: GG1E60
University: Budapest University of Technology and Economics
Faculty: Faculty of Mechanical Engineering
Department: Department of Fluid Mechanics
Major/Minor: MSc in Mechanical Engineering Modelling
Fluid Mechanics major / Solid Mechanics minor
Project Report Title: CFD analyses of an air-jet loom
Academic year of submission: 2010 / 2011 - II.
I, the undersigned, hereby declare that the Project Report submitted for assessment and
defence, exclusively contains the results of my own work assisted by my supervisor. Further to
it, it is also stated that all other results taken from the technical literature or other sources are
clearly identified and referred to according to copyright (footnotes/references are chapter and
verse, and placed appropriately).
I accept that the scientific results presented in my Project Report can be utilised by the
Department of the supervisor for further research or teaching purposes.
Budapest, 13 May, 2011
__________________________________
(Signature)
FOR YOUR INFORMATION
The submitted Project Report in written and in electronic format can be found in the Library
of the Department of Fluid Mechanics at the Budapest University of Technology and Economics.
Address: H-1111 Budapest, Bertalan L. 4-6. „Ae” building of the BME.
ACKNOWLEDGEMENT
It is a pleasure to thank those who made this project possible with their guidance and support.
I offer my regards to my supervisor Gergely KRISTÓF for all the help and advices he ensured
I also want to thank all the members of the Department of Fluid Mechanics who gave me
advices at the evaluation team meetings and supported me to progress in my project. I would like
to highlight the help of Viktor SZENTE at constructing the pneumatic arrangement and András
GULYÁS at the hot-wire measurements.
And I would like to thank for the weaving equipments to Lóránt SZABÓ from the University
of Óbuda.

ii
ABSTRACT
The study is focused on the analysis of the flow induced by an air-jet loom’s sub-nozzle, in
the framework of the project a CFD simulation is presented, along with laboratory experiments
aim at the validation of the CFD results.
The thesis begins with a brief presentation of the weaving process, the development of a
weaving loom and operation of an air-jet loom. Subsequently, a hot-wire measurement is
introduces, during which the velocity distribution of a sub-nozzle placed at a reed is determined,
and the document shows another performed measurement, which goal was to specify drag force
acting on a weft while located in its place in the reed. After the description of evaluating the
mass-flow rate at the sub-nozzles inlet - an important input parameter of the simulation- in the
next chapter the finite-volume model is described, including the geometry and modeling
parameters. Out of the modeling aspects the substitution of the reed with a porous zone is a
curiosity.
The simulation was done with two different mesh densities and the weft was interpreted by a
rigid body at one of the calculations. The results conclude that, although the measured and
simulated air velocities are converging by mesh refinement, the mesh independent solution is not
yet achieved. There is a large discrepancy between the measured and the simulated drag forces,
therefore the corresponding mathematical model should be reconsidered.
KIVONAT
A dolgozat témája a légsugaras szövőgép mellékfúvókájánál kialakuló áramlás vizsgálata,
aminek keretein belül a tárgyról készült CFD szimuláció kerül bemutatásra, valamint annak
validálásához elvégzett mérések.
A munka elején a szövés menete, a szövőgépek fejlődése és a légsugaras szövőgép működése
kerül röviden bemutatásra. Ezt követően a borda mellett elhelyezett segédfúvóka
sebességterének felvételére készített hődrótos mérést és az áramlásba helyezett fonalra ható erő
meghatározását ismerteti a munka. A szimuláció bemeneti paraméteréhez fontos tömeg-áram
meghatározása után, magáról a létrehozott véges-elemes modellről olvashatunk, ezen belül a
kialakított geometriáról, a beállított modellezési paraméterekről, melyek közül érdekesség a
fúvóka melletti borda porózus zónával való helyettesítése.
A szimuláció különböző hálósűrűség mellett és a fonal merev testként való behelyezésével is
megtörtént. Az eredményekből arra következtethetünk, hogy bár a valós és szimulált
sebességprofilok kezdik közelíteni egymást, a hálófüggetlen megoldást még nem értük el.

iii
CONTENTS
DECLARATION ______________________________________________________________________ I
ACKNOLEDGEMENT _________________________________________________________________ I
ABSTRACT _________________________________________________________________________ II
CONTENTS ________________________________________________________________________ III
1. THE SHORT HISTORY OF LOOMS_________________________________________________1
2. THE AIR-JET LOOM ______________________________________________________________3
2.1 The operation of an air-jet loom 3
3. MEASUREMENT OF THE VELOCITY FIELD________________________________________5
3.1 Equipment 5
3.1.1 Pressure transducer 5
3.1.2 Ohmic thermometer 7
3.1.3 Hot wire 8
3.2 Hot wire measurement 8
3.2.1 Hot wire calibration 8
3.2.2 Hot wire results 9
4. MEASUREMENT OF THE FORCE ACTING ON THE WEFT __________________________ 11
4.1 Measurement arrangement 11
4.2 Force measurement 13
5. MASS FLOW RATE MEASUREMENT______________________________________________ 13
6. SIMULATION OF SIMPLE FLOW FIELD___________________________________________ 16
6.1 Geometry of the model 16
6.1.1 The nozzle 16
6.1.2 The reed 16
6.1.3 Enclosure 17
6.2 Meshing 18
6.3 Simulation settings 18
6.4 Results 19
6.4.1 Velocity distributions 19
6.4.2 Visualized flow field 21
6.5 Pressure at the mass-flow inlet 22
7. SIMULATION OF WEFT__________________________________________________________ 23
7.1 Geometry of the model 23
7.2 Simulation with weft 23
7.3 Results of weft simulation 23
SUMMARY __________________________________________________________________________ 24
BIBLIOGRAPHY_____________________________________________________________________ 26
APPENDIX __________________________________________________________________________ 27

iv
LIST OF FIGURES
1.1. Figure Waving frame 1
1.2. Figure Parts of a loom 1
1.3. Figure Ancient and modern loom 2
1.4. Figure Punched card loom 2
2.1. Figure Airjet loom 3
2.2. Figure The composition of the machine's waving part 3
2.3. Figure Subnozzles along the reed 4
2.4. Figure Subnozzle's location, explonation of parts [13] 4
2.5. Figure Different types of sub-nozzle outlets 4
3.1. Figure Measurement arrengement 5
3.2. Figure Oleaginous calibrator with Bourdon manometer 6
3.3. Figure Measured pressures for calibration 6
3.4. Figure Fitted curve for pressure transducers 6
3.5. Figure Calibration of the thermometer 7
3.6. Figure Hot-wire calibration equipment 8
3.7. Figure Hot-wire calibration's King's law 9
3.8. Figure Right-hand side measured velocity distribution 9
3.9. Figure The two measurement positions at the right-hand side 9
3.10. Figure Velocity distribution measured in the middle 10
3.11. Figure Positions of the measurements in the middle 10
3.12. Figure Left-hand side measured velocity distribution 10
3.13. Figure The two measurement positions at the left-hand side 11
4.1. Figure Force measurement arrengement 11
4.2. Figure Calibration with 2.5 g (left) and 6.5 g (right) 12
4.3. Figure Calibration for force measurement 13
4.4. Figure Force measurement on the weft 13
5.1. Figure Mass of air in the reservoir in time 15
6.1. Figure Pictures for modell parameter determination and the coordinate-system 16
6.2. Figure Distances between reedteeth 17
6.3. Figure Geometry and hirher resolution target volume 18
6.4. Figure Boundary conditions 19
6.5. Figure Locations of observed lines 19
6.6. Figure Velocity distribution on the left-hand side (sparse mesh) 20
6.7. Figure Velocity distribution on the left-hand side (denser mesh) 20
6.8. Figure Velocity distribution in the middle-lines (sparse mesh) 20
6.9. Figure Velocity disrtibution on the middle-lines (denser mesh) 20
6.10. Figure Velocity distribution at the right-hand side (sparse mesh) 20
6.11. Figure Velocity distribution at the right-hand side (denser mesh) 20
6.12. Figure Pathlines from inlet of simulated flow-field 21
6.13. Figure Pathlines from reed close nozzle outlet of simulated flow-filed 21
6.14. Figure X velocity distribution on the back of reed 21
6.15. Figure Contour plots of the simulated flow field's z-velocity 22
6.16. Figure Pressure at mass-flow inlet 22
7.1. Figure Position of the weft in the model 23
LIST OF TABLES
3.1. Table Fitting parameters for pressure calibration 7
3.2. Table Fitting parameters for thermometer 7
4.1. Table Data at force measurement 12
4.2. Table Fitting parameters for force measurement 13
5.1. Table Fitting parameters for the mass-flow rate 15
7.1. Table Forces acting on the weft (from simulation) 23
8.1. Table Comparison of measured and simulated velocity distribution 24

1
1. The short history of looms
The process of waving is known since a long time, from BC 8-9, it stands of two distinct sets
of yarns or threads to form a fabric or cloth. The threads which run lengthways are called the
warp yarns and the ones running across from side to side are the weft yarns or fillings. They
passing the weft yarn though the warps in a perpendicular direction, in a way that those are
avoiding the warp yarns alternately on top and bottom side. The fiber after passing is pushed to
the already woven textile, and the next turn is going the other way creating a kind of mesh,
meanwhile the textile (see 1.1. Figure).
1.1. Figure Waving frame
As the woven techniques progressed the cloth was woven on looms, a device that holds the
warp threads in place while filling threads are woven through them. It fastened the process a lot,
because the warp yarns did not have to be separated every time when crossing the weft, instead
they were hold by the so called heddles and could be reordered by a lathe (see 1.2. Figure)
1.2. Figure Parts of a loom
1. Wood frame
2. Seat for weaver
3. Warp beam- let off
4. Warp threads
5. Back beam or platen
6. Rods – used to make a
shed
7. Heddle frame - heald
frame - harness
8. Heddle- heald - the eye
9. Shuttle with weft yarn
10. Shed
11. Completed fabric
12. Breast beam
13. Batten with reed comb

2
Firstly the yarn was taken from one side to the other by hand, which limited the width of the
textile, sometime assistants (mainly children) were sat there to help, later the yarn was put into a
capsule called the warp at passing through. At the industrial revolution the flying shuttle was
invented by John Key, which is a warp that could be thrown along. On 1.3. Figure you can see
two looms operated by mancraft.
1.3. Figure Ancient and modern loom
The idea of machine operated looms appeared already in 1678, but was realized only in the
18th
century. The first water-power supplied device is dated to 1788; later in the 19th
century also
steam-powered was used in England.
The pattern woven technique by punched card machine was invented by Joseph Marie
Jacquard already in 1805, and this was also the first step in automation and control technique.
1.4. Figure Punched card loom
Till the middle of the 20th
century the looms with flying shuttle were the most efficient, but
had the disadvantage of big noise and high energy consumption because of the weft’s weight.
The idea of waving without a weft showed up already in the middle of the 19th
century, but it
could not be realized that time. Nowadays it is already developed and still improved all the time,
but loom with wefts are still used some places.
Among the nowadays used looms we distinguish the ones with simple weft, with microweft,
with rotating weft or with nozzles. Among looms with nozzles there are two types, one with air

3
and one with water-jet, but the later can be used only at materials which physical properties are
not affected by the water, like synthetic yarns.
2. The air-jet loom
The power of air was used already 2000 years ago, its industrial usage got significant in the
18th
– 19th
century, while the industrial revolution such devices were invented like pneumatic
post, pneumatic railway break system and jackhammer. The pneumatic systems are still under
development [1], one of the big inventions is in the focus of my paper. The air-jet loom’s
operation principle was patented in 1946 by the Swiss company Maxbom and soon it begun to be
produced. One of the nowadays used machines can be seen on Figure 2.1.
2.1. Figure Airjet loom
2.1 The operation of an air-jet loom
The machine is working in a way that, it shoots out the weft yarn from the main nozzle to the
gap between the warps with the help of an air-jet. Firstly they did not use sub-nozzles, but after
assembling them the speed of waving and the possible width of textile highly increased. These
small devices are located along the reed (see Figure 2.2. Figure -2.4) and help the transportation
of the weft yarn to the other side.
2.2. Figure The composition of the machine's waving part
weft yarn
fillings
jets of sub-nozzles
main-nozzle
magnet valve sub-nozzles

4
On Figure 2.4 we can see the two position of the reed casket. As already mentioned the
process starts with the main nozzle shooting out the yarn, and then it is passing along the reed in
its “tunnel” and after or -at some machines- meanwhile reaching the other end it is pushed to the
already woven textile – changing from 1st
to 2nd
position. As at the other type of waving
instruments the next step is the reordering of the heddle yarns with the eyes and then the process
can be repeated again and again.
The usage of the sub-nozzles made 541 cm reedlength - and with this textile width - possible,
the present air-jet looms can reach a 2000-3000 m/min weft transport velocity, depending on the
type of yarn [10], this means that the weft yarn pass over a 5 m wide reed 400-600 times a
minute.
At the optimization of the operation many aspects need to be considered and the criteria can
change depending on the type of the yarn. E.g. the load carrying capacity is different for silk,
cotton or wool. For the main nozzle we can find more investigations both experimental and
computational [2-4], these are dealing mostly with the main nozzle’s tube length [4-7]. Other,
like Kim Chae-Min Lim and his coworkers were publishing about the shear layer and shockwave
boundary layer interaction [8], in it an interesting result was the fact that their model did not
work and gave back the reality [9] above the pressure ration 1.93, where the pressure ratio was
defined as the ratio of the static pressure in tube and environment. For the sub-nozzle we can
hardly find an article, probably there are just industrially concealed results yet and as told some
of the settings are based on practical experimentations. The most interesting parameters could be
the pressure supply, the direction of the jet and the necessary operating time. We can also find
many types of outlets and orientations on the picture below.
2.5. Figure Different types of sub-nozzle outlets
The nozzle investigated in this paper is a one holed type
2.3. Figure Subnozzles along the 2.4. Figure Subnozzle's location, explonation of parts
sub-nozzle
textil
reed
weft yarne gap
heddle yarne
eye
1st
position
2nd
position
reed
cascet

5
3. Measurement of the velocity field
For measuring the velocity distribution of the sub-nozzle’s flow field hot wire measurements
has been made. The measurement was done on the following arrangement:
The pressure at the tube before the nozzle (p2) was kept on constant with the help of the
pressure controller (PC), and the reservoir was kept on a higher p0 pressure by the compressor.
To have more information about the boundary conditions of the model not only the pressure, but
the temperature was measured as close to the nozzle as possible (p2,T2) with an ohmic
thermometer and a pressure transducer, whose signal was sampled by computer. Finally the
nozzle was fixed to the read and got the supply through pipes similar to the industrial ones.
For assembling the read and the nozzle together the industrial arrangement was the base,
naturally at constructing the model for simulation we considered our dimensions to decrease the
differences of the model and measured reality.
3.1 Equipment
At the measurement the following equipment has been used:
- Compressor
- Pressure transducer
- Ohmic thermometer
- Pressure controller
- Hot-wire
3.1.1 Pressure transducer
I have used Nivelco NIPRESS DH1-7324 type pressure transducer, which had to be first
calibrated. The calibration device is shown on the following picture:
pr
(t)
T
T p2
PC
Compressor
p0
T1
nozzle
3.1. Figure Measurement arrengement

6
3.2. Figure Oleaginous calibrator with Bourdon manometer
The calibration was managed by a hydraulic oil calibrator. The results show some deviance
from a linear characteristic, but there was no hysteresis, which means the pressure can be
determined univocal.
0 1 2 3 4 5 6 7 8
0,5
0,6
0,7
0,8
0,9
1,0
1,1
1,2
1,3
U1(V)
p (bar)
U1
U1m
Ub
Reservoir's pressure transducer
0 1 2 3 4 5 6 7
0,4
0,5
0,6
0,7
0,8
0,9
1,0
1,1
1,2
1,3
Channel's pressure transducer
U(V)
p (bar)
U1
U1m
Ub
3.3. Figure Measured pressures for calibration
On the graph the two voltage values measured while increasing the pressure U1 and U1m
refers to the small fluctuation in the signal, U1 is the highest and U1m is the smallest value at a
given pressure, we can see, that the fluctuation was quite small and can be neglected. The Ub
values show the measured voltage while decreasing the pressure from 7 to zero bars. After taking
the average of the three data for both transducers an exponential curve was fitted. The
parameters of the curves and the plots of the fits are shown in 3.4. Figure and 3.1. Table
0,5 0,6 0,7 0,8 0,9 1,0 1,1 1,2
0
1
2
3
4
5
6
7
Reservoir's pressure transducer
p(bar)
U (V)
p
Fitted line
0,5 0,6 0,7 0,8 0,9 1,0 1,1 1,2 1,3
0
1
2
3
4
5
6
7
tube's pressure transducer
p(bar)
U (V)
p
Fitted curve
3.4. Figure Fitted curve for pressure transducers
pressure transducer
weigths
Bourdon manometer

7
Equation of fitted curve: p[bar]= A1*exp(-U[V]/t1) + y0
for tube for reservoir
Value
Standard
Error
Value
Standard
Error
y0 -3.0013 0.13069 -4.50539 0.38443
A1 1.40198 0.07575 2.36366 0.26211
t1 -0.62303 0.01356 -0.77555 0.03939
R2
0.9998 0.99939
3.1. Table Fitting parameters for pressure calibration
Where R2
is a Q factor of the fit (closer to value 1 is better), for further details see appendix.
3.1.2 Ohmic thermometer
The ohmic thermometers had a wide measurement range; it was
earlier calibrated between -50 and 630 °C, where it came up that the
temperature is almost linear with the resistance (1.1% highest
deviance). The computer measures the voltage on the resistance for
given current supply, which will be also proportional with the
temperature. To be sure I have made a calibration for both
thermometers with 0°C ice-water mixture and water cooling down
from 100°C to 95°C.
Finally for these two points a lline was fitted to the voltage (U)-
temperature (T) connection, this can be obtained on the following
figure.
0,85 0,90 0,95 1,00 1,05 1,10 1,15
0
20
40
60
80
100
Temperature(°C)
Voltage1 (V)
Temperature reservoir
Temperature tube
3.5. Figure Calibration of the thermometer
The lines are described by the equation T=A+B·U, which parameters are in table 3.2.
parameter Reservoir Tube
A (intercept) -349.94404 -310.06094
B (slope) 410.73244 356.39189
3.2. Table Fitting parameters for thermometer

8
3.1.3 Hot wire
Hot wire is a well-known velocity measurement device, which is based on the cooling
property of the gas flow with given temperature. The technique depends on the convective heat
loss to the surrounding fluid from an electrically heated sensing element or probe. If only the
fluid velocity varies, then the heat loss can be interpreted as a measure of that variable. Hot-wire
sensors are, as the name implies, made from short lengths of resistance wire and are circular in
section. The rate of heat loss to the fluid is equal to the electrical power delivered to the sensor
V2
/R where V is the voltage drop across the sensor and R is its electrical resistance. Meanwhile
the measurement the voltage is recorded, and from that value the perpendicular component of the
velocity can be calculated. For further details see [14].
3.2 Hot wire measurement
3.2.1 Hot wire calibration
For the measurement the hot wire needs to be calibrated every time, when the properties of
the environment are expected to be changed (e.g. the temperature increased in the room). This is
done by its own calibration equipment, which includes a Laval nozzle connected to a pressure
transducer and a stand that holds the wire’s handle (see on Figure below):
3.6. Figure Hot-wire calibration equipment
After entering the environmental temperature, pressure and the cold resistance of the wire for
the program, we can start the calibration by increasing the supply pressure, and thereby the
velocity at the nozzle. The program itself calculates the corresponding velocity and registers the
measured voltage.
At the end we can fit the calibration curve regarding the King’s law, which can be considered
valid at a wider region than the calibration was done. The fitted curve for one of the
measurements can be seen below.

9
3.7. Figure Hot-wire calibration's King's law
3.2.2 Hot wire results
After calibration the measurements could be done along the 9 lines parallel to the reed, which
start from the outlet of the nozzle and goes for the different distances from the inner side of the
pit. The velocity distribution along all measurement lines are shown on the following graphs
with the punctual positions, which can be observed on the pictures below the diagrams.
At the right-hand side:
0 25 50 75 100 125 150 175 200 225
0
10
20
30
40
50
60
70
80
90
100
110
v(m/s)
x (mm)
2mm
5mm
3.8. Figure Right-hand side measured velocity distribution
3.9. Figure The two measurement positions at the right-hand side

10
In the middle:
0 25 50 75 100 125 150 175 200 225
0
20
40
60
80
100
120
140
v(m/s)
x (mm)
2mm
5mm
8mm
12mm
3.10. Figure Velocity distribution measured in the middle
3.11. Figure Positions of the measurements in the middle
At the left-hand side:
0 20 40 60 80 100 120 140 160 180 200 220
0
10
20
30
40
50
60
70
80
90
100
v(m/s)
x (mm)
2mm
5mm
8mm
3.12. Figure Left-hand side measured velocity distribution

11
3.13. Figure The two measurement positions at the left-hand side
At the last measurements we can see that the data go only 45 mm close to the nozzle outlet.
The reason was the fear from broking the wire, because at the second data series a good quality
wire was damaged at the velocity of 120 m/s, and for the next one we could not be sure to stand
such a high velocity.
At this measurement the pressure in the tube before the nozzle (on Figure 3.1. p2) was
3.62±0.03 bar, which is about the lower limit for supply pressure in industrial applications.
Therefore lower pressure measurements would not have sense. A higher pressure measurement
should be done, but it was not possible, because the hot-wire would not be able to handle an even
higher velocity.
4. Measurement of the force acting on the weft
First the weft should be purchased; the textiles are characterized by their specific density for
length. The unit is the so called tex, and it gives the weight of a one kilometer long yarn. We can
also take difference between simple and multifilament strings; we have investigated the latter
one, this is a multitude of fine, continuous filaments, with some twist, and it is clamped together
every 1-2 centimeter. The average diameter of the weft was measured [13] as da,w=0.634 mm.
The measurement was done with the help of a pendulum, the force acting on the weft was
pulling the end of the pendulum, and the angle of rotation could be observed and used to
calculate the searched value.
4.1 Measurement arrangement
The measurement arrangement can be seem in the picture below:
4.1. Figure Force measurement arrengement
weftnozzlereed
pendulum
scale

12
The weft was bound to the end of the pendulum, and it was lead through the tunnel created for
it in the reed. At the other end it was lead over a beam and a small hook was fixed there, which
made possible to hang weights there. The weight of the hook is so small, that it can be neglected
regarding to the other errors coming from the friction and value reading.
The constructed device had to be first calibrated with very small weights from 0.5 to 7 grams,
from which the force could be easily calculated by simply multiplying it with the gravitational
acceleration, 9.8 m/s. At every loading a picture was taken from which the angle of rotation
could be read out with the help the reference line - the 90° line on calibrator picture.
Two of the pictures from the calibration can be seen below.
4.2. Figure Calibration with 2.5 g (left) and 6.5 g (right)
The forces respects to the pendulum’s angle of rotation are present on 4.3. Figure with the
fitted line. The data are shown below:
m g 0 0,5 1 1,5 2 2,5 3
F mN 0 4,9 9,8 15 20 25 29
αrel ° 0,49 0,67 0,64 1,67 2,40 2,45 2,71
α ° 0,00 0,18 0,15 1,17 1,91 1,96 2,22
m g 3,5 4 4,5 5 5,5 6 6,5 7
F mN 34 39 44 49 54 59 64 69
αrel ° 3,85 4,14 4,39 4,30 4,34 4,59 5,01 5,21
α ° 3,36 3,65 3,90 3,81 3,85 4,10 4,52 4,72
4.1. Table Data at force measurement
- αrel [°] Relative angle from reference line
- α [°] Angle of rotation
- m [g] Hanged mass
- F [mN] Force acting on the yarn

13
0 1 2 3 4 5
0
10
20
30
40
50
60
70 F
Linear Fit of F
F(mN)
alpha (°)
4.3. Figure Calibration for force measurement
where
- α [°] pendulum’s angle of rotation
- F [mN] force acting on the yarn
And the parameters of the fitted line F= B·alpha are below:
R2
B
Value Value Standard Error
0.99914 12.966 0.457
4.2. Table Fitting parameters for force measurement
The most probable source of error is the presence of Coulomb friction between the yarn and
the rod and the end of the reed. Although we tried to choose the smoothest rod and, every time a
small wobble was done on it, to let the yarn move easier, the deviance from linear is significant.
4.2 Force measurement
When the calibration was finished the pressure
was gain on the nozzle and as the jet started to act
on the weft a considerable rotation could be
observed on the pendulum, the force was evaluated
by taking a picture (Figure 4.4) and analyzing it.
The angle of rotation was 3.97°, which meant
F = (12.966±0.457)·3.97 = 51.47±1.813 mN
This sounded realistic based on some previous
measurements [13] for the whole system.
5. Mass flow rate measurement
As the nozzle was supplied from a huge reservoir, the mass flow rate was derived from the
pressure and temperature change in it. Counter to the hot-wire measurement, when continuous
refill was ensured by compressor, in this case the tank was filled up to 5.5 bars and let deflated –
4.4. Figure Force measurement on the weft

14
higher pressure could not be controlled. Unfortunately only after a certain time has the pressure
in the pipe and thus the flow reached its stationer mode, and since the reservoir was not allowed
to be refilled only a short time remained to done the measurement. The parameters were
recorded till the pressure at the tube was constant (and its value was the same as at the
measurements, 3.62 bar).
The air was considered as ideal gas which meant from the gas law the mass follows the
expression
( ) ( )
( )tTR
tpV
tm
air ⋅
⋅
=
5.1
Where
- m [kg] Mass
- V [m3] Volume
- p [Pa] Pressure
- Rair [J/(kg·K)] Specific Gas Constant of Air
- T [K] Temperature
And volume of the reservoir was 50 m3
, and the gas constant for air was taken for 286.9
J/(kg·K).
The pressure went from 4.4 to 3.8 bars and the temperature from 22.5 to 21 °C. Both the
pressure and the temperature have an error, what have to be considered. Taking the quadratic
error propagation, we can say for the relative error of mass:
22





 ∆
+




 ∆
=
∆
p
p
T
T
m
m
5.2
- ∆m [kg] Error of the mass
- ∆T [K] Error of temperature 5
- ∆p [Pa] Error of pressure 0.2·105
For the pressure error I considered the steepest part of the corresponding exponential curve (at
4.4 bar) and multiplied it with the fluctuation width of the voltage.
For the temperature error I have taken the difference of the starting and ending value, this is a
very huge over-estimation of error, but the time reaction of the thermometer was not responsible.
Considering these respectively high errors we will have still just 6% relative error in the mass.
The pressure data can be considered as proper data in time, but the thermometer had inertia at
response for temperature change. These give some more deviation from the real values, but we
can say it will remain about a 10% relative error.
From the mass (m)-time (t) graph seen below the mass flow could be easily calculated via
finding the slope of the linear fit on the data. The original curve was a bit noisy, therefore
smoothing was done before evaluating.

15
5.1. Figure Mass of air in the reservoir in time
The fitted m=A+B·t line had the parameters
R2
A B
Value Value Standard Error Value Standard Error
0.99914 2.92619 9.97762E-5 -0.00177 3.40522E-7
5.1. Table Fitting parameters for the mass-flow rate
The source of errors in this measurement is mainly the inertia of the thermometer’s response.
Probably the temperature changed faster than it was registered, but we can consider it as part of
the error.
Finally the mass-flow rate can be derived as qm = 1.77 ±0.177 g/s.
175 200 225 250 275 300 325 350 375 400
2,1
2,2
2,3
2,4
2,5
2,6
2,7
2,8
mass(kg)
time (s)
Smothened curve
Linear fit

16
6. Simulation of simple flow field
The simulation was done by ANSYS Workbench. Started with the creation of the geometry
and went on with the mesh generation. With the ready mesh the next step could be done, i. e. the
simulation parameters and the initial conditions were set. And finally the simulations could be
run and evaluated.
6.1 Geometry of the model
The geometry – as already mentioned – was based on the measurement arrangement.
6.1.1 The nozzle
The CAD model of the nozzle was available [13] and its accurate position was specified by
taken pictures, for distances with the presence of a graph paper as seen below on 6.1. Figure.
6.1. Figure Pictures for modell parameter determination and the coordinate-system
Although the distances could be quite well defined this way, they still have an uncertainty,
especially in angles was hard to define.
6.1.2 The reed
The read stands of small slabs called reedtheeth, and they would be hard to implement one by
one, therefore the whole lamella was modeled by a continuous porous zone. The basis to set the
porosity parameter in Fluent was the approximation of the velocity profile between the
reedtheeth with the one belonging to a flow field between two flat planes.
This meant a parabolic distribution reaching its maxima at the midline among the lamellas,
and acquire zero at the walls. Considering the x axis perpendicular to the reed and the z axis
parallel, starting from the wall (as they are in Fluent, and as it can be seen above), the following
expressions can be written:
( )2
2
max
2/D
zDz
v=v
−
⋅ 6.1
Where
- vmax [m/s] Maximum value of velocity
- D [m] The distance between the reedtheeth
- z [m] z coordinate
From this the average velocity, vaverage with integration
z
x
y
z
x
D

17
∫⋅
D
average v=vdz
D
=v
0
max
3
21
6.2
The wall shear stress (τ) looks like
dz
dv
µ=τ 6.3
where µ is the viscosity.
From the equilibrium of the force exerted by the pressure difference (∆p) along an L distance
and the wall shear stress
τ⋅=⋅∆ LDp 2 6.4
This means
2
max
0=z D
v
µ12=
D
4v
µ
D
2
=
dz
dv
µ
D
2
=
L
∆p
6.5
The porous zone is represented in Fluent with an S source term introduced to the standard fluid
flow equations, where its component in the i direction is
ii vS
α
µ
−= 6.6
where α, the permeability is defined with the nexus
∑−
3
1=j
j
i
i
v
α
µ
=
L
∆p
6.7
If assuming that the pressure drop depends only on the velocity magnitude in the same direction
we can compare the equation 6.5 and 6.7 resulting






⋅ 2
7
2
1
10655.6
1
12
m
=
D
=α 6.8
Where D = 0.424 mm was predicted from the real reed shown below.
6.2. Figure Distances between reedteeth
In the other direction a one order higher porosity was set to model the imprenetlability.
6.1.3 Enclosure
Around the nozzle and read an enclosure volume was created, where the distances were based
on previous simulations. The sizes of the bounding box are in the (x,y,z) directions (0.05, 0.093,
0.26) meter.

18
6.2 Meshing
At meshing different dense resolutions were created, but at both a target volume was
performed at the nozzle outlet to ensure a higher resolution for outflow, as seen on 6.3. Figure.
6.3. Figure Geometry and hirher resolution target volume
First a very simple 300 000 celled one was generated than a denser one with 1.2 million cells,
both with tetrahedral elements.
6.3 Simulation settings
As first try steady simulation was done, but it seemed unstable, therefore the final project had
time dependence, which seemed stable. The further settings can be red below
- Time dependent solver
- Density-based solver
- Realizable k-ε model
- Standard Wall function as wall treatment
- Energy equation was also implemented
The air was considered as compressible, ideal gas with the basic set properties of ANSYS
Fluent.
The Fluent sets for basic properties of air:
- Cp [J/(kg·K)] Specific Heat 1006.43
- λ [W/(m·K)] Thermal Conductivity 0.0242
- υ [kg/(m·s)] Viscosity 1.7894·10-05
- M [kg/kgmol] Molecular Weight 28.966
The boundary conditions were set to pressure farfield, beside the inlet of the nozzle was
considered as a mass flow inlet, which value was originated from the measurement. On the
figures bellow the farfields are colored by brown and the mass-flow inlet by blue, the green
colored part is the reed.
target volume

19
6.4. Figure Boundary conditions
6.4 Results
The most important results were the velocity distribution at the measurement lines. From the
pictures of the measurement the accurate positions of the lines were located. In order to have the
same variable a custom field function had to be defined, i.e. the component perpendicular to the
reed was taken out, and with this the new variable vrel is
22
zyrel vvv += 6.1
where
- vy [m/s] the y component of velocity
- vz [m/s] the z component of velocity
6.4.1 Velocity distributions
On the following graphs we can see the velocity distributions along different lines parallel to
the reed (z axis). These lines had the butting point as it shown on the picture below, and they are
noted with the numbers near to the points.
6.5. Figure Locations of observed lines
At the graphs the number after the vrel refers to the line number on the picture above.
mass-flow inlet
1
2
4
3
5
6
7
8
9

20
Coarser mesh Denser mesh
At the left-hand side
0,00 0,05 0,10 0,15 0,20 0,25
0
10
20
30
40
50
60
70
vrel(m/s)
z (m)
vrel1
vrel2
vrel3
6.6. Figure Velocity distribution on the left-hand side
(sparse mesh)
0,00 0,05 0,10 0,15 0,20 0,25
0
20
40
60
80
100
120
140
vrel1
z (m)
vrel1
vrel2
vrel3
6.7. Figure Velocity distribution on the left-hand side
(denser mesh)
In the middle line:
0,00 0,05 0,10 0,15 0,20
0
10
20
30
40
50
60
70
80
90
vrel(m/s)
z (m)
vrel4
vrel5
vrel6
vrel7
6.8. Figure Velocity distribution in the middle-lines
(sparse mesh)
0,00 0,05 0,10 0,15 0,20 0,25
0
20
40
60
80
100
120
vrel(m/s)
z (m)
vrel5
vrel6
vrel7
6.9. Figure Velocity disrtibution on the middle-lines
(denser mesh)
At the right-hand-side
0,00 0,05 0,10 0,15 0,20 0,25
0
10
20
30
40
50
vrel(m/s)
z (m)
vrel8
vrel9
6.10. Figure Velocity distribution at the right-
hand side (sparse mesh)
0,00 0,05 0,10 0,15 0,20 0,25
0
10
20
30
40
50
60
70
80
vrel(m/s)
z (m)
vrel8
vrel9
6.11. Figure Velocity distribution at the right-
hand side (denser mesh)

21
We can see that for the denser mesh the velocities reach a higher value, that is why we cannot
state that our solution is mesh-independent. Further investigation should be done, with denser
and higher quality meshes. Unfortunately because of the lack of time this was not possible yet.
The source of the fluctuation on the distributions can be because of the distorted cells.
6.4.2 Visualized flow field
Techplot was used while the below pictures were created. The pathlines coming out from the
nozzles have been visualized as below at 8.8 s flowtime:
6.12. Figure Pathlines from inlet of simulated flow-field
6.13. Figure Pathlines from reed close nozzle outlet of simulated flow-filed
We can see that the pathlines are situated at first in the tunnel for the yarn as expected, but
after that they are disappearing in the reed or turning back and generating a kind of vortices. To
gain further knowledge about the air departing through the reed the reed perpendicular velocity
component is plotted on the next picture.
6.14. Figure X velocity distribution on the back of reed
We can see that the main part stands of a small, varying inflow-outflow part – velocities
between [-1,1] m/s –,there is a more significant outflow where the pathlines reach the reed and
also a bit more intensive inflow where the pathlines are separating and starting to form the
vortices.
XZ
Y

22
For first sight we could be suspicious that the solution is not converged yet, but after running
the simulation for further 4.2 seconds we had still the same results.
For further investigations I made contour plots of the reed parallel velocity component in
different heights:
6.15. Figure Contour plots of the simulated flow field's z-velocity
We can see what the pathlines showed too, the nozzle blows the air against the reed and then a
kind of separation appears and the flow does not contain its way along the hollow. One of the
reasons can be the too high porosity of the reed.
6.5 Pressure at the mass-flow inlet
The pressure has been checked at the mass-flow inlet, to have a baseline for comparison with
real pressure in the tube before the nozzle.
6.16. Figure Pressure at mass-flow inlet
y=48mm
y=46mm
y=42mm
y=44mm
YZ
X

23
The pressure on the inlet was between 3.654 and 3.652 bar, which is quite close to the
measured value on the transducer before the nozzle (p2 pressure on Figure 3.2).
7. Simulation of weft
7.1 Geometry of the model
The base geometry was the same as for the previous described case, but the weft as a rigid
body was put into the picture realized as a cylinder along the reed. In reality the weft is more or
less changing its position, but from consultation [13] the usual position of it was given as 3 mm-s
from the top and 2 mm-s from the inner side of the tunnel in the reed. The diameter of the
cylinder was equal to the average thickness of the weft, 0.634 mm.
7.1. Figure Position of the weft in the model
7.2 Simulation with weft
The main properties were the same as at the previous simulation, the only difference was in
the mesh, which need to have a higher resolution at the weft.
7.3 Results of weft simulation
Unfortunately as we did not have a satisfying velocity distribution without the weft, therefore
we could not have high expectations for this simulation. The resultant integrals on the weft are
summarized in the following table:
X-Force: -2.062099e-003
Y-Force: -4.819360e-004
Z-Force: 1.260997e-004
7.1. Table Forces acting on the weft (from simulation)
We can see the forces do not reach the order of magnitude of the real one, of course till the
original flow-field is not reliable, but such a huge difference is not justified. Probably the rigid
body model is too simple to treat this case.
3 mm
2 mm

24
8. Summary
Firstly the velocity distributions should be compared, these are summarized in 8.1. Table.
Hot-wire measurement Simulated
right-hand side
0 25 50 75 100 125 150 175 200 225
0
10
20
30
40
50
60
70
80
90
100
110
v(m/s)
x (mm)
2mm
5mm
0 25 50 75 100 125 150 175 200 225
10
20
30
40
50
60
70
80
90
100
110
v(m/s) z (mm)
5mm
2mm
middle-line
0 25 50 75 100 125 150 175 200 225
0
20
40
60
80
100
120
140
v(m/s)
x (mm)
2mm
5mm
8mm
12mm
0 25 50 75 100 125 150 175 200 225
0
20
40
60
80
100
120
140
v(m/s)
z (m)
2mm
5mm
8mm
left-hand side
0 20 40 60 80 100 120 140 160 180 200 220
0
10
20
30
40
50
60
70
80
90
100
v(m/s)
x (mm)
2mm
5mm
8mm
0 20 40 60 80 100 120 140 160 180 200 220
0
20
40
60
80
100
120
140
v(m/s)
z (mm)
2mm
5mm
8mm
8.1. Table Comparison of measured and simulated velocity distribution

25
We can immediately see that the velocities are higher at the reality, this can be a result of the
not properly set mass-flow inlet or as well the unsatisfactory mesh quality. The latter opportunity
is more probable, because the pressure at inlet for the set mass-flow rate was quite close to the
measured value not far from the nozzle inlet. As we saw for denser mesh the velocity values
increased, therefore an even higher cell numbered and better quality mesh could help to have
more realistic results.
The second peak at the measured velocity profile can be due to a kind of reflection of the
original air-jet, which can be observed at the z-velocity contour plots of the simulation on 6.15.
Figure as weel. but the two peaks do not appear.
The reason of this can be the not properly set angle of the nozzle or another source of this
error can be the difference between the spreading rate of simulated and real jet. If we assume that
the jet in reality is more narrow the hot-wire measurements can be considered as the flow is
firstly propagating to the read, than changing its direction while separating and this is why we
see a “gap” after the main peak.
And since the simulation gives a wider jet, it covers also the “gap” and result a continuous
peak in the velocity distribution.
According to the simulation of the weft we can say that, although the velocity profiles do not
differ in orders of magnitude, the forces do. This can be originating from inadequate model that
the weft was substituted with a rigid body. Probably a porous zone would give a better solution,
but till easy to implement.

26
BIBLIOGRAPHY
[1] Szabó Lóránt: A sűrített levegő a textiltechnológiában, Magyar Textiltechnika LXII. ÉVF.
2009/1
[2] Korea Textile Machinery Research Institute: High Performance Shuttleless Loom System
Development, 2003
[3] Lim, C. M.; Lee, K. H; Kim, H. D.: The Study of the Gas Flow through a Texturing
Nozzle, Proceedings of KSME Fall Meeting, Pyeongchang, pp. 2163—2168, (2005)
[4] Lim, C. M.; Lee, H. J.; Lee, K. H.; Kim, H. D.; Chun, D. H.: A Computational Study of
the Air-Texturing Nozzle Flow, Proceedings of KSME Spring Meeting, Seogwipo, pp.3417—
3421, (2006).
[5] Pianthong, K.; Zakrzewski, S.; Behnia, M.; Milton, B. E.: Characteristics of Impact
Driven Supersonic Liquid Jets, Shin,
[6] C. H.; Kim, K. H.; Kwon, Y. H.; Kim, S. J.: Flow Characteristics of the Main Nozzle with
Different Tube Lengths in an Air-Jet Loom, Proceedings of KFS Spring Meeting, Seoul, pp.99—
102, (1996).
[7] Kim, K. H.; Kim, Y. S.; Kim, S. J.: A Study on the Analysis and Design of Air Flow
Behavior in the Nozzle of Air Jet Loom(III)-Natural Suction of the Double Coaxial Jets, Journal
of the Korean Fiber Society, 35(4), pp. 249—256, (1998).
[8] Kim, Chae-Min Lim, Ho-Joon Lee, Doo-Hwan Chun, Heuy-Dong: A Study of the Gas
Flow through Air Jet Loom,
[9] Matsuo, K.; Miyazato, Y.; Kim, H. D.: Shock train and pseudo-shock phenomena in
internal gas flows, Progress in Aerospace Sciences, 35(1), pp. 33—100, (1999).
[10] Based on the article International Textile Bulletin 2002/5. composed Szabó Rudolf:
Vetülékbeviteli rendszerek Magyar textiltechnika 2003/3 page 76.
[11] Szabó Lóránt: Kutatási terv, Nyugat-Magyarországi Egyetem Faipari Mérnöki Kar
Cziráki József Faanyagtudomány és Technológiák Doktori Iskola, Budapest, 4th
june 2007.
[12] ANSYS FLUENT Theory Guide
[13] Oral consultation with Szabó Lóránt, Budapesti Műszaki Főiskola, adjunct
[14] University of Cambridge Turbomachinery Department, webserver of current researches
http://www-g.eng.cam.ac.uk/whittle/current-research/hph/hot-wire/hot-wire.html, Cited 3rd
May,
2011.
[15] Origin theory guide

27
Appendix
Quality of Fit [15]
“One obvious metric for the quality of the fit is how close the fitted curve is from the actual
data points. The value of residual sum of square (RSS) varies from dataset to dataset, making it
necessary to rescale this value to a uniform range. On the other hand, one may want to use the
mean of y value to describe the data feature. If it is the case, the fitted curve is a horizontal line
, and the predictor x, cannot linearly predict the y value. To verify this, we first calculate
the variation between data points and the mean, the "total sum of squares" about the mean, by
In least-squares fitting, the TSS can be divided into two parts: the variation explained by
regression and that not explained by regression:
• The regression sum of squares, SSreg, is that portion of
the variation that is explained by the regression model.
• The residual sum of squares, RSS, is that portion that is
not explained by the regression model.
Clearly, the closer the data points are to the fitted curve, the smaller the RSS and the greater
the proportion of the total variation that is represented by the SSreg. Thus, the ratio of SSreg to
TSS can be used as one measure of the quality of the regression model. This quantity -- termed
the coefficient of determination -- is computed as:
”

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