wake of tandem cylinders
TRANSCRIPT
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drag. Hoerner reviewed many of theories developed for LAR wings of non-delta
platforms.
The most important consequence of work at low Reynolds numbers is increasing
in drag, but lift coefficient will be constant approximately and this leads todecreasing lift to drag. In research which Kunz and Kroo [3] have performed at
low Reynolds numbers, they studied NACA0002 to NACA0008 and showed that
for Reynolds number 2000 drag coefficient is much more than Reynolds number
6000 but the lift coefficient is about the same order. Generally, drag growth is
proportional to thickness increase and it will increase as Reynolds number
decreases, but rate of increasing in drag related to zero-thickness drag are
similar in both Reynolds number.
Also, the addition of 2% camber results in a 2.0-2.5 deg shift in the zero lift
angle of attack. It means that cambered airfoil at zero angle of attack has a lift
equal to the lift of the airfoil without camber at 2 to 2.5deg angle of attack [3].
Mueller and Torres have studied Zimmerman wing models and rectangular
wing at tree aspect ratios as 0.5, 1 and 2 experimentally. They showed that
increasing in lift coefficient will continue even after 30 deg of angle of attack
for 0.5 and 1 aspect ratios, but for aspect ratio of 2, after 12 deg angle of attack
it will be halted [4].
Furthermore, according to the extensive application of turbulent boundary
layer, knowing the physics of boundary layer and analyzing turbulence
parameters is important. A turbulence study in the wake of a model wind
turbine placed in a boundary layer developed over rough and smooth surfaces
were performed using hot-wire anemometry, by Chamorro and Porte-Angel[5].
This study showed that the effect of turbine on the velocity defect and added
turbulence intensity is not negligible even in the very far wake, at a distance of
fifteen times the rotor diameter.
Hot-wire anemometry data are much reliable that have been used to validate a
Particle Image Velocimetry (PIV) work by Foucaut, et al [6]in order to study
unsteady characteristics of near-wall turbulent boundary layer. Their aim was
building dynamic boundary conditions near a solid wall,
Farsimadan and Mokhtarzadeh [7] performed an experimental investigation on
flow over NACA 0012 airfoil placed at upstream of a 90 bend. They focused on
in order to reduce the
large eddy simulation spatial resolution that is necessary in this region.
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upper surface boundary layer and downstream vorticities and studied mean
velocity and stream wise turbulent intensity taken in the span wise direction.
In the present work, boundary layer has been studied experimentally and effects
of free stream velocity, angle of attack and also distances between two wing'shave been shown on the main wing's boundary layer. Also, Artificial Neural
Networks have been applied to estimate some values in boundary layer.
1.1. Introduction to Turbulence parameters
To study of a turbulent boundary layer, one needs to analyze some turbulence
parameters such as mean velocity and turbulence intensity [8]. Mean velocity
shows the time averaged velocity and is related to velocity u(t) and velocity
fluctuations u'
(t) as u(t)=Umean + u'
Which N is the number of velocity samples. Standard deviation of flow velocity
determines the turbulence intensity and is known as root-mean-squared
velocity:
(t). Mean velocity can be obtained asequation 1:
=1
()
1
(1)
= ( 11 (() )21
)0.5 (2)
Using velocity standard deviation, we can calculate turbulence intensity as
equation 3:
= 100 (3)There are two other important parameters which are used to study fluids flow
qualitatively; Skewness and Kurtosis. Skewness is a measure of symmetry, or
more precisely, the lack of symmetry of distribution function. Here, skewness
shows the symmetry of velocity related to flow mean velocity. When skewness is
not zero, data is not symmetry related to mean velocity and it cannot be
modeled by a normal distribution. Kurtosis is a measure of whether the data are
peaked or flat relative to a normal distribution. That is, data sets with high
kurtosis tend to have a distinct peak near the mean, decline rather rapidly, and
have heavy tails. Data sets with low kurtosis tend to have a flat top near the
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mean rather than a sharp peak. Skewness and kurtosis are shown in equations 4
and 5 respectively.
= 1
(())3
3
1 (4)
= 1 (())44
1 (5)
2.Experiment details
2.1. Wing model
A two-wing MAV, based on our studies whose wings are reverse Zimmerman
and rectangular have been tested. The main wing's area and chord are about 83
cm2and 10 cm respectively. The aspect ratio is 1 and GOE 723 has been used
for its root airfoil (figure 1). Also, the upper wing which has horizontal
stabilizer role has about 42 cm2
First, boundary layer has been studied for single main wing at three different
free stream velocities and three different angles of attack. The main wing and
stations in which boundary layer has been measured through them are shown in
figure 2 schematically. Free stream velocities are 10, 15 and 20 m/s and anglesof attack are 0, 2 and 4 degrees.
area, and GOE344 has been used for its root
airfoil.
Then, effects of existence of upper wing have been studied on main wing's
boundary layer. There are three positions for the upper wing in which distances
between main wing's trailing edge and upper wing's trailing edge is 3.5, 3 and
2.5 cm that called up1, up2 and up3 respectively.
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Figure1. The wing which is used in present work
2.2. wind Tunnel
Measurements were conducted in a low-speed, open-circuit wind tunnel located
at the Sabzevar Tarbiat Moalem University. Tunnel has a maximum speed of 30
m/s. Over the speed range used for experiments, the turbulence intensity in the
test section has been determined to be approximately 0.1%.
Figure 2. Schematic of the root airfoil and the stations
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A 1.7-m-long test section with a rectangular cross-sectional area of 0.40.4 m
is located downstream of the inlet. Downstream of the test section is a diffuser
that slows the flow. Figure 3 shows a schematic of the wind tunnel.
Figure 3. Schematic of the low-speed wind tunnel in the present work
2.3. measurments
Parameters measured by the flow of hot tungsten 1-D wire anemometer with
diameter 5 m, length of 1.25mm in a constant temperature circuit. The
frequency of the probe calibrated is 5 KHz. Figure 4 shows a schematic of the
1-D hot wire anemometer.
Figure 4. Schematic of the 1-D hot wire anemometer
2.4. Data Acquisition
All experiments data were acquired using a PC-based data acquisition system
performed by FARA SANJESH SABA using the LABVIEW graphical
programming language. An analog/digital (A/D) card was used.
2.5. Neural Network
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ANNs are formed by input data vectors, neurons and output functions. Input
data to the neuron are transformed by means of a base function and leave by an
activation function. Each connection between input and output data and
neurons is made by weight factors.
Each Neural Network applied in this work is solved with three Neurons, basedon a feed forward calculation and using Marquardt non-linear fitting method
[9].
3.Results and Discussion
3.1. Experiments results
Figure 5 shows the effects of different free stream velocities on wing's boundary
layer at zero degree angle of attack. In this figure, velocity profiles for 10 m/s
free stream velocity are shown by symbol + and also they are shown for 15 and
20 m/s by symbols and respectively. As free stream velocity increases,
separation point shifts toward the trailing edge and also boundary layer
thickness decreases. For 10 m/s velocity, the boundary layer thickness reaches
up to 10 mm at the trailing edge of the wing; but for two other velocities, it
seems that results are near to each other and far different from 10 m/s velocity
results.
It is important to say that because of single 1-D hot-wire anemometer, reverse
flows cannot be measured and so velocity profiles from x/c=0.65 to x/c=0.95
are much different from the actual ones. Separation has been occurred and flowis reverse at these stations.
Turbulence intensity for 7 stations in wing's boundary layer is shown in figure
6. As it is mentioned in figure 5, boundary layer thickness is much thicker for 10
m/s free stream velocity. According to the figure 6, there is one maximum peak
for turbulence intensity in each station which is in mean velocity gradient area.
Maximum turbulence intensity is greater for 15 m/s velocity than other two
velocities and it shifts upward as x/c increases. Also, when free stream velocity
is 15 m/s, the range of turbulence area is greater than the other velocities.
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Furthermore, maximum turbulence intensity in the first and second stations (i.e.
x/c=0.45 and x/c=0.55)is greater for 20 m/s velocity than 15 m/s velocity; it
seems that when separation is not occurred, turbulence intensity in the
boundary layer increases as free stream velocity increases.
Figures 7 and 8 show the effects of angle of attack on wing's boundary layer at
10 m/s free stream velocity. In these figures, profiles for zero degree angle of
attack are shown by symbol + and also they are shown for 2 and 4 degrees by
symbols and respectively. Figure 7 shows that increasing in angle of attack
increases probability of separation and shifts the separation point toward the
leading edge. Also, increasing in angle of attack increases the boundary layer
thickness.
According to the figure 8 which shows the turbulence intensity in wing's
boundary layer, increasing in angle of attack increases turbulence intensity and
distance from wing's surface to maximum peak of turbulence intensity.
Effects of upper wing on main wing's boundary layer have been studied in
figures 9 and 10 at zero angle of attack and 10 m/s free stream velocity. In these
work, there were three positions for the upper wing which are shown in these
figures. When distance between trailing edge of upper wing and that of main
wing is 3.5 cm, it is called up1 and shown by symbol. Also, this distance is 3and 2.5 for up2 and up3 and is shown by symbols and respectively.
Considering the figure 9, existence of upper wing leads to decreasing in
boundary layer thickness; furthermore decreasing in distance between two
wings amplifies this. From figure 9 we can conclude that existence of the upper
wing will delay separation and shifts the separation point toward the trailing
edge.
Figure 10 shows the effects of upper wing on main wing's boundary layerturbulence intensity. According to this figure, existence of the upper wing
decreases turbulence intensity so much; and as distance between two wings
decreases both turbulence intensity peak and area will decreases. Hence, in up3
when distance between two wings is 2.5, turbulence intensity in the main wing's
boundary layer is minimum.
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Figure 5- boundary layer velocity profiles at zero degree angle of attack
Figure 6- boundary layer turbulence intensity profiles at zero degree angle of attack
0.50
0.00 1.00
2.00
6.00
10.00
14.00
0.00
4.00
8.00
12.00
Y(mm)
0.50
0.00 1.000.50
0.00 1.000.50
0.00 1.00
U/Uref
x/c=0.45 x/c=0.55
x/c=0.65
x/c=0.75
Boundary layer profiles at 0deg angle
10 m/s
15 m/s
20 m/s
0.50
0.00 1.00
x/c=0.85
0.00 1.00 0.00 1.00
x/c=0.9
x/c=0.95
1.00 3.00
0.00 2.00
Tu
2.00
6.00
10.00
14.00
0.00
4.00
8.00
12.00
Y(mm)
1.00 3.00
0.00 2.00 4.00
Tu
2.50 7.50
0.00 5.00 10.00
Tu
2.50 7.50
0.00 5.00 10.00
Tu
x/c=0.45
x/c=0.55
x/c=0.65
x/c=0.75
Turbulence intensity in boundary layer at 0deg angle of attack
10 m/s
15 m/s
20 m/s
5.00 15.00
0.00 10.00
Tu
x/c=0.85
0.00 10.00 20.00
Tu0.00 10.00 20.00
Tu
x/c=0.9
x/c=0.95
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Figure 7- boundary layer velocity profiles at 10 m/s free stream velocity
Figure 8- boundary layer turbulence intensity profiles at 10 m/s free stream velocity
0.50
0.00 1.00
2.00
6.00
10.00
14.00
0.00
4.00
8.00
12.00
Y(mm)
0.50
0.00 1.000.50
0.00 1.000.50
0.00 1.00
U/Uref
x/c=0.45 x/c=0.55
x/c=0.65
x/c=0.75
Boundary layer profiles at 10m/s velocity
0 deg
2 deg
4 deg
0.50
0.00 1.00
x/c=0.85
0.00 1.00
x/c=0.95
0.50 1.50
0.00 1.00 2.00
Tu
2.00
6.00
10.00
14.00
0.00
4.00
8.00
12.00
Y(mm)
1.00 3.00
0.00 2.00
Tu
2.00 6.00
0.00 4.00
Tu
2.00 6.00
0.00 4.00
Tu
x/c=0.45x/c=0.55
x/c=0.65x/c=0.75
Turbulence Intensity in Boundary layer at 10m/s velocity
0 deg
2 deg
4 deg
5.00 15.00
0.00 10.00
Tu
x/c=0.85
0.00 10.00 20.00
Tu
x/c=0.95
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Figure 9- boundary layer velocity profiles at 10 m/s free stream velocity and zero
degree angle of attack and effects of upper wing
Figure 10- boundary layer turbulence intensity profiles at 10 m/s free stream velocity
and zero degree angle of attack and effects of upper wing
0.50
0.00 1.00
2.50
7.50
12.50
0.00
5.00
10.00
15.00
Y(mm)
0.50
0.00 1.00
U/Uref
0.50
0.00 1.00
x/c=0.85 x/c=0.95x/c=0.9
Boundary layer profiles at 0deg and 10 m/s
Single wing
Up1
Up2
Up3
2.50 7.50
0.00 5.00 10.00
5.00
15.00
0.00
10.00
20.00
Y(m
m)
5.00 15.00
0.00 10.00
Tu
5.00 15.000.00 10.00 20.00
x/c=0.85
x/c=0.95x/c=0.9
Turbulence Intensity at 0deg and 10 m/s
Single wing
Up1
Up2
Up3
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3.2. Artificial Neural Network
First, an artificial Neural Network is trained to determine turbulence
parameters in x/c=0.9 for 10 m/s free stream velocity, zero degree angle of
attack and up3. We picked up3 because the minimum turbulence intensity wascaptured in the boundary layer; hence that is the best location for upper wing
from turbulence intensity point of view. As it shows in table 1, Hot-wire results
and Neural Network results for a point (y=4.2 mm) are compared. Now using
this network, turbulence intensities for mid-points for x/c=0.9 at 10 m/s velocity
and zero degree angle of attack is shown in figure 11.
Table1. Comparison between hot-wire and Neural Network results for one wing's boundary
layer point (y=4.2 mm, x/c=0.9 at 10 m/s free stream velocity, up3)
Results Tu Skewness Kurtosis Urms
Hot wire 4.09106 -0.00551 0.0873 0.409106
Neural
Network
4.0908 -0.0060 0.0874 0.40908
Error 0.006% 9% 0.11% 0.006%
As mentioned in figure 6, turbulence intensities in main wing's boundary layer
at zero degree angle of attack and 10 m/s free stream velocity has been studied.Maximum turbulence intensity measured using Hot-wire anemometer, in each
station (x/c) is shown in table 2. For other points through the wing's chord (x/c),
turbulence intensities are estimated and shown in figure 12.
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Figure 11- Turbulence intensity at x/c=0.9 and up3, Hot-wire results and Neural Network
estimated values
Table2. Hot-wire results for maximum turbulence intensities in single wing's boundarylayerat 10m/s free stream velocity and zero degree angle of attack
x/c 0.55 0.65 0.75 0.85 0.9 0.95
Max. Tu 2.23312 4.58271 6.13497 8.07906 9.39714 19.08466
0 1 2 3 4 5 6 7 8 9 100
1
2
3
4
5
6
Y(mm)
Tu
HoT-wire
NeuralNeTwork
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Figure 12- Maximum turbulence intensities single wing's boundarylayer at 10m/s freestream velocity and zero degree angle of attack, Hot-wire results and Neural Network
estimated values
4. Conclusion
In the present work, effects of free stream velocity and angle of attack have been
studied on a single wing's boundary layer. Boundary layer thickness increases
as free stream velocity decreases and angle of attack increases. Also,
separation point shifts toward the trailing edge as free stream velocity increases
or angle of attack decreases. Furthermore, existence of the upper wing
decreases both boundary layer thickness and turbulence intensity; for up3,
which distance between two wings is 2.5 cm, turbulence intensity is minimum.
Moreover, Artificial Neural Networks have been applied to estimate maximum
turbulence intensities in the single wing's boundary layer and mid-points for
turbulence intensity profile of up3.
5.Acknowledgments
Authors appreciate SABZEVAR TARBIYAT MOALLEM UNIVERSITY for
cooperation. Also, we are thankful of the editor and reviewers of the
'Experimental Thermal and Fluid Science' journal for their time and
cooperation.
0.4 0.5 0.6 0.7 0.8 0.9 10
5
10
15
20
25
30
35
x/c
max.Tu
HoT-wire
NeuralNeTwork