Study on Effect of Semi Circular Dimple on Aerodynamic Characteristics of NAC...
Final v1.0
1. 1
Investigation of the limitations of XFLR5 for aerodynamic
predictions at low Reynolds numbers
3Philip Chan, 2Francisco Gomez, 1Hugo Villafana,
Advisors: 1*Wilson Chan, 1Tyler Davis, 1Joseph Tank, 1Geoff Spedding, 1Denise Galindo
1Department of Aerospace and Mechanical Engineering, University of Southern California,
Los Angeles, CA 90089
2Department of Mechanical and Aerospace Engineering, University of California, Irvine,
Irvine, CA 92697
3Department of Mechanical Engineering, University of California, Riverside,
Riverside, CA 92521
August 2016
Abstract
Over the past decades, Unmanned Air Vehicles (UAVs) have become popular within the
industrial, military, and consumer community. The ability to deliver packages to any location in
the world by remote access has created a number of significant benefits to these communities.
Typically, larger air vehicles have been used for accomplishing these autonomous tasks due to
the familiarity with its aerodynamic characteristics: lift and drag. However, these communities
wish to make the vehicles more compact, while still maintaining its aerodynamic performance.
Creating smaller air vehicles becomes advantageous to these communities due to its increase in
stealth and maneuverability. With smaller vehicles the Reynolds numbers are smaller. Programs
like XFLR5 have been shown to give accurate estimates of aerodynamic characteristics, at
Reynolds numbers above 2.0 × 105
. The objective of the project is to investigate if XFLR5 can
accurately predict aerodynamic characteristics of a standard airfoil (NACA0010) at Reynolds
numbers lower than 2.0 × 105
. This investigation will be supported with airfoil testing in the
Biegler Hall of Engineering wind tunnel. If the results in the wind tunnel are similar to the results
in XFLR5, then XFLR5 can be used as a resourceful technique in designing and manufacturing
efficient airfoils and Micro Air Vehicles (MAV). If this were not the case, then adjustments on
XFLR5’s parameters would have to be made in order to obtain similar results to those of the
wind tunnel.
Keyword(s): UAV, MAV, XFLR5, Reynolds number, airfoil, aerodynamic, lift, drag.
2. 2
Table of Contents
Abstract.........................................................................................................................................1
1 Introduction................................................................................................................................ 1
1.1 Approach .................................................................................................................................2
2 Materials and Methods.............................................................................................................. 3
2.1 XFLR5.......................................................................................................................................3
2.2 Calibration and Alignment........................................................................................................3
2.3 Experimental Corrections..........................................................................................................3
3 Characterization of the Test Flow............................................................................................ 5
3.1 Wind Tunnel Characterization...................................................................................................5
3.2 Boundary Layer ........................................................................................................................6
3.3 Effect of Sampling Time............................................................................................................7
3.4 Test Repeatability.....................................................................................................................8
3.5 Boundary Layer Calculations.....................................................................................................9
4 Results & Discussion................................................................................................................ 10
4.1 Tests at Re of 180,000.............................................................................................................10
4.2 Tests of Re at 100,000.............................................................................................................10
4.3 Tests of Re at 40,000...............................................................................................................11
4.4 Discussion..............................................................................................................................12
4.5 XFLR5 Correction....................................................................................................................13
5 Conclusions............................................................................................................................... 14
Appendix...................................................................................................................................... 15
Calculation #1..............................................................................................................................15
Calculation #2..............................................................................................................................15
Test Matrix #1..............................................................................................................................16
Test Matrix #2..............................................................................................................................16
References.................................................................................................................................... 18
3. 3
Figures
Figure 1: Flow around an airfoil with respect to its angle of attack (Hall, Inclination Effects on
Lift, 2015) ............................................................................................................................... 1
Figure 2: Wake deficit without correction factor............................................................................ 4
Figure 3: Wake deficit with correction factor................................................................................. 4
Figure 4: Top view of the WT with flow heading left in the x direction........................................ 5
Figure 5: Side view of the WT........................................................................................................ 5
Figure 6: Boundary layer development at u = 30 m/s..................................................................... 6
Figure 7: Boundary layer development at u = 5 m/s....................................................................... 7
Figure 8: Recording t (s) at 0.05s and 1.00s such that, y=37cm, z=23cm, and u=30m/s ............. 8
Figure 9: Results of repeatability at t=1.00s such that, y=37cm, z=23cm, and u=30m/s ............... 8
Figure 10: Angle of attack versus coefficient of lift for Re of 180,000........................................ 10
Figure 11: Angle of attack versus coefficient of drag for Re of 180,000 ..................................... 10
Figure 12: Angle of attack versus coefficient of lift for Re of 100,000........................................ 11
Figure 13: Angle of attack versus coefficient of drag for Re of 100,000 ..................................... 11
Figure 14: Angle of attack versus coefficient of lift for Re of 40,000.......................................... 11
Figure 15: Angle of attack versus coefficient of drag for Re of 40,000 ....................................... 11
Figure 16: diagram of laminar separation bubble ......................................................................... 12
Figure 17: Laminar Separation Bubbles theory results................................................................. 13
Figure 18: Laminar Separation Bubbles XFLR5 results at 8°...................................................... 13
Figure 19: Re of 40,000 with correction factor............................................................................. 14
Figure 20: Re of 100,000 with correction factor........................................................................... 14
Figure 21: Re of 180,000 with correction factor........................................................................... 14
4. 1
1 Introduction
For the past century, applied aerodynamics has been used to study airfoil design and its
significance for constructing unique applications, like Micro Air Vehicles (MAVs) (Talay,
1975). The primary interests for fixed-wing MAVs include surveillance, detection,
communication, and the placement of antenna sensors (Mueller, 1999) (Selig, 2003). The
increase of potential applications for MAVs, has led to an increase in research on the
aerodynamic characteristics of airfoils at low Reynolds number (Re). A vital component for
characterizing the flow for MAVs is through the equation (1) used for calculating Re:
𝑅𝑒 = 𝜌
𝑢𝑥
𝜇
(1)
where x is the characteristic length of the airfoil chord, and µ is dynamic viscosity of the fluid it
is traveling in. The following equations (2) and (3) will examine the variables that play a role in
finding the forces of L and D:
𝐿 =
1
2
𝜌𝑢2
𝑆𝐶 𝐿 (2)
𝐷 =
1
2
𝜌𝑢2
𝑆𝐶 𝐷 (3)
where, is the fluid density, u is the velocity of the object traveling through the fluid, S is the
planform area, and CL and CD are coefficients of lift and drag, respectively (Anderson, 2001).
Since MAVs are smaller scale unmanned air vehicles, the coefficients of drag and lift are more
difficult to predict since at low Re, the aerodynamics become more complex tend to form
complex fluid dynamics, such as laminar flow separation, laminar separation bubbles, etc.
Consequently, the aerodynamic behavior is not the same as larger air vehicles (e.g. Boeing 747).
For instance, MAV wings tend to stall at lower angles of attacks () than larger air vehicles
(McArthur, 2007). Stall occurs when an airfoil reaches its critical , causing greater flow
separation, resulting in high drag and low lift, as shown in Figure 1 (McArthur, 2007).
Determining what the stall angle at low Re’s is part of the crucial component in assessing and
characterizing its aerodynamic characteristics.
Figure 1: Flow around an airfoil with respect to its angle of attack (Hall, Inclination Effects on Lift, 2015)
5. 2
Re is a non-dimensional value that describes the ratio of inertial to viscous forces. MAVs,
generally fall in the range of 1.0 × 104
~1.0 × 105
are required (Mueller, 1999). A program
called XFLR5 is typically used for predicting aerodynamic characteristics of airfoils. However,
XFLR5 has not been proven for Re below 2.0 × 105
; the typical range MAVs operate in (Selig,
2003). For these reasons, the objective of this research is to examine if XFLR5 is capable of
predicting the aerodynamics characteristic of a standard airfoil below Re of 2.0 × 105
.
1.1 Approach
The approach for the project involves conducting XFLR5 simulations for a standard airfoil,
NACA 0010, to predict lift and drag coefficients over a range of Re and . The effect has on
the lift and drag coefficient will be interpreted. In addition, the 𝐶 𝐿 vs 𝛼 and 𝐶 𝐷 vs 𝛼 graph
illustrates the lift and drag coefficients resulting in a depiction of the stall angle. The lift and drag
curves, stalling characteristics, and the aerodynamic performances are important individual
factors that must be considered when analyzing an airfoil. Experiments were conducted in the
Biegler Hall of Engineering (BHE) wind tunnel at three Re’s of 4.0 × 104
, 1.0 × 105
, and 2.0 ×
105
over a range of ’s from −4° to 13°.
XFLR5 results will then be compared with experimental lift and drag measurements taken on the
NACA 0010 airfoil in the BHE wind tunnel to see if there are any correlations. The free stream
velocity will range from 6.5m/s – 30m/s and Re of 40,000 – 180,000. The experimental velocity
inside the wind tunnel is measured using a device called a Pitot tube, a hollow L shape metal rod
that concentrates air through the tube where a pressure sensor can calculate the difference
between total and static pressure (Shih, Lourenco, Van Dommelen, & Krothapalli, 1992). Once
the static pressure is measured, we can calculate the density of the air using the ideal gas law (4):
𝜌 𝑎𝑖𝑟 =
𝑃
𝑅𝑇
(4)
where 𝜌 𝑎𝑖𝑟 is the density of air, P is the static pressure, T is the temperature, R is the universal
gas constant of air: 287
J
kg∙K
. By using Bernoulli’s equation (5),
𝑢1
2
2
+ 𝑔ℎ1 +
𝑃1
𝜌1
=
𝑢2
2
2
+ 𝑔ℎ2 +
𝑃2
𝜌2
= 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 (5)
and by setting ℎ1 = ℎ2, 𝜌1 = 𝜌2 = 𝜌 𝑎𝑖𝑟, 𝑃1 = 𝑃 𝑇, 𝑃2 = 𝑃𝑆, and 𝑢2
2
= 0, we are able to rearrange
and calculate the velocity inside the wind tunnel (6) where the subscript indicate states 1 and 2:
𝑢 = √
2𝑃 𝐷
𝜌 𝑎𝑖𝑟
(6)
6. 3
𝑃 𝐷 = 𝑃 𝑇 − 𝑃𝑆,
(7)
where 𝑃 𝐷is dynamic pressure, calculated by subtracting the total pressure, 𝑃 𝑇, from the static
pressure, 𝑃𝑆, which is approximately 101kPa, as shown in equation (8).
Before testing begins, the location of stall angle on XFLR5 must be noticed in order to relate the
theory to experimental data. Stall angle is where an airfoil reaches its maximum CL. This
phenomenon results in a rapid increase of drag, while simultaneously decreasing the lift
significantly (Anderson, Jr, 2001) (Chen & Bernal, 2008). These are aerodynamic characteristics
that are expected in order to be able and relate it to the experimental values from the wind tunnel.
With extensive research and testing, it will be possible to confidently confirm whether the
program XFLR5 and the BHE wind tunnel results match.
2 Materials and Methods
2.1 XFLR5
XFLR5 is a computer program created by M. Drela, designed to calculate the different
aerodynamic characteristics of an airfoil, such as lift and drag for different angles of attack and
Re. To do this, XFLR5 divides the airfoil into a preset number of panels (e.g. 100) and solves for
the pressure for every individual panel. From the pressure, XFLR5 can extrapolate lift and drag
forces, lift and drag coefficients, and generate plots, such as CL vs α, CD vs α, or CL/CD vs α.
XFLR5 does a tremendous job illustrating accurate aerodynamic characteristics such as stall
angle, maximum lift, or the efficiency of an airfoil for Re above 2.0 × 105
. However, XFLR5
has not been deemed a reliable instrument for Re below 2.0 × 105
. Therefore, testing has been
conducted in the Biegler Hall Wind Tunnel to characterize the NACA0010 airfoil and compare it
to XFLR5 results.
2.2 Calibration and Alignment
With the NACA0010 mounted on the force balance, various necessary precautions had to be
taken. For example, calibrating the force balance became a crucial experimental precaution due
the heavy dependence on its measurements. The force balance used in the BHE Wind Tunnel is a
device that determines forces applied in the x, y, and z direction. With the force balance correctly
calibrated, the next step is to align the airfoil to the direction of the wind tunnels airflow. A VI
made it possible to acquire real-time force measurements, where the user can manually rotate the
airfoil until the forces orthogonal to the airfoil result in 0°. The forces orthogonal to the airfoil
represent lift and weight, therefore, if the forces do not equal zero, the airfoil is not properly
aligned to 0°. Once the force balance and airfoil position are correctly calibrated, then and only
then, can data acquisition begin.
2.3 Experimental Corrections
A total of eighteen sweeps for each Re were made across the airfoil to determine the
aerodynamic behaviors of lift and drag. After each sweep, the VI would save the Pitot tube
7. 4
measurements on an Excel file, where it was later uploaded to MATLAB and further analyzed.
Since the force balance has a resolution of 200 mN, the lift forces could be applied directly from
the Excel sheet. However, the drag measurements were well below the force balance’s
resolution, therefore a different approach had to be implemented.
When over plotting, there is a clear difference between upstream and downstream velocity
profiles. The difference of velocities is due to the force the airfoil exerts on the flow. This is
called the wake deficit. The wake deficit is the disturbance to the average flow caused by the
airfoil. Therefore, the wake deficit can be thought of as loss of momentum. Therefore, one can
imply that the force of on a solid object must be equal to the rate of change of momentum in the
fluid (Anderson, Jr, 2001). The equation calculating the drag using the momentum balance is:
𝐷𝑟𝑎𝑔 = 𝜌𝑈0
2
𝑏∫ [
𝑢 𝑤(𝑦)
𝑈0
− (
𝑢 𝑤(𝑦)
𝑈0
)
2
] 𝑑𝑦
ℎ 2⁄
−ℎ 2⁄
(8)
Where 𝜌 is the density of the fluid, 𝑈0 is the free stream velocity, b is the airfoil span, and 𝑢 𝑤(𝑦)
is the velocity within the wake.
However, even with equation (8), there is still a correction factor that needs to be applied in
order to calculate accurate drag values. Throughout all eighteen sweeps, there is a slight offset
between the upstream and downstream Pitot tube as seen in Figure 2. To correct this, a
MATLAB script was written to average 10 data points on both sides of the wake profile. The
velocity from the upstream Pitot tube was then subtracted from the calculated velocities. The
difference is then averaged again and increments each velocity data point by that the calculated
value (see Appendix for sample code).
Figure 2: Wake deficit without correction factor Figure 3: Wake deficit with correction factor
The result is an adjusted over plot of the both the upstream and downstream Pitot tube, where the
downstream Pitot tube sits over the wake (Figure 3). Furthermore, with such a small test area,
higher angles of attack result in greater pressure differences. This causes the velocity to increase
on the leeward side of the airfoil and decrease on the windward side. However, the only valuable
27.5 28 28.5 29 29.5 30 30.5 31
velocity for alpha (5)
0
5
10
15
20
25
30
35
40
horizontal
velocity vs. horizontal @ 200,000 Re
27 27.5 28 28.5 29 29.5 30 30.5
velocity for alpha (5)
0
5
10
15
20
25
30
35
40
horizontal
velocity vs. horizontal @ 200,000 Re
8. 5
part of the graph is the wake itself, therefore, the values on either side of the wake can be
omitted. Therefore, the limits of integration are reduced to only integrate between the regions of
the wake deficit.
3 Characterization of the Test Flow
With the Pitot tube inside the test section, the wind tunnel can be tested repeatedly without an
airfoil to test the uniformity of the airflow. It is crucial constantly monitor results when analyzing
the uniformity of the airflow inside the wind tunnel, to record optimum data when the airfoil is
placed inside the test sections. Once the wind tunnel is working to the projects specifications, an
airfoil can be added and its lift and drag forces measured.
Figure 4: Top view of the WT with flow heading left in the x direction
Figure 5: Side view of the WT
3.1 Wind Tunnel Characterization
9. 6
The BHE Wind Tunnel has many characteristics that must be acknowledged before the airfoil is
mounted. One of the characteristics involves analyzing the limitations of the traverse system that
is attached to the downstream Pitot tube. The downstream Pitot tube moves in the y and z
direction and is used to record the velocity of the fluid in test section area (Figure 4,5). The Pitot
tube could only move 37 cm in the y-axis, leaving it unreachable about 8cm-9 cm from the wall
facing the y-axis. Lastly, both Pitot tubes have a diameter of approximately 3.3 ± 0.1mm.
Therefore, the range of the downstream Pitot tube within the test area is from 0.165 ± 0.1mm to
37 cm in the y direction.
The program that is used for controlling the traverses and performing data acquisition is
Laboratory Virtual Instrument Engineering Workbench (LabVIEW). This allows the Pitot tube to
be set at a certain location, sweep for data recordings, and detect what the upstream and
downstream flow of the fluid is at a predetermined location.
3.2 Boundary Layer
It is very important when testing inside the wind tunnel to plot the velocity profile in order to
justify where the boundary layer is. The wind tunnel has four boundary layers, over each of the
inside walls of the test area. The boundary layer creates a thin layer of fluid near the surface
where the velocity increases from zero at the surface of the object to the free stream value away
from the surface (Hall, 2006). A relationship between velocity and horizontal distance can be
used to determine the average boundary layer thickness. As the Pitot tube moves away from the
wall, it increases in velocity. Therefore, the distance the Pitot tube moves to reach the upstream
velocity is the actual distance of the boundary layer.
Figure 6: Boundary layer development at u = 30 m/s
When velocity matches 95% of the upstream velocity, it indicates that the Pitot tube is outside
the boundary layer, resulting in the boundary layer edge. As the Pitot tube moves in the positive
z-axis the boundary layer starts to develop as it moves away from the floor. The midway point,
23cm away from the test area floor, is where the average boundary layer thickness remains
consistent and will act as initial z-axis location for future tests with the NACA0010 airfoil. Once
the Pitot tube is outside the boundary layer, a consistent boundary layer profile appears. With
0 5 10 15 20 25 30 35 40
Horizontal distance (cm)
22
23
24
25
26
27
28
29
30
31
Velocity(m/s)
Z=23cm
10. 7
lower Re, the airflow experiences more disturbances, which result in an inconsistent velocity
profile, as seen in Figure 7.
Figure 7: Boundary layer development at u = 5 m/s
The development of the boundary layer at 5 m/s is not nearly as clear as at 30 m/s. The boundary
layers from bottom and left of the test area overlap, causing a greater disturbance in the airfield.
Ultimately, lower velocities make the air flow more susceptible to disturbances. However,
despite these vortices, a boundary layer profile can still be measured and present valuable data.
By comparing the calculations to both Figure 6 and Figure 7, one can determine whether the
boundary layers are laminar or turbulent. When looking at the boundary layer at 30 m/s (Figure
6), the boundary layer edge can be estimated at about 1.8 cm. By referring back to the
calculations made earlier for boundary layer thickness, it is safe to say that the boundary layer is
neither laminar nor turbulent. Therefore, the boundary layer must be transitioning from laminar
to turbulent within the wind tunnel. By comparing the boundary layer thickness calculations to
the boundary layer graph at 5 m/s (Figure 7), the boundary layer edge can be estimated to be 1.00
cm. Therefore, at 5 m/s, the boundary layer matches the calculation made earlier for laminar.
3.3 Effectof Sampling Time
A LabVIEW Virtual Instrument (VI) is programmed to take reading of the Pitot tube at
predetermined locations. The Pitot tube moves in increments and delays in-between those
increments for Δt(s), in order to effectively calculate the velocity at that location. An
investigation was conducted to discover, the sensitivity of results to Δt used. This is crucial
because it show that using a Δt of 0.05s does not change the velocity measurements.
0 5 10 15 20 25 30 35 40
Horizontal distance (cm)
3
3.5
4
4.5
5
5.5
Velocity(m/s)
Z=23cm
11. 8
Figure 8: Recording t (s) at 0.05s and 1.00s such that, y=37cm, z=23cm, and u=30m/s
Upon analyzing the results, the direction and the velocity remained consistent as t changed. At
first, when looking at Figure 8, there is no noticeable difference. Generally, there will not be a
significant difference between sweeping at t = 0.05s and t= 1.00s besides the time of each
sweep. When t = 0.05s, the total time for one sweep is approximately 7 minutes. Whereas when
t = 1s, the total time to complete one sweep is approximately 14 minutes. Therefore, to achieve
a more time effective sweep, while still maintain the integrity of the data, sweeps should be
conducted at the lower t of 0.05s.
3.4 TestRepeatability
Before proceeding with any results, it is vital to make sure the results are repeatable. In other
words, will the experimental reading be the same if it is tested at the same boundaries multiple
times under the same conditions? For sweeps 7 and 8 (Figure 9) the direction, velocity, and time
are kept constant to compare whether or not there is a difference in the velocity profile. Clearly,
there is no observable difference in either case. Therefore, it is safe to say that the sweeps are
repeatable.
Figure 9: Results of repeatability at t=1.00s such that, y=37cm, z=23cm, and u=30m/s
12. 9
3.5 Boundary Layer Calculations
Prior to mounting the airfoil, boundary layer thickness is measured in order to determine whether
the boundary layer is laminar or turbulent. In order to interpret these characteristics, different Re
values were tested inside the wind tunnel. The test section temperature is assumed to be 20°C,
where density and viscosity are obtained from Appendix D in Anderson’s Fundamentals of
Aerodynamics. When calculated using equation (1), the Re at 5 m/s becomes 4.5𝑥104
and the Re
at 30 m/s becomes 2.8𝑥105
.
Since there are two types of flow in the wind tunnel, turbulent flow (9) and laminar (10) what
type of boundary layer appears had to be assumed (White, 2002):
( 𝑡𝑢𝑟𝑏𝑢𝑙𝑒𝑛𝑡)
𝛿
𝑥
=
0.16
𝑅𝑒
1
7
(9)
( 𝑙𝑎𝑚𝑖𝑛𝑎𝑟)
𝛿
𝑥
=
5.0
𝑅𝑒
1
2
(10)
where 𝛿 is the boundary layer thickness, x is the distance downstream from the start of the
boundary layer, and Re is the Reynolds number. Moreover, since Re is a unit less value, 𝛿 is
divided by x to achieve the same unit less result.
When analyzing the Re of 2.8 × 106
, the boundary layer thickness for turbulent flow became
2.62cm and the boundary layer thickness for laminar flow became 0.412cm. Moreover, when
calculating results for Re of 4.5 × 105
, a boundary layer thickness for turbulent flow transitioned
to 3.38cm and a boundary layer thickness for laminar flow also transitioned to 1.01cm.
With the theoretical results completed, the next step is to examine the thickness of the boundary
layer experimentally within the wind tunnel. The airfoil was not mounted because we want an
empty test section to measure flow non-uniformity and not to measure flow disturbance. By
doing so, experimental data can be used to calculate the thickness of the boundary layer while
simultaneously determining the quality of airflow inside the test area. When comparing the
experimental results alongside the theoretical results, the higher Re experienced a turbulent
behavior, whereas the lower Re experienced a hybrid of laminar and turbulent behavior. In fact,
with lower Re, the boundary is in a transitional state, where it transitions from a laminar
boundary layer to a turbulent boundary layer. After the wind tunnel testing was conducted, a
boundary layer thickness of around 1.2 cm was obtained at a velocity of 30 m/s (Figure 6) which
differs from the boundary thickness calculation at turbulent flow, 2.6cm. In the case of the 5m/s,
the experimental boundary layer thickness was around 0.5cm. Interestingly in both cases the
experimental results do not match any of our theoretical results for both fully laminar and
turbulent flow. This may be due to the fact that the velocities in which the wind tunnel was
operated, 5 m/s and 30m/s, produces a Re equal to 4.5 × 104
and 2.8 × 105
, which fall within
the range of Re where the transition from laminar flow to turbulent flow occurs. Therefore,
13. 10
causing a phenomenon where fully turbulent flow or laminar flows are not present, but rather a
combination of both.
4 Results & Discussion
After completing the 18 sweeps for each Re, the values for lift and drag were over plotted for the
wind tunnel, force balance, and XFLR5.
4.1 Tests atRe of 180,000
Figure 10 shows an over plot of the 𝐶 𝐿 versus the α for XFLR5 results and experimental data for
Re of 1.8 × 105
. Moreover, Figure 11 shows an over plot of 𝐶 𝐷 versus α for the force balance
results, XFLR5 results, and experimental data When looking at the 𝐶 𝐿 uncertainty of the wind
tunnel, it is not within that of XFLR5. That is because the uncertainty increases as the Re
decreases. Moreover, there is a decrease in 𝐶 𝐿 for the experimental data, causing separation from
the XFLR results. When analyzing Figure 11, XFLR5’s drag values are within the wind tunnels
uncertainty from α’s of −4° to 3°. But, the experimental 𝐶 𝐷 increases and also separates from
the XFLR5 results.
Figure 10: Angle of attack versus coefficient of lift
for Re of 180,000
Figure 11: Angle of attack versus coefficient of drag
for Re of 180,000
4.2 Tests ofRe at 100,000
Figure 12 also shows 𝐶 𝐿 versus the α for XFLR5 results and experimental data but for Re of
1.0 × 105
. Moreover, Figure 13 shows the same over plot of 𝐶 𝐷 versus α for the force balance
results, XFLR5 results, and experimental data. Looking at experimental 𝐶 𝐿, it continues to flow
the trend of separation from the XFLR5 results. Figure 12 also shows the accuracy of XFLR5
when predicting the stall angle (10°). One thing to also note is the inaccuracy of the force
balance for drag measurements. When analyzing Figure 11, XFLR5’s drag values are within the
wind tunnels uncertainty from α’s of −4° to 3°, however, not for the force balance. With such
small Re, it is expected to record very small drag forces. As mentioned before, the force balance
14. 11
only has a resolution of 200 mN. Regardless, the XFLR5 results and experimental results have
followed a similar linear trend.
Figure 12: Angle of attack versus coefficient of lift for
Re of 100,000
Figure 13: Angle of attack versus coefficient of drag
for Re of 100,000
4.3 Tests ofRe at 40,000
Once again, Figure 14 illustrates the 𝐶 𝐿 versus 𝛼 relationship whereas Figure 15 illustrates the 𝐶 𝐷
versus 𝛼. Both Figure 14 and Figure 15 continue to show a linear trend with XFLR5. At Re
4.0 × 104
, the 𝐶 𝐷 values for XFLR5 are within the uncertainty of the experimental wake deficit
results. Whereas in the previous two Re, the experimental results and force balance results are
larger and not within the uncertainty.
Figure 14: Angle of attack versus coefficient of lift for
Re of 40,000
Figure 15: Angle of attack versus coefficient of drag
for Re of 40,000
The reason why the force balance drag measurements do not follow the trend is due to the gap on
the top and bottom on the airfoil. The airfoil is about 2.0 ± 0.10mm away from the wall, which
15. 12
may develop a vortex that applies an induced drag onto the force balance. Neither the momentum
integral nor XFLR5 take into consideration this effect, resulting in an increase in drag on the
force balance. Overall, the results attained from the force balance cannot be deemed reliable for
drag because it does not take the same parameters as that of XFLR5 and wake.
4.4 Discussion
The wind tunnel results tend to follow the same trend as that of XFLR5 for Figure 10, Figure 12,
and Figure 14. So, the lower the Re, the longer the trend holds. When related back to theory, it
makes perfect sense because the larger the Re, the more linear the graph should look for 𝐶 𝐿. So
far, XFLR5 can give accurate trend lines that the experimenter can base his or her results and
hold them reliable or not.
To continue analyzing the separation occurring in each graph, the idea of a laminar separation
bubble (LSB) must be introduced. When analyzing Figure 12, there is a sudden increase in lift at
about 2° whereas for Figure 14, the increase of lift happens at about 3°. An inflection angle is
where the gradient of the velocity changes rapidly. This is a result of the LSB. The phenomenon
happens at low Re where the laminar boundary layer separates transitions to turbulent, then
reattaches to the airfoil surface. A laminar boundary layer develops on the leading edge of the
airfoil and transitions into a turbulent boundary layer shortly after. The difference of pressure
causes a reverse flow under the boundary layer that, in time, develops into a vortex. The
boundary layer then reattaches to the airfoil and continues through the trailing edge.
Furthermore, as the angle of attack increases, the LSB travels from the trailing edge to the
leading edge only to burst, which in return, causes stall.
Figure 16: diagram of laminar separation bubble
When further observing Figure 10, Figure 12, and Figure 14, an evident trend is revealed, further
strengthening the assumption that an LSB is affecting 𝐶 𝐿. Each 𝐶 𝐿 graph has a sudden sharp
increase in 𝐶 𝐿. According to Mueller, the sharp rise at low Re is believed to be the result of a
laminar separation bubble on the upper surface of the wing (Figure 16). Furthermore, O’Meara
and Mueller (1987) showed that the length of the separation bubble tends to increase with a
16. 13
reduction in Re. A reduction in the turbulence intensity also tends to increase the length of the
bubble, resulting in the lift-curve slope is affected. (Mueller, 1999).
In order to justify whether or not XFLR5 is reliable for predicting aerodynamic characteristic at
low Re, the presence of a LSB must be investigated with the program XFLR5. In order to do so,
a plot needs to be generated to compare the airfoils chord position (
𝑥
𝑐
) and coefficient of pressure
(𝐶 𝑃).
Figure 18 illustrates the three main components of characterizing a LSB. The three different
gradients represent three different things: separation point, transition point, and reattachment
point. The graph fully demonstrates the development of the LSB the closer it approaches its
chord length. This means, that XFLR5 does in fact take into consideration LSB. Therefore, the
separation seen by the graphs must be due to dimensional inconsistences. Where as the force
balance measures three dimensions, XFLR5 only operates in two dimensions. This means that
XFLR5 is not fully characterizing the LSB. However, XFLR5 still does not predict accurate
results in for lift since the lift measurements are higher after the rapid increase in lift shown in
Figure 10, Figure 12, and Figure 14
4.5 XFLR5 Correction
As stated before, the XFLR5 results did not match the lift values. However, by multiplying the
XFLR5 lift results by a correction factor of 0.75, the graphs were able to match. Not only are the
graphs following the same trends, but a stall angle can be obtained from both data sets, and both
data sets contain a rapid increase in lift. Lastly, all three experimental data uncertainties fall
within nearly every XFLR5 result. With the implantation of the correction factor of 0.75, XFLR5
can effectively predict aerodynamic characteristics at low Re.
Figure 17: Laminar Separation Bubbles theory results Figure 18: Laminar Separation Bubbles XFLR5
results at 𝟖°
Separation point
Transition point
Reattachment point
17. 14
Figure 19: Re of 40,000 with
correction factor
Figure 20: Re of 100,000 with
correction factor
Figure 21: Re of 180,000 with
correction factor
5 Conclusions
With extensive characterization of the wind tunnel and airfoil, a well-developed argument has
been made on whether XFLR5 can accurately predict aerodynamic characteristics at low Re.
Aerodynamic theory assisted the understanding and dependability of testing with the NACA0010
airfoil. With careful and precise data acquisition methods, six very crucial plots were analyzed. It
was safe to say that XFLR5 can be used to compare aerodynamic trends of both lift and drag for
the NACA0010. Furthermore, the ability for XFLR5 to accurately predict the development of a
laminar separation bubble from the large increase of lift is significant. Lastly, XFLR5 accurately
predicts the stall angle, which can be monumental in developing effective and reliable MAV’s.
Lastly, with the help of the correction factor, XFLR5 can be used to predict actual lift values that
is crucial when testing airfoils at low Re. Nonetheless, XFLR5 has demonstrated comparative
test reliability, as well as test precision, for the development and manufacturing of MAV’s
navigating in Re lower than 2.0 × 105
.
20. 17
Sample code
% adjust data for alpha of negative 4
%find average offset and creat correction factor
Indn4b = data(195:205,3,1)-data(195:205,1,1);
Indn4t = data(235:245,3,1)-data(235:245,1,1);
Indn4 = [Indn4b; Indn4t];
avgIndn4 = mean(Indn4);
%momentum integral
for j= 205:235
u_u0(j,1) = (data(j,3,1)-avgIndn4)/data(j,1,1);
u_u0_2(j,1) = ((data(j,3,1)-avgIndn4)/data(j,1,1))^2;
diff_u(j,1)= (u_u0(j,1) - u_u0_2(j,1));
sum_u(:,1) = sum(diff_u(:,1));
theta(1) = sum_u(1)*0.001;
end
c = 0.0915;
c_d(:,1) = (2*theta(1))/c;
%graph
figure()
plot(data(:,1,1),y(:,:),'-');
hold on
plot(data(:,3,1)-avgIndn4,y(:,:),'-');
title('velocity vs.horizontal @ 200,000 Re')
alphalabel = ['velocity for alpha (', num2str(nAlpha(1)), ')'];
xlabel(alphalabel)
ylabel('horizontal')
grid minor
grid on
21. 18
References
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McGraw-Hill.
Chen, W., & Bernal, L. P. (2008). Design and Performance of Low Reynolds Number Airfoils for
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Hall, N. (2006, May 5). Boundary Layer. Retrieved July 27, 2016, from National Aeronautics
and Space Administration: https://www.grc.nasa.gov/www/k-12/airplane/boundlay.html
McArthur, J. (2007). Aerodynamics of Wings at Low Reynolds Numbers. PhD thesis, University
of Southern California, California, US.
Mueller, T. (1999). Aerodynamics Measurements at Low Reynolds Numbers for Fixed Wing
Micro-Air Vehicles. Belgium: VKI Lecture Series, NATO-RTO-AVT.
Selig, M. (2003). Low Reynolds Number Airfoil Design. Belgium: VKI Lecture Series, NATO-
RTO-AVT.
Shih, C., Lourenco, L., Van Dommelen, L., & Krothapalli, A. (1992). Unsteady flow past an
airfoil pitching at a constant rate. . AIAA Journal.
Talay, T. (1975). Introduction to the aerodynamics of flight. Washington, D.C.: Scientific and
Technical Information Office, National Aeronautics and Space Administration.
White, F. (2002). Fluid Mechanics . Boston, MA, US: McGraw-Hill.
