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.

1

Table of ContentsAbstract...........................................................................................................................................1

1 Introduction........................................................................................................................11.1 Approach...................................................................................................................................2

2 Materials and Methods........................................................................................................32.1 XFLR5.........................................................................................................................................32.2 Calibration and Alignment..........................................................................................................32.3 Experimental Corrections...........................................................................................................3

3 Characterization of the Test Flow.......................................................................................53.1 Wind Tunnel Characterization....................................................................................................63.2 Boundary Layer..........................................................................................................................63.3 Effect of Sampling Time..............................................................................................................73.4 Test Repeatability......................................................................................................................83.5 Boundary Layer Calculations.......................................................................................................9

4 Results & Discussion.........................................................................................................104.1 Tests at Re of 180,000...............................................................................................................104.2 Tests of Re at 100,000...............................................................................................................104.3 Tests of Re at 40,000................................................................................................................114.4 Discussion................................................................................................................................124.5 XFLR5 Correction......................................................................................................................13

5 Conclusions........................................................................................................................14

Appendix..............................................................................................................................15Calculation #1................................................................................................................................15Calculation #2................................................................................................................................15Test Matrix #1................................................................................................................................16Test Matrix #2................................................................................................................................16

References............................................................................................................................18

2

FiguresFigure 1: Flow around an airfoil with respect to its angle of attack (Hall, Inclination Effects on

Lift, 2015)................................................................................................................................1Figure 2: Wake deficit without correction factor............................................................................4Figure 3: Wake deficit with correction factor..................................................................................4Figure 4: Top view of the WT with flow heading left in the x direction........................................5Figure 5: Side view of the WT........................................................................................................5Figure 6: Boundary layer development at u = 30 m/s.....................................................................6Figure 7: Boundary layer development at u = 5 m/s.......................................................................7Figure 8: Recording t (s) at 0.05s and 1.00s such that, y=37cm, z=23cm, and u=30m/s..............8Figure 9: Results of repeatability at t=1.00s such that, y=37cm, z=23cm, and u=30m/s................8Figure 10: Angle of attack versus coefficient of lift for Re of 180,000.........................................10Figure 11: Angle of attack versus coefficient of drag for Re of 180,000......................................10Figure 12: Angle of attack versus coefficient of lift for Re of 100,000.........................................11Figure 13: Angle of attack versus coefficient of drag for Re of 100,000......................................11Figure 14: Angle of attack versus coefficient of lift for Re of 40,000...........................................11Figure 15: Angle of attack versus coefficient of drag for Re of 40,000........................................11Figure 16: diagram of laminar separation bubble..........................................................................12Figure 17: Laminar Separation Bubbles theory results.................................................................13Figure 18: Laminar Separation Bubbles XFLR5 results at 8 °......................................................13Figure 19: Re of 40,000 with correction factor..............................................................................14Figure 20: Re of 100,000 with correction factor............................................................................14Figure 21: Re of 180,000 with correction factor............................................................................14

3

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:

ℜ=ρ uxμ (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=12

ρ u2 SC L (2)

D=12

ρ u2 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)

1

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 CL vsα∧CD vsαgraph 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):

ρair=P

RT (4)

where ρair is the density of air, P is the static pressure, T is the temperature, R is the universal gas

constant of air: 287 Jkg ∙ K . By using Bernoulli’s equation (5),

u12

2+g h1+

P1

ρ1=

u22

2+g h2+

P2

ρ2=constant (5)

and by setting h1=h2, ρ1= ρ2=ρair, P1=PT , P2=PS, and u22=0, we are able to rearrange and

calculate the velocity inside the wind tunnel (6) where the subscript indicate states 1 and 2:

u=√ 2 PD

ρair(6)

2

PD=PT−PS, (7)

where PDis dynamic pressure, calculated by subtracting the total pressure, PT , 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

3

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 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=ρU 02 b ∫

−h /2

h/2 [uw( y)U 0

−( uw( y )U 0 )

2]dy (8)

Where ρ is the density of the fluid, U 0 is the free stream velocity, b is the airfoil span, and uw ( 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,

4

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 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

5

3.1 Wind Tunnel Characterization

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

6

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 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 (Figure6), 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 Effect of 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.

7

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 Test Repeatability

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

8

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 4.5 x 104 and the Re at 30 m/s becomes 2.8 x105.

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 ) δx=0.16

ℜ17

(9)

(laminar ) δx=5.0

ℜ12

(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 of4.5 × 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∧2.8× 105, which fall within the range of Re where the transition from laminar flow to turbulent flow occurs. Therefore, causing a

9

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 at Re of 180,000

Figure 10 shows an over plot of the CL versus the α for XFLR5 results and experimental data for Re of 1.8 ×105. Moreover, Figure 11 shows an over plot of CD versus α for the force balance results, XFLR5 results, and experimental data When looking at the CL 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 CL 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 °¿3°. But, the experimental CD 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 of Re at 100,000

Figure 12 also shows CL 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 CD versus α for the force balance results, XFLR5 results, and experimental data. Looking at experimental CL, 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 °¿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

10

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 of Re at 40,000

Once again, Figure 14 illustrates the CL versusα relationship whereas Figure 15 illustrates the CD versus α . Both Figure 14 and Figure 15 continue to show a linear trend with XFLR5. At Re 4.0 × 104, the CD 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 ± 0.10 mm away from the wall, which

11

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 CL. 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 CL. Each CL graph has a sudden sharp increase in CL . 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

12

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 ( xc ) and coefficient of

pressure (CP).

Error: Reference source not found 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.

Separation point

Figure 17: Laminar Separation Bubbles theory results Figure 18: Laminar Separation Bubbles XFLR5 results at 8 °

Transition point

Reattachment point

13

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.

14

Appendix

Calculation #1

ℜ= ρuxμ

ℜ=(1.20 kg

m3 )(5 ms ) (1.36 m )

1.80 x10−5 N m2

s

=4.533 x105

ℜ=(1.20 kg

m3 )(30 ms ) (1.36 m )

1.80 x10−5 N m2

s

=2.720 x 106

Calculation #2

For Re = 1.8 ×105

δ=0.16(1.36 m)

(2.720 x 106)1 /7 =0.0262 m=2.620 cm (Turbulent)

δ=5.0(1.36 m)

(2.720 x106)1 /2 =0.0410 m=0.412 cm (Laminar)

For Re = 4.0 × 104

δ=0.16(1.36 m)

(4.533 x 105)1/7 =0.0338 m=3.38 cm (Turbulent)

δ=5.0(1.36 m)

(4.533 x 105)1/2 =0.01009 m=1.01 cm (Laminar)

15

Test Matrix #1

Sweep # y (cm) z (cm) u (m/s) t (s)0 37 23 0 0.051 37 0 30 0.052 37 1 30 0.053 37 2 30 0.054 37 3 30 0.055 37 4 30 0.056 37 5 30 0.057 37 23 30 0.058 37 23 5 0.059 37 23 30 0.0510 37 23 30 1

Test Matrix #2

Sweeps Y(cm) Z(cm) U(m/s) Δt(s)1 37 10 30 0.052 37 15 30 0.053 37 28 30 0.054 37 33 30 0.055 37 0 5 0.056 37 1 5 0.057 37 2 5 0.058 37 3 5 0.059 37 4 5 0.0510 37 5 5 0.0511 37 7 5 0.0512 37 10 5 0.0513 37 15 5 0.0514 37 28 5 0.0515 37 33 5 0.0516 37 7 30 0.05

16

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 integralfor 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;endc = 0.0915;c_d(:,1) = (2*theta(1))/c; %graphfigure()plot(data(:,1,1),y(:,:),'-');hold onplot(data(:,3,1)-avgIndn4,y(:,:),'-');title('velocity vs. horizontal @ 200,000 Re')alphalabel = ['velocity for alpha (', num2str(nAlpha(1)), ')'];xlabel(alphalabel)ylabel('horizontal')grid minorgrid on

17

References Anderson, Jr, J. D. (2001). Fundamentals of Aerodynamics (Third Edition ed.). Boston, MA:

McGraw-Hill.Chen, W., & Bernal, L. P. (2008). Design and Performance of Low Reynolds Number Airfoils for

Solar Powered Flight. Reno, Nevada, US.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.htmlMcArthur, 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.

18