FindingtheOptimumAngleof AttackforaClark-yAirfoilto
OmerSyed
Grade12:DIAEmiratesHills
LaboratorySupervisor:Mr.MohammedKhateeb Instructorat‘EmiratesAviationUniversity’
05/08/2023
MaximizeLiftForce
Aerodynamics is the study of how things move through air. Its four main principlesareWeight, Lift, Drag, and Thrust, each being a different type of force. Weight is adownwardsforcewhich acts on every object due to gravity. Weight is the product of a body’smassandthegravitational force acting on that body: . Aircraftsneedtoovercometheirweightinordertofly.On �� = ���� the other hand,liftisanupwardforceopposingweight.Itcausesthebodytomoveupwards.The lift coefficient is a dimensionless value that relates the lift force to the fluid density, fluid velocity, and the area the lift force acts on. The formula for lift force is:
(“The Lift Coefficient”). Depending on the shape of the body, the �� = 1 2× �� �� × ρ ×��2 × ��
magnitude of lift force changes. Aerodynamics is used to analyze the properties of airfoils and wingstomaximizeliftforce.
Next, drag is the force opposing the direction of motion of a body. It existsineveryfluidandis also affected by the shape ofabody.Inasimilarfashiontolift,itisdesiredtominimizethedrag force as it slows down a body. A coefficient of drag also exists andrelatestheliftforcetoforce produced by dynamic pressure and the area. The drag force can be calculated through the formula:
(“TheDragCoefficient”).
Finally, to counteract the drag force, a thrust force is present. In ordertoaccelerateforward,the thrust force needs to be greater than drag. In aircrafts it is generated through an engine and a propulsionsystemsuchasapropellerorturbine.
AerodynamicsPrinciplesExplained
When a fluid flows past a body, or a body moves through afluid,therearetwotypesofstressit experiences. Shear stress from the frictional forces acting onthebodyduetotheviscosityofthe fluid. It is tangential to the direction the fluid is moving in. The second type of stress is the Pressure stress caused by the uneven distribution of pressure around the body. It acts perpendicular to the body’s surface.Thesestressesarekeyfactorsincreatingliftanddragforces (“UnderstandingAerodynamicLift”).
Lift
The lift force is the result of these two stresses, mainly pressure stress. In the context of an airfoil, there will be lower pressure above the airfoil and higher pressure below the airfoil (“Understanding Aerodynamic Lift”). The difference in pressure can be illustrated through a pressuredistributioncurvewhichmapsthepressureprofileonthetopandbottomoftheairfoil.
Introduction
�� = 1 2 ×�� �� × ρ ×��2 × ��
The diagram above shows the pressure distribution
a
The y-axis is the coefficient of pressure and increases in magnitude as you go down. The blue colored line represents the pressure at the bottom oftheairfoilandtheyellowcoloredlinerepresentsthetop. According to the graph, the top of the airfoil experiences negative pressure. Thismeansthatthe pressure at the top of the airfoil is lower than atmospheric pressure, and the pressure at the bottom, being positive, is higher than atmospheric pressure. Due to thisdifferenceinpressure,a netforceintheupwardsdirectioniscreated,beingtheliftforce.
This phenomena can be explained through two different theories, Bernouli’s equation and Newton’s third law. Aroundtheleadingedgeoftheairfoil,thereisapointwhereflowvelocityis zero due to the dispersion of flow around the airfoil known as the stagnation point. Its position changesdependingontheangleofattackandtheshapeoftheairfoil.
Theairflowsfasteroverthestagnationpointthanunderthestagnationpoint.Thishappensasthe streamlines above the airfoil are closer together Since air is not compressible and the flow rate of air is constant, it means that the air has a smaller passage to travel through and therefore
Figure 1: Pressure distribution around NACA 2412 airfoil (Source: Xfoil)
around
NACA 2412 airfoil.
(Source: Helicopters and aircrafts)
increases the velocity of air. According to Bernouli’s principle,thehigherthevelocityoftheair, the lower the pressure in that region. Thus, a pressure difference is createdbelowandabovethe airfoil.
Drag
Drag, similar to lift, is caused by the pressureandshearstresses.Therefore,thedragforcecould be split into two different categories, pressure drag, and friction drag. Pressure drag is most notable for blunt bodies such as spheres. Thisisduetoahighdifferenceinpressurebetweenthe front and back of the object. A high pressure difference is created if there is significant flow separationcausedbytheobject(“UnderstandingAerodynamicDrag”).
The curved arrows in the separation region represent recirculation of airflow due to the detachment of the boundary layer from the surface of the object. Ideally, flow separationwould be minimized to reduce drag and other adverse effects such as vortex sheddings causing vibrationsandinstabilityintheairflow
Diving in more detail, as the flow passes over the top of the body, it accelerates and causes a decrease in pressureinthedirectionofflow Afteracertainpointonthetopofthebody,theflow starts to decelerate whichcausesanincreaseinpressure.Ifthepressurebecomeslargeenough,it causes the flow to reverse direction, making it travel backwards. However, this is not possible due to the incoming flow of air in the positive direction, causing the flow to detach from the surface of the body and inducing flow separation. Although the sphere is an extreme case, it provides a more comprehensive understanding of the concept of flow separation and pressure drag (“UnderstandingAerodynamicDrag”).
Secondly, friction drag is due to the viscosity of the fluid and its interaction with the surface of the body. It is more relevant to this study as it is present for bodies which have a large surface areaaligningwiththedirectionoftheflow,suchasanairfoil.
(Source: Tecscience)
ResearchQuestion
How does theangleofattack(5°,7°,9°,11°,13°,15°,17°,19°,21°,23°,25°,27°)ofaClark-Y airfoilaffecttheliftforce(N)experiencedbyit?
AimoftheExperiment
The aim of the investigation is to find the angle of attack that maximizes lift force, ie. the optimumangle.
Variables
Independent Variable: Angle ofAttack(5°,7°,9°,11°,13°,15°,17°,19°,21°,23°,25°,27°) (±0.5°)
DependentVariable: LiftForce(N)
ControlVariables:
Variable Howisitcontrolled? Whyisitcontrolled?
AirFlowSpeed(m/s) Ensure the fan speed of the wind tunnel is controlled, to maintain the same flowspeed ofair.
Velocity of air flow should remain constant to prevent differences in property flow (laminar or turbulent), which can cause lift force to change duetorecirculationofflow.
Temperature(°C)
Method
InsertingtheModel:
Ensure the room is kept at a constant temperature throughout the procedure and the airfoil is not heated up priortotheexperiment.
The temperature of air can have an effect on airflow and its characteristics. For example, heating can cause flowseparation.
1. Makesuretheelectricalsupplytothewindtunnelisdisconnected.
2. Removethesidewindowoppositetothethree-componentbalance.
3. Tighten the balance locks of the three-componentbalance.Fromoutsidethewindtunnel, insert the airfoils into the collet of the three-component balance, so that its supportshaft passes into the wind tunnel test section. The airfoil should be inserted “upside down” with the trailing edge facing the frontofthewindtunnel.Thisisbecausethewindtunnel takes measurements through a scale which functions by measuring the tension on the stringsthattheairfoilisattachedto.
4. Inside the test section, measure the distance from the center of the airfoil to the bottom surface of thetestsection.Thisis152.5mm.Tightenthemodelclampofthebalance.The airfoilisnowsetaszeroangleofattack(α=0°).
5. Usetheangleadjustmentofthebalancetorotatetheairfoilandcheckthatitrotatesfreely inthetestsection,withoutrubbingthesidesofthetestsection.
6. Refitthesidewindowofthetestsection.
StartinguptheWindTunnel:
1. Switchontheelectricalisolatoronthecontrolandinstrumentationframe.
2. Setthespeedcontroltotheminimumposition(fullyanticlockwise)
3. Pressthegreen“START”button
4. Graduallyturnthespeedcontrolclockwiseuntilthetunnelisoperationalat15m/s.
WindTunneltestprocedure
1. Recordtheambienttemperatureandpressure.
2. Releasebalancelockbeforetest
3. Startthewindtunnel,setfree-streamvelocityasassignedtoeachteam.
4. Record the Lift, Drag and Pitching moment readings from the Three componentbalance displayunit
5. Adjust the angle of attack in steps of 1 ° from -5 ° upwards until the lift passed its maximummagnitudeduetothestall
6. The airfoil is flown “upside down” in the three-component balance. This is normal and allows more accurate balance design. (The sign of angle of attack in this balance is the oppositewhichappearsinyourtextbook)
7. Tightenbalancelockaftertest.
SpecificationsforAirfoilModel
Span:300mm
Chord:150mm
DataAnalysis
The raw data consists of datatakendirectlyfromtheVDASsoftware,andshowstheliftforceas well as the lift coefficients at each angle of attack. Three readings were taken for each angle of attacktoreducetheeffectofrandomerrorsonthedataandprovideamoreaccurateliftforce.
In the raw data, theangleswereincreasinginincrementsof2°until21°whereitincreasedby1 ° once to ensure that the optimum angle of attack was not skipped. However, this was not ultimatelynecessaryas21°provedtocausethemaximumliftforce.
To process the data, an average lift force was calculated and recorded from the three readings takenforeachangleofattack.
AngleofAttackvsAverageLiftForce-Graph
Figure 1: Angle of Attack vs Average Lift Force (Source: Logger Pro [plotted by me{?}])
SampleCalculationfrom5°: 341+341+339 3 = 3.403
Figure 1 shows the relationship between the angle of attack and average lift force. A best fit curve was plotted to better summarize the relationship between the two variables. It is aquintic curve with its equation shown in figure 1. As shown in the window presented in the graph, the curve has a correlation of 0.9947 to the data points which is considered high. This means the curveisanaccuratedepictionoftherelationshipbetweenangleofattack.
As the angle of attackincreases,theliftforceincreasestillamaximumpointandgraduallystarts decreasing after said point. This is caused by exceeding the optimum angle of attack causing airflow to become separated along the trailing edge of the airfoil. This causes a pressure difference between theleadingandtrailingedgeoftheairfoilandalossoflift.Alongtheleading edge, flow is still attached to the surface of theairfoil.Asattachedflowexertsmorepressureon the airfoil than separated flow, there is higher pressure against the surface of the airfoilnearthe leading edge compared to the trailing edge (Anderson). This causes a larger downwards force rootedattheleadingedgeincomparisontothedownwardsforceatthetrailingedge,pointingthe leadingedgedownwardsandresultinginalossoflift.
From Table 2andFigure1,aclearoptimumangleofattackcanbeobservedat21° Atthispoint, the lift force is 11.260 N. A clear decreasing trend in lift force is observed after this point, provingitisthepointofmaximumlift.
Uncertainties
The independent variable has an uncertainty of ±0.5 ° The protractor on the wind tunnel increases in increments of 1 ° The uncertainty was calculated by taking half of this increment. As there are no major calculations performed in order to obtain data, the uncertainty on the independentvariableisnotpropagatedanddoesnotmajorlyaffecttheinvestigation.
The percentageuncertaintythereforerangesfrom10%to1.9%,goingfrom5°to27°.Theseare relatively low values of percentage uncertainty indicating the measurements are precise and the relationship observed between the two variables is accurate in the context of this experiment. This is because there is high certainty that the angles reported in the data are close totheactual anglesofattack.
Theuncertaintyoftheindependentvariableisdisplayedinfigure1througherrorbars.
According to the lab instructor associated with this experiment, the values of lift are extremely precise and do not have any notable uncertainties. Therefore the measured values for the dependentvariabledonothaveuncertainties.
When calculating an average, an uncertainty ( ) stems from the small fluctuations in recorded △ values.Thisiscalculatedthroughthefollowingformula:
When calculating these uncertainties, the values came out to be exceptionally small and their effect on the findings was decided to be insignificant. The percentage uncertaintiesrangedfrom 0%to1.35%.
These very low uncertainty values show that the data gatheredishighlypreciseandthefindings can be considered reliable. This can be attributed to the preciseequipmentused,specificallythe AF100subsonicwindtunnel.
ComparingFindingswithaSimulation
The findings of this investigation will be compared to data fromXfoil-aprogramthatprovides data on the aerodynamic performances of various airfoils. The data is provided on the online databaseknownas“AirfoilTools”.Thedatafromthesimulationisprovidedbelow.
As seen in the graph, the optimum angle found by the simulation is around 15 ° which islower thantheoptimumangleofattackfoundinthisinvestigation.
The Reynold’s number used in the simulation is similar to the Reynold’s number in the conductedexperiment.
TheReynold’snumberintheinvestigationwascalculatedthroughthefollowingformula:
������������������������ ������������������������ 2 = △
Figure 2: Coefficient of Lift vs Angle of Attack of a Clark-y airfoil (Source: Xfoil)
�� = ρ���� µ
-Reynold’sNumber��
-FluidDensity=ρ 1.23������ 1
-Flowspeed=�� 25���� 1
-CharacteristicDistance=�� 0.6��
-DynamicViscosityofAir= (EngineersEdge) µ 1.802 ×10 5����/�� ��
5 = 1.02 ×10
On Xfoil, the Reynold’s number was set to , which is very close to the Reynold’s 1.00 ×106 numberinthewindtunnelusedfortheinvestigation.
Discrepancies between this investigation’s findings and the data provided by Xfoil must be due toerrorsintheexperiment.Systematicandrandomerrorsarepresentintheexperiment.
LimitationsandErrors
ConstructionoftheAirfoil
A source of error is the construction of the airfoil. As mentioned before, the airfoil was 3d printed and was not constructed from the highest quality of material. This may have resulted in the surface of the airfoil beingrough,whereasanidealairfoilwouldbecompletelysmooth.This may have caused turbulent airflow asroughedgesorslightimperfectionsinthemodelmayhave obstructed the smooth flow of air Lift force depends on smooth airflow around the airfoil and therefore turbulent airflow would reduce lift. This would cause the datatohavelowerliftforces than with smooth airflow It may contribute to the discrepancy between Xfoil and this investigationasthesimulatorassumeslaminarairflow
Although the model was rubbed with sandpaper toweakenthiseffect,itcouldhavebeensanded moretofurtherreducethiserror
ObstructionsinFrontofWindTunnel
As the wind tunnel used in the investigation is a suction-type, it can presentawindowforerror. As the tunnel is sucking in air, if there are any obstructions in front of the suction duct, it will disrupt the airflow before it enters the testing section. At times there may have been people walking in front of the suction duct which could have caused there to be slightly turbulent, affectingtheliftforceasdiscussed.
�� = 123×25×06 1802×10
6
GroundEffectandCirculation
The ground effect is caused by the air trapped between the bottom side of the airfoil and the ground, or the bottom of the test section in this case. It serves as a cushion of air under the airfoil. Thisdisruptstheliftforceasthegroundeffectindirectlyopposestheforcescausedbythe pressure stresses on the topoftheairfoil.Itthereforedoesnotprovideanaccuraterepresentation of how a clark-y wing on an aircraft would perform. This could be avoided by using a wind tunnelwithalargertestsectionasthetestsectionoftheusedwindtunnelwasquitesmall.
Although not exactly a limitation, circulation is not accounted for in Xfoil and therefore may contribute to the differences in results. Circulation occurs as airflow going around the trailing edge and is directed downwards, ultimately circulating around the airfoil. Circulationcancreate lift as it increases the speed of the air above the airfoil and subtracts from it underneath the airfoil, creating a higher pressure difference and more lift. Circulation also increases with angle of attack which may explain why it takes a higher angle of attack to generate the maximum lift ontheairfoil.
IssuewithHoneycombStructureofWindTunnel
The wind tunnel used has a honeycomb structure used for flow settling. In other words, the honeycomb structure is used to straighten the airflow that is sucked in from itssurroundings.In the wind tunnel used for this investigation, the honeycomb structure had slight issues as the design had some rough edges. This would cause the airflow to not be perfectly straight and laminarwhichwouldagainmakeresultsinaccurateduetotheeffectonlift.
SignificanceofthisInvestigation
The angle of attack is a very important parameter forairplanesandflight.Itcontributestomany different aspects of flight such as lift generation, stall control, aerodynamic efficiency, stability, andmore.
Additionally, the Clark-y airfoilisoneofthemostwidelyusedandinfluentialairfoilsinaviation history It is a simple and stable airfoil used in research, the aviation industry, and beyond. Airfoil designs like the Clark-y have applications in wind turbines due to its positive aerodynamic qualities. Such principles are also used in automotive design, marine engineering, architecture,etc.
Therefore, findingtheoptimumangleofattackforaClark-yairfoilwasaworthyinvestigationto conduct.
The findings of this investigation are fruitful in providing more insight into the Clark-y’s aerodynamic performance, helping with maximizing lift, stall prevention, aircraft stability, and more. Additionally, finding such parameters can aid in further research and development of existing and new airfoil designs to improve performance. It can lead to inquiring about the practicalityofsuchairfoildesignsonwingsandconsideringtheirdifferentuses.
For example, high-speed aircraftsandvehiclesbenefitfromalowangleofattackasitminimizes drag force and air resistance. This would influence the designs of such airfoils to have lower optimumanglesofattack.
Conclusion
This investigation used an AF100 subsonic wind tunnel to test a 3D printed model of a Clark-y airfoil. The angle of attack was varied and the lift force was measured in order to find the optimumangleofattackwhereliftforceismaximized.
The findings of this investigation express that the angle of attack to maximize lift on a Clark-y airfoilis21°.ThisrelativelyhighangleofattacksuggeststheconclusionthattheClark-yisused forlow-speedaircrafts.Thisisbecausethehighangleofattackwouldcausealargedragforce.
The coefficient of drag at the optimum angle was around 0.58 (drag coefficient was recorded alongsidetheliftcoefficient)whichisconsideredslightlyhigh,provingtheconclusionabove.
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