Pressure distribution over an airfoil

Shubham Maurya

Indian Institute of Space Science and Technology, Thiruvananthapuram, Kerala, 695547, India

The pressure distribution over a symmetric NACA 66(2)-015 airfoil placed in a subsonicsuction type wind tunnel is determined for various angle of attack while keeping the speedof the fan constant and vice versa. Using various non-dimensional constants results wereplotted for Coefficient of drag and Coefficient of lift at different angle of attack and Reynoldsno. in the test section. Coefficient of lift is observed to increase to a maximum value andthen decrease with angle of attack, whereas coefficient of drag is observed to increase withangle of attack. Both co-efficient of lift and drag decreased with increasing Re at fixedangle of attack. The airfoil is observed to stall at an Angle of attack of 9 for Reynolds no.around 100,000.

Nomenclature

cl Co-efficient of liftcd Co-efficient of dragL Lift per unit span, N/mD Drag per unit span, N/mN Normal force per unit span, N/mA Axial force per unit span, N/mc Chord length, cq∞ Dynamic pressure, PaS Frontal area, m2

v Freestream velocity, m/sRe Reynolds numberρ Density of air, kg/m3

ρe Density of ethanol, kg/m3

µ Dynamic viscosity, N s/m2

α Angle of attack, degreehi Height of ethanol in i’th manometer, mPi Static pressure at i’th manometer, PaSubscripti Variable number

I. Introduction

An airfoil is the shape of a wing, which when moved through a fluid produces an aerodynamic force.There are various ways to describe an airfoil. The NACA-terminology is a well-known standard, whichdefines the following airfoil properties (Fig.??).

• Leading Edge: The part of the airfoil which meets the airflow first.

• Upper Chamber: Also called Up wash. It is the deflection of the oncoming airstream upward and overthe wing.

• Lower Chamber: Also called downwash. Its the downward deflection of the airstream as it passes overthe wing and moves towards the trailing edge.

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Figure 1. Airfoil nomenclature

• Trailing Edge: The portion of the airflow where the airflow over the upper surface re-joins the lowersurface airflow.

• Mean Chamber: The curves of the upper and lower body of the airfoil.

• Chord c: It is an imaginary line drawn through the airfoil starting from the leading edge going up tillthe trailing edge.

• Angle of attack: This is the relative angle formed by the wing. This is the angle formed between anairfoil and the oncoming wind. The chord lines and relative wind is called the angle of attack. As aircirculates around the wings surface where the pressure is less than atmospheric, and regions where thepressure is greater than atmospheric. This specific pressure distribution varies the angle of attack. Asthe angle of attack grows larger, the lift reaches a maximum at some angle; increasing the angle ofattack beyond this critical angle of attack causes the air to become turbulent and separate from thewing; there is less deflection downward so the airfoil generates less lift. The airfoil is said to be stalled.

Sufficient airspeed must be maintained in flight to produce enough lift to support the airplane withoutrequiring too large an angle of attack. At a specific angle of attack, called the critical angle of attack, airgoing over a wing will separate from the wing causing the wing to lose its lift (stall). The airspeed at whichthe wing will not support the airplane without exceeding this critical angle of attack is called the stallingspeed. This speed will vary with changes in wing configuration (flap position). Excessive load factors causedby sudden manoeuvres, steep banks, and wind gusts can also cause the aircraft to exceed the critical angle ofattack and thus stall at any airspeed and any attitude. Speeds permitting smooth flow of air over the airfoiland control surfaces must be maintained to control the airplane. To recover from a stall attack the smoothairflow must be restored by decreasing the angle of attack to a point below the critical angle of attack so thatyou can allow the wings to regain lift. The lowest possible velocity at which the airplane can maintain steady,level flight is defined as the stalling velocity, Vstall and it is dictated by the value of maximum coefficient oflift clmax. In order to achieve a steady flight clmax should be increased ,which in-turn decreases the stallingvelocity. Mechanical devices called high lifting devices namely flaps, slats and slots on the wing are deployedby the pilot, serve to increase clmax.

The drag and lift forces depend on the density r of the fluid, the upstream velocity V, and the size, shape,and orientation of the body. Drag and lift coefficients are given by

cl =L

1

2ρv2(c)(1)

cd =D

1

2ρv2(c)(1)

The drag coefficient, in general, depends on the Reynolds number, especially for Reynolds numbers belowabout 104. At higher Reynolds numbers, the drag coefficients for most geometries remain essentially constant.(Fig.??)

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Figure 2. cd for geometry

This is due to the flow at high Reynolds numbers becoming fully turbulent. However, this is not the casefor rounded bodies such as circular cylinders and spheres. The drag coefficient exhibits different behaviourin the low (creeping), moderate (laminar), and high (turbulent) regions of the Reynolds number.The inertia effects are negligible in low Reynolds number flows (Re approx 1), called creeping flows, andthe fluid wraps around the body smoothly. At low Reynolds numbers, the shape of the body does not havea major influence on the drag coefficient but orientation of the body relative to the direction of flow has amajor influence on the drag coefficient.For Lift Coefficient,

Figure 3. cl vs. α

The lift coefficient increases almost linearly with the angle of attack a, reaches a maximum at about a =160, and then starts to decrease sharply. (Fig.??) This decrease of lift with further increase in the angle ofattack is called stall, and it is caused by flow separation and the formation of a wide wake region over thetop surface of the airfoil.The drag coefficient also increases with the angle of attack, often exponentially (Fig.??). So large angleof attack should be preferred sparingly. At zero angle of attack, the lift coefficient is zero for symmetricalairfoils but nonzero for non-symmetrical ones with greater curvature at the top surface. Therefore, planeswith symmetrical wing sections must fly with their wings at higher angles of attack in order to produce thesame lift.

II. Experimental details

• The experiment was done on a typical suction type wind tunnel.

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Figure 4. cd vs. Re

• The set up mainly consists of an axial flow fan, converging duct, test section.

• The bell mouth section is fitted with honeycomb mesh to reduce the turbulence and impurities withincoming air.

• The NACA 66(2)-015 airfoil was placed in test section.

• Multi-tube manometer with 45 ◦ inclination is used to measure the pressure at various cross section ofthe wind tunnel.

• The manometer fluid used is ethyl alcohol in order to measure even small changes in pressure.

III. Model

Derivation of cl and cd from pressure distribution

Figure 5. Normal and Axial force on the airfoi

Let

Pavg =p2 + p1

2(1)

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Axial force on the element (A) = Pavg × (y2 − y1) (2)

Normal force on the element (N) = Pavg × (x2 − x1) (3)

The Lift is be calculated using

L = Ncosα−Asinα (4)

The Drag is be calculated using

D = Nsinα+Acosα (5)

IV. Procedure

• All equipments were checked and then power was switched on.

• The NACA airfoil was placed in test section with initial angle of attack of −6 ◦ .

• The Reynold’s number was maintained at 660 RPM and angle of attack was varied from −6 ◦ to 9 ◦

with a interval of 3 ◦.After 9 ◦ the AOA was varied with interval of 1 ◦ till to get the installing point.After installing point 2 more readings were taken for different successive AOA.

• The values of the pressures at all pressure nodes of the test section were noted down.These readingswere used to measure the pressure distribution with AOA at constant RPM.

• Same procedure was repeated at constant RPM 960.

• To measure the pressure distribution at different RPM, the airfoil was placed at constant AOA of 5 ◦

and RPM was varied from 560-960.

• For various RPM, manometer readings were noted down.These readings were used to measure thepressure distribution with RPM at constant AOA.

V. Results

1. Variation of lift per span and drag per span for various angle of attack was plotted for Re=104050 andRe=154340 (Fig.?? and Fig.??)

2. cl and cd are plotted against angle of attack. (Fig.?? and Fig.??) cl for thin airfoil is also plotted andis found to have minimal variation with the measured cl for the region corresponding to −3 < α < 8.

3. Ratio of lift and drag is plotted against angle of attack.(Fig.??)L/D ratio directly gives the requiredangle of attack for maximum lift for a unit drag. L/D attains peak of 23 at α = 60. As Re increased,L/D also increased.

4. L/D is plotted for a particular angle of attack of 50 while Re is varied. (Fig.??) Maxima is obtainedat around Re=140000 which corresponds to L/D=26.

5. cl and cd are plotted against angle of attack. (Fig.??) Both cl and cd tend to decrease with increasein Re.

6. The XFLR5 is used to numerically solve viscous flow over the NACA 66(2)-015 airfoil. The numericalpredictions, however does not converge for some angle of attacks, even though it gives reasonable results

and varies the same way as experimental results. The plots for cl andclcd

vs. α for Re=100000 and

Re=150000 are obtained as shown in (Fig.?? and Fig.??).

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Figure 6. Lift per span vs. angle of attack

Figure 7. Drag per span vs. angle of attack

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Figure 8. Cl vs. angle of attack

Figure 9. Cd vs. angle of attack

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Figure 10.Cl

Cdvs. angle of attack

Figure 11.L

Dvs. Reynolds number for α = 50

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Figure 12. cl and cd vs. Reynolds number for α = 50

Figure 13. cl and vs. α for Re=100000 (blue) and Re=150000 (red)

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Figure 14.cl

cdand vs. α for Re=100000 (blue) and Re=150000 (red)

7. As found out by experiment, the maximumclcd

is equal to 23 which occurs at around 60. Also, by

XFLR5 predictions,clcd

has maximum of around 23.

8. However, cl plotted numerically predicts stall to occur at around 60 which is not validated by theexperiment.

VI. Discussion and Conclusions

A. Conclusions

1. Stalling was found to happen at an angle of attack of approximately 90. At this angle of attack, flowseparation begins to occur close to the leading edge. As a result, the separated regions on the top ofthe wing increase in size and hinder the wing’s ability to create lift. The large wake region thus createdstalls the lift of the airfoil. At the critical angle of attack, separated flow is so dominant that furtherincreases in angle of attack produce less lift and vastly more drag. Hence, cl drops after stalling isreached which is evident from our results.

2. The drag obtained in throughout the experiment is not total drag as it does not account the drag dueto viscosity.

B. Limitations

1. While taking readings, at higher RPM, the level of ethanol in manometer was fluctuating too much.

2. Manometer readings may also get effected due to disturbance of ethanol in the source bottle by acci-dental movement of table.

3. Boundary effects are dominant and hence the reliability of the experimental results is doubtful.

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Appendix

1. Sample calculation

Sample calculation is done for the airfoil with an angle of attack of 60 and the fan operated at 660 rpm.Pressure points 11 and 12 are considered for the calculation.

Height of ethanol in the manometer corresponding to the points 11 and 12 are 10.2 cm, 11 cm respectivelyand that of reference is 7.3 cm.

Static pressure at point 11 is,

P11 = Patm + ρ× g × (7.3 − 10.2) × cos450 × 0.01

= 99991.77 + 789 × 9.81 × (−0.029) × cos45◦

= 99833.08N/m2

Static pressure at point 12 is,

P12 = Patm + ρethanol × g × (7.3 − 11) × cos45◦ × 0.01

= 99991.77 + 789 × 9.81 × (−0.037) × cos450

= 99789.3N/m2

Pavg =p11 + p12

2= 99811.2N/m2

(x11,y11) ≡ (0.006 m, 0.0034 m)(x12,y12) ≡ (0.012 m, 0.0047 m)

dy = y12 − y11

dx = x12 − x11

Normal force(per unit span) acting on the area element, N = Pavgdx

= 598.86N/m

Axial force(per unit span) acting on the element, A = Pavgdy

= 129.04N/m

Lift per unit span, L =∑

(Ncosα−Asinα)

= 10.18N/m

Drag per unit span, D =∑

(Nsinα+Acosα)

= 0.439N/m

2. Error Analysis

For 660 rpm and 6◦ angle of attack,Lift:

L = Ncosα−Asinα =∑ (Pi + Pi+1)(dxicosα− 101dyisinα)

2000

∆Lα =(Pi + Pi+1)(−dxi sinα− 101dyicosα)dα

2000

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∆Lhref=

2(dxicosα− 101dyisinα)ρegsin450dhref2000

∆Lhref=

−(dxicosα− 101dyisinα)ρegsin450dhi2000

∆Lhref=

−(dxicosα− 101dyisinα)ρegsin450dhi+1

2000

∆L =∑√

(∆Lα)2 + (∆Lhref)2 + (∆Lhi))

2 + (∆Lhi+1))2 = ±1.4022N/m

Drag:

D = Nsinα+Acosα =∑ (Pi + Pi+1)(dxisinα+ 101dyicosα)

2000

∆Dα =(Pi + Pi+1)(dxi cosα− 101dyisinα)dα

2000

∆Dhref=

2(dxisinα+ 101dyicosα)ρegsin450dhref2000

∆Dhref=

−(dxisinα+ 101dyicosα)ρegsin450dhi2000

∆Dhref=

−(dxisinα101dyi + cosα)ρegsin450dhi+1

2000

∆D =∑√

(∆Dα)2 + (∆Dhref)2 + (∆Dhi))

2 + (∆Dhi+1))2 = ±0.1653N/m

Acknowledgments

We would like to acknowledge all the persons involved directly or indirectly in completion of this experi-ment. We would like to thank our lab supervisor Dr.B.R.Vinoth for their guidance and clearing our doubts.We would also like to thank our instructors Roshan Kumar and Prasanthi for providing us the needful forconducting the experiment.

References

1Yunus A. Cengel and John M. Cimbala, Fluid Mechanics 2e., McGraw Hill Education, New York, 2010.2Ascher Shapiro, National Committee for Fluid Mechanics Films, MIT, 19613Houghton, et al Aerodynamics for Engineering students 6e., Butterworth Heinemann, Oxford, 2013.

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