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Aerodynamics of Winglet: a Computational Fluid Dynamics Study

Md Saifuddin Ahmed Atique1, Md. Abdus Salam2, Asif Shahriar Nafi3, Nafisa Nawal Probha4, Shuvrodeb Barman*5

The concept of mounting wingtip devices to reduce induced drag; as applied to a model commercial Boeing 737-800 wing is investigated through a planned computational study. The design and simulation was done using commercial software. The effect of mounting winglet was seen to have greatly affecting the induced drag and vortices formation at the wing tip. The result came out with a positive effect of reducing induced drag ranging from 3.47% at 0.50 Mach up to 40.13% at 0.35 Mach. A flow visualization study substantiates, rather spectacularly, the effectiveness of the concept.

Field of research: Aeronautical Engineering

Keywords: Winglet, CFD, Induced Drag

1. IntroductionWinglets are considered as a powerful means of improving fuel efficiency for modern aircraft. It defines the small fins or vertical extensions at the end of the wing known as wing tips. Winglet improves the aircraft efficiency by reducing induced drag which is being caused by the vortices generated at the tip of the wing. This type of device (winglet) usually increases the effective aspect ratio of the wing without increasingthe structure loads drastically. From several experiment it is seen that around 25% part of the conventional aircraft wing (without winglet) actually produce no lift but increase drag due to the wing tip vortices.

1 Md Saifuddin Ahmed Atique, Undergraduate Student, Department of Aeronautical Engineering, Military Institute of Science & Technology (MIST), Bangladesh, Email: saifaerospace@gmail.com

2 Md. Abdus Salam, Professor & Head, Department of Aeronautical Engineering, Military Institute of Science & Technology (MIST), Bangladesh, Email: head@ae.mist.ac.bd

3 Asif Shahriar Nafi, Undergraduate Student, Department of Aeronautical Engineering, Military Institute of Science & Technology (MIST), Bangladesh, Email: asifnafi@ymail.com

4 Nafisa Nawal Probha, Undergraduate Student, Department of Aeronautical Engineering, Military Institute of Science & Technology (MIST), Bangladesh, Email: probha112266@gmail.com

*5 Shuvrodeb Barman, Undergraduate Student, Department of Aeronautical Engineering, Military Institute of Science & Technology (MIST), Bangladesh, Email: shuvrodebbarman@gmail.com

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Both experimental and computational approach shows that an aircraft that use the winglet is much safer from the attack of induced drag than the aircraft which does not use winglet. For computational fluid dynamics (CFD) simulation purpose here a comparison will be made between the wing models of Boeing 737-800 aircraft which does not have any winglet with Boeing 737-800 real wing model which is blessed with conventional designed winglet. Solid Works flow simulation was done in this experiment with a view to finding out the positive effect of mounting winglet in conventional aircraft wing.

2. Literature Review

The concept of wingtip device was first introduced by English engineer Frederick W. Lanchester. He patented the endplate concept in 1897 and his research results demonstrated that significant amount of induced drag could be diminished by placing vertical surface at the wingtip under high-lift condition. Although it was a promising approach to induced drag reduction technique, the benefits of this concept was suppressed because of large generation of profile drag at cruise condition.

Unfortunately, there wasn’t any major contribution in the field of winglet concept until World War II. Dr. Sighard F. Hoerner, a German aeronautical engineer developed “Hoerner Tips” which was used in Heinkel He 162 jet aircraft. In 1952, he published a technical paper regarding drooped wingtips also called as “Hoerner Tips”.

In the early 1970, Richard T. Whitcomb, an American aeronautical engineer started working on wingtip vortex elimination. He along with a team of researchers including Stuart G. Flechner and Peter F. Jacobs initiated a research program on wingtip vortices at NASA’s Langley Research Center. Their studies and experiments on winglets validated the acceptability of winglet concept in the case of induced drag reduction.

Basing on Whitcomb’s studies, NASA successfully flight-tested KC-135 aircraft at Dryden Flight Research Center in 1979-80. The outcome of the research was positive and it turned out that 7 percent increase of an aircraft's range is possible at cruise speed.

Now-a-days winglets are used in most commercial and military transport jets including the Gulfstream III, IV and V business jets, Boeing 747-400 and McDonnell Douglas MD-11 airliners, the McDonnell Douglas C-17 military transport and Embraer aircraft.

However, one of the major technical challenges still exists regarding incorporating winglet to the existing wing designs because of precipitating large profile drag which is of great research interest. Beneficial factor in winglet performance is largely dependent on wing design as well as the design of winglet itself. Basing on this fact

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there has been many modifications of winglet and these are conveniently being used by commercial aircraft manufacturers.

3. The Methodology and Model

Dimensions and specifications of winglet mounted modelwing:

Span (cm) 34.027524Surface Area (cm2) 246.806684 Aspect Ratio 4.691414231Taper Ratio 0.159Root Chord(cm) 7.880016Tip Chord(cm) 1.250009M.A.C.(cm) 3.960027

Dimensions and specifications of model wing without winglet:

Span (cm) 30Surface Area (cm2) 230.842376Aspect Ratio 3.898764237Taper Ratio 0.159Root Chord(cm) 7.880016

Tip Chord(cm) 1.250009M.A.C.(cm) 3.960027

Unit System followed:

All dimensions, parameters and calculations here are done in CGS (Centimeter, Gram, Second) System of units.

Choice of Airfoil:

We have chosen the Boeing 737-800 airfoil. Three different types of airfoil has been used which are relevant to real Boeing 737-800 wing. The root airfoil, midsection airfoil and the tip airfoil were different and were customized for different chord lengths. The airfoil used for winglet was the same as the tip airfoil.

Figure-1: Root airfoil (b737a) of 7.880016 cm chord length

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Figure-2: Midsection airfoil (b737c) of 3.960027 cm chord length

Figure-3: Tip airfoil (b737d) of 1.250009 cm chord length

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Figure-4: Winglet airfoil (b737d) of 1cm chord length

Designing 3D Wing:

For designing 3D wing model lofting tool was used. Due to the choice of customized airfoils it has become possible to createa complex wing surface. Carbon fiber composites were used as wing model material. Composite materials provide high “strength to weight” or “stiffness to weight” ratio. So, weight savings are significant ranging from 25-45% of the weight of the traditional metallic machine design. It also has improved friction and wear properties. These have given us better chance for accurate analysis.

Figure-5: Half Wing model without winglet with dimensions (in cm) (Top View)

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Figure-6: Half Wing model without winglet with dimensions (in cm) (Front View)

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Figure-7: Full Wing model without winglet (Isometric View)

Figure-8: Full winglet mounted Wing model (Isometric View)

Material used: Carbon fiber-Hexcel AS4C (3000 filaments)

Simulation:

To complete this simulation, adaptive mesh refinement technique was used. Adaptive mesh refinement, or AMR, is actually a method of adapting the accuracy of a solution within certain sensitive or turbulent regions of simulation, dynamically and during the time the solution is being calculated. When solutions are calculated numerically, they are often limited to pre-determined quantified grids as in the Cartesian plane which constitute the computational grid, or 'mesh'. Adaptive mesh refinement provides such a dynamic programming environment for adapting the precision of the numerical computation based on the requirements of a computation problem in specific areas of multi-dimensional graphs which need precision while leaving the other regions of the multi-dimensional graphs at lower levels of precision and resolution.

The conditions set before the simulation was done:

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Thermodynamic parameters:

Pressure: 1013250 dyne / cm2

Temperature: 20.05˚C

Result resolution was set to high as we need more accurate result. Finer mesh was used near the wing body for increased accuracy.

Mesh refinement level was set to 2[1].

Air density at 20.05˚C and 1013250 dyne / cm2:

T = (20.05 + 273.15) K

= 293.2 KSubstituting the values in ideal gas law:

ρ=Moleculer weight ×PR×T

¿ 29×10132508.3145×107×293.2

gmgmmole

× dynecm2

ergsKmole

× K

= 1.205353704 × 10 – 3gm / cm3

4. Calculations and Findings

Figure-9: Airflow Trajectories at 4˚ AOA, 0.60 Mach simulation for wing model without winglet

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Here in at figure – 9and 10it is noticed that if there is no existence of winglet at the end then Vorticity is near about 19157.10 (1 / s) which is quite high and responsible for curl flow behind wingtip region generating massive induced drag.

Figure-10: Vorticity strength that 4˚ AOA, 0.60 Mach simulation for wing model without winglet

Figure-11: Airflow Trajectories at 4˚ AOA, 0.60 Mach simulation for winglet mounted wing model

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But from Figure -11 and 12it is seen that due to mounting winglet the Vorticity strength at wingtip has been drastically reduced to 9873.282 ( 1 / s ). So the airflow trajectory is far smoother and far straight than compared to the previous one.

Figure-12: Vorticity strength that 4˚ AOA, 0.60 Mach simulation for winglet mounted wing model

For analytical simplicity half wing model has been considered for both winglet mounted and without winglet analysis.

Result for lift after simulating for 0.60 Mach at 4˚ AOA condition on wing model without winglet:

Table -1

Lift (dyn) Averaged value(dyn)

Minimum Value(dyn)

Maximum Value(dyn)

Delta(dyn)

Criteria(dyn)

2465436.663 2468840.534 2460377.563 2481128.538 20750.97423 335791.818

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Iterations: 310

Analysis Interval: 144

Result for lift after simulating for 0.60 Mach, 4˚ AOA condition on winglet mounted wing model:

Table -2

Lift (dyn) Averaged value(dyn)

Minimum Value(dyn)

Maximum Value(dyn)

Delta(dyn)

Criteria(dyn)

2411001.879 2416257.467 2396209.034 2444038.393 47829.35827 253965.4638

Iterations: 333

Analysis Interval: 144

Calculation of Induced Drag:

Total Drag = (cD0 + kcL2) 12ρV2S

= 12ρV2ScD0 +

12ρV2S kcL

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L = W = 12ρV2ScL

2W = ρV2ScL

cL = 2WρV 2S

Putting the value of cLin Total drag equation:

Total Drag = 12ρV2ScD0+

12ρV2S k 4W

2

ρ2V 4S2

=12ρV2ScD0 + 2k L

2

ρV 2S

From the above equation Lift dependent drag/ Induced Drag, Di = 2k L2

ρV 2S

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Surface area of half span of wing model without winglet = 120.365619 cm2

Surface area half span of winglet mounted wing model = 129.772226cm2

As our flow simulation condition met the subsonic criterion we assumed k = constant = 1

Velocity of sound through air = 33200 cm / s

Using the induced drag formula calculated D i for model wing without winglet is:

Table –3

For 4˚ AOA situation

Mach number Velocity (cm / s) Lift (dyn) Induced drag (dyn)

0.35 11620 1018544.181 105915.7445

0.40 13280 1111906.611 96639.24092

0.45 14940 1361723.925 114522.2775

0.50 16600 1632596.73 133338.2355

0.55 18260 2017834.538 168338.1661

0.60 19920 2465436.663 211165.0634

0.65 21580 3025685.594 270992.7983

Using the induced drag formula calculated Di for winglet mounted model wing is:

Table –4

For 4˚ AOA situation

Mach number Velocity (cm / s) Lift (dyn) Induced drag (dyn)

0.35 11620 818290.2303 63406.85473

0.40 13280 1039340.719 78316.68655

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0.45 14940 1359935.881 105942.3018

0.50 16600 1665524.158 128712.1164

0.55 18260 2009226.325 154806.7551

0.60 19920 2411001.879 187305.3422

0.65 21580 2830351.88 219943.7969

Figure – 13 Effect of mounting winglet on Induced Drag

Figure 13 shows a comparative study on the effect of mounting winglet by using induced drag values for both the defined cases. It is clearly evident from the graph that Induced drag is significantly reduced after mounting winglet.

Drag reduction due to mounting winglet is found by the formula

Drag reduction=InducedDrag without winglet−Induced Dragwithwinglet

Percentage of Drag reduction due to mounting winglet is found by the formula

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Induced Dragwithout winglet−InducedDragwithwingletInduced Dragwithout winglet

×100%

Reynolds number is given by ℜ= ρVDμ

For 0.60 Mach Re = 402.64× 106 where standard values are assumed.

Table –5

For 4˚ AOA situation

Mach number Velocity(cm / s) Induced drag Reduction(dyn)

Reduction Percentage

0.35 11620 42508.88977 40.13 %

0.40 13280 18322.55437 18.96 %

0.45 14940 8579.9757 7.49 %

0.50 16600 4626.1191 3.47 %

0.55 18260 13531.411 8.04 %

0.60 19920 23859.7212 11.30 %

0.65 21580 51049.0014 18.84 %

Figure 14 – Induced Drag Reduction Percentage vs. Flight Mach number

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After setting up a winglet at the tip of Boeing 737-800 model wing; for Mach number 0.35 the reduction of induced drag was 40.13% and after that it decreases continuously up to 0.50 Mach number and this it was about 3.47%. After that again the reduction in induced drag was increased and at Mach number 0.60 and 0.65 it was about 11.30% and 18.84% respectively. So at a steady and level flight condition at 0.65 Mach the reduction in induced drag which we obtained that was beyond doubt the debt of mounting winglet at the tip of conventional Boeing 737-800 model wing. Figure – 14shows the graphical representation of this phenomena.

5. Conclusion. Computational Fluid Dynamics (CFD) simulation shows that mounting a simple winglet at the tip of the aircraft wing can reduce the induced drag significantly that is always desired. Though this theoretical concept was established by the flow simulation over a same model aircraft wing when one of them was equipped with a winglet at the wing tip & another one is not. Result obtained from flow simulation describes here that, if angle of attack, thermodynamics and other parameters are being kept constant then a conventional Boeing 737-800 model aircraft wing having winglet will significantly generate less induced drag than compared to a conventional Boeing 737-800 model aircraft wing having no winglet. This can be considered as a great achievement with aerodynamics point of view. Simulation was done at 4 degree angle of attack (AoA) and it shows that induced drag reduction is maximum at 0.35 mach and minimum at 0.45 mach. From 0.5 to 0.6 mach reduction in induced drag was not too much significant but a potential result is obtained when it fly at 0.65 mach and the reduction in induced drag that was gained at this mach number was sounds promising. So, from here a well conclusion can be brought that an aircraft/aircraft wing having winglet, mounted at the tip of the wing will definitely generate less induced drag than compared to the aircraft/aircraft wing having no winglet provided all other the parameters (angle of attack, thermodynamics) are kept same

End Notes

[1] Mesh refinement level defines how fine mesh is generated for fluid flow analysis. The higher the level of refinement the more accurate is the analysis.

[2] All the symbols in the equations used in this paper bear conventional meaning.

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