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NumericalAnalysisoftheWingTipVor8cesofaCommercialAircra:
XVConvergenceANSYSMexico2016
RicardoHernandezRiveraPh.D.StudentattheUniversityofGuanajuato
Mo8va8on
[1]DiscoveryChannel,Giantoftheskies-BuildingtheAirbusA380,2006.
(a)SmokeflowvisualizaQon[2].
WingTipVortexForma8on
[2]J.Boehrer,CFDStudyofWingTipVortexGeneraQon,2005.[3]J.BerQn,AerodynamicsforEngineers,1998.
(b)WingQpvortexemergingatthewingQp[3].
Li:-InducedDrag
[3]J.BerQn,AerodynamicsforEngineers,1998.
Induceddrag
Li^ EffecQveli^
Chordline
Undisturbedfree-stream
Resultantvelocity
Descrip8on
Inthisproject, thetangenQalvelociQesand li^-induceddragsofthewingQpvorQcesofacommercialaircra^wereanalyzednumerically.
TwodifferentkindsofwingletswereadaptedtotheoriginalwinginordertoanalyzetheireffectsonthewingQpvorQces.
TovisualizethewingQpvortexformaQon.
ToanalyzethetangenQalvelociQesoftheQpvorQces.
Toevaluatetheli^anddragforces.
Objec8ves
Figura7.Generacióndelarrastreinducidoporlasustentación.
1/144aircra^plasQcmodeloftheBoeing767-300/ER.
3DModeling
WingDesign
Wingplanform.
Frontviewofthewingshowingtheangleofdihedral.
Figura7.Generacióndelarrastreinducidoporlasustentación.
WingDesign
Geometricfeaturesofthewing.
Descrip8on Variable Value
Rootchord Cr 10.9m
Rootincidenceangle αr 4°15´
Tipchord Ct 2.16m
Tipincidenceangle αt 0°
Sweepangle Λ 31°30´
Dihedralangle Φ 6°
Wingarea S 283.3m2
AspectraQo AR 8
TaperraQo λ 0.1981
Wingspan b 47.4m
SupercriQcalairfoilDFVLRR-4ofthewingroot.
SupercriQcalairfoilRAE(NPL)5212ofthewingQp.
Supercritical airfoil NPL 9510 of the horizontal stabilizer root.
Supercritical airfoil NPL de ARC CP 1372 of the horizontal stabilizer tip.
Symmetric supercritical airfoil NACA/LANGLEY N0011SC of the vertical stabilizer.
HorizontalStabilizer
Ver8calStabilizer
Figura7.Generacióndelarrastreinducidoporlasustentación.
Geometricfeaturesofthewing.
EngineCF6-80C2GeneralElectric
Front view. Side View.
Upper view. Rear view.
3DModeloftheAircra:underAnalysis
(a)
(c) (d)
(b)
ModifiedcommercialBoeing767-300/ERaircra^:(a)lowerview;(b)isometricview;(c)lateralview;(d)frontview.
B747-400Winglet
Descrip8on Variable Value
Rootchord Cr 2.15m
Tipchord Ct 0.88m
Sweepangle Λ 56.32°
AnglewiththeverQcal β 33.04°
Wingletarea S 2.8m2
TaperraQo λ 0.4074
Wingletspan b 2.12m
GeometricdataoftheB747winglet.
[4]hlps://commons.wikimedia.org
AirbusA380Winglet(TipFence)
Upperpartofthewinglet Variable Value
Rootchord Cr 1.19m
Tipchord Ct 0.29m
Sweepangle Λ 64.34°
AnglewiththeverQcal β 9.13°
TaperraQo λ 0.25
Wingletspan b 0.86m
GeometricdataoftheA380winglet.
Lowerpartofthewinglet Variable Value
Rootchord Cr 1.19m
Tipchord Ct 0.29m
Sweepangle Λ 57.89°
AnglewiththeverQcal β 23.52°
TaperraQo λ 0.25
Wingletspan b 0.61m
[5]hlps://en.wikipedia.org/wiki/Airbus_A380
FluidDomain
(a) (b)
MeshGenera8on
(a) (b)
(c) (d)
StructuredHexaMeshing
(a) (b)
(c)
StructuredHexaMeshing
(d) (e)
StructuredHexaMeshing(ScanPlane)
(f)
(g)
StructuredHexaMeshing(ScanPlane)
(h)
(i)
StructuredHexaMeshing-B747Winglet
(j) (k)
(l)
StructuredHexaMeshing-A380Winglet
(m) (n)
(o)
Considera8onsoftheAnalysis
Steadystate. Cruiseflight. Compressibleflow. Theaircra^wasconsideredarigidbody. Turbulencemodel:shearstresstransport. Energytransfermodel:totalenergy.
Descrip8on Analysis Elements
B767 Originalaircra^ 1,790,631
A380Winglet Aircra^withadaptaQonoftheA380winglet 2,195,241
B747Winglet Aircra^withadaptaQonoftheB747-400winglet 2,028,975
Numberofhexahedralelementsforeachcasestudied.
Property Value
Aircra^velocity 851km/h AlQtude 10.66km(35,000^)
Machnumber 0.8
Density 0.3809kg/m3
Dynamicviscosity 1.434x10-5kg/ms
Temperature 218.92K(-54.12°C)
Atmosfericpressure 0.23648atm(23.3kPa)
Speedofsound 1,068.84km/h
AirProper8es
Equation of state: ideal gas
Ideal gas equation of state gives good accuracy if:
air pressure (23.3 kPa) < air critic pressure (pc=3770 kPa) air temperature (218.92 K) > air critic temperature (Tc=133 K)
BoundaryCondi8ons
Inlet: velocity = 851 km/h. Static temperature: 219 K.
Outlet: static pressure = 0 Pa.
Adiabatic walls with free slip. Adiabatic walls with no slip.
Inlet: velocity = 1,322 km/h. Static temperature: 214 K.
Outlet: static pressure = 0 Pa.
Inlet: velocity = 1,730 km/h. Static temperature: 505 K.
BoundaryCondi8onsoftheEngine
Incompressibleflow:convergencecriteria:1x10-5. Compressibleflow:convergencecriteria:2x10-5.
HistoryofConvergence
AccumulatedTimeStep
Varia
bleVa
lue
(a) (b)
(c) (d)
Sta8cPressure(Pa)–B747Winglet
(a) (b)
(c) (d).
Sta8cPressure(Pa)–A380Winglet
VelocityVectors(m/s)
2DStreamlines(m/s)
(a) 1.5 m downstream from wing tip. (b) 11.5 m downstream from wing tip.
(c) 21.5 m downstream from wing tip. (d) 31.5 m downstream from wing tip.
VelocityComponent“w”inZAxis(m/s)
(a) 1.5 m downstream from wing tip. (b) 11.5 m downstream from wing tip.
(c) 21.5 m downstream from wing tip. (d) 80 m downstream from wing tip.
StreamlinesoftheWingTipVor8ces(m/s)
(a)
(b)
StreamlinesoftheWing(m/s)
(a) Original Aircraft. (b) B747 Winglet.
(c) A380 Winglet.
MaximumTangen8alVeloci8esdownstreamoftheWingTipVor8ces(m/s)
Distance (m)
Velo
city
(m/s
) OriginalAircra^B747WingletA380Winglet
The maximum tangential velocity of an Airbus A340 for cruise speed is about 60 m/s at the wing tip [6].
[6]Adib,InteracQonbetweentheWingTrailingVortexandtheEnginePlume,2006.
Li:andDragForces
The drag of both wings is about 50% of the total drag of the aircraft. The lift-induced drag is about 40% of the total drag of the aircraft for cruise speed [3].
The maximum weight of the original aircraft is 175.54 ton [7].
The lift of both wings of the original aircraft is 1,651.9kN (168.38 ton), about 96% of the maximum weight.
Descrip8on Aircra: Wing
Drag(kN) Drag(kN) Li:(kN) Es8matedϵ
Originalaircra^ 190.00 100.70 1,651.90 2.63° Aircra^withtheA380winglet 185.20 90.80 1,677.60 2.53° Aircra^withtheB747winglet 183.40 87.80 1,691.50 2.48°
[3]J.BerQn,AerodynamicsforEngineers,1998.[7]hlp://www.airliners.net/aircra^-data/
Winglets reduce the pressure gradients in the wing tip. As a consequence, the strength of the vortex is slightly decreased.
The B747-400 winglet: • decrease the angle of downwash up to 5.7% • increased the lift up to 2.39% • decreased the total aircraft drag up to 3.47% • decreased the vortex core velocity up to 15.38%
The A380 winglet: • decrease the angle of downwash up to 3.8% • increased the lift up to 1.55% • decreased the total aircraft drag up to 2.52% • decreased the vortex core velocity up to 5.76%
Conclusions
Thanks
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