MAE 150B - 05A - Incompressible Flow over Finite Wings

MAE 150B - 05A - Incompressible Flow over Finite Wings -...

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MAE 150B - Chap 5 Part A  Incompressible Flow Over Finite Wings

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Effects of Finite Wings Airfoil: Higher P at lower surface The pressure at the wing tips need to be balance It causes a rollup motion at the tip First, the flow is not two- dimensional any more (see Fig 5.3) However, the local 2-D could still be a good approximation
Effects of Finite Wings

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AA 587 November 12, 2001 AA 587 (Airbus A300-605R) Taking off from JFK Flew into a JAL B-747 turbulent wake NTSB concluded that the enormous stress on the rudder was due solely to the first officer's over- aggressive rudder inputs, and not the wake caused by the earlier Japan Airlines 747 that had crossed that area.

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Effects of Finite Wings Vortex will induce velocity Question: what’s the effects to the wing air flows There is a downwash velocity component This component not only affects the flow behind the vehicle, it also added to the incoming flow The downwash causes a different (smaller) effective angle of attack (Fig 5.6) Note: you should have Fig 5.6 in mind all the time while considering finite wing aerodynamics
Downwash and Induced Drag (5.1) Inviscid flow implies no force in the flow direction (drag) The induced angle of attack a force normal to the local relative wind It leads to a net horizontal force (drag) and a smaller vertical force (actual lift) α eff = α - α i The downwash leads to an induced drag (even only inviscid flow is considered)

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Induced Drag Inviscid flow over a finite wing has induced drag D’Alembert paradox does not occur for a finite wing Induced drag is a type of “Pressure drag” The wing-tip vortices contains kinetic energy. From energy conservation, the energy needs to come from some where (engine) The induced drag leads to a power loss of the engine (just like the friction drag) i D d D C c C , + = S q D D c P f d + = c d is from the 2-D airfoil data

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Biot-Savart Law A segment of vortex filament with length of dl and a constant circulation value of Γ will induce a velocity of dV at a point P that has a radius vector r from the filament ) 5 . 5 ( 4 3 r r dl dV × Γ = π
For an infinitely long straight vortex  filament

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Semi-infinite vortex filament For a semi-infinite vortex filament of circulation Γ The induced velocity is V= Γ / (4 π h) (half of the infinite vortex line) Note: the definition of h The strength of a vortex is constant along a its length A vortex filament cannot end in a fluid. It must extend to the boundaries or form a loop
Lift on a finite wing The pressure at the tip must balanced no lift at y= -b/2 and b/2 Lift varies along the span of the wing Geometrical twist : change the shape to allow different angle of attack (like a propeller) Aerodynamic twist : different zero-lift angle of attack ( α L=0 )along the wing

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This note was uploaded on 10/09/2009 for the course MAE 150B taught by Professor D during the Spring '09 term at UCLA.

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MAE 150B - 05A - Incompressible Flow over Finite Wings -...

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