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
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    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
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    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
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    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
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    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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