lec28 - Aerodynamics Lecture 28 Finite Wing Vortex Filament...

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Aerodynamics Finite Wing Vortex Filament Helmholtz Vortex Theorems Induced Drag 28.1 Lecture 28 Aerodynamics Wing AE311 Aerodynamics Manoj T. Nair IIST

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Aerodynamics Finite Wing Vortex Filament Helmholtz Vortex Theorems Induced Drag 28.2 Agenda 1 Finite Wing 2 Vortex Filament 3 Helmholtz Vortex Theorems 4 Induced Drag
Aerodynamics Finite Wing Vortex Filament Helmholtz Vortex Theorems Induced Drag 28.3 Finite Wing I Induced Angle of Attack and Drag Pressures on the upper surface are in general less than those on the lower surface This pressure imbalance creates lift Due to this pressure imbalance, the flow near the wing tips tends to curl around the tips Air flows from high pressure lower surface to low pressure upper surface This leaking of flow around the wing tips introduces a circulatory motion that trails down the downstream of the wing This is called trailing vortices

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Aerodynamics Finite Wing Vortex Filament Helmholtz Vortex Theorems Induced Drag 28.4 Finite Wing II The vortices tend to drag the surrounding air with them This introduces a small velocity component in the downward direction at the wing This downward component is called downwash w
Aerodynamics Finite Wing Vortex Filament Helmholtz Vortex Theorems Induced Drag 28.5 Finite Wing III Downwash combines with freestream velocity V to produce a local relative wind Local relative wind is canted downward in the vicinity of each aerofoil section of the wing Angle between the chord line and direction of V is α α is the geometric angle of attack α i is the induced angle of attack

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Aerodynamics Finite Wing Vortex Filament Helmholtz Vortex Theorems Induced Drag 28.6 Finite Wing IV The presence of downwash has the following effects inclining of the local wind in downward direction even though the wing is at an Aoa α , the local airfoil sees a smaller angle α eff α eff = α - α i
Aerodynamics Finite Wing Vortex Filament Helmholtz Vortex Theorems Induced Drag 28.7 Finite Wing V Local lift vector is aligned perpendicular to the local relative wind It is inclined behind the vertical by α i Therefore, there is a component of local lift vector in the direction of V i.e., there is a drag created by downwash This drag is called induced drag D i Will there be induced drag in supersonic flow?

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Aerodynamics Finite Wing Vortex Filament Helmholtz Vortex Theorems Induced Drag 28.8 Finite Wing VI Hence downwash reduces Aoa introduced induced drag
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