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MAE 150B - 04B - Incompressible Flow over Airfoils

# MAE 150B - 04B - Incompressible Flow over Airfoils - MAE...

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MAE 150B - Chap 4 part B Incompressible Flow Over Airfoils

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Airfoil Characteristics (4.3) Velocity difference leads to pressure difference and that results with a net lift The lift coefficient varies linearly within a range of α Separation (stall) leads to a drop of lift Stall is a viscous effect, its occurrence is a function of Re
Flying upside down Flying upside down is achieved by having negative α for a “negative” lift. It is harder because stall occurs more easily.

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Airfoil Characteristics (4.3) Moment at aerodynamic center is independent of α within a range of α at aerodynamic center
Examples 4.1 4.2 and 4.3 (pp. 305-307) 4.1: NACA 2412 c=0.64m, standard sea level, V =70m/s L=1254 N/m, find α and the drag per unit span 4.2: Calculate moment per unit span 4.3: L/D ratio for α =0, 4, 8,12

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Kutta Condition For fluid flow around a body with a sharp corner the Kutta condition refers fluid approaches the corner from both directions, meets at the corner, and then flows away from the body. The sharp TE will be either a stagnation point or having same velocity from both surfaces for a cusp TE. At TE, Kutta condition means γ (TE)=0
Kelvin’s Circulation Theorem and  the Starting Vortex (4.6) Kelvin’s circulation theorem: In an flow that is inviscid, barotropic [ ρ= ρ( p 29 ], conservative body forces the circulation around a closed curve moving with the fluid remains constant with time 0 = Γ Dt D

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Kelvin’s Circulation Theorem and  the Starting Vortex (4.6) Having a loop enclosed the airfoil that is stationary in a still fluid Γ =0 (why?) The starting motion of the airfoil will generate two circulations Γ 3 and Γ 4 . Γ 3 stays with the airfoil and Γ 4 is a trialing vortex Kevin’s circulation theorem implies Γ 3 + Γ 4 =0 (why?) The starting vortex has a circulation Γ 4 = - Γ 3
Theoretical solution for low-speed flow  over airfoil: Outlines Theory Basis Vortex sheet representation (4.4) Kutta condition (4.5) Kevin’s theorem *4.6) Vortex sheet representation of a thin airfoil (4.7a) Symmetric airfoil results (4.7b) Cambered airfoils (4.8) Aerodynamic center (4.9) Vortex panel method for arbitrary body(4.10)

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Vortex Sheet of Thin Airfoil (4.7a)
Vortex Sheet of Thin Airfoil (4.7a)

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MAE 150B - 04B - Incompressible Flow over Airfoils - MAE...

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