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3241 Lecture 9

# 3241 Lecture 9 - MAE 3241 AERODYNAMICS AND FLIGHT MECHANICS...

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1 MAE 3241: AERODYNAMICS AND FLIGHT MECHANICS Summary of Incompressible Flow Over Airfoils Summary of Thin Airfoil Theory Example Airfoil Calculation Mechanical and Aerospace Engineering Department Florida Institute of Technology D. R. Kirk

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2 KEY EQUATIONS FOR c l , α L=0 , c m,c/4 , and x cp Within these expression we need to evaluate A 0 , A 1 , A 2 , and dz/dx ( 29 ( 29 ( 29 ( 29 - + = - = - - = + = = 2 1 1 2 4 , 0 0 0 0 1 0 1 4 4 1 cos 1 2 A A c c x A A c d dx dz A A c l cp c m L l π π θ θ π α π π
3 A 0 , A 1 , and A 2 COEFFICIENTS = - = π π θ θ π θ π α 0 0 0 0 0 0 cos 2 1 d n dx dz A d dx dz A n = = - = π π π θ θ π θ θ π θ π α 0 0 0 2 0 0 0 1 0 0 0 2 cos 2 cos 2 1 d dx dz A d dx dz A d dx dz A

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4 CENTER OF PRESSURE AND AERODYNAMIC CENTER Center of Pressure: It is that point on an airfoil (or body) about which the aerodynamic moment is zero Thin Airfoil Theory: Symmetric Airfoil: Cambered Airfoil: Aerodynamic Center: It is that point on an airfoil (or body) about which the aerodynamically generated moment is independent of angle of attack Thin Airfoil Theory: Symmetric Airfoil: Cambered Airfoil: ( 29 - + = = 2 1 1 4 4 A A c c x c x l cp cp π 4 4 . . . . c x c x C A C A = =
5 ACTUAL LOCATION OF AERODYNAMIC CENTER NACA 23012 x A.C. < 0.25c NACA 64212 x A.C. > 0.25 c x/c=0.25 x/c=0.25

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6 EXAMPLE OF LEADING EDGE STALL NACA 4412 Airfoil (12% thickness) Linear increase in c l until stall At α just below 15º streamlines are highly curved (large lift) and still attached to upper surface of airfoil At α just above 15º massive flow-field separation occurs over top surface of airfoil → significant loss of lift Called Leading Edge Stall Characteristic of relatively thin airfoils with thickness between about 10 and 16 percent chord
7 EXAMPLE OF TRAILING EDGE STALL NACA 4421 (21% thickness) Progressive and gradual movement of separation from trailing edge toward leading edge as α is increased Called Trailing Edge Stall

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8 THIN AIRFOIL STALL Example: Flat Plate with 2% thickness (like a NACA 0002) Flow separates off leading edge even at low α ( α ~ 3º) Initially small regions of separated flow called separation bubble As a increased reattachment point moves further downstream until total separation
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3241 Lecture 9 - MAE 3241 AERODYNAMICS AND FLIGHT MECHANICS...

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