MAE 3241: AERODYNAMICS AND FLIGHT MECHANICS

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MAE 3241 AERODYNAMICS ANDFLIGHT MECHANICS

• Flow Over Rotating Cylinders and Applications
• February 21, 2007
• Mechanical and Aerospace Engineering Department
• Florida Institute of Technology
• D. R. Kirk

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INVISCID VS. VISCOUS FLOWS
Theoretical Beautifully behaved but
mythically thin boundary layer and wake region
Actual High separated Flow and large wake region
NO DRAG
HIGH DRAG
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COMPARISON OF DRAG FORCES
d
d
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GOLF BALL AERODYNAMICS
Large Wake of Separated Flow, High Pressure
Drag Laminar B.L. Separation Point
Reduced Size Wake of Separated Flow, Lower
Pressure Drag Turbulent B.L. Separation Point
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GOLF BALL AERODYNAMICS
Laminar B.L.
Turbulent B.L.
Laminar B.L.
Turbulent B.L.

• Pressure drag dominates sphere
• Dimples encourage formation of turbulent B.L.
• Turbulent B.L. less susceptible to separation
• Delayed separation ? Less drag

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LIFTING FLOW OVER A CYLINDER
Kutta-Joukowski Theorem
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STAGNATION POINTS
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SUMMARY OF ROTATING CYLINDER IN CROSS-FLOW

• Rotating Cylinder Generates Lift
• Velocity is faster over the top of the cylinder
  than bottom
• Pressure is higher on the bottom than over the
  top
• lifting force is directed perpendicular to the
  cylinder velocity (or the free stream velocity if
  the cylinder is stationary)
• Predicts Zero Drag
• Notice vertical plane symmetry
• Inviscid flow approximation does not model drag
  physics

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SUMMARY OF STREAM AND POTENTIAL FUNCTIONSTABLE
3.1
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IMPLICATIONS

• Lift theorem applies in general to cylindrical
  bodies of any cross-section
• Lift per unit span of airfoil is directly
  proportional to circulation around body
• Circulation also defined from pressure
  distribution
• Circulation is an alternate way of thinking about
  generation of lift on body
• Physical source of lift is pressure distribution

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APPLICATION TO AIRFOILS
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FLETTNER ROTOR SHIP
Length 100 ft Displacement 800 tons Rotors 50
ft high, 9ft diameter
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FLETTNER SHIP

• Flettner rotor ship in NYC harbor, May 9, 1926
• Since power to propel a ship varies as cube of
  its speed, 50 hp used for this auxiliary
  propulsion system represented a large increase in
  fuel efficiency

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OTHER EXAMPLES OF MAGNUS EFFECTS

• Spin-damping and Magnus dynamic effects are
  important when determining targeting accuracy of
  missiles, artillery rounds, and re-entry vehicles

• Energy waves strike proton on underside and
  because of its spin are forced around it, result
  is a difference of pressure between each side of
  proton.

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APPLICATION BASEBALL PITCH
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EXAMPLES

• Pitch Overhand curveball

• Pitch Split-Finger Fastball
• MLB Speed 85-90 MPH
• 1300 RPM (10 Revolutions)

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CURVE BALL BATTER PERCEPTION

• Perception plays a big role in the curve ball
  The typical curveball goes through only 3.4
  inches of deviation from a straight line drawn
  between the pitchers hand and the catchers
  glove. However, from the perspective of the
  pitcher and batter, the ball moves 14.4 inches.
  This proves that a curve ball really curves.

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WIND TUNNEL TEST OF SPINNING BASEBALL
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CURVEBALL EFFECTIVENESS

• Coors Field, Denver
• 1.047 kg/m3
• 14.5 less

Yankee Stadium, Bronx r 1.225 kg/m3
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EXAMPLE FOOTBALL

• Fluent 5 Simulation of Football in Flight
  (Sliding Mesh Geometry)
• Forward velocity 40 MPH
• Rotation rate 300 RPM
• High pressure region in front of ball, long
  trailing wake
• Laces cause B.L. to separate and rotates with
  call
• Even if ball is thrown straight, ultimately will
  begin to wobble