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**MAE 3241: AERODYNAMICS AND FLIGHT MECHANICS**

Flow Over Rotating Cylinders and Applications February 23, 2011 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**

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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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**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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STAGNATION POINTS

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**SUMMARY OF STREAM AND POTENTIAL FUNCTIONS TABLE 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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**FLETTNER ROTOR SHIP: EXAMPLE**

Flettner Rotor Ship Data: Approximately 100 ft long, displaced 800 tons and wetted area of 3,500 ft2 Two rotors each 50 ft tall and 9 ft diameter rotating at approximately 750 RPM Measured ‘lift’ coefficient was 10 and measured ‘drag’ coefficient was 4 Water drag resistance coefficient of boat CD = 0.005 Question 1: If the ship is moored (tied to a dock) and subject to a 25 ft/s cross-wind what forces parallel and normal to the ship’s center line are generated? Question 2: How fast will the ship ‘sail’ in open water if the keel aligns itself with the resulting force of the rotors? Note: Keep in mind that boat is now moving and there is a relative velocity that rotors see, which is combination of wind and motion of boat

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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: 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 pitcher’s hand and the catcher’s 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 = kg/m3 14.5 % less Yankee Stadium, Bronx r = 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

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