1. 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

2. 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

3. COMPARISON OF DRAG FORCES

4. 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

5. 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

6. LIFTING FLOW OVER A CYLINDER
Kutta-Joukowski Theorem

7. 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

8. STAGNATION POINTS

9. SUMMARY OF STREAM AND POTENTIAL FUNCTIONS TABLE 3.1

10. 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

11. APPLICATION TO AIRFOILS

12. FLETTNER ROTOR SHIP Length: 100 ft Displacement: 800 tons
Rotors: 50 ft high, 9ft diameter

13. 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

14. 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

15. 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.

16. APPLICATION: BASEBALL PITCH

17. EXAMPLES Pitch: Overhand curveball Pitch: Split-Finger Fastball
MLB Speed: MPH
1300 RPM (10 Revolutions)

18. 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.

19. WIND TUNNEL TEST OF SPINNING BASEBALL

20. CURVEBALL EFFECTIVENESS
Coors Field, Denver
= kg/m3
14.5 % less
Yankee Stadium, Bronx
r = kg/m3

21. 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