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1/8/2016
1
ME 326 G. Ahmadi ME 326 G. Ahmadi
ME 326 G. Ahmadi
Outline• Forces and Toques• Drag of Spheres• Drag of Cylinders• Drag Coefficient for 2D Objects• Drag Coefficient for 3D Objects• Lift Force for an Airfoil
ME 326 G. Ahmadi
1/8/2016
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ME 326 G. Ahmadi
(Re)CC DD (Re)CC DD
VLRe
VLRe
AV21
ForceDragC2
D
AV21
ForceDragC2
D
Fric,DessPr,DD CCC Fric,DessPr,DD CCC ME 326 G. Ahmadi
ME 326 G. Ahmadi ME 326 G. Ahmadi
1/8/2016
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ME 326 G. Ahmadi ME 326 G. Ahmadi
ME 326 G. Ahmadi ME 326 G. Ahmadi
L/D CD0 1.90.1 1.90.5 2.51.0 2.22.0 1.73.0 1.3
L/D CD0.5 1.21.0 0.92.0 0.74.0 0.7
L/D CD Laminar CD Turb2.0 0.6 0.24.0 0.35 0.158.0 0.25 0.1
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ME 326 G. Ahmadi
Karman Vortices
ME 326 G. Ahmadi
Karman Vortices
ME 326 G. Ahmadi ME 326 G. Ahmadi
circular cylinder : boundary layer
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ME 326 G. Ahmadi ME 326 G. Ahmadi
ME 326 G. Ahmadi ME 326 G. AhmadiTwo-Dimensional Bodies
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ME 326 G. AhmadiThree-Dimensional Bodies ME 326 G. Ahmadi
0
1
10
100
1000
CD
0 1 10 100 1000 10000 Re
Stokes Eq. (5)
Oseen
Newton
Experiment
Drag Coefficient for a Sphere
ME 326 G. Ahmadi ME 326 G. Ahmadi
1/8/2016
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ME 326 G. Ahmadi ME 326 G. Ahmadi
ME 326 G. Ahmadi
Shape Variation for Drag Reduction
Leaf Curls with Wind
Speed
ME 326 G. Ahmadi
Start-Up
Separation/ Vortex Formation
Vortex is Shed
Full Lift
Kutta Condition
1/8/2016
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ME 326 G. Ahmadi
Small Angle of Attack High Angle of Attack
Flow Visualization
ME 326 G. Ahmadi
ME 326 G. Ahmadi ME 326 G. Ahmadi