outline • forces and toques • drag of spheres • drag of cylinders … ·  ·...

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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

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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

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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

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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

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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

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ME 326 G. Ahmadi ME 326 G. Ahmadi

Concluding Remarks

• 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