Download Vortex Shedding

기계공학실험
Ch. 12 Measurements for Flow Passing over a Cylinder
Introduction


Purpose: Understanding and observation on flows behind a circular cylinder
 Boundary layer
 Flow separation
 Vortex shedding
 Vortex shedding frequency
Experimental setup
 Pitot‐tube & micro‐manometer (기압계)
 Hot‐wire probe & hot‐wire anemometer (풍속계)
 A/D convertor
 Circular cylinder
 Wind tunnel
References
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Frank M. White, “Viscous Fluid Flow,” 2nd Ed., McGraw‐Hill, New York, 1991.
Robert W. Fox and Alan T. Mcdonald, “Introduction to Fluid Mechanics,” 4th
Ed., John Wiley & Sons, 1994.
기계공학실험
Physical Phenomena
Boundary layer Flow separation
Flows behind a circular cylinder
Wake flow
Mountain Halla: cylindrical obstacle in flow
Jeju island
Flow past a cylinder at Re (ρVD/μ) = 2,000
Numerical simulation
Alternating low‐pressure vortices on the downstream side of the object  The object will tend to move toward the low‐pressure zone. Eventually, if the frequency of vortex shedding matches the resonance frequency of the structure, the structure will begin to resonate  Can damage or destroy the chimney
기계공학실험
Flow Separation

Bernoulli’s theorem Flows over the surface of a cylinder
Increase of flow velocity  Decrease of pressure
Decrease of flow velocity  Increase of pressure
2
2
V1
p
V
p
 1  gh1  2  2  gh2
2 g
2 g
Symmetric
stream lines
Pressure force momentum
shear force
(zero viscosity)
• Since the pressure decreases continuously between points A and B, a fluid element inside the boundary layer experiences a net force in the direction of flow. • In the region between A and B, this net force is sufficient to overcome the resisting shear force (μ(∂V/∂n)), and the motion of the element in the flow direction is maintained.
• After point B, since the pressure increases in the direction of flow, the fluid element experiences a net pressure force opposite to its direction of motion.
• At some point (point C), the momentum of the fluid in the boundary layer is insufficient to carry the element further into the region of increasing pressure.
• The fluid layers adjacent to the solid surface are brought to rest and the flow separates from the surface at the point C.
• Boundary layer separation results in the formation of a relatively low‐pressure region behind a body; this region, which is deficient in momentum, is called the wake.
기계공학실험
Pressure and Drag Coefficients
Pressure along the cylinder surface
Drag vs Re (Velocity)
D  CD A
U
2
2
Low form drag
High form drag
(inviscid flow)
Laminar flow  High form drag  Early separation
Turbulent flowLow form drag
Late separation
 Turbulent flow  Small wake area of low pressure  Drag decrease
 Rough surface/Turbulent freestream  Small wake area of low pressure  Drag decrease
기계공학실험
Influence of the “Dimple” on the Golf Ball
Influence on drag
Influence on lift
Without dimple effect
With dimple effect
기계공학실험
Experimental Process
Pressure hole #20
Cylinder
Pressure holes
Pressure hole #1
Flow
Flow
Pressure tubes
Selection box
+ ‐
+ ‐
Micromanometer
AD converter / PC
Sectional view of the cylinder
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

Pressure distribution
Flow separation point
Drag coefficient
기계공학실험
Vortex Shedding
Vortex shedding
Repeating pattern of swirling vortices caused by the unsteady separation of flow of a fluid over bluff bodies
The wake consists of pairs of vortices shed alternately from the upper and lower part after separation point (Karman vortex streets).
Timeline and streamlines at Re=170

The effect of the Re on the flow past a cylinder

Strouhal number
St s 
fs D
U
f s : shedding frequency
U : free stream velocity
D : cylinder diameter
As Re increases, the wake becomes more complex and turbulent, but the alternating shedding can still be detected at Re=107.
기계공학실험
Vortex Shedding of Chimney
 Laminar flow: Large area of wake flow  High force on
chimney  Vortex shedding: resonance 
Danger ↑
 Turbulent flow: Small area of wake flow  Low force on
chimney  Vortex shedding: resonance 
Danger ↓
기계공학실험
Vortex Shedding Frequency

Strouhal number
Experiments region
St s  0.2
f s  0.2
U
D
The shedding cycle takes place during the time that the free stream moves approximately five cylinder diameters.
Experimental process
Hot‐wire
U
Velocity change 
Frequency of vortex shedding
기계공학실험
Review Questions
1.
2.
3.
4.
5.
6.
7.
The pressure at A is ( ) than at B.
The pressure at B is ( ) than at C.
The wake has a very ( ) pressure, and consequently ( ).
Dimples on golf ball cause a ( ) size of wake, and consequently low ( ).
The wake consists of ( ), which shows a phenomenon known as ( ).
Vortex shedding frequency can be expressed in the term of the dimensionless ( ) number.
What is the title of this music and who is its composer?
기계공학실험