Basic Bluff-Body - Wind Engineering - Lecture Slides, Slides of Environmental Law and Policy

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Basic bluff-body aerodynamics II

• Pressures on prisms in turbulent boundary layer :
  • drag coefficient (based on Uh )  0.

-0.20 -0.10 -0.

-0. (^23) -0.18 -0. x x x

-0.20 x -0.20x

x x x

Sym.about CL

-0.

-0.

-0.

-0.

-0. -0.

-0.

Wind

windward wall

side wall

leeward wall roof

• Circular cylinders :

Complexity due to interacting effects of surface roughness, Reynolds

Number and turbulence in the approach flow

Flow regimes in smooth flow :

Re < 2  105 Cd = 1.

Sub-critical

Laminar boundary layer Separation

Subcritical regime : most wind-tunnel tests - separation at about 90o^ from the

windward generator

• Circular cylinders :

Complexity due to interacting effects of surface roughness, Reynolds

Number and turbulence in the approach flow

Flow regimes in smooth flow :

Supercritical : flow in boundary layer becomes turbulent -

separation at 140o^ - minimum drag coefficient

Re  5  105 Cd  0.

Super-critical

Laminar Turbulent Separation

• Circular cylinders :

Pressure distributions at sub-critical and super-critical Reynolds Numbers

20 60 100 140

0

-0.

-1.

-1.

-2.

-2.

U

q degrees

q

C p

Drag coefficient mainly determined by pressure on leeward side (wake)

• Circular cylinders :

Effect of surface roughness :

Increasing surface roughness : decreases critical Re - increases minimum Cd

U (^) b

104 2 4 8 10^5 2 4 8 10^6 2 4 8 10^7

k/b = 0.

k/b = 0.

k/b = 0.

Sanded surface Smooth surface

Cd

Re

increasing surface roughness

• Fluctuating forces and pressures on bluff bodies :

Sources of fluctuating pressures and forces :

• Freestream turbulence (buffeting)
  • associated with flow fluctuations in the approach flow
• Vortex-shedding (wake-induced)
• unsteady flow generated by the bluff body itself
• Aeroelastic forces
• forces due to the movement of the body (e.g. aerodynamic damping)

• Buffeting - the Quasi-steady assumption :

Fluctuating pressure on the body is assumed to follow the

variations in wind velocity in the approach flow :

p(t) = Cpo (1/2) a [U(t)]

2

Cpo is a quasi-steady pressure coefficient

Expanding :

p(t) = Cpo (1/2) a [U + u(t) ]

2

= Cpo (1/2) a [U^2 + 2U u(t) + u(t)^2 ]

Taking mean values :

p = Cpo (1/2) a [U

2

+ u

2

]

• Peak pressures by the Quasi-steady assumption :

Quasi-steady assumption gives predictions of either maximum

or minimum pressure, depending on sign of Cp

Time

p(t)

pˆ

p

pˆ^ orp C (1/2)ρ [Uˆ ] C (1/2)ρ [Uˆ ]

2 p a

2

 po a 

• Vortex shedding :

On a long (two-dimensional) bluff body, the rolling up of

separating shear layers generates vortices on each side

alternately

• Occurs in smooth or turbulent approach flow
• may be enhanced by vibration of the body (‘lock-in’)
• cross-wind force produced as each vortex is shed

• Vortex shedding - circular cylinder :
  • vortex shedding not regular in the super-critical Reynolds

Number range

• Vortex shedding - other cross-sections :

0.

2b

2.5b

~10b

0.

0.

0.

• fluctuating cross-wind sectional force coefficient for

circular cylinder :

dependecy on Reynolds Number

105 106 107

0

Fluctuating side force coefficient Cl

Reynolds number, Re

• Quasi-steady fluctuating pressure coefficient :
• Quasi-steady drag coefficient :

p u 2 a

2 p a

2 a

2

p 2 C I ρ U 2

1

C ρ U u

ρ U 2

1

p C 

 

 



CD  2 CDIu