Chapter 7.4 Bluff Body

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Chapter 7.4 Bluff Body

Fluid flows are broadly categorized:

1. Internal flows such as ducts/pipes, turbomachinery, open channel/river, which are bounded by walls or fluid interfaces:

Chapter 6. 2. External flows such as flow around vehicles and structures, which are characterized by unbounded or partially bounded domains and flow field decomposition into viscous and inviscid regions: Chapter 7.

a. Boundary layer flow: high Reynolds number flow around streamlines bodies without flow separation.

b. Bluff body flow: flow around bluff bodies with flow

separation.

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3. Free Shear flows such as jets, wakes, and mixing layers, which are also characterized by absence of walls and development and spreading in an unbounded or partially bounded ambient domain: advanced topic, which also uses boundary layer theory.

Basic Considerations

Drag is decomposed into form and skin-friction contributions:

( )

 



 

 ∫ − ⋅ + ∫ τ ⋅ ρ

=

_∞

S w

2 S

D

p p n iˆ dA t iˆ dA

A 2 V

1 1 C

C

Dp

C

f

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( )

 



 

 ∫ − ⋅ ρ

= p p

_∞

n jˆ dA A

2 V 1 1

C

L 2 S

c t << 1 C

f

> > C

Dp

streamlined body

c t ∼ 1 C

Dp

> > C

f

bluff body Streamlining: One way to reduce the drag

 reduce the flow separation  reduce the pressure drag

 increase the surface area  increase the friction drag

 Trade-off relationship between pressure drag and friction drag

Trade-off relationship between pressure drag and friction drag

Benefit of streamlining: reducing vibration and noise

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Drag of 2-D Bodies

First consider a flat plate both parallel and normal to the flow

( p p ) n iˆ 0 A

2 V 1 1

C

Dp 2 S

∫ − ⋅ = ρ

=

_∞

∫ τ ⋅ ρ

=

S w

f 2

t iˆ dA

A 2 V

1 1 C

=

₁_/₂

Re

L

33 .

1 laminar flow

=

₁_/₅

Re

L

074 . turbulent flow

where C

p

based on experimental data

vortex wake

typical of bluff body flow

flow pattern

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( )

∫ − ⋅

ρ

=

_∞

2 S

Dp

p p n iˆ dA

A 2 V

1 1 C

= ∫

S

C

p

dA A

1 = 2 using numerical integration of experimental data C

f

= 0

For bluff body flow experimental data used for C

D

.

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In general, Drag = f(V, L, ρ , µ , c, t, ε , T, etc.) from dimensional analysis

c/L

 

 



 ε

= ρ

= , T , etc .

, L L , t Ar Re, A f

2 V 1 Drag

C

D 2

scale factor

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Potential Flow Solution: _ ^θ



 



 −

−

=

ψ

_∞

sin

r r a

U

²

2

U

2 p 1

2 V

p + 1 ρ =

_∞

+ ρ

_∞

2 2 2r

p 2

U

u 1 u

2 U 1 p C p

∞ θ

∞

+

−

= ρ

= −

( = ) = −

²

θ

p

r a 1 4 sin

C surface pressure

u r r u

_r

1 ∂ ψ

− ∂

=

θ

∂ ψ

= ∂

θ

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< 0.3 flow is incompressible, i.e., ρ ∼ constant

Effect of Compressibility on Drag: CD = CD(Re, Ma)

a Ma = U

^∞

speed of sound = rate at which infinitesimal disturbances are propagated from their