03Lect8BluffBodyAero

8/2/2019 03Lect8BluffBodyAero

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Basic bluff-body aerodynamics I

Wind loading and structural response

Lecture 8 Dr. J.D. Holmes


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Basic bluff-body aerodynamics

Streamlined body - flow follows contours of body :

Bluff body

- flow separates :

vortices formed by rolling up of shear layers - may re-attach


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Bernoullis equation :

applicable in inviscid(zero viscosity)and irrotational (zero vorticity) flow

- outside of boundary layers and free shear layers

constanta2

1 2 Up a

2

00

2

2

1

2

1UpUp aa

p0 and U0 are pressure and velocity in region outside of influence of body


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Surface pressure coefficient :

in regions in which Bernoullis Equation is valid :

approximately valid in separated flows if U is taken as velocity in flow just

outside adjacent shear layer

2

0

0

2

1U

ppC

a

p

2

02

0

22

0

1

2

1

2

1

U

U

U

UU

C

a

a

p

U = 0 Cp = 1.0 (stagnation point)

U > U0 Cp < 0


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Force coefficient :

reference area, A, - arbitary but often projected area

b = reference length - often projected width normal to wind

Force per unit length coefficient :

AU

FC

a

F2

0

2

1

bU

fC

a

f2

0

2

1


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Wind axes :

= angle of attack

Body axes :


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Relationship between force coefficients in two axes systems :

Fx = D cos - L sin

Fy = D sin - L cos


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Dependence of pressure/force coefficients on other non-dimensionalgroups :

Cp = f(1, 2, 3etc)

Examples ofs :

h/zo - Jensen Number (h is height of building)

Iu, Iv, Iw - turbulence intensities

lu/h, lv/h, lw /h - turbulence length scale ratios

Uh/ - Reynolds Number ( is kinematic viscosity)

In wind tunnel testing - try to match s in full scale and model scale


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Reynolds Number

Re = Uh/ = aUh/

= kinematic viscosity = dynamic viscosity

Reynolds Number represents a ratio of inertial forces to viscous

forces in the flow

full-scale values of Re cannot be matched in wind tunnel tests

dependence of flow on Re - less for sharp-edged bluff bodies,

and very turbulent flow


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Jensen Number

Je = h/z0

z0 = roughness length

Applicable only to bluff bodies immersed in a turbulent boundary

layer (full-scale or wind-tunnel)

Lower values of Je - steeper mean speed profile, higher turbulence

Ref. Lecture 6, Chapter 3


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Flat plates and walls normal to flow

Advertising hoardings, free-standing walls

Drag force, D = (pW - pL) A

pW = average pressure on windward wall

pL = average pressure on leeward wall

dividing both sides by (1/2) a U2

A :

CD = Cp,WCp,L = Cp,W + (Cp,L)


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Turbulence decreases (more negative) leeward side or base

pressure by increasing entrainment of flow from wake by

shear layers

Smooth flow

CD = 1.1

SQUARE PLATE

Turbulent flow

CD = 1.2

Shear layer


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No flow path around the sides (out of screen) - strong vortex generationand shedding - lower base pressure - higher drag

CD = 1.9

Smooth flow

TWO-DIMENSIONAL PLATE


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Splitter plate induces re-attachment of flow - weaker, smaller vortices -lower drag

TWO-DIMENSIONAL PLATE

CD = 1.4

splitter plate


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walls normal to flow

Walls on ground - boundary layer flow : U taken as Uh (top of wall)

CD = 1.2

TWO-DIMENSIONAL WALL

Ground

SQUARE WALL

CD = 1.1

Ground


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walls normal to flow

Only slight dependency of CD

on length / height (b/h)


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two square plates in series normal to flow

acts like a single plate

Spacing 0

b Combined Cd 1.1

1.5b

Combined Cd 0.8combined drag is less

than single plate

(critical spacing = 1.5b)Spacing

Combined Cd 2.2

acts like two single plates


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porous plate

CD, = CD . Kp

Kp = porosity factor,

Kp 1- (1-)2

Kp : not sensitive to shape of openings

(plate could be a truss with linear members)

= solidity = solid area/total area


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inclined plate

Primarily normal force

(negligible tangential component)

For angle of attack, < 10 degrees,

Centre of pressure at h/4 from leading edge

CN 2( in radians)

CN 2

4

h

reference area : plan area normal to surface


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inclined plate

As increases, centre of pressure movestowards centre of plate

CN = 1.5

45o

0.4h


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rectangular prism (two dimensional)

Maximum Cd at d/b 0.7

3

2

1

00 1 2 3 4 5

d/b

Cd

Smooth flow

105


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rectangular prism (two dimensional)

Effect of turbulence

With increasing turbulence intensity, d/b ratio for maximum Cd falls

4

3

2

1

0 0 4 8 12 16 20Iu(%)

Cd

0.330.50

0.62

1.0

b

d

Turbulence promotes increased curvature of shear layers -

reattachment occurs at lower d/b ratio (shorter after-body length)


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rectangular prism (two dimensional)Effect of turbulence

Partialreattachment

lower drag

Higher

drag

d/b 0.5

Higherdrag

Lower

drag

Decreased radius of curvature andhence lower pressure due toincreased rate of entrainment ofwake fluid into the more turbulentshear layer.

d/b = 0.1

b

d

Lowturbulence

Highturbulence


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End of Lecture 8

John Holmes225-405-3789 [email protected]

03Lect8BluffBodyAero

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