Basic bluff-body aerodynamics I

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Basic bluff-body aerodynamics I. Wind loading and structural response Lecture 8 Dr. J.D. Holmes. 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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### Basic bluff-body aerodynamics I

Lecture 8 Dr. J.D. Holmes

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
Basic bluff-body aerodynamics
• Bernoulli’s equation :

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

- outside of boundary layers and free shear layers

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

Basic bluff-body aerodynamics
• Surface pressure coefficient :

in regions in which Bernoulli’s Equation is valid :

U = 0 Cp = 1.0 (stagnation point)

U > U0 Cp < 0

approximately valid in separated flows if U is taken as velocity in flow just outside adjacent shear layer

Basic bluff-body aerodynamics
• Force coefficient :

reference area, A, - arbitary but often projected area

Force per unit length coefficient :

b = reference length - often projected width normal to wind

Basic bluff-body aerodynamics
• Wind axes :
• Body axes :

 = angle of attack

Basic bluff-body aerodynamics
• Relationship between force coefficients in two axes systems :

Fx = D cos  - L sin 

Fy = D sin  - L cos 

Basic bluff-body aerodynamics
• Dependence of pressure/force coefficients on other non-dimensional groups :

Cp = f(1, 2, 3etc…)

Examples of ’s :

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

Basic bluff-body aerodynamics
• 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

Basic bluff-body aerodynamics
• 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

Basic bluff-body aerodynamics
• Flat plates and walls normal to flow

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 U2A :

CD = Cp,W – Cp,L = Cp,W + (– Cp,L)

SQUARE PLATE

Shear layer

Turbulent flow

Smooth flow

CD = 1.1

CD = 1.2

Basic bluff-body aerodynamics
• Flat plates and walls normal to flow

Turbulence decreases (more negative) leeward side or ‘base’ pressure by increasing entrainment of flow from wake by ‘shear’ layers

TWO-DIMENSIONAL PLATE

Smooth flow

Basic bluff-body aerodynamics
• Flat plates and walls normal to flow

CD = 1.9

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

TWO-DIMENSIONAL PLATE

splitter plate

Basic bluff-body aerodynamics
• Flat plates and walls normal to flow

CD = 1.4

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

CD = 1.1

Ground

Ground

TWO-DIMENSIONAL WALL

SQUARE WALL

Basic bluff-body aerodynamics
• walls normal to flow

CD = 1.2

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

Basic bluff-body aerodynamics
• walls normal to flow

Only slight dependency of CD on length / height (b/h)

Spacing  0

Combined Cd 1.1

b

1.5b

Combined Cd 0.8

Spacing 

Combined Cd 2.2

Basic bluff-body aerodynamics
• two square plates in series normal to flow

acts like a single plate

combined drag is less than single plate (critical spacing = 1.5b)

acts like two single plates

Basic bluff-body aerodynamics
• porous plate

CD, = CD . Kp

Kp = porosity factor,

Kp 1- (1-)2

 = solidity = solid area/total area

Kp : not sensitive to shape of openings

(plate could be a truss with linear members)

CN  2

a

Basic bluff-body aerodynamics
• inclined plate

Primarily normal force

(negligible tangential component)

For angle of attack,  < 10 degrees,

CN 2

reference area : plan area normal to surface

Centre of pressure at h/4 from leading edge

CN = 1.5

0.4h

45o

Basic bluff-body aerodynamics
• inclined plate

As  increases, centre of pressure moves towards centre of plate

b

3

2

1

0

d

Smooth flow

105<Re<106

Cd

0 1 2 3 4 5

d/b

Basic bluff-body aerodynamics
• rectangular prism (two dimensional)

Maximum Cd at d/b 0.7

For d/b > 0.7, shear layers re-attach to sides of prism - drag is lower

4

3

2

1

0

b

d

0.33

0.50

Cd

0.62

1.0

0 4 8 12 16 20

Iu(%)

Basic bluff-body aerodynamics
• rectangular prism (two dimensional)

Effect of turbulence

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

Turbulence promotes increased curvature of shear layers - reattachment occurs at lower d/b ratio (shorter after-body length)

Decreased radius of curvature and hence lower pressure due to increased rate of entrainment of wake fluid into the more turbulent shear layer.

Partial reattachment lower drag

Higher drag

b

d

Lower drag

Higher drag

d/b = 0.1

d/b  0.5

Low turbulence

High turbulence

Basic bluff-body aerodynamics
• rectangular prism (two dimensional)

Effect of turbulence