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

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Basic bluff-body aerodynamics I

• Streamlined body
• • flow follows contours of body :
    • Bluff body
    • • flow separates :
      • vortices formed by rolling up of shear layers - may re-attach

• Surface pressure coefficient :

in regions in which Bernoulli’s 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

1 U

p p C a

p 

 

02 0

2 2 0 1 2

1

2

1



 

  

  U

U U

U U C a

a p 



U = 0 Cp = 1.0 (stagnation point)

U > U 0 Cp < 0

• Force coefficient :

reference area, A, - arbitary but often projected area

b = reference length - often projected width normal to wind

Force per unit length coefficient :

U A

F C a

F (^) 2 2 0



U b

f C a

f (^) 2 2 0

1 



• Relationship between force coefficients in two axes systems :

Fx = D cos  - L sin  Fy = D sin  - L cos 

• Dependence of pressure/force coefficients on other non-dimensional

groups :

Cp = f( 1 ,  2 ,  3 etc…)

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

• Jensen Number

Je = h/z 0

z 0 = 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

• 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 U^2 A :

CD = Cp,W – Cp,L = Cp,W + (– Cp,L)

• Flat plates and walls normal to flow

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

CD = 1.

Smooth flow

TWO-DIMENSIONAL PLATE

• Flat plates and walls normal to flow

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

TWO-DIMENSIONAL PLATE

CD = 1.

splitter plate

• walls normal to flow

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

• two square plates in series normal to flow

acts like a single plate

Spacing  0

b Combined Cd ^ 1.

1.5b

Combined Cd  0.8 combined drag is^ less than single plate (critical spacing = 1.5b) Spacing  

Combined Cd  2.

acts like two single plates

• 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

• inclined plate

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

C N = 1.

45 o

0.4h