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

2. 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

3. 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

4. Basic bluff-body aerodynamics
Surface pressure coefficient :
in regions in which Bernoulli’s Equation is valid :
U = Cp = (stagnation point)
U > U0 Cp < 0
approximately valid in separated flows if U is taken as velocity in flow just outside adjacent shear layer

5. 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

6. Basic bluff-body aerodynamics
Wind axes :
Body axes :
 = angle of attack

7. Basic bluff-body aerodynamics
Relationship between force coefficients in two axes systems :
Fx = D cos  - L sin 
Fy = D sin  - L cos 

8. Basic bluff-body aerodynamics
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

9. 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

10. 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

11. Basic bluff-body aerodynamics
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 U2A :
CD = Cp,W – Cp,L = Cp,W + (– Cp,L)

12. Basic bluff-body aerodynamics
Flat plates and walls normal to flow
Smooth flow
CD = 1.1
SQUARE PLATE
Turbulent flow
CD = 1.2
Shear layer
Turbulence decreases (more negative) leeward side or ‘base’ pressure by increasing entrainment of flow from wake by ‘shear’ layers

13. Basic bluff-body aerodynamics
Flat plates and walls normal to flow
Smooth flow
TWO-DIMENSIONAL PLATE
CD = 1.9
No flow path around the sides (out of screen) - strong vortex generation and shedding - lower base pressure - higher drag

14. Basic bluff-body aerodynamics
Flat plates and walls normal to flow
TWO-DIMENSIONAL PLATE
splitter plate
CD = 1.4
Splitter plate induces re-attachment of flow - weaker, smaller vortices - lower drag

15. Basic bluff-body aerodynamics
walls normal to flow
CD = 1.2
SQUARE WALL
CD = 1.1
Ground
TWO-DIMENSIONAL WALL
Ground
Walls on ground - boundary layer flow : U taken as Uh (top of wall)

16. Basic bluff-body aerodynamics
walls normal to flow
Only slight dependency of CD on length / height (b/h)

17. Basic bluff-body aerodynamics
two square plates in series normal to flow
Spacing  0 b
Combined Cd  1.1
acts like a single plate
1.5b
Combined Cd  0.8
combined drag is less than single plate (critical spacing = 1.5b)
Spacing  
Combined Cd  2.2
acts like two single plates

18. 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)

19. Basic bluff-body aerodynamics
inclined plate
Primarily normal force
(negligible tangential component)
CN  2 a
For angle of attack,  < 10 degrees,
CN  2 
( in radians)
reference area : plan area normal to surface
Centre of pressure at h/4 from leading edge

20. Basic bluff-body aerodynamics
inclined plate
CN = 1.5
45o
0.4h
As  increases, centre of pressure moves towards centre of plate

21. Basic bluff-body aerodynamics
rectangular prism (two dimensional) 3 2 1
d/b Cd
Smooth flow
105<Re<106 b d
Maximum Cd at d/b 0.7
For d/b > 0.7, shear layers re-attach to sides of prism - drag is lower

22. Basic bluff-body aerodynamics
rectangular prism (two dimensional)
Effect of turbulence 4 3 2 1
Iu(%) Cd
0.33
0.50
0.62
1.0 b d
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)

23. Basic bluff-body aerodynamics
rectangular prism (two dimensional)
Effect of turbulence
Higher drag
Lower drag
Decreased radius of curvature and hence lower pressure due to increased rate of entrainment of wake fluid into the more turbulent shear layer.
d/b = 0.1 b d
Low turbulence
High turbulence
Partial reattachment lower drag
Higher drag
d/b  0.5

24. End of Lecture 8 John Holmes 225-405-3789 JHolmes@lsu.edu