1. Basic bluff-body aerodynamics II
Wind loading and structural response
Lecture 9 Dr. J.D. Holmes
Basic bluff-body aerodynamics II

2. Basic bluff-body aerodynamics
Pressures on prisms in turbulent boundary layer :
-0.20
-0.10
-0.23
-0.18 x
Sym.about CL
-0.2
-0.5
-0.8
-0.6
-0.7
0.7
0.5
0.0
Wind
leeward wall
roof
side wall
windward wall
drag coefficient (based on Uh )  0.8

3. Basic bluff-body aerodynamics
Pressures on prisms in turbulent boundary layer :
x 0.4
0.3 x
0.9 x
0.5 x
Windward wall
x -0.6 x
-0.5
-0.6
-0.7
Wind
Side wall
-0.5
-0.4 to –0.49
Leeward wall
-0.6
-0.56 to –0.59 x
Wind
Roof
shows effect of velocity profile
nearly uniform

4. Basic bluff-body aerodynamics
Circular cylinders :
Complexity due to interacting effects of surface roughness, Reynolds Number and turbulence in the approach flow
Flow regimes in smooth flow :
Re < 2  105
Cd = 1.2
Sub-critical
Laminar boundary layer
Separation
Subcritical regime : most wind-tunnel tests - separation at about 90o from the windward generator

5. Basic bluff-body aerodynamics
Circular cylinders :
Complexity due to interacting effects of surface roughness, Reynolds Number and turbulence in the approach flow
Flow regimes in smooth flow :
Re  5  105
Cd  0.4
Super-critical
Laminar
Turbulent
Separation
Supercritical : flow in boundary layer becomes turbulent - separation at 140o - minimum drag coefficient

6. Basic bluff-body aerodynamics
Circular cylinders :
Complexity due to interacting effects of surface roughness, Reynolds Number and turbulence in the approach flow
Flow regimes in smooth flow :
Re  107
Cd  0.7
Post-critical
Turbulent
Separation
Post-critical : flow in boundary layer is turbulent - separation at about 120o

7. Basic bluff-body aerodynamics
Circular cylinders :
Pressure distributions at sub-critical and super-critical Reynolds Numbers
1.0
0.5
-0.5
-1.0
-1.5
-2.0
-2.5 U
q degrees q Cp
Drag coefficient mainly determined by pressure on leeward side (wake)

8. Basic bluff-body aerodynamics
Circular cylinders :
Effect of surface roughness :
increasing surface roughness
1.2
0.8
0.4 U b
k/b = 0.02
k/b = 0.007
k/b = 0.002
Sanded surface
Smooth surface Cd Re
Increasing surface roughness : decreases critical Re - increases minimum Cd

9. Basic bluff-body aerodynamics
Circular cylinders :
Effect of aspect ratio on mean pressure distribution :
Cp b h
Silos, tanks in atmospheric boundary layer
Decreasing h/b : increases minimum Cp (less negative)

10. Basic bluff-body aerodynamics
Fluctuating forces and pressures on bluff bodies :
Sources of fluctuating pressures and forces :
Freestream turbulence (buffeting)
- associated with flow fluctuations in the approach flow
Vortex-shedding (wake-induced)
- unsteady flow generated by the bluff body itself
Aeroelastic forces
- forces due to the movement of the body (e.g. aerodynamic damping)

11. Basic bluff-body aerodynamics
Buffeting - the Quasi-steady assumption :
Fluctuating pressure on the body is assumed to follow the variations in wind velocity in the approach flow :
p(t) = Cpo (1/2) a [U(t)]2
Cpo is a quasi-steady pressure coefficient
Expanding :
p(t) = Cpo (1/2) a [U + u(t) ]2
= Cpo (1/2) a [U2 + 2U u(t) + u(t)2 ]
Taking mean values :
p = Cpo (1/2) a [U2 + u2]

12. Basic bluff-body aerodynamics
Buffeting - the Quasi-steady assumption :
Small turbulence intensities :
(e.g. for Iu = 0.15, u2 = U2 )
p  Cpo (1/2) aU2 =Cp (1/2) aU2
i.e. Cpo is approximately equal to Cp
Fluctuating component :
p' (t) = Cpo (1/2) a [2U u'(t) + u'(t)2 ]
Squaring and taking mean values :
 Cp2 (1/4) a2 [4U2 ]= Cp2 a2 U2 u2

13. Basic bluff-body aerodynamics
Peak pressures by the Quasi-steady assumption :
Time
p(t)
Quasi-steady assumption gives predictions of either maximum or minimum pressure, depending on sign of Cp

14. Basic bluff-body aerodynamics
Vortex shedding :
On a long (two-dimensional) bluff body, the rolling up of separating shear layers generates vortices on each side alternately
Occurs in smooth or turbulent approach flow
may be enhanced by vibration of the body (‘lock-in’)
cross-wind force produced as each vortex is shed

15. Basic bluff-body aerodynamics
Vortex shedding :
Strouhal Number - non dimensional vortex shedding frequency, ns :
b = cross-wind dimension of body
St varies with shape of cross section
circular cylinder : varies with Reynolds Number

16. Basic bluff-body aerodynamics
Vortex shedding - circular cylinder :
vortex shedding not regular in the super-critical Reynolds Number range

17. Basic bluff-body aerodynamics
Vortex shedding - other cross-sections :
0.08 2b
2.5b
~10b
0.12
0.06
0.14

18. Basic bluff-body aerodynamics
fluctuating pressure coefficient :
fluctuating sectional force coefficient :
fluctuating (total) force coefficient :

19. Basic bluff-body aerodynamics
fluctuating cross-wind sectional force coefficient for circular cylinder :
0.7
0.6
0.5
0.4
0.3
0.2
0.1
Fluctuating side force coefficient Cl
Reynolds number, Re
dependecy on Reynolds Number

20. Basic bluff-body aerodynamics
Quasi-steady fluctuating pressure coefficient :
Quasi-steady drag coefficient :

21. Basic bluff-body aerodynamics
Correlation coefficient for fluctuating forces on a two-dimensional body :
Correlation length :
y is separation distance between sections

22. Basic bluff-body aerodynamics
Correlation length for a stationary circular cylinder (smooth flow) : 6 4 2
Reynolds number, Re
Correlation length / diameter
cross-wind vibration at same frequency as vortex shedding increases correlation length

23. Basic bluff-body aerodynamics
Total fluctuating force on a slender body : L
We require the total mean and fluctuating forces on the whole body

24. Basic bluff-body aerodynamics
Total fluctuating force on a slender body :
mean total force : F = fi yi
instantaneous total fluctuating force : F(t) =  fi  (t) yi
= f1 (t) y1 + f2 (t) y2 + ……………….fN (t) yN
Squaring both sides : [F(t)]2 = [ f1 (t) y1 + f2 (t) y2 + ……………….fN (t) yN]2
= [f1 (t) y1]2 + [f2 (t) y2]2 ..+ [fN (t) yN]2 + f1 (t) f2(t) y1y2 + f1 (t) f3(t) y1y3 +...

25. Basic bluff-body aerodynamics
Total fluctuating force on a slender body :
Taking mean values :
As yi, yj tend to zero :
writing the integrand (covariance) as :
This relates the total mean square fluctuating force to the sectional force

26. Basic bluff-body aerodynamics
Total fluctuating force on a slender body :
Introduce a new variable (yi - yj) :
Special case (1) - full correlation, (yi-yj) = 1 :
fluctuating forces treated like static forces
Special case (2) - low correlation, correlation length l is much less than L :
mean square fluctuating force is proportional to the correlation length - applicable to slender towers

27. Basic bluff-body aerodynamics
Total fluctuating force on a slender body :
The double integral : is represented by the volume under the graph : yi yj
Symmetric about diagonal since (yj-yi) = (yi-yj ). Along the diagonal, the height is 1.0
On lines parallel to the diagonal, height is constant

28. Basic bluff-body aerodynamics
Total fluctuating force on a slender body :
Consider the contribution from the slice as shown :
Volume under slice = (z)(L-z)2
Length of slice = (L-z)2
z/2
z /2 L
yi-yj=0
yi-yj= z yj yi
Total volume =
(reduced to single integral)

29. End of Lecture 9 John Holmes 225-405-3789 JHolmes@lsu.edu