basic bluff-body aerodynamics i wind loading and structural response lecture 8 dr. j.d. holmes
TRANSCRIPT
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
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
constanta2
1 2 Up a
200
2
2
1
2
1UpUp aa
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 :
approximately valid in separated flows if U is taken as velocity in flow just outside adjacent shear layer
20
0
21
U
ppC
a
p
2
020
220
1
21
21
U
U
U
UUC
a
a
p
U = 0 Cp = 1.0 (stagnation point)
U > U0 Cp < 0
Basic bluff-body aerodynamics
• 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
F202
1
bU
fC
a
f202
1
Basic bluff-body aerodynamics
• Wind axes :
= angle of attack
• Body axes :
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, 3 etc…)
Examples of ’s :
h/zo - Jensen Number (h is height of building)
Iu, Iv, Iw - turbulence intensities
u/h, v/h, w/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
Advertising hoardings, free-standing walls
Drag force, D = (pW - pL) A
pW = average pressure on windward wallpL = average pressure on leeward wall
dividing both sides by (1/2) a U2A :
CD = Cp,W – Cp,L = Cp,W + (– Cp,L)
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
Smooth flow
CD = 1.1
SQUARE PLATE
Turbulent flow
CD = 1.2
Shear layer
Basic bluff-body aerodynamics
• 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 = 1.9
Smooth flow
TWO-DIMENSIONAL PLATE
Basic bluff-body aerodynamics
• Flat plates and walls normal to flow
Splitter plate induces re-attachment of flow - weaker, smaller vortices - lower drag
TWO-DIMENSIONAL PLATE
CD = 1.4
splitter plate
Basic bluff-body aerodynamics
• 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
Basic bluff-body aerodynamics
• walls normal to flow
Only slight dependency of CD on length / height (b/h)
Basic bluff-body aerodynamics
• 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
Basic bluff-body aerodynamics
• 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
Basic bluff-body aerodynamics
• 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
Basic bluff-body aerodynamics
• inclined plate
As increases, centre of pressure moves towards centre of plate
CN = 1.5
0.4h
Basic bluff-body aerodynamics
• rectangular prism (two dimensional)
Maximum Cd at d/b 0.7
3
2
1
00 1 2 3 4 5
d/b
Cd
Smooth flow105<Re<106
b
d
For d/b > 0.7, shear layers re-attach to sides of prism - drag is lower
Basic bluff-body aerodynamics
• 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 20
Iu(%)
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)
Basic bluff-body aerodynamics
• rectangular prism (two dimensional)Effect of turbulence
Partial reattachment lower drag
Higher drag
d/b 0.5
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
