Lecture 4
Flow Patterns and
Wind Forces
Tokyo Polytechnic University
The 21st Century Center of Excellence Program
Yukio Tamura
Flows Around Bluff Bodies
1
Flow Patterns Around
Bluff Bodies
Stream Lines
2
Flow pattern around a square prism (Particle
paths, 2D, Uniform flow, CFD)
Flow pattern around a square prism (Streak
Lines, 2D, Uniform Flow, CFD)
3
Flow pattern between building models
(Streak Lines)
K. Shimada
Periodic vortices shed from a square prism
(Streak Lines, CFD)
4
Flow pattern around a square prism
(Stream lines, Wind tunnel, by T. Mizota)
Temporal variation of flow pattern around
a square prism (Stream lines, 2D, Uniform flow, CFD)
5
Temporally averaged flow pattern around
a square prism (Stream lines, 2D, Uniform flow, CFD)
A: Front stagnation
point
B: Rear stagnation
point
1, 2: Separation
point
Temporally averaged flow pattern
around a square prism
6
SP
RP
FP
SP
Temporally averaged flow pattern around a
circular cylinder
Reattachment
Temporally averaged flow pattern around a
rectangular cylinder
with a large side ratio
7
Inflow and outflow into an infinitesimal
hexahedron
Inflow through the (dy × dz) plane:
1 ∂u
1 ∂u
ρ(u − ⎯ ⎯⎯dx )dydz − ρ(u + ⎯ ⎯⎯dx )dydz
2 ∂x
2 ∂x
∂u
= − ρ ⎯⎯ dxdydz
(1)
∂x
Inflow through the (dz × dx) plane:
∂v
= − ρ ⎯⎯ dxdydz
(2)
∂y
Inflow through the (dx × dy) plane:
∂w
= − ρ ⎯⎯ dxdydz
(3)
∂z
8
Law of Conservation of Mass
(Incompressive Fluid) : Eq.(1)+Eq.(2)+Eq.(3)=0
∂u
∂v
∂w
− ρ ⎯⎯dxdydz − ρ ⎯⎯dxdydz − ρ ⎯⎯dxdydz = 0
∂x
∂y
∂z
Equation of Continuity:
∂u
∂v
∂w
⎯⎯ + ⎯⎯ + ⎯⎯ = 0
∂x
∂y
∂z
(div v = 0)
„ Vorticity Vector ω :
ω = (ξ, η, ζ ) = rot v
∂w
∂v
ξ = ⎯⎯ − ⎯⎯
∂y
∂z
∂u
∂w
η = ⎯⎯ − ⎯⎯
∂z
∂x
∂v
∂u
ζ = ⎯⎯ − ⎯⎯
∂x
∂y
ξ, η, ζ = 2ωx , 2ωy ,2ωz : Vorticity
ωx , ωy ωz : Rotational angular velocity
about x, y and z axes
9
y
∂u
– ⎯⎯ δt
∂y
Angular Velocity of Rotation
∂ v − ⎯⎯
∂u)
1 (⎯⎯
ωz = ⎯
2 ∂x
∂y
1
=⎯ζ
2
average
ζ : Vorticity
∂v
⎯⎯ δt
∂x
x
„ Non-viscous and Irrotational Fluid
ω = rot v = 0
„ Velocity potential φ can be
assumed:
∂φ
∂φ
∂φ
u = ⎯⎯, v = ⎯⎯, w = ⎯⎯
∂x
∂y
∂z
10
„ Equation of Continuity:
∂u
∂v
∂w
⎯⎯ + ⎯⎯ + ⎯⎯ = 0
∂x
∂y
∂z
∂φ
∂φ
∂φ
u = ⎯⎯ , v = ⎯⎯ , w = ⎯⎯
∂x
∂y
∂z
φ : Velocity potential
„ Laplace Equation:
∂ 2φ ∂ 2φ ∂ 2φ
⎯⎯2 + ⎯⎯2 + ⎯⎯
=0
2
∂x
∂y
∂z
Flow Pattern
and Pressure
11
l i ne
stream
a
a
stre
in e
ml
b
Stream line and flow velocity
Pressure: PB
UB
Sectional Area: AB
Pressure: PA
UA
zB
Sectional Area: AA
Closed
Curve:C
zA
Stream tube and flow velocity
12
Incompressive Flow (Law of conservation of mass)
ρAAUA = ρABUB = m
m : Air mass of inflow and outflow portions
Increase of kinetic energy during unit time
m (U 2 − U 2)
—
B
A
2
(1)
mg (zB − zA)
(2)
Increase of potential energy during unit time
Work done by pressure difference during unit
time
(PA AA)UA − (PB AB)UB
ρ : Air density,
(3)
Ui : Wind speed at point i
Pi : Pressure at point i, g : Gravity acceleration
zi : Altitude of point i
For the same stream tube:
1
— ρ UA2 + PA + ρ gzA
2
1
= — ρ UB2 + PB + ρ gzB
2
ρ : Air density
Ui : Wind speed at point i
Pi : Pressure at point i
g : Gravity acceleration
zi : Altitude of point i
Eq.(1)+Eq.(2)= Eq.(3)
13
Bernoulli’s Equation (Steady / Ideal flow)
1
— ρ U 2 + P + ρ g z = HT (constant)
2
ρ : Air density
U : Wind speed
P : Pressure
g : Gravity acceleration
z : Altitude
HT : Total pressure
(On Stream
Li )
Bernoulli’s equation:
1
— ρ U 2 + PS = HT (constant)
2
ρ : Air density
U : Wind speed
PS : Static pressure = P + ρgz
1 ρU 2 : Dynamic pressure
—
2
HT : Total pressure
14
Bernoulli’s equation:
1
— ρ U 2 + PS = HT (constant)
2
U : Large (Small)
PS : Small (Large)
Low Pressure
Resultant
Force
High Pressure
Pressure distribution and resultant force
acting on a fluid cell
15
U2 ∂ P
ρ
+
=0
r ∂n
High Pressure
Force
Low Pressure
Curved stream line and
pressure gradient
„ Wind Pressure at point i
pi = Pi − PR
Pi : Pressure at point i
PR : Pressure at reference point R far
away from the body, where there
is no effect of the body on the flow
field
16
Wind Pressure : pi = Pi – PR
PR
PA >PR (pA >0)
PB >PR (pB >0)
PD <PR (pD <0)
PE <PR (pE <0)
Stream lines around a square prism and
spatial variation of pressure
pA = PA − PR = PA −PG =
= (1/2)ρUR2 : Dynamic pressure (Velocity
pressure) of the reference point
→ UR = √ 2pA / ρ (Reference wind speed)
→ Anemometer
Flow around Pitot static tube
and pressure
17
Navier-Stokes Equation
Substantial DifferentiationQ(x+δx,y+δy,z+δz,t+δt)
Vδt
Velocity components
u = u(x,y,z,t)
v = v (x,y,z,t)
P(x,y,z,t)
w = w(x,y,z,t)
Displacement of a small element of fluid at
point P during an infinitesimal interval δ t
δ x = u(x,y,z,t)δ t
δ y = v(x,y,z,t) δ t
Eq.(a)
}
δ z = w(x,y,z,t)δ t
18
35
Changing rate (δ f /δ t ) of a property f
f + δ f = f(x + δ x , y + δ y , z + δ z, t + δ t )
∂f
∂f
∂f
∂f
= f(x, y, z, t) + — δ x + — δ y + — δ z + —δ t
∂x
∂y
∂z
∂t
+ O(δ t2)
δ t → 0, substituting Eq.(a)
Df
∂f
∂f
∂f
∂f
—— = —— + u —— + v —— + w ——
Dt
∂t
∂x
∂y
∂z
Substantial Acceleration
Du
∂u
∂u
∂u
∂u
—— = —— + u —— + v —— + w ——
∂x
∂y
∂z
Dt
∂t
Changing rate (δ f /δ t ) of a property f
f + δ f = f(x + δ x , y + δ y , z + δ z, t + δ t )
∂f
∂f
∂f
∂f
= f(x, y, z, t) + — δ x + — δ y + — δ z + —δ t
∂x
∂y
∂z
∂t
+ O(δ t2)
δ t → 0, substituting Eq.(a)
Df
∂f
∂f
∂f
∂f
—— = —— + u —— + v —— + w ——
Dt
∂t
∂x
∂y
∂z
Substantial Acceleration
Du
∂u
∂u
∂u
∂u
—— = —— + u —— + v —— + w ——
∂x
∂y
∂z
Dt
∂t
19
dU
τ = µ ⎯⎯
dn
Newton’
Newton’s Law
of Viscosity
Coefficient of Viscosity 15°
15°C
µ = 1.78×
1.78×10–5 kg/m/s (Air)
(Air)
µ = 114 ×10–5 kg/m/s (Water)
(Water)
Velocity gradient and viscous stress
(Newtonian fluid)
Shear deformation velocity
in xy - plane
20
∂v ∂u
τxy= τyx = µ (⎯ + ⎯)
∂u
τxx= 2µ ⎯
∂x
∂x ∂y
Shear stresses acting on
an infinitesimal hexahedron of fluid
„Total shear forces acting x-direction:
∂τ
∂τ
∂τ
xx
yx
zx
( ⎯⎯
+ ⎯⎯
+ ⎯⎯
) dxdydz
∂x
∂y
∂z
21
„Navier Stokes Equations:
Convective acceleration
Inertial force per unit volume
∂u
∂u
∂u
∂u
ρ [⎯⎯ + u ⎯⎯ + v ⎯⎯ + w ⎯⎯ ]
∂t
∂x
∂y
∂z
Substantial acceleration
Local (Instantaneous)
Instantaneous) acceleration
2u
2u
p
∂p
∂ u
= − ⎯⎯ + µ [ ⎯⎯2 +
∂x
∂x
Pressure
gradient
∂ u
⎯⎯
+
2
∂y
Viscous
stress
∂ 2u
⎯⎯
]
2
∂z
„Navier Stokes Equations:
∂u
∂u
∂u
∂u
ρ [⎯⎯ + u ⎯⎯ + v ⎯⎯ + w ⎯⎯ ]
∂t
∂x
∂y
∂z
∂p
∂ 2u ∂ 2u
∂ 2u
= − ⎯⎯ + µ [ ⎯⎯2 + ⎯⎯
+ ⎯⎯
]
∂x
∂x
∂ y2
∂ z2
∂v
∂v
∂v
∂v
ρ [⎯⎯ + u ⎯⎯ + v ⎯⎯ + w ⎯⎯ ]
∂t
∂x
∂y
∂z
2
2
∂p
∂ v
∂ v
∂ 2v
= − ⎯⎯ + µ [ ⎯⎯
+
⎯⎯
+
⎯⎯
]
∂y
∂ x2
∂ y2
∂ z2
∂w
∂w
∂w
∂w
ρ [⎯⎯ + u ⎯⎯ + v ⎯⎯ + w ⎯⎯ ]
∂t
∂x
∂y
∂z
2
2
∂p
∂ w
∂ w ∂ 2w
= − ⎯⎯ + µ [ ⎯⎯
+
⎯⎯
+ ⎯⎯ ]
∂z
∂ x2
∂ y2 ∂ z2
22
„ Non-dimensional expression of Navier Stokes
Equations:
∂ u*
∂ u*
∂ u*
∂ u*
*
*
*
⎯⎯* + u ⎯⎯* + v ⎯⎯* + w ⎯⎯
∂t
∂x
∂y
∂ z*
∂ p* 1 ∂ 2u* ∂ 2u* ∂ 2u*
= − ⎯⎯* + ⎯ [ ⎯⎯
+ ⎯⎯ + ⎯⎯ ]
∂ x Re ∂ x* 2 ∂ y* 2 ∂ z* 2
x
y
z
tU
p
x*= ⎯ , y* = ⎯ , z* = ⎯ , t* = ⎯ , p* = ⎯⎯2
L
L
L
L
ρU
u
v
w
ρUL
u*= ⎯ , v* = ⎯ , w* = ⎯ , Re = ⎯⎯
µ
U
U
U
„ Reynolds Number
T = 15°
15°C, P = 1013hPa
ρ = 1.22 kg/m3
µ = 1.78×
1.78×10–5 kg/m/s (Air)
µ = 114 ×10–5 kg/m/s (Water)
ρUL = ⎯⎯
UL
Re = ⎯⎯
µ
ν
Dynamic Viscosity
3
2
ρL U / L
ν = µ /ρ = 1.45×
1.45×10
= ⎯⎯⎯⎯⎯
ν = µ /ρ = 1.14×
1.14×10
L 2 µU / L
Inertial Force
= ⎯⎯⎯⎯⎯⎯⎯
Viscous Force
(Air)
≈ 7 × 104 L U
–5
m2/s (A)
–6 m2/s (W)
(m/s) Reference Speed
(m) Reference Length
≈ 9 × 105 L U
(Water)
23
- Laminar flow
- A parabola profile
- Quantity of flowing
r 4∆p
Q ∝ ⎯⎯⎯
µ
- r : Radius of tube
- Viscosity meter
Hagen-Poiseuille flow in a straight circular
tube
Decelerate
Accelerate
L.P.
(RP)
H.P.
(FP)
H.P.
Flow around a circular cylinder
in an ideal flow (Non-viscous)
24
Surface Boundary Layer
ity
e lo c
v
w
F lo
d
un
Bo
ar
Wall
er
ay
l
y
Surfa
ce
Flow near surface of body
Decelerate
Accelerate
L.P.
(RP)
H.P.
(FP)
H.P.
Flow around a circular cylinder
in an ideal flow (Non-viscous)
25
- Separated shear layer
- Vortex sheet
- Shear layer instability
Separation
Point
Flow near the separation point
- Separated shear layer
- Vortex sheet
- Shear layer instability
Separation
Point
Flow near the separation point
26
SP
FP
Flow separation from body surface
(Viscous Flow)
- ΓC = 2ω0 A
- Vorticity ω = 2ω0
= ΓC /A
Area: A
Closed
Curve:C
Circulation
ΓC = ∫C Ucosθ ds
(a) Definition of circulation
Angular
Velocity
r
Closed
rω0
Curve: C
ΓC = rω0 · 2π r
= 2ω0 · π r2 = 2ω0A
(b) Rigid vortex and Circulation
Circulation and vorticity
27
- Circulation
ΓC = − (UA − UB )
Line of Velocity
Discontinuity
Closed Curve:C
Unit Length : 1
Circulation along a line of
velocity discontinuity
Causes of Wind Forces
28
Decelerate
Accelerate
L.P.
(RP)
H.P.
(FP)
H.P.
Flow around a circular cylinder
in an ideal flow (Non-viscous)
- D’Alambert’s Paradox
Pressure distribution on a circular cylinder in
the ideal non-viscous flow
29
SP
FP
Flow separation from body surface
(Viscous Flow)
Pressure distribution on a circular cylinder in
actual viscous flow
30
Uniform
Flow
Circulation
Superimposition of a rotational flow around a
circular cylinder with a uniform flow
KuttaKutta-Joukowski’
Joukowski’s Theorem
L.P.
Flow
Velocity
Lift Force: ρ UΓ
H.P.
Stream lines around a circular cylinder
in a uniform ideal flow superimposed on
a clockwise circulation
31
- Starting vortex
Γ=0
Γ=0
Γ = –Γ
Γ = +Γ
Lift
+Γ
Just after starting
Γ=0
–Γ
Starting vortex
( Kutta’
Kutta’s Condition,
Joukowski’
Joukowski’s Hypothesis )
A starting vortex and a remaining
circulation around an airfoil
( Kelvin’
Kelvin’s TimeTime-Invariant Circulation
Theorem )
A vortex generated when an airfoil starts to
move in a stationary flow
Sudden stop of motion
Release of a vortex stuck to an airfoil
by sudden stop of motion
32
2 .5 m /s e c
2 .5 m /s e c
無風
Turbulence after airplane
Reynolds Number
and
Flow Patterns
33
Re < 5
5×103 < Re
5 < Re < 30
30
3×105 < Re
30 < Re <
5×
5×103
Sub-critical
<
3×
3×105
CD=1.2, θs = 85°
85°
<
6×
6×105
CD=0.3, θs = 120°
120°
6×105 < Re
Supercritical
Postsupercritical
CD=0.6, θs = 100°
100°
Variation of flow pattern around a circular
cylinder due to Reynolds number
Important Regimes for Structures
„ Sub-critical 5×103 < Re < 3×105
Surface boundary layer : Laminar
Separation points: θS = 85º
Separated shear layer: Turbulent in wake (Widest wake)
Drag Coefficient : CD = 1.2
Vortices : Very periodic
„ Supercritical 3×105 < Re < 6×105
Surface boundary layer : Laminar →Turbulent θ > 85º
Separation points: θS = 120º
Separated shear layer: Narrow Wake-width
Drag Coefficient : CD = 0.3
Vortices : Lose periodicity
„ Post-supercritical 6×105 < Re
Surface boundary layer : Fully turbulent
Separation points: θS = 100º
Separated shear layer: Wider wake-width
Drag Coefficient : CD = 0.6 (Re ≈ 4 × 106)
Vortices : Periodic
34
Drag Coefficient CD
Rcr : Critical Reynolds
Number
- d : Diameter of particles
attached to the surface
- D : Diameter of a circular
cylinder
Okajima
105 Rcr 106
Reynolds Number : Re members
102
10
103
107
104
buildings
Variation of drag coefficient of a circular
cylinder due to Reynolds number
Drag Coefficient CD
Turbulence
Intensity
Smooth
Flow
Reynolds Number Re
Variation of mean drag coefficient of a
circular cylinder with turbulence
intensity and Reynolds number (2D)
35
Turbulence Index Iu(D/Ly)1/5
Sphere (Dryden et
al.)
Circular
Cylinder
Critical Reynolds Number Rcr
3.2.15
Drag Coefficient CD
Variation of the critical Reynolds
numbers of a sphere and a circular
cylinder with turbulence index
Iu(D/Ly)1/5(Bearman, 1968)
106
107
Reynolds Number Re
108
Field data of mean drag coefficients of
actual circular structures (chimneys etc.)
36
Vortices Shed From Bluff
Bodies
Karman vortices shed from
a square prism
37
wv / pv = 0.281
Karman vortex streets
Γ
FL
Γ
–Γ
FL
FL = ρ UΓ
–Γ
KuttaKutta-Joukowski’
Joukowski’s Theorem
Periodic lateral force due to alternate
vortex shedding
38
U
fv = S ⎯ ,
B
- fv
-S
-U
-B
fv B
S = ⎯⎯
U
: Shedding frequency of Karman vortices
: Strouhal number
: Wind Speed
: Reference Length
U
B
CFD by K. Shimada
Strouhal Number S
Vortex shedding and Strouhal Number
105
106
107
Reynolds Number Re
Variation of Strouhal number
with Reynolds number
(Circular cylinder, 2D, Uniform flow, Shewe 1983)
39
(a) front side
(b) rear side
Flow around a building
(T.Tamura)
B
B
H
H
(a) Small H/B (Aspect Ratio) (b) Large H/B
Vortex formation behind building models
40
Static Wind Forces
Velocity Pressure
and
Wind Pressure Coefficient
41
UR
PR
SP
U0 = 0, P0
Wind speed at reference point
far away
bodyatand
stagnation
Wind form
Pressure
Stagnation
Pointpoint
p0 = P0 −PR = (1/2)ρ UR2
Velocity Pressure (Dynamic
„
Wind Pressure Coefficient
pk
Cpk = ⎯⎯⎯⎯
1 ρU 2
⎯
R
2
pk = Pk − PR
pk :
Pk :
PR :
ρ :
UR :
Velocity Pressure : qR
Wind pressure at point k
Static pressure at point k
Reference static pressure
Air density
Reference wind speed
42
Stagnation point of a 3D building
Internal Pressure Coefficient
and
External Pressure Coefficient
43
− 0.5
Cpe = + 0.8
Cpi = − 0.34
− 0.4
Internal Space
− 0.5
External pressure coefficient Cpe and internal
pressure coefficient Cpi
Equilibrium Equation of Flows
Through Gaps:
- The flow is proportional to the velocity
at each gap.
- The velocity is assumed to be
proportional to the square root of the
pressure difference between the gap.
√⏐0.8 − Cpi⏐
= 2√⏐Cpi + 0.5⏐ + √⏐Cpi + 0.4⏐
Cpi = − 0.34
44
Mean Internal Pressure ((hPa
hPa))
Ground
7th story
13th
18th
24th
7th
Ground
13th
18th
24th
pi
mmAq))
Difference From Reference Pressure ((mmAq
Temporal variations of mean internal pressures
(Full-scale, Kato et al., 1996)
Internal
Pressure Coefficient
Cpi = pi / qR
24th story
18th
13th
(Office)
13th
7th
(after altitude compensation)
Mean Velocity Pressure at Top :
qR
Variation of mean internal pressures with reference
velocity pressure (Full-scale, Kato et al., 1996)
45
Wind Force Coefficient
FY
MZ
U
y
FX
Projected
Width: B
θ
p
x
(Body Length:
h)
3.2.3
Wind pressure and wind forces
defined for axes fixed to body
46
„ Wind Forces
FX = ∫S p cosθ h ds
FY = ∫S p sinθ h ds
h : Body length
„ Wind Force Coefficients
FX
FY
CFX = ⎯⎯⎯⎯ , CFY = ⎯⎯⎯⎯
1 ρ U 2A
1 ρ U 2A
⎯
⎯
R
R
2
2
A : Projected area = Bh
Aerodynamic Moment Coefficients
MZ
CMZ = ⎯⎯⎯⎯⎯
1 ρ U 2AL
⎯
R
2
MZ : Aerodynamic Moment
A : Projected area
L : Reference Length
47
Across-wind Force: FL
(Lift)
Along-wind Force: FD
(Drag)
Along-wind force and across-wind force
defined for the axes fixed to wind
Cpe,S
Cpi
Cpe,L
AlongAlong-wind Force Coefficient
CF = Cpe,W − Cpe,L
Cpe,W
Cpe,S
Wind pressure coefficient and wind force
coefficient for a building
with an internal space
48
Lift Coefficient CL
Drag Coefficient CD
Static Wind Forces
Acting On Bluff Bodies
Smooth
Flow
Turbulent Flow
Turbulent
Flow
Smooth
Flow
Variations of mean drag and lift coefficients
with attacking angle (2D)
49
Drag Coefficient CD
Turbulence Intensity Iu
(%)
Effects of turbulence on mean drag
coefficients of 2D prisms
Entrainment effects of turbulence
Small Drag
Large Drag
Smooth Flow
Turbulent Flow
Large Drag
Small
Drag
(a)Flat plate (D/B = 0.1) (b) Prism (D/B = 0.5)
Effects of turbulence on separated shear
layers (Laneville et al., 1975)
50
Drag Coefficient
CD
Back--pressure coefficient – Cpb
Back
Wake stagnation point
Xws
Back pressure
Cpb
0.62
D/B
Variation of mean drag coefficient, backpressure coefficient, and wake stagnation
point with side ratio (2D, Uniform flow)
Drag Coefficient CD
Turbulent
Uniform
D/B : Side Ratio
H/B : Aspect Ratio
B
H
H/B
Variation of mean drag coefficients of 3D
rectangular prisms with aspect ratio
51
Shimizu Corp.
Mean pressure distribution
on a low-rise building model
Instantaneous pressure distribution
on a low-rise building model (45° Wind)
Shimizu Corp.
52
Instantaneous pressure distribution
on a low-rise building model (45° Wind)
Shimizu Corp.
Conical Vortices
Mean pressure distributions Shimizu Corp
on a low-rise building model (45° Wind)
53
- 0.4
- 0.3
- 0.5
- 0.6
- 0.4 - 0.5 - 0.7 - 0.1
- 0.8
- 0.9 0.1
- 1.0
0.2
- 0.4
- 0.5
- 0.3
- 0.3
- 0.4
- 0.4
- 0.5
- 0.5
- 0.8
- 0.8
- 1.3 1.1 - 1.2
0.4
0.3
0.3
0.2
(a) 0° Wind
- 0.3
- 0.4
- 0.5
- 0.8
- 0.6 - 0.6
- 0.4
- 1.4
0.5
- 0.6
0.4
- 0.6
- 0.6 - 0.7
- 0.8 - 0.9 - 1.0 - 1.4
- 0.3
- 0.1
0.1
0.2
0.4
(b) 45° Wind
Mean pressure distributions
on a low-rise building model
Conical vortices generated
from corner eaves
54
Instantaneous pressure distribution
on a high-rise building model
Shimizu Corp.
- 0.8- 0.9
- 0.7 - 0.8
- 0.9
- 0.8 - 0.8- 0.7
- 0.3
- 1.2
- 0.7
- 0.7
- 0.7
0.8
- 0.8
0.7
- 0.6
0.8
- 0.6
- 0.6 - 0.5
0.7
- 0.5
- 0.8
0.6
- 1.0
0.6
- 0.8 - 0.6 - 0.6 - 0.8
- 0.6
0.5
0.5
- 0.6
0.4 0.4
- 0.5
0°
(a) 0° Wind
0°
- 0.4
- 0.5
- 0.90.5 15
0.3 °
0.4
- 0.5
15
°
(b) Glancing Wind
Mean pressure distributions
on a high-rise building model
55
SP
180º
180º
Surface flow pattern near the tip of
3D circular cylinder (Oil film technique, view
obliquely from behind, Lawson, 1980)
D
Distance from tip z/D
z
H
Drag Coefficient CD
Drag Coefficient CD
(a) PostPost-supercritical Regime (b) SubSub-critical Regime
Re = 2.7∼5.4×106
Re =1.33×104
Vertical distributions of local mean drag
coefficients of 3D circular cylinders
56
Mean Pressure Coefficient Cp
Supercritical
SubSub-critical
3.2.18
Potential Flow
Mean Pressure Coefficient Cp
Mean pressure distribution
on a circular cylinder (Sach, 1972)
Surface Wind
Roughness Speed
Smooth 10 m/s
1mmφ
5 m/s
1mmφ
10 m/s
10 m/s
2mmφ
FullFull-scale 12–
12–40 m/s
1mmφ bar
Pressure
tap
2mmφ bar
Pressure
tap
Mean pressure distributions on a fullscale chimney and wind tunnel models
with different surface roughnesses
57