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Optimization of tree canopy model for CFD Optimization of tree canopy model for CFD application toapplication to
local area wind energy predictionlocal area wind energy prediction
Akashi MochidaAkashi MochidaLBEE ( Laboratory of Building Environment Engineering )LBEE ( Laboratory of Building Environment Engineering )
Tohoku University, JapanTohoku University, JapanEmail : [email protected]
T. Iwata, A. Kimura, H. Yoshino, and S. MurakamiT. Iwata, A. Kimura, H. Yoshino, and S. Murakami
NATO ASI, May 6
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Factors affecting the flow around a hilly terrain
Separation Separation
Circulation
Circulation
Re-circulation
Convex Convex
Concave Concave
Roughness Recirculation
Sea Surface
Inlet flow
Wake of windmill
CollisionAcceleration way
・ Existence of trees changes wind speed at a windmill height considerably. ・ So, the effects of trees should be considered carefully for the selection of a site for wind power plant
The canopy model for reproducing the aerodynamic effects of trees was optimized for the use of local area wind energy prediction.
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In order to reproduce the aerodynamic effects of trees, i.e. 1) decrease of wind velocity 2) increase of turbulence,extra terms are added to model equations.
Here, a revised k- model is used as a base.
Modelling of aerodynamic effects of trees
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Formulations of extra terms for expressing Formulations of extra terms for expressing the aerodynamic effects of tree canopythe aerodynamic effects of tree canopy
・ was given by Willson and Shaw (1977),
by applying the space average to the
basic equations for DSM ( Differential
Stress Model ),
・ the expressions for Mellor-Yamada level
2.5 model was proposed by Yamada(1982)
・ the expressions for k – model was
proposed by Hiraoka (1989 in Japanese,
1993 in English).
・ several revisions (1990’s ~)
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Modelling of aerodynamic effects of tree canopy
k – model with tree canopy model decreases in velocity increases in turbulence increases in dissipation
0
i
i
x
u
ii
j
j
it
jij
jii Fx
u
x
u
xk
p
xx
uu
t
u
3
2
kkj
t
jj
jFP
x
k
xx
ku
t
k
FCPCkxxx
u
t kj
t
jj
j
21
j
i
i
j
j
itk x
u
x
u
x
uP
[Continuity equation]
[k transport equation]
[ transport equation]
[Average equation]
Fi
Fk ii Fu
F kp FCk
2
jif uuaC
: fraction of the area covered with trees
Cf: drag coefficient for canopy
a : leaf surface area density
Cp1: model coefficient for F
- Fi: extra term added to the momentum equation
+ Fk: extra term added to the transport equation of k
+ F: extra term added to the transport equation of
aa
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Extra terms for incorporating aerodynamic effects of tree canopy
a : leaf surface area density
Cf : drag coefficient for canopy
: fraction of the area covered with trees
CpCp : model coefficients in turbulence modeling
Fi Fk F
typeA
typeB
typeC
2 jif uuaC
ii Fu
24 jfii uaCFu
L
kC
kp
23
1
iip FuCk
1
2
21 4 jfpiip uaCCFuCk
Hiraoka : Cp1=2.5
Uno : Cp1=1.5
Yamada : Cp1=1.0
Green :Cp1=Cp=1.5
Liu : Cp1=1.5 , Cp2=0.6
ii Fu Svensson : Cp1=1.95
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Difference in Fk (types A & B VS type C)
In types A and B, Fk=<ui>Fi ( < > : ensemble-average )
So-called “wake production term”
this form can be analytically derived (Hiraoka)
Fi Fk F
typeA
typeB
typeC
2 jif uuaC
ii Fu
24 jfii uaCFu
L
kC
kp
23
1
iip FuCk
1
2
21 4 jfpiip uaCCFuCk
Hiraoka : Cp1=2.5
Uno : Cp1=1.5
Yamada : Cp1=1.0
Green :Cp1=Cp=1.5
Liu : Cp1=1.5 , Cp2=0.6
ii Fu Svensson : Cp1=1.95
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Difference in Fk (type A & B VS type C)
24 jf uaC
In types C, Fk = Production(Pk) - Dissipation(Dk) Pk: production of k within canopy (=<ui >Fi) Dk: a sink term to express the turbulence energy loss within canopy (Green) (Dk= )This terms also appears in F
Fi Fk F
typeA
typeB
typeC
2 jif uuaC
ii Fu
24 jfii uaCFu
L
kC
kp
23
1
iip FuCk
1
2
21 4 jfpiip uaCCFuCk
Hiraoka : Cp1=2.5
Uno : Cp1=1.5
Yamada : Cp1=1.0
Green :Cp1=Cp=1.5
Liu : Cp1=1.5 , Cp2=0.6
ii Fu Svensson : Cp1=1.95
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Difference in F (type A VS type B & C)In type A, length scale within canopy L=1/a (a : leaf surface area density )
F ∝
(here = k/ )
L
k 23
1
Fi Fk F
typeA
typeB
typeC
2 jif uuaC
ii Fu
24 jfii uaCFu
L
kC
kp
23
1
iip FuCk
1
2
21 4 jfpiip uaCCFuCk
Hiraoka : Cp1=2.5
Uno : Cp1=1.5
Yamada : Cp1=1.0
Green :Cp1=Cp=1.5
Liu : Cp1=1.5 , Cp2=0.6
ii Fu Svensson : Cp1=1.95
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In type B, F (here ∝ = k/ )
In type C, F= Production(P) – Dissipation(D)
P , D∝ ∝
Difference in F (type A VS type B & C)
kF1
kP1
kD1
Fi Fk F
typeA
typeB
typeC
2 jif uuaC
ii Fu
24 jfii uaCFu
L
kC
kp
23
1
iip FuCk
1
2
21 4 jfpiip uaCCFuCk
Hiraoka : Cp1=2.5
Uno : Cp1=1.5
Yamada : Cp1=1.0
Green :Cp1=Cp=1.5
Liu : Cp1=1.5 , Cp2=0.6
ii Fu Svensson : Cp1=1.95
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24 jfii uaCFu
CpCp
:
type B type C
Fi
Fk
F
2
jif uuaC
ii Fu
iip FuCk
1
model coefficients in turbulence modeling, which should be optimized, for prescribing the time scale of the process of energy dissipation in canopy layer
parameters to be determined according to the real conditions of trees
, a, Cf :
Extra terms Fi, Fk, F
2
21 4 jfpiip uaCCFuCk
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1) revision of modelling of eddy viscosityReynolds stress :
Modifying eddy viscosity
A mixed time scale, m , proposed by Nagano et al.
iji
j
j
itji k
3
2
x
u
x
uuu
mt kC
Revised k- model adopted here -mixed time scale model-
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A harmonic balance of , i.e. an
d
s (timescale of mean velocity gradient)
s
s
m
C
1211
2) Introduction of the mixed time scale (Nagano et al.)
Cs=0.4
kk
Mixed time scale
22s
2
S
ijij2
i
j
j
iij x
u
x
u
21
ijij SSS 2
i
j
j
iij x
u
x
uS
21
s , time scale of mean velocity gradient
k
, turbulence time scale
Revised k- model based on mixed time scale concept
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Results of CFD computations Results of CFD computations with tree canopy modelswith tree canopy models
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16model tree
Comparison between types A and B・ Results of wind velocity behind a model tree were
compared.
・ Wind tunnel experiment was carried out by Ohashi
・ Exact value of leaf area density “a” of the model
tree was given
30cm
30cm
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Case No. type Cp
1-1 typeA 1.0
1-2 1.5
1-3 4.0
2-1 typeB 1.0
2-2 1.5
2-3 2.0
2-4 3.0
2-5 4.0
typeA L
kC
k p
23
1
Leaf surface area density
a=17.98[m2/m3]
Drag coefficient
Cf =0.8[-]
Expressions for F
typeB kp FCk 1
2
jifi uuaCF
(L=1/ a)
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Comparison between types A and BDistribution of mean wind velocity (at 0.6m height)
0
1
2
3
- 0.8 - 0.6 - 0.4 - 0.2 0 0.2 0.4 0.6 0.8 1
[m/s
]平
均風
速
実測値case1- 1 (TypeA,Cpε =1.0)case1- 2 (TypeA,Cpε =1.5)case1- 3 (TypeA,Cpε =4.0)
Tree modelexperiment
p1
p1
p1
0
1
2
3
- 0.8 - 0.6 - 0.4 - 0.2 0 0.2 0.4 0.6 0.8 1
測定位置x 1 [m]
[m
/s]
平均
風速
実測値case2- 1 (TypeB,Cpε =1.0)case2- 2 (TypeB,Cpε =1.5)case2- 3 (TypeB,Cpε =2.0)case2- 4 (TypeB,Cpε =3.0)case2- 5 (TypeB,Cpε =4.0)
Tree model experimentp1
p1
p1
p1
p1
Mea
n w
ind
velo
city
[m
/s]
Mea
n w
ind
velo
city
[m
/s]
0.6m
TypeA TypeBx1 [m]x1 [m]
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Distribution of mean wind velocity (at 0.8m height)
0.8m
2
3
4
- 0.8 - 0.6 - 0.4 - 0.2 0 0.2 0.4 0.6 0.8 1
[m
/s]
平均
風速
実測値case1- 1 (TypeA,Cpε =1.0)case1- 2 (TypeA,Cpε =1.5)case1- 3 (TypeA,Cpε =4.0)
p1
p1
p1
2
3
4
- 0.8 - 0.6 - 0.4 - 0.2 0 0.2 0.4 0.6 0.8 1
測定位置x 1 [m]
[m
/s]
平均
風速
実測値case2- 1 (TypeB,Cpε =1.0)case2- 2 (TypeB,Cpε =1.5)case2- 3 (TypeB,Cpε =2.0)case2- 4 (TypeB,Cpε =3.0)case2- 5 (TypeB,Cpε =4.0)
p1
p1
p1
p1
p1
TypeA TypeB
Mea
n w
ind
velo
city
[m
/s]
Mea
n w
ind
velo
city
[m
/s]
x1 [m]
Cp =4.0
Tree model Tree modelexperiment experiment
Cp =1.0
Cp =1.5
x1 [m]
Cp =1.0
・ Effect of difference in Cp1 value is large compared to the difference of model type (types A or B)・ Type B model corresponds well with experiment in the range Cp1=1.5 ~ 2.0.・ Type B was selected in this study ・ More detailed optimizations for Cp1 were done
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Fi
Fk
F
Optimization of model coefficient Cpfor typeB
Tsuijimatu ( Rectangular-cutted-pine-trees as wind-break )
2
jif uuaC
ii Fu
kp FCk 1
・ By comparing CFD results with measurements, Cp was optimized.
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x1
Hb=9[m]
Ub=5.6[m/s]
U(z)=Ub(z/Hb)0.22
H=7m 5.8m
1.2m
2m
0.7m
1.2m
0
0
x3
x1
Hb=9[m]
Ub=5.6[m/s]
U(z)=Ub(z/Hb)0.22
H=7m 5.8m
1.2m
2m
0.7m
1.2m
0
0
x3
Computational domain : 100m(x1:streamwise)×100m (x3:vertical)
CL
2D computation is carried out at the central section
Comparison of flow behind pine trees
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(x/H=5)(x1/H=4)(x1/H=3)(x1/H=2)(x1/H=1)
(x/H=5)(x/H=4)(x/H=3)(x/H=2)(x/H=1)
(x1/H=5)(x1/H=4)(x1/H=3)(x1/H=2)(x1/H=1)
(x/H=5)(x/H=4)(x/H=3)(x/H=2)(x/H=1)
(x/H=5)(x1/H=4)(x1/H=3)(x1/H=2)(x1/H=1)(x1/H=5)(x1/H=4)(x1/H=3)(x1/H=2)(x1/H=1)
Comparison of vertical velocity profiles behind tree
: measurement : CFD with type B model
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
(1) Cp=1.5
(2) Cp=1.6
(3) Cp=1.7
(4) Cp=1.8
(5) Cp=1.9
(6) Cp=2.0
a=1.17[m2/m3] Cf =0.8[-]
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Type B model(Cp=1.8)measurement
Comparison of vertical velocity profiles behind tree (Cp=1.8)
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
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(1) Cp=1.5
(2) Cp=1.6
(3) Cp=1.7
(4) Cp=1.8
(5) Cp=1.9
(6) Cp=2.0
(x/H=5)(x1/H=4)(x1/H=3)(x1/H=2)(x1/H=1)
(x/H=5)(x/H=4)(x/H=3)(x/H=2)(x/H=1)
(x1/H=5)(x1/H=4)(x1/H=3)(x1/H=2)(x1/H=1)
(x/H=5)(x/H=4)(x/H=3)(x/H=2)(x/H=1)
(x/H=5)(x1/H=4)(x1/H=3)(x1/H=2)(x1/H=1)(x1/H=5)(x1/H=4)(x1/H=3)(x1/H=2)(x1/H=1)
Comparison of vertical profiles of k behind tree
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
: measurement : CFD with type B modela=1.17[m2/m3] Cf =0.8[-]
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0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
Comparison of vertical profiles of k behind tree (Cp=1.8)
Type B model(Cp =1.8)measurement
k is underestimated in this area by type B model
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Performance of Type C model in which the energy loss in canopy is also considered
24 jf uaC
In types C, Fk = Production(Pk) - Dissipation(Dk) Pk: production of k within canopy (=<ui >Fi) Dk: a sink term to express the turbulence energy loss within canopy (Green) (Dk= )
Similar term also appears in F
Fi Fk F
typeA
typeB
typeC
2 jif uuaC
ii Fu
24 jfii uaCFu
L
kC
kp
23
1
iip FuCk
1
2
21 4 jfpiip uaCCFuCk
Hiraoka : Cp1=2.5
Uno : Cp1=1.5
Yamada : Cp1=1.0
Green :Cp1=Cp=1.5
Liu : Cp1=1.5 , Cp2=0.6
ii Fu Svensson : Cp1=1.95
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model F ε
Type B
Optimization of model coefficient Cpfor typeC
Green : Cp1= Cp2=1.5
Liu et al. : Cp1=1.5, Cp2= 0.6
kuaCCFuC
k jfpiip
2
21 4
typeC
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: measurement : CFD with type C model
(x1/H=5)(x1/H=4)(x1/H=3)(x1/H=2)(x1/H=1)
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
(x1/H=5)(x1/H=4)(x1/H=3)(x1/H=2)(x1/H=1)
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
(x1/H=5)(x1/H=4)(x1/H=3)(x1/H=2)(x1/H=1)
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
(x1/H=5)(x1/H=4)(x1/H=3)(x1/H=2)(x1/H=1)
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
0
6
12
0 0.2 0.4k/ UH
2
Hei
ght[
m]
Green : Cp1= Cp2=1.5
Liu et al. : Cp1=1.5, Cp2= 0.6
vertical profiles of k behind tree
vertical profiles of k behind tree
vertical velocity profiles behind tree
vertical velocity profiles behind tree
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29
Computed Casesmodel F ε
Type B
kuaCCFuC
k jfpiip
2
21 4
typeC
Cp1=1.8( optimized value for type B )
case type Cp1 Cp2C-1 0.6C-2 0.7C-3 0.8C-4 0.9C-5 1C-6 1.1C-7 1.2C-8 1.3C-9 1.4
C-10 1.5C-11 1.6C-12 1.7C-13 1.8
type C 1.8
Optimization of model coefficient Cpfor typeC
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Comparison of numerically predicted drag coefficient CD
Pf Pb
tree
treeD
dzzV
dzzP
C2
21
)(
V(z)bf PPP
■Pressure difference ⊿P
■Drag coefficient of tree CD
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1.30
1.35
1.40
1.45
1.50
0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8
model F ε
Type B
kuaCCFuC
k jfipiip
2
21 4
Cp2
C
D
Comparison of numerically predicted drag coefficient CD ( Cp1=1.8 )
typeC
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0
0. 020. 04
0. 06
0. 080. 1
0. 12
0. 14
0. 160. 18
0. 2
- 2 - 1 0 1 2 3 4 5
0
0. 2
0. 4
0. 6
0. 8
1
1. 2
1. 4
1. 6
- 2 - 1 0 1 2 3 4 5
experiment
Cp2 =1.6Cp2 =1.4Cp2 =0.6
Cp2 =1.8
tree
ε/ (
UH
3 /H
)k/
UH
2
Cp2 =0.6
Cpe2 =1.4
X1/H
X1/H
4.5 m
Comparison of streamwise profiles of k & around tree ( type C, Cp1=1.8 )
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0
6
12
0 0.025 0.05/ (UH
3/ H)
[m]
高さ
0
6
12
0 0.025 0.05/ (UH
3/ H)
[m]
高さ
0
6
12
0 0.025 0.05/ (UH
3/ H)
[m]
高さ
0
6
12
0 0.025 0.05/ (UH
3/ H)[m
]高
さ
0
6
12
0 0.025 0.05/ (UH
3/ H)
[m]
高さ
(x1/H=1) (x1/H=2) (x1/H=3) (x1/H=4) (x1/H=5)
Cp2=1.6Cp2=1.4 Cp2=1.8Cp2=0.6
Comparison of vertical profiles of behind tree ( type C, Cp1=1.8 )
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0
6
12
0 0.1 0.2k/ UH
2
Hei
ght[
m]
0
6
12
0 0.1 0.2k/ UH
2
Hei
ght[
m]
0
6
12
0 0.1 0.2k/ UH
2
Hei
ght[
m]
0
6
12
0 0.1 0.2k/ UH
2
Hei
ght[
m]
0
6
12
0 0.1 0.2k/ UH
2
Hei
ght[
m]
(x1/H=1) (x1/H=2) (x1/H=3) (x1/H=4) (x1/H=5)
Comparison of vertical profiles of k behind tree ( type C, Cp1=1.8 )
measurement Cp2=1.6Cp2=1.4 Cp2=1.8Cp2=0.6
Result with CResult with Cpp22=1.4 shows good =1.4 shows good agreement.agreement.
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0
6
12
0 0.7 1.4U/ UH
[m]
高さ
0
6
12
0 0.7 1.4U/ UH
[m]
高さ
0
6
12
0 0.7 1.4U/ UH
[m]
高さ
0
6
12
0 0.7 1.4U/ UH
[m]
高さ
0
6
12
0 0.7 1.4U/ UH
[m]
高さ
(x1/H=1) (x1/H=2) (x1/H=3) (x1/H=4) (x1/H=5)
measurement Cp2=1.6Cp2=1.4 Cp2=1.8Cp2=0.6
Comparison of vertical velocity profiles behind tree ( type C, Cp1=1.8 )
Result with CResult with Cpp22=1.4 shows good =1.4 shows good agreement.agreement.
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within tree canopy behind tree
decrease
k decrease
increase
k decrease
Mean wind velocity decrease
When Cp2 is decreased ・・・
kuaCCFuC
kF jfpiip
2
21 4
Effects of Cp
Cp2=1.4 was selected under the condition of Cp1=1.8..
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Comparison of vertical velocity profiles behind tree
Comparison of vertical profiles of k behind tree
0
6
12
0 0.1 0.2k/ UH
2
Hei
ght[
m]
0
6
12
0 0.1 0.2k/ UH
2
Hei
ght[
m]
0
6
12
0 0.1 0.2k/ UH
2
Hei
ght[
m]
0
6
12
0 0.1 0.2k/ UH
2
Hei
ght[
m]
0
6
12
0 0.1 0.2k/ UH
2
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
0
6
12
0 0.7 1.4U/ UH
Hei
ght[
m]
type C model ( Cp1 =1.8 , Cp2 =1.4 )
experiment type B model ( Cp1 =1.8 )
(x1/H=5)(x1/H=4)(x1/H=3)(x1/H=2)(x1/H=1)
(x1/H=5)(x1/H=4)(x1/H=3)(x1/H=2)(x1/H=1)
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39
Topographic effect on wind (slow down)
Collision to ground surface
Effect of surface roughness by plants
Topographic effect on wind (speed up)
Prediction of local area wind distributionPrediction of local area wind distribution
The tree canopy model ( type B ) optimized here was incorporated into “Local Area Wind Energy Prediction System (“Local Area Wind Energy Prediction System (LAWEPS)”LAWEPS)”
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40
LAWEPS : Local Area Wind Energy Prediction System Developed by NEDO through the Four-Year Project (1999-2003) New Energy and Industrial Technology Development Organization of Japan
( Project Leader: S.Murakami Members: Y.Nagano, S.Kato, A.Mochida, M.Nakanishi, etc.)
The Goal of the Project: To Develop a wind prediction Model which is Applicable to Complex Terrain including Steep Slopes, Able to Predict the Annual Mean Wind Speed with the Prediction Error of less than10%.
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41
2nd Domain
1st Domain
Five-stage Grid Nesting ( One-way)
3rd Domain
3rd Domain 4th Domain5th Domain
5th Domain Wind Turbines
500km100km
10km
10km
1~2km
0.5~1km
5km
10km
50km
Outline of LAWEPS
tree canopy model is incorporated into the model for 5th Domain
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Table : Five sub-domains in LAWEPS
Domains Horizontal Area Horizontal Resolution
1 500×500 km 5 km 2 100×100 km 1 km 3 50×50 km 500 m 4 10×10 km 100 m 5 1×1 km 10 m
Domains 1-3: Meso-scale Meteorological Model( revised Mellor-Yamada Level 2.5 )
Domains 4-5: Engineering Model (revised k- (SΩ) ) ( Domain 5: tree canopy model is coupled )
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43
Long term measurements of wind velocities at Shionomisaki Peninsula of Wakayama Prefecture, Japan.
Field observation
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44
(a)
(b)
Testing Area: Shionomisaki Peninsula, Japan
1st-3rd Domain
1st
2nd
3rd
9km
11km
A B
5th Domain
4th Domain
A & B are Obs. SitesDoppler Sodar Observations are done at site B
N
W E
S
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45
Leaf surface area density a is given from a = LAI/H LAI : Leaf Area Index (here assumed to be 5)
H : tree height (given from the aircraft measurements) Cf = 0.2 (typical value for plant community ( stands of tree )
Cp = 1.8
Fi
Fk
F
2
jif uuaC
ii Fu
kp FCk 1
H
dz z a LAI0)) ( (
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2001.12.15.15JST (Site A)
0
50
100
150
200
250
300
0 10 20 30 40wind speed[m/s]
Alt
itud
e (m
)
3rd domain4th domain5th domainObservation
2001.12.15.15JST (site B)
0
50
100
150
200
0 5 10 15 20 25Wind Speed (m/s)
Alti
tude
(m)
5th domain
Observation
2000.10.28.12JST (site A)
0
50
100
150
200
0 5 10 15 20 25Wind Speed (m/s)
Alti
tude
(m
) 5th domain
Observation
Comparison of the 1st-5th Full Nesting Calculation with the Ground Observations
2001 Dec. 15th 15JST 2000 Oct 28th 12JST 2001 Dec. 15th 15Jst
Site A Site A Site B
5th Domain ModelObservation
Vertical distributions of the calculated wind speed are compared with the tower observations.
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Results of the Annual Mean Wind Calculation
Annual Mean Wind Speed (Year of 2000)
Observation LAWEPS Error(%)
Site A 5.31m/s 5.51m/s +3.77%
Site B 4.31m/s 4.17m/s -3.27%
Frequency of the Occurrence of Wind Speed
site A
05
1015202530
0 5 10 15 20 25 30Wind speed(m/s)
Fre
qu
ency
(%)
5th domainObservation
site B
05
1015202530
0 5 10 15 20 25 30Wind speed(m/s)
Fre
qu
ency
(%)
5th domainObservation
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48
Annual Mean Wind Speed Map 30m above the Ground
0
1
2
3
4
5
6
7
8
10 20 30 40 50 60 70 80 90 100
10
20
30
40
50
60
70
80
90
100
0
1
2
3
4
5
6
7
8
10 20 30 40 50 60 70 80 90 100
10
20
30
40
50
60
70
80
90
100
4th Domain
5th Domain(a) 5th Domain(b)
0~8m/s
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49
Conclusions ( tentative )
1) Type B model predicted well the velocity distributions behind tree canopies in the range Cp
1=1.5 ~ 2.0 .
2) The value of 1.8 was selected for Cp1 in LAWEPS. The vertical velocity profiles above the real complex terrain predicted by LAWEPS with type B model showed close agreement with measurements.
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50
Conclusions
3) But, turbulence energy k tended to be underpredicted in the wake of trees by type B.
4) The model that considers the effect of energy loss within canopy (Type C) was also tested.
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51
Conclusions
5) Results with the combination of Cp1=1.8 and Cp2=1.4 for type C showed fairly good agreement with measurement in the case of flow behind pine trees.
6) Further systematic optimization is necessary for reproducing the turbulence quantities more accurately.
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APPENDIX
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Prediction of thermal effects Prediction of thermal effects of planted treesof planted trees
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Following effects are considered :
Model for tree canopy
decrease of velocity and increase of turbulence
generation of water vapor from leaf
shading effect on long-wave radiation
shading effect on short-wave (solar) radiation
Tree crown (樹冠)
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Shading effects of solar and long-wave radiations
The present model is based on the following assumptions:
1. Only the effect of tree crown is modelled. The effects of stem and branches are assumed to be negligibly small.
2. The ratio of absorbed radiations to the total incident radiation on the tree crown is given by the function
321 x,x,xakexp1
Tree crown ・Leaf area density a [m2/m3] ・Absorption coefficient k’ [-]
l [m] ℓ
(1) Distance through the tree crown ℓ [m]
(2) Leaf area density a [m2/m3]
(3) Absorption coefficient k’ [-] (here, k’=0.6)Tree crown= 樹冠
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Generation (transpiration) of water vapor and heat balance at leaf surface・ The heat balance equation at leaves that compose the tree
crown
(1)
SP : Absorbed solar radiation [W]
RDP : Absorbed long-wave radiation [W]
HP : Sensible heat [W]
LEP : Latent heat [W]
SP
HP
LEP RDP
・ Using Eqs. (1), (2) and (3), leaf surface temperature TP is obtained. HP, LEP and TP are used as boundary conditions for CFD computation.
PaPcPP TTAH
sPaPPWPP ffLALE
0LEHRS PPDPP
(2)
(3)
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Coupled simulation of radiation, conduction and convection
Prediction of thermal effects of trees planted on a main street in Sendai city
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25m
1.7m
10m
25m 9m 15m 15m 9m 25m
2.5m
N
E
S
W
Higashi-Nibancho Street in Sendai City (東二番丁通,仙台)
(1) Plan
(2) Section
building
sidewalkroadway
tree
median strip
tree
buildingroadwaysidewalk
0.3m
center
Prediction of thermal effects of trees planted on a main street in Sendai city
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Computed casesN
S
W E
(1) Case 1 (2) Case 2
(3) Case 3
Condition of Tree Planting
Case 1 Not Planted
Case 2 Present Situation
Case 3 Densely Planted
N
S
W E
N
S
W ETable Computed cases
Wind Wind
Wind
building
sidewalk
roadway
tree
median strip
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Physical processes to be considered and model equations to be solved
1 Momentum transfer by wind and turbulence diffusion
2 Heat transfer by wind and turbulence3 Contaminant diffusion by wind and turbulence4 Moisture transfer by wind and turbulence5 Radiative heat transfer in outdoor space6 Heat conduction to underground and inside of bu
ilding7 Heat energy balance at urban surface (ground su
rface and building surface )→all processes listed here are considered
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[3] Calculation of SET* for evaluating the themal environment based on prediction results
[2] Coupled simulation of convection (CFD) and radiation Radiation
calculation ・ Surface temperature ・ Convective Heat ・ Latent Heat
CFD simulation for convection
Feedback
[1] Input Condition
Input data 2 Geometry of boundary condition ・Building coverage ・Floor area ratio ・Floor height, etc.
Input data 1 Solar radiation data ・solar location ・judgment of direct sunshine or
shading by building etc.
Input data 3 Boundary conditions of ground surface, building wall ・Albedo ・Soil moisture ・Heat conductivity, etc.
①Wind velocity ②Temperature ③Radiation ④Humidity ⑤Clothing ⑥Metabolism
・MRT ・Operative temperature
assumed
SET* Thermal comfort index
Flowchart for assessing outdoor human comfort
based on CFD
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All heat balance components to calculate the surface temperature
Si:Solar radiation[W]Ri:Longwave radiation[W]Hi:Sensible heat flux[W]Ci:Heat gain by heat conducttion[W]LE i:Latent heat flux[W]
Monte-Carlo simulation
LE i LE i
Ci Ci Ci
Ci
Ci
HiRi
Ri Ri
Si
Si
LE i
Ci
CiCi
Ci Hi
Hi
Hi
Si
LE i
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(1) Case 1(Not Planted)
(2) Case 2(Present Situation )
(3) Case 3(Densely Planted)
N
S
W E
N
S
W E
Wind
N
S
W E
N
S
W E
Wind
N
S
W E
N
S
W E
Wind
Distribution of surface temperature( August 4, 12:00 )
[C]
N
E
S
W
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[3] Calculation of SET* for evaluating the themal environment based on prediction results
[2] Coupled simulation of convection (CFD) and radiation Radiation
calculation ・ Surface
temperature ・ Convective Heat ・ Latent Heat
CFD simulation for convection
Feedback
[1] Input Data
Input data 2 Geometry of boundary condition ・Building coverage ・Floor area ratio ・Floor height, etc.
Input data 1 Meteorological data ・ Solar location ・ Air temperature and
humidity in atmosphere.
Input data 3 Boundary conditions of ground surface, building wall ・Albedo ・Soil moisture ・Heat conductivity, etc.
①Wind velocity ②Temperature ③Radiation (MRT) ④Humidity ⑤Clothing ⑥Metabolism
・Operative temperature
assumed
SET* Thermal comfort index
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(1) Case 1(Not Planted)
(2) Case 2(Present Situation )
(3) Case 3(Densely Planted)
N
S
W E
N
S
W E
Wind
N
S
W E
N
S
W E
Wind
N
S
W E
N
S
W E
Wind
Horizontal Distributions of Velocity Vectors at the Height of 1.5m ( August 4, 13:00 )
A A’
N
E
S
W
Wind Velocity is decreased by trees
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(1) Case 1(Not Planted)
(2) Case 2(Present Situation )
(3) Case 3(Densely Planted)
N
S
W E
N
S
W E
Wind
N
S
W E
N
S
W E
Wind
N
S
W E
N
S
W E
Wind
Vertical Distribution of Wind Velocity Vectors at A-A’ sections ( August 4,
13:00 )
Case 3
Case 1 Case 2
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air temperature
(1) Case 1 (Not Planted)
(2) Case 2 (Present Situation )
(1) Case 1 (Not Planted)
(2) Case 2 (Present Situation )
Wind Velocity Vectors
[C]29.0 32.030.5
Vertical Distribution ( August 4, 13:00 )
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Evaluation of Standard Effective Temperature (SET*)
・ Velocity
・ Temperature
・ Humidity
・ Mean Radiative
Temperature (MRT)
Index for thermal comfort
( SET*)
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N
E
S
W
25.0 35.030.0 [ ]℃
(1) Case 1(Not Planted)
(2) Case 2(Present Situation )
(3) Case 3(Densely Planted)
N
S
W E
N
S
W E
Wind
N
S
W E
N
S
W E
Wind
N
S
W E
N
S
W E
Wind
Horizontal distribution of SET* (Standard Effective Temperature) at the height of 1.5m
( August 4, 13:00 )
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(Case 2) - (Case 1)(Present Situation ) - (Not Planted)
N
E
S
W
[ ]℃-5.0 5.00.0
Difference of SET* at the height of 1.5m (August 4, 13:00)
N
S
W E
N
S
W E
Wind
N
S
W E
N
S
W E
Wind
① SET* is decreased by trees
② But SET* is increased by trees in these areas
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(1) Case 1(Not Planted)
(2) Case 2(Present Situation )
(3) Case 3(Densely Planted)
N
S
W E
N
S
W E
Wind
N
S
W E
N
S
W E
Wind
N
S
W E
N
S
W E
Wind
Horizontal Distributions of Velocity Vectors at the Height of 1.5m ( August 4, 13:00 ) N
E
S
W
Wind Velocity is decreased by trees
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Change of SET* by greening
•The effect of wind velocity on the outdoor thermal environment is significantly large.
•Overly dense arrangement of planted trees may not necessarily improve the outdoor environment.
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Gas diffusion within street canyon
Median Strip
Center
tree
0.3m
2.5m
25m 9m 15m 15m 9m 25m
Building
Sidewalk
Roadway
• Gas is released from all roadway area (red area) at height of 0.15m
Condition of Tree Planting
Case 1 Not Planted Case 2 Present Situation Case 3 Densely Planted
Computed cases
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(1) Case 1(Not Planted)
(2) Case 2(Present Situation )
(3) Case 3(Densely Planted)
N
S
W E
N
S
W E
Wind
N
S
W E
N
S
W E
Wind
N
S
W E
N
S
W E
Wind
Vertical Distribution of Wind VelocityUsing these velocities, contaminant diffusion is predicted
Case 3
Case 1 Case 2
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(2) Case 2 (Present Situation )
(3) Case 3 (Densely Planted)
歩道歩道 歩道歩道
歩道歩道
0.0 3.01.5
Average value in CV: 0.84 Average value in CV : 0.74
Average value in CV : 0.76
(1) Case 1(Not Planted)Sidewalk Sidewalk Sidewalk Sidewalk
Sidewalk Sidewalk
CV CV
CV
Vertical distribution of gas concentration
W E
Gas is diffused to upper region in Cases 2 and 3
-> In case 1, Gas is convected to sidewalk area
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Averaged values in CV and PS
歩道歩道Sidewalk Sidewalk
CV
PSPS : Pedestrian Space (from 0.3m to 1.8m height on sidewalk)
• Gas is not convected to sidewalk area so much in Case2 and Case3 by the effects of trees on flowfield
Case 1 (Not planted)
Case 2 (Present situation)
Case 3 (Densely planted)
Averaged gas concentration in CV [-]
0.826 0.732 0.750
Averaged gas concentration in PS [-]
4.452 1.233 1.021
Normalized values