Transcript Optimization of tree canopy model for CFD application to

NATO ASI, May 6
Optimization of tree canopy model for
CFD application to
local area wind energy prediction
Akashi Mochida
LBEE ( Laboratory of Building Environment Engineering )
Tohoku University, Japan
Email : [email protected]
T. Iwata, A. Kimura, H. Yoshino, and S. Murakami
1
Factors affecting the flow around a hilly terrain
Inlet flow
Circulation
Separation
Acceleration way
Sea Surface
Wake of windmill
Separation
Recirculation Roughness
Convex
Convex
Collision
Concave
Concave
Circulation
Re-circulation
・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.
2
Modelling of aerodynamic effects
of trees
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-e model is used as a base.
4
Formulations of extra terms for expressing
the 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 – e model was
proposed by Hiraoka (1989 in Japanese,
1993 in English).
・several revisions (1990’s～）
5
Modelling of aerodynamic effects of tree canopy
k – e model with tree canopy model
[Continuity equation]
 ui
xi
 decreases in velocity
 increases in turbulence
 increases in dissipation
0
[Average equation]
 ui
t

 ui u j
x j


xi
[k transport equation]
 p 2  

 k
  3  x j


 
   ui  u j

 t 

x
xi

  j

k  u j k



t
x j
x j
  k 
 t
  P e  F
k
  x j  k


[e transport equation]


  Fi

a
e  u j e



t
x j
x j
  e  e
 t
  C P  C e   F
2e
e
  x j  k 1e k


 u
 u j   ui

i
Pk   t 

xi  x j
 x j


Fi
Fk
Fe
C f a ui
uj
2
u i Fi
e×
C p e1 Fk
k
: fraction of the area covered with trees
－Fi: extra term added to the momentum equation
a : leaf surface area density
+ Fk: extra term added to the transport equation of k
Cf: drag coefficient for canopy
+ Fe: extra term added to the transport equation of e
Cpe1: model coefficient for Fe
6
Extra terms for incorporating
aerodynamic effects of tree canopy
：fraction of the area covered
with trees
Cf：drag coefficient for canopy
Cpe1, Cpe2 ： model
coefficients in turbulence
modeling
a： leaf surface area density
Fi
Fk
typeC
e
 ui  Fi
typeA
typeB C
Fe
f
a  ui   u j 
2
k
e
 ui  Fi
 ui  Fi  4C f a  u j  2
k
e
3
k 2
L
Hiraoka：
Cpe1=2.5
Yamada：
Cpe1=1.0
C pe 1  ui  Fi
Uno：Cpe1=1.5
 C pe 1
 4C a  u 2 


C

u

F

C


p
e
1
i
i
p
e
2
f
j

k


Svensson：
Cpe1=1.95
Green：
Cpe1=Cpe2=1.5
Liu：Cpe1=1.5，
Cpe2=0.6
7
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
typeC
e
 ui  Fi
typeA
typeB C
Fe
Fk
f
a  ui   u j 
2
k
e
 ui  Fi
 ui  Fi  4C f a  u j  2
k
e
3
k 2
L
Hiraoka：
Cpe1=2.5
Yamada：
Cpe1=1.0
C pe 1  ui  Fi
Uno：Cpe1=1.5
 C pe 1
 4C a  u 2 


C

u

F

C


p
e
1
i
i
p
e
2
f
j

k


Svensson：
Cpe1=1.95
Green：
Cpe1=Cpe2=1.5
Liu：Cpe1=1.5，
Cpe2=0.6
8
Difference in Fk (type A & B VS type C)
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= 4C a  u  )
This terms also appears in Fe.
Fi
Fk
Fe
2
f
typeC
e
 ui  Fi
typeA
typeB C
j
f
a  ui   u j 
2
k
e
 ui  Fi
 ui  Fi  4C f a  u j  2
k
e
3
k 2
L
Hiraoka：
Cpe1=2.5
Yamada：
Cpe1=1.0
C pe 1  ui  Fi
Uno：Cpe1=1.5
 C pe 1
 4C a  u 2 


C

u

F

C


p
e
1
i
i
p
e
2
f
j

k


Svensson：
Cpe1=1.95
Green：
Cpe1=Cpe2=1.5
Liu：Cpe1=1.5，
Cpe2=0.6
9
Difference in Fe (type A VS type B & C)
In type A,
length scale within canopy
L=1/a (a： leaf surface area
density )
Fe∝
Fi
Fk
typeC
f
a  ui   u j 
2
e
k
e
 ui  Fi
 ui  Fi  4C f a  u j  2




(here t = k/e )
Fe
 ui  Fi
typeA
typeB C
3
2
1
k

t 
L

k
e
3
k 2
L
Hiraoka：
Cpe1=2.5
Yamada：
Cpe1=1.0
C pe 1  ui  Fi
Uno：Cpe1=1.5
 C pe 1
 4C a  u 2 


C

u

F

C


p
e
1
i
i
p
e
2
f
j

k


Svensson：
Cpe1=1.95
Green：
Cpe1=Cpe2=1.5
Liu：Cpe1=1.5，
Cpe2=0.6
10
Difference in Fe (type A VS type B & C)
1
Fe ∝ t F
(here t = k/e )
Fe= Production(Pe) – Dissipation(De)
In type B,
k
In type C,
Pe ∝
Fi
typeC
t
Pk
a  ui   u j 
2
t
e
k
e
 ui  Fi
 ui  Fi  4C f a  u j  2
1
Dk
Fe
 ui  Fi
f
, De ∝
Fk
typeA
typeB C
1
k
e
3
k 2
L
Hiraoka：
Cpe1=2.5
Yamada：
Cpe1=1.0
C pe 1  ui  Fi
Uno：Cpe1=1.5
 C pe 1
 4C a  u 2 


C

u

F

C


p
e
1
i
i
p
e
2
f
j

k


Svensson：
Cpe1=1.95
Green：
Cpe1=Cpe2=1.5
Liu：Cpe1=1.5，
Cpe2=0.6
11
Extra terms Fi, Fk, Fe
Cpe 1, Cpe 2 ： model coefficients in turbulence modeling,
which should be optimized, for
prescribing the time scale of the process of
energy dissipation in canopy layer
, a, Cf ： parameters to be determined according
to the real conditions of trees
type B
C f a ui
Fi
Fk
Fe
ui Fi
e
k
C pe 1 u i Fi
type C
uj
2
 ui  Fi  4C f a  u j  2
e

2 
C pe 1  ui  Fi   C pe 2  4C f a  u j  
k


12
Revised k-e model adopted here
-mixed time scale model1) revision of modelling of eddy viscosity
Reynolds stress :
 u

u
j
i

 u i u j   t

 x j
x i

 2
  k
ij
 3

Modifying eddy viscosity
A mixed time scale, tm , proposed by Nagano et al.
 t  C kt m
13
Revised k-e model based on
mixed time scale concept
2) Introduction of the mixed time scale (Nagano et al.)
Mixed time scale
ts , time scale of mean velocity gradient
A harmonic balance of t , i.e. ek
and
ts (timescale of mean velocity gradient)
1  1 Cs 



t m 2  t  t s 
ts 
2
S2 
2
1
Cs=0.4
S  Sij Sij
1   ui  u j
S ij 


2 x j
xi





2  ij ij
1   ui  u j
 ij 


2 x j
xi





2
t , turbulence time scale
t 
k
e
14
Results of CFD computations
with tree canopy models
15
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
model tree
16
Fi  C f a ui
2
uj
Leaf surface area density
Case No.
1-1
1-2
1-3
2-1
2-2
2-3
2-4
2-5
type
Cpe1
typeA
1.0
1.5
4.0
typeB
1.0
1.5
2.0
3.0
4.0
a=17.98[m2/m3]
Drag coefficient
Cf =0.8[-]
Expressions for Fe
3
e
k2
typeA Cpe 1
k
L
typeB
e
k
(L=1/ a)
C pe 1 Fk
17
Comparison between types A and B
Distribution of mean wind velocity (at 0.6m height)
0.6m
velocity [m/s]
Mean wind
平均風速 [m/s]
2
1
0
-0.8
-0.6
-0.4
-0.2
0
0.2
x [m]
1 x 1 [m]
測定位置
TypeA
0.4
0.6
0.8
1
3
velocity
Mean wind
平均風速
[m/s] [m/s]
実測値
experiment
case1-1 (TypeA,Cpε=1.0)
pe1
case1-2 (TypeA,Cpε=1.5)
pe1
case1-3 (TypeA,Cpε=4.0)
pe1
3
実測値
experiment
pe1
case2-1 (TypeB,Cpε=1.0)
case2-2 (TypeB,Cpε=1.5)
pe1
case2-3 (TypeB,Cpε=2.0)
pe1
case2-4 (TypeB,Cpε=3.0)
pe1
pe1
case2-5 (TypeB,Cpε=4.0)
Tree model
Tree model
2
1
0
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
x [m]
測定位置x11 [m]
TypeB
18
Distribution of mean wind velocity (at 0.8m height)
0.8m
Tree model
平均風速
[m/s] [m/s]
velocity
Mean wind
4
experiment
実測値
case1-1 (TypeA,Cpε=1.0)
pe1
case1-2 (TypeA,Cpε=1.5)
pe1
case1-3 (TypeA,Cpε=4.0)
pe1
Cpe1 =4.0
3
Cpe1 =1.0
Cpe1 =1.5
2
[m/s]
velocity
Mean wind
平均風速
[m/s]
Tree model
4
experiment
実測値
case2-1
case2-2
case2-3
case2-4
case2-5
(TypeB,Cpε=1.0)
pe1
(TypeB,Cpε=1.5)
pe1
(TypeB,Cpε=2.0)
pe1
(TypeB,Cpε=3.0)
pe1
(TypeB,Cpε=4.0)
pe1
3
Cpe1 =1.0
2
-0.8
-0.6
-0.4
-0.2
0
0.2
x1 [m]
測定位置
x1
0.4
[m]
0.6
0.8
1
-0.8
-0.6
-0.4
-0.2
0
0.2
x1 [m]
測定位置
x [m]
1
0.4
0.6
0.8
1
TypeA
TypeB
・Effect of difference in Cpe1 value is large compared to the difference
of model type (types A or B)
・Type B model corresponds well with experiment in the range
Cpe1=1.5～2.0.
・Type B was selected in this study
・More detailed optimizations for Cpe1 were done
19
Optimization of model coefficient Cpe1 for typeB
・ By comparing CFD results with measurements,
Cpe1 was optimized.
Fi
Fk
Fe
C f a ui
uj
2
ui Fi
e
k
C pe 1 Fk
Tsuijimatu （Rectangular-cutted-pine-trees as wind-break ）
20
Comparison of flow behind pine trees
CL
2D computation is carried out at
the central section
Computational domain：100m(x1:streamwise)×100m (x3:vertical)
21
Comparison of vertical velocity profiles behind tree
: measurement
12
12
Height[m]
(x/H=5)
12
Height[m]
(x1/H=4)
12
Height[m]
(x1/H=3)
12
Height[m]
(x1/H=2)
12
Height[m]
(x1/H=1)
12
Height[m]
(x1/H=5)
12
Height[m]
(x1/H=4)
12
Height[m]
(x1/H=3)
12
Height[m]
(x1/H=2)
: CFD with type B model
Height[m]
(x1/H=1)
a=1.17[m2/m3]
Cf =0.8[-]
6
6
6
6
6
6
6
6
6
6
0
0
0
0.7
U/UH
0
0
0
1.4
0.7
U/UH
1.4
0
0.7
U/UH
0
0
1.4
0.7
U/UH
1.4
0
0
0
0.7
U/UH
1.4
0
0.7
U/UH
0.7
U/UH
(1) Cpe1=1.5
0
0.7
U/UH
0
0
1.4
0.7
U/UH
1.4
0
12
12
12
12
12
12
Height[m]
Height[m]
6
6
6
6
6
6
6
6
6
6
0
0
0.7
U/UH
0
0
0
1.4
0.7
U/UH
1.4
0
0.7
U/UH
0
0
1.4
0.7
U/UH
1.4
0
0
0
0.7
U/UH
1.4
0
0.7
U/UH
0.7
U/UH
1.4
0
0.7
U/UH
0
0
1.4
0.7
U/UH
1.4
0
12
12
12
12
12
12
Height[m]
Height[m]
Height[m]
6
6
6
6
6
6
6
6
6
6
0
0
0.7
U/UH
1.4
0
0
0
0.7
U/UH
1.4
0
0.7
U/UH
1.4
(3) Cpe1=1.7
1.4
(x/H=5)
12
Height[m]
(x/H=4)
12
Height[m]
(x/H=3)
12
Height[m]
(x/H=2)
Height[m]
(x/H=1)
Height[m]
(x/H=5)
Height[m]
(x/H=4)
12
0
0.7
U/UH
(5) Cpe1=1.9
(x/H=3)
Height[m]
(x/H=2)
0
0
0
1.4
(2) Cpe1=1.6
(x/H=1)
1.4
(x/H=5)
12
Height[m]
(x1/H=4)
12
Height[m]
(x1/H=3)
12
Height[m]
(x1/H=2)
Height[m]
(x1/H=1)
Height[m]
(x1/H=5)
Height[m]
(x1/H=4)
12
0
0.7
U/UH
(4) Cpe1=1.8
(x1/H=3)
Height[m]
(x1/H=2)
1.4
Height[m]
(x1/H=1)
0
0
0
1.4
0
0
0.7
U/UH
1.4
0
0
0
0.7
U/UH
1.4
0
0.7
U/UH
1.4
0
0
0
0.7
U/UH
1.4
0
0.7
U/UH
1.4
0
0
0.7
U/UH
(6) Cpe1=2.0
1.4
0
0.7
U/UH
1.4
22
Comparison of vertical velocity profiles
behind tree (Cpe1=1.8)
measurement
Type B model(Cpe1=1.8)
12
12
12
12
0
0.7
U/UH
1.4
Height[m]
0
Height[m]
0
Height[m]
6
Height[m]
Height[m]
12
6
6
6
6
0
0
0
0.7
U/UH
1.4
0
0.7
U/UH
1.4
0
0
0.7
U/UH
1.4
0
0.7
U/UH
1.4
23
Comparison of vertical profiles of k behind tree
: measurement
12
12
Height[m]
(x/H=5)
12
Height[m]
(x1/H=4)
12
Height[m]
(x1/H=3)
12
Height[m]
(x1/H=2)
12
Height[m]
(x1/H=1)
12
Height[m]
(x1/H=5)
12
Height[m]
(x1/H=4)
12
Height[m]
(x1/H=3)
12
Height[m]
(x1/H=2)
: CFD with type B model
Height[m]
(x1/H=1)
a=1.17[m2/m3]
Cf =0.8[-]
6
6
6
6
6
6
6
6
6
6
0
0
0
0.2
k/UH2
0
0
0
0.4
0.2
k/UH2
0.4
0
0.2
k/UH2
0
0
0.4
0.2
k/UH2
0.4
0
0
0
0.2
k/UH2
0.4
0
0.2
k/UH2
0.2
k/UH2
(1) Cpe1=1.5
0
0.2
k/UH2
0
0
0.4
0.2
k/UH2
0.4
0
12
12
12
12
12
12
Height[m]
Height[m]
6
6
6
6
6
6
6
6
6
6
0
0
0.2
k/UH2
0
0
0
0.4
0.2
k/UH2
0.4
0
0.2
k/UH2
0
0
0.4
0.2
k/UH2
0.4
0
0
0
0.2
k/UH2
0.4
0
0.2
k/UH2
0.2
k/UH2
0.4
0
0.2
k/UH2
0
0
0.4
0.2
k/UH2
0.4
0
12
12
12
12
12
12
Height[m]
Height[m]
Height[m]
6
6
6
6
6
6
6
6
6
6
0
0
0.2
k/UH2
0.4
0
0
0
0.2
k/UH2
0.4
0
0.2
k/UH2
0.4
(3) Cpe1=1.7
0.4
(x/H=5)
12
Height[m]
(x/H=4)
12
Height[m]
(x/H=3)
12
Height[m]
(x/H=2)
Height[m]
(x/H=1)
Height[m]
(x/H=5)
Height[m]
(x/H=4)
12
0
0.2
k/UH2
(5) Cpe1=1.9
(x/H=3)
Height[m]
(x/H=2)
0
0
0
0.4
(2) Cpe1=1.6
(x/H=1)
0.4
(x/H=5)
12
Height[m]
(x1/H=4)
12
Height[m]
(x1/H=3)
12
Height[m]
(x1/H=2)
Height[m]
(x1/H=1)
Height[m]
(x1/H=5)
Height[m]
(x1/H=4)
12
0
0.2
k/UH2
(4) Cpe1=1.8
(x1/H=3)
Height[m]
(x1/H=2)
0.4
Height[m]
(x1/H=1)
0
0
0
0.4
0
0
0.2
k/UH2
0.4
0
0
0
0.2
k/UH2
0.4
0
0.2
k/UH2
0.4
0
0
0
0.2
k/UH2
0.4
0
0.2
k/UH2
0.4
0
0
0.2
k/UH2
(6) Cpe1=2.0
0.4
0
0.2
k/UH2
0.4
24
Comparison of vertical profiles of k
behind tree (Cpe1=1.8)
measurement
Type B model(Cpe1 =1.8)
Height[m]
12
Height[m]
12
Height[m]
12
Height[m]
12
Height[m]
12
6
6
6
6
6
0
0
0
0
0
0
0.2
k/UH2
0.4
0
0.2
k/UH2
0.4
0
0.2
k/UH2
0.4
0
0.2
k/UH2
0.4
0
0.2
k/UH2
0.4
k is underestimated in
this area by type B model
25
Performance of Type C model in which the energy loss in
canopy is also considered
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= 4C a  u  )
2
f
Similar term also appears in Fe.
Fi
Fk
typeB C
typeC
f
a  ui   u j 
2
k
e
 ui  Fi
 ui  Fi  4C f a  u j  2
Fe
e
 ui  Fi
typeA
k
e
j
3
k 2
L
Hiraoka：
Cpe1=2.5
Yamada：
Cpe1=1.0
C pe 1  ui  Fi
Uno：Cpe1=1.5
 C pe 1
 4C a  u 2 


C

u

F

C


p
e
1
i
i
p
e
2
f
j

k


Svensson：
Cpe1=1.95
Green：
Cpe1=Cpe2=1.5
Liu：Cpe1=1.5，
Cpe2=0.6
26
Optimization of model coefficient Cpe2 for typeC
model
Fε
Type
typeCB

2
e 
C pe 1 ui Fi  C pe 2  4C f a u j  k 

k 

Green
：Cpe1= Cpe2=1.5
Liu et al. : Cpe1=1.5, Cpe2= 0.6
27
: measurement
12
Height[m]
(x1/H=5)
12
Height[m]
(x1/H=4)
12
Height[m]
(x1/H=3)
12
Height[m]
(x1/H=2)
12
Height[m]
(x1/H=1)
12
Height[m]
(x1/H=5)
12
Height[m]
(x1/H=4)
12
Height[m]
(x1/H=3)
12
Height[m]
(x1/H=2)
12
Height[m]
(x1/H=1)
: CFD with type C model
6
6
6
6
6
6
6
6
6
6
0
0
0
0.7
U/UH
0
0
0
1.4
0.7
U/UH
1.4
0
0.7
U/UH
0
0
1.4
0.7
U/UH
1.4
0
0
0
0.7
U/UH
1.4
vertical velocity profiles behind tree
0
0.2
k/UH2
0
0
0
0.4
0.2
k/UH2
0.4
0
0.2
k/UH2
0
0
0.4
0.2
k/UH2
0.4
0
0.2
k/UH2
0.4
vertical profiles of k behind tree
Green ：Cpe1= Cpe2=1.5
Height[m]
(x1/H=5)
12
Height[m]
(x1/H=4)
12
Height[m]
(x1/H=3)
12
Height[m]
(x1/H=2)
12
Height[m]
(x1/H=1)
12
Height[m]
(x1/H=5)
12
Height[m]
(x1/H=4)
12
Height[m]
(x1/H=3)
12
Height[m]
(x1/H=2)
12
Height[m]
(x1/H=1)
12
6
6
6
6
6
6
6
6
6
6
0
0
0
0.7
U/UH
1.4
0
0
0
0.7
U/UH
1.4
0
0.7
U/UH
1.4
0
0
0.7
U/UH
1.4
0
0
0
0.7
U/UH
1.4
vertical velocity profiles behind tree
0
0.2
k/UH2
0.4
0
0
0
0.2
k/UH2
0.4
0
0.2
k/UH2
0.4
0
0
0.2
k/UH2
0.4
0
0.2
k/UH2
0.4
vertical profiles of k behind tree
Liu et al. : Cpe1=1.5, Cpe2= 0.6
28
Optimization of model coefficient Cpe2 for typeC
Computed Cases
Cpe1=1.8
( optimized
value for type B )
case
C-1
C-2
C-3
C-4
C-5
C-6
C-7
C-8
C-9
C-10
C-11
C-12
C-13
model
Fε
Type B
typeC

2
e 
C pe 1 ui Fi  C pe 2  4C f a u j  k 

k 

type
Cpe1
type C
1.8
Cpe2
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
29
Comparison of numerically
predicted drag coefficient CD
■Pressure difference ⊿P
P  Pf  Pb
V(z
)
Pf
Pb
■Drag coefficient of tree CD
CD 
 P( z)dz
tree
1
2
  V z dz
2 tree
30
Comparison of numerically predicted
drag coefficient CD ( Cpe1=1.8 )
1.50
CD
1.45
1.40
1.35
1.30
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
Cpe2
model
Fε
2
Type B e  C u F  C  4C a u  k 
typeC
 pe1 i i pe 2 fi

j
k

31
Comparison of streamwise profiles of k & e
around tree ( type C, Cpe1=1.8 )
tree
ε/ (UH3/H)
1.6
1.4
experiment
Cpe2 =0.6
1.2
4.5 m
1
0.8
0.6
Cpe2 =1.4
0.4
0.2
Cpe2 =0.6
Cpe2 =1.4
Cpe2 =1.6
Cpe2 =1.8
k/UH2
0
-2
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
-2
-1
-1
0
0
1
1
2
3
4
X1/H
5
2
3
4
5
X1/H
32
Comparison of vertical profiles of e
behind tree ( type C, Cpe1=1.8 )
高さ[m]
6
(x1 /H=1) 6
(x1 /H=2) 6
(x1 /H=3) 6
0
0
0
0
0
0.025 0.05
e/(UH3 /H)
0
0.025 0.05
e/(UH3 /H)
Cpe2=1.8
12
高さ[m]
12
高さ[m]
12
Cpe2=1.6
高さ[m]
12
Cpe2=1.4
0
0.025 0.05
e/(UH3 /H)
12
高さ[m]
Cpe2=0.6
(x1/H=4)
(x1 /H=5)
6
0
0
0.025 0.05
e/(UH3 /H)
0
0.025 0.05
e/(UH3 /H)
33
Comparison of vertical profiles of k
behind tree ( type C, Cpe1=1.8 )
Cpe2=1.4
Cpe2=0.6
12
12
12
Height[m]
Height[m]
Height[m]
Height[m]
12
6
(x1 /H=1) 6
(x1 /H=2) 6
(x1/H=3) 6
0
0
0
0
0
0.1
k/UH2
0.2
0
0.1
k/UH2
0.2
Cpe2=1.8
Cpe2=1.6
0
0.1
k/UH2
0.2
12
Height[m]
measurement
(x1 /H=4)
(x1 /H=5)
6
0
0
0.1
k/UH2
0.2
0
0.1
k/UH2
0.2
Result with Cpe2=1.4 shows good agreement.
34
Comparison of vertical velocity profiles
behind tree ( type C, Cpe1=1.8 )
measurement
Cpe2=1.4
Cpe2=0.6
12
12
Cpe2=1.8
Cpe2=1.6
12
12
高さ[m]
高さ[m]
高さ[m]
高さ[m]
高さ[m]
12
6
(x1 /H=1) 6
(x1 /H=2) 6
(x1 /H=3) 6
(x1 /H=4) 6
0
0
0
0
0
0
0.7
U/UH
1.4
0
0.7
U/UH
1.4
0
0.7
U/UH
1.4
0
0.7
U/UH
1.4
(x1/H=5)
0
0.7
U/UH
1.4
Result with Cpe2=1.4 shows good agreement.
35
Effects of Cpe2
When Cpe2 is decreased ･･･
within tree canopy
behind tree
e
increase
e
decrease
k
decrease
k
decrease
Mean wind velocity
decrease

2
e 
Fe  C pe 1 ui Fi  C pe 2  4C f a u j  k 

k 

Cpe2=1.4 was selected under the condition of Cpe1=1.8..
36
type B model
（Cpe1 =1.8 , Cpe2 =1.4）
（Cpe1 =1.8）
6
6
(x1/H=1)
0
0.7
U/UH
0
1.4
12
6
6
6
(x1/H=2)
(x1/H=3)
(x1/H=4)
0
0
0
0
12
Height[m]
Height[m]
12
Height[m]
12
Height[m]
12
type C model
Height[m]
experiment
0.7
U/UH
1.4
0
0.7
U/UH
0
0
1.4
(x1/H=5)
0.7
U/UH
1.4
0
0.7
U/UH
1.4
Comparison of vertical velocity profiles behind tree
6
(x1/H=1)
6
(x1/H=2)
0
0
0
0.1
k/UH2
0.2
12
6
(x1/H=3)
0.1
k/UH2
0.2
Height[m]
6
(x1/H=4)
0
0
0
12
Height[m]
Height[m]
12
Height[m]
12
Height[m]
12
0
0.1
k/UH2
0.2
6
(x1/H=5)
0
0
0.1
k/UH2
0.2
0
0.1
k/UH2
Comparison of vertical profiles of k behind tree
0.2
38
Prediction of local area wind distribution
The tree canopy model ( type B ) optimized here
was incorporated into
“Local Area Wind Energy Prediction System (LAWEPS)”
Topographic effect on wind
(slow down)
Topographic effect on wind
(speed up)
Collision to ground surface
Effect of surface roughness by plants
39
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%.
40
Outline of LAWEPS
Five-stage Grid Nesting ( One-way)
500km
100km
1st Domain
2nd
Domain
3rd
Domain
10km
50km
10km
3rd Domain
4th
Domain
5th Domain
tree canopy model is
incorporated into the
model for 5th Domain
5th Domain
Wind Turbines
1~2km
10km
5km
0.5~1km
41
Table : Five sub-domains in LAWEPS
Domains
1
2
3
4
5
Horizontal Area
500×500 km
100×100 km
50×50 km
10×10 km
1×1 km
Horizontal Resolution
5 km
1 km
500 m
100 m
10 m
Domains 1-3: Meso-scale Meteorological Model
( revised Mellor-Yamada Level 2.5 )
Domains 4-5: Engineering Model (revised k- e
(SΩ)）
( Domain 5: tree canopy model is coupled )
42
Field observation
Long term measurements of wind velocities at
Shionomisaki Peninsula of Wakayama
Prefecture, Japan.
43
Testing Area: Shionomisaki Peninsula, Japan
1st-3rd Domain
4th Domain
11km
1st
9km
N
2nd
W
(b)
E
S
(a)
3rd
5th Domain
A
B
A & B are Obs. Sites
Doppler Sodar Observations are done at site B
44
Leaf surface area density a is given from
a = LAI/H
LAI : Leaf Area Index (here assumed to be 5)
LAI   (a( z ))dz
0
H
H : tree height (given from the aircraft
measurements)
Cf = 0.2 (typical value for plant community
( stands of tree )
Fi
C f a ui
uj
Cpe1 = 1.8
ui Fi
Fk
Fe
e
k
2
C pe 1 Fk
45
Comparison of the 1st-5th Full Nesting Calculation
with the Ground Observations
Site A
Site A
2001.12.15.15JST (Site A)
Site B
2000.10.28.12JST (site A)
300
2001.12.15.15JST (site B)
200
200
150
150
3rd domain
4th domain
5th domain
Observation
150
100
50
5th domain
Altitude(m)
200
Altitude (m)
Altitude (m)
250
Observation
100
100
50
50
5th domain
Observation
0
0
0
0
10
20
30
wind speed[m/s]
40
2001 Dec. 15th 15JST
0
5
10
15
Wind Speed (m/s)
20
25
2000 Oct 28th 12JST
0
5
10
15
20
Wind Speed (m/s)
25
2001 Dec. 15th 15Jst
5th Domain Model
Observation
Vertical distributions of the calculated wind speed
are compared with the tower observations.
46
Results of the Annual Mean Wind Calculation
Annual Mean Wind Speed (Year of 2000)
Site A
5.31m/s
5.51m/s
+3.77%
Site B
4.31m/s
4.17m/s
-3.27%
site A
30
25
20
15
10
5
0
Frequency(%)
Frequency(%)
Observation LAWEPS Error(%)
5th domain
Observation
0
5
10 15 20 25
Wind speed(m/s)
30
site B
30
25
20
15
10
5
0
5th domain
Observation
0
5
10 15 20 25
Wind speed(m/s)
30
Frequency of the Occurrence of Wind Speed
47
Annual Mean Wind Speed Map 30m above the Ground
4th Domain
0~8m/s
5th Domain(a)
5th Domain(b)
100
8
90
7
100
8
90
7
80
80
6
6
70
70
5
60
50
40
5
60
4
50
4
3
40
3
30
30
2
20
2
20
1
10
1
10
10
20
30
40
50
60
70
80
90
100
0
10
20
30
40
50
60
70
80
90
100
0
48
Conclusions ( tentative )
1) Type B model predicted well the velocity
distributions behind tree canopies in the
range Cpe1=1.5～2.0 .
2) The value of 1.8 was selected for Cpe1 in
LAWEPS. The vertical velocity profiles above
the real complex terrain predicted by
LAWEPS with type B model showed close
agreement with measurements.
49
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.
50
Conclusions
5) Results with the combination of Cpe1=1.8 and
Cpe2=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.
51
APPENDIX
52
Prediction of thermal effects
of planted trees
53
Model for tree canopy
Following effects are considered :
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）
54
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
ℓ
1  exp kax1, x 2 , x3 
(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
55
Generation (transpiration) of water
vapor and heat balance at leaf surface
・The heat balance equation at leaves that compose the tree
crown
SP  R DP  HP  LEP  0
SP
RDP
HP
LEP
SP
(1)
: Absorbed solar radiation [W]
: Absorbed long-wave radiation [W]
: Sensible heat [W]
: Latent heat [W]
HP  APc TaP  TP 
LEP  LAPWP faP  fsP 
RDP
LEP
HP
(2)
(3)
・Using Eqs. (1), (2) and (3), leaf surface temperature TP is
obtained. HP, LEP and TP are used as boundary conditions for
CFD computation.
56
Coupled simulation of
radiation, conduction and convection
Prediction of thermal effects of trees planted
on a main street in Sendai city
57
Prediction of thermal effects of
trees planted on a main street in
Sendai city
sidewalk
roadway
median strip
building
N
W
E
S
25m
9m
15m
15m
9m
25m
2.5m
tree
(1) Plan
center
tree
Higashi-Nibancho Street in Sendai City
（東二番丁通，仙台）
0.3m
building
sidewalk roadway
(2) Section
58
Computed cases
building
median strip
N roadway
N
W
W
E
S
S
Wind
(1) Case 1
N
W
E
tree
sidewalk (2) Case 2
Table
E
Wind
Computed cases
Condition of Tree Planting
S
Wind
Case 1
Not Planted
Case 2
Present Situation
Case 3
Densely Planted
(3) Case 3
59
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 turbulence
3 Contaminant diffusion by wind and turbulence
4 Moisture transfer by wind and turbulence
5 Radiative heat transfer in outdoor space
6 Heat conduction to underground and inside of
building
7 Heat energy balance at urban surface (ground
surface and building surface )
→all processes listed here are considered
60
Flowchart for assessing outdoor human comfort
based on CFD
61
All heat balance components to
calculate the surface temperature
S i：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
62
Distribution of surface temperature
（August 4, 12:00）
N
W
E
[C]
S
(1) Case 1
(2) Case 2
(3) Case 3
(Not Planted)
(Present Situation )
(Densely Planted)
N
W
N
E
W
S
N
E
W
S
Wind
E
S
Wind
Wind
63
64
Horizontal Distributions of Velocity Vectors
at the Height of 1.5m （August 4, 13:00）
N
W
E
S
Wind Velocity is
decreased by trees
A’
A
W
(1) Case 1
(2) Case 2
(3) Case 3
(Not
Planted)
N
(Present
Situation )
N
(Densely Planted)
E
W
S
E
W
S
Wind
N
E
S
Wind
Wind
65
Vertical Distribution of Wind Velocity
Vectors at A-A’ sections （August 4, 13:00）
(1) Case 1
(2) Case 2
(Not Planted)
(Present Situation )
N
W
N
E
W
S
E
S
Wind
Wind
N
W
Case 1
Case 2
E
S
(3) Case 3
(Densely Planted)
Wind
Case 3
66
Vertical Distribution （August 4, 13:00）
29.0
30.5
32.0
[C]
(1) Case 1 (Not Planted)
(1) Case 1 (Not Planted)
(2) Case 2 (Present Situation )
(2) Case 2 (Present Situation )
Wind Velocity Vectors
air temperature
67
Evaluation of Standard Effective
Temperature (SET*)
・Velocity
・Temperature
・Humidity
・Mean Radiative
Temperature (MRT)
Index for
thermal
comfort
（ SET*）
68
Horizontal distribution of SET* (Standard
Effective Temperature) at the height30.0
of 1.5m
35.0 [℃]
25.0
N
（August 4, 13:00）
W
E
S
(1) Case 1
(2) Case 2
(3) Case 3
(Not Planted)
(Present Situation )
(Densely Planted)
N
W
N
E
W
S
N
E
W
S
Wind
E
S
Wind
Wind
69
Difference of SET* at the height of 1.5m
(August 4, 13:00)
0.0
-5.0
5.0
[℃]
① SET* is
decreased by trees
N
W
E
S
② But SET* is
increased by trees
in these areas
(Case 2) －(Case 1)
(Present Situation ) －(Not Planted)
N
N
W
W
E
E
S
S
Wind
Wind
70
Horizontal Distributions of Velocity Vectors
at the Height of 1.5m （August 4, 13:00）
N
W
E
Wind Velocity is
decreased by trees
S
W
(1) Case 1
(2) Case 2
(3) Case 3
(Not
Planted)
N
(Present
Situation )
N
(Densely Planted)
E
W
S
E
W
S
Wind
N
E
S
Wind
Wind
71
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.
72
Gas diffusion within street canyon
Sidewalk
Median Strip
Roadway
Building
Building
Center
• Gas
is released from
all
25m
roadway area (red area)
tree
at height of 0.15m
Computed
cases
10m
10m
1.7m
Condition
Sidewalk
25m
9m
15m
15m
2.5m
9m
25m
Case 1
Case 2
Case 3
0.3m
of Tree
Planting
Roadway
Not Planted
Present Situation
Densely Planted
73
Vertical Distribution of Wind Velocity
Using these velocities, contaminant diffusion is predicted
(1) Case 1
(2) Case 2
(Not Planted)
(Present Situation )
N
W
N
E
W
S
E
S
Wind
Wind
N
W
Case 1
Case 2
E
S
(3) Case 3
(Densely Planted)
Wind
Case 3
74
Vertical distribution of gas concentration
0.0
1.5
3.0
E
W
Average value in CV：0.84
CV
歩道
Sidewalk
CV
歩道
Sidewalk
歩道
Sidewalk
(1) Case 1(Not Planted)
-> In case 1,
Gas is convected
to sidewalk area
Average value in CV ：0.74
歩道
Sidewalk
(2) Case 2 (Present Situation )
CV
歩道
Sidewalk
Average value in CV ：0.76
歩道
Sidewalk
(3) Case 3 (Densely Planted)
Gas is diffused to upper region in Cases 2 and 3
75
Averaged values in CV and PS
CV
PS : Pedestrian Space
(from 0.3m to 1.8m height
on sidewalk)
PS
歩道
Sidewalk
歩道
Sidewalk
Case 1
（Not planted）
Averaged gas concentration
in CV [-]
Averaged gas concentration
in PS [-]
Case 2
Case 3
（Present situation） （Densely planted）
0.826
0.732
0.750
4.452
1.233
1.021
 Normalized values
• Gas is not convected to sidewalk area so much in Case2 and Case3
by the effects of trees on flowfield
76