1

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 : mochida@sabine.pln.archi.tohoku.ac.jp

T. Iwata, A. Kimura, H. Yoshino, and S. MurakamiT. Iwata, A. Kimura, H. Yoshino, and S. Murakami

NATO ASI, May 6

2

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.

4

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

5

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 ～）

6

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

7

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

8

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

9

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

10

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

11

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

12

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

13

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-

14

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

15

Results of CFD computations Results of CFD computations with tree canopy modelswith tree canopy models

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

17

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)

18

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]

19

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

20

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.

21

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

22

(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[-]

23

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]

24

(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[-]

25

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

26

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

27

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

28

: 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

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

30

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

31

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

32

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 )

33

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 ) 　

34

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.

35

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.

36

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..

38

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)

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)”

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%.

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

42

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 )

43

Long term measurements of wind velocities at Shionomisaki Peninsula of Wakayama Prefecture, Japan.

Field observation

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

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)) ( (

46

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.

47

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

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

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.

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.

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.

52

APPENDIX

53

Prediction of thermal effects Prediction of thermal effects of planted treesof planted trees

54

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）

55

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

56

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)

57

Coupled simulation of radiation, conduction and convection

Prediction of thermal effects of trees planted on a main street in Sendai city

58

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

59

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

60

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

61

[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

62

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

63

(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

64

[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

65

(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

66

(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

67

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 ）

68

Evaluation of Standard Effective Temperature (SET*)

・ Velocity

・ Temperature

・ Humidity

・ Mean Radiative

Temperature (MRT)

Index for thermal comfort

（ SET*）

69

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 ）

70

(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

71

(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

72

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.

73

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

74

(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

75

(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

76

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