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

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**Factors affecting the flow around a hilly terrain**

Separation Circulation Re-circulation Convex Concave Roughness Recirculation Sea Surface Inlet flow Wake of windmill Collision Acceleration 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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**A birdview over the planted park**

This study focuses on modelling of aerodynamic effects of tree canopy ( effects on wind flow and turbulence ) A birdview over the planted park and surroundings CFD prediction (revised k-εmodel)

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**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.

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**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～）

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**Modelling of aerodynamic effects of tree canopy**

decreases in velocity increases in turbulence increases in dissipation k – e model with tree canopy model [Continuity equation] [Average equation] [k transport equation] [ transport equation] F i F k i F u k p F C e1 e × F e : 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

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**Extra terms for incorporating aerodynamic effects of tree canopy**

h：fraction of the area covered with trees Cpe1, Cpe2 ： model coefficients in turbulence modeling Cf：drag coefficient for canopy a： leaf surface area density Fi Fk Fe typeA typeB typeC Hiraoka： Cpe1=2.5 Yamada： Cpe1=1.0 Uno：Cpe1=1.5 Svensson： Cpe1=1.95 Green： Cpe1=Cpe2=1.5 Liu：Cpe1=1.5， Cpe2=0.6

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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 Fe typeA typeB typeC Hiraoka： Cpe1=2.5 Yamada： Cpe1=1.0 Uno：Cpe1=1.5 Svensson： Cpe1=1.95 Green： Cpe1=Cpe2=1.5 Liu：Cpe1=1.5， Cpe2=0.6

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**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= ) This terms also appears in Fe. Fi Fk Fe typeA typeB typeC Hiraoka： Cpe1=2.5 Yamada： Cpe1=1.0 Uno：Cpe1=1.5 Svensson： Cpe1=1.95 Green： Cpe1=Cpe2=1.5 Liu：Cpe1=1.5， Cpe2=0.6

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**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∝ (here t = k/e ) Fi Fk Fe typeA typeB typeC Hiraoka： Cpe1=2.5 Yamada： Cpe1=1.0 Uno：Cpe1=1.5 Svensson： Cpe1=1.95 Green： Cpe1=Cpe2=1.5 Liu：Cpe1=1.5， Cpe2=0.6

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**Difference in Fe (type A VS type B & C)**

In type B, Fe∝ (here t = k/e ) In type C, Fe= Production(Pe) – Dissipation(De) Pe ∝ , De ∝ Fi Fk Fe typeA typeB typeC Hiraoka： Cpe1=2.5 Yamada： Cpe1=1.0 Uno：Cpe1=1.5 Svensson： Cpe1=1.95 Green： Cpe1=Cpe2=1.5 Liu：Cpe1=1.5， Cpe2=0.6

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**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 h, a, Cf ： parameters to be determined according to the real conditions of trees type B type C Fi Fk Fe まず、モデル係数Cpeの最適化について説明します。

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**Revised k-e model adopted here -mixed time scale model-**

1) revision of modelling of eddy viscosity Reynolds stress : Modifying eddy viscosity A mixed time scale, m , proposed by Nagano et al.

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**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 , i.e and s (timescale of mean velocity gradient) Cs=0.4 t , turbulence time scale

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

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**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 model tree

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**1-1 1-2 1-3 2-1 2-2 2-3 2-4 2-5 Leaf surface area density**

a=17.98[m2/m3] Drag coefficient Cf =0.8[-] Expressions for Fe Case No. type Cpe1 1-1 typeA 1.0 1-2 1.5 1-3 4.0 2-1 typeB 2-2 2-3 2.0 2-4 3.0 2-5 typeA (L=1/ a) typeB

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**Distribution of mean wind velocity (at 0.6m height)**

Comparison between types A and B Distribution of mean wind velocity (at 0.6m height) 0.6m Tree model experiment pe1 Tree model experiment pe1 Mean wind velocity [m/s] Mean wind velocity [m/s] x1 [m] x1 [m] TypeA TypeB

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**Distribution of mean wind velocity (at 0.8m height)**

Tree model Tree model pe1 pe1 experiment experiment Cpe1 =4.0 Mean wind velocity [m/s] Mean wind velocity [m/s] Cpe1 =1.0 Cpe1 =1.5 Cpe1 =1.0 x1 [m] x1 [m] 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

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**Optimization of model coefficient Cpe1 for typeB**

・ By comparing CFD results with measurements, Cpe1 was optimized. Fi Fk Fe 本研究では、Cpeの最適値をより詳しく調べるために、黒谷らが実測結果を報告している出雲地方の黒松によるスクリーン状の屋敷囲いである築地松の後方の風速分布を対象とする数値解析を行った。モデル係数Cpeを1.5～2.0の間で段階的に変化させ、実測と比較した。 Tsuijimatu （Rectangular-cutted-pine-trees as wind-break ）

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**Computational domain：100m(x1:streamwise)×100m (x3:vertical)**

Comparison of flow behind pine trees CL 2D computation is carried out at the central section 本解析では、風向が築地松と直交する場合を対象とし、築地松中心軸上の鉛直断面内の流れを２次元で解析した。 Computational domain：100m(x1:streamwise)×100m (x3:vertical)

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**Comparison of vertical velocity profiles behind tree**

a=1.17[m2/m3] : measurement : CFD with type B model Cf =0.8[-] (x1/H=1) (x1/H=2) (x1/H=3) (x1/H=4) (x1/H=5) (x1/H=1) (x1/H=2) (x1/H=3) (x1/H=4) (x/H=5) (1) Cpe1=1.5 (4) Cpe1=1.8 (x1/H=1) (x1/H=2) (x1/H=3) (x1/H=4) (x1/H=5) (x1/H=1) (x1/H=2) (x1/H=3) (x1/H=4) (x/H=5) (2) Cpe1=1.6 (5) Cpe1=1.9 平均風速の鉛直分布 です。 いずれの場合もかなりよく実測値と一致しているが、詳しく比較するとCpe=1.8～2.0がより実測値に近い分布となっており、樹木風下後方の風速分布を非常によく再現している。 (x/H=1) (x/H=2) (x/H=3) (x/H=4) (x/H=5) (x/H=1) (x/H=2) (x/H=3) (x/H=4) (x/H=5) (3) Cpe1=1.7 (6) Cpe1=2.0

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**Comparison of vertical velocity profiles**

behind tree (Cpe1=1.8) measurement Type B model(Cpe1=1.8) 特に、1.8の場合を抜き出してみると、黒谷らの実測とよく一致していることがわかります。

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**Comparison of vertical profiles of k behind tree**

a=1.17[m2/m3] : measurement : CFD with type B model Cf =0.8[-] (x1/H=1) (x1/H=2) (x1/H=3) (x1/H=4) (x1/H=5) (x1/H=1) (x1/H=2) (x1/H=3) (x1/H=4) (x/H=5) (1) Cpe1=1.5 (4) Cpe1=1.8 (x1/H=1) (x1/H=2) (x1/H=3) (x1/H=4) (x1/H=5) (x1/H=1) (x1/H=2) (x1/H=3) (x1/H=4) (x/H=5) (2) Cpe1=1.6 (5) Cpe1=1.9 (x/H=1) (x/H=2) (x/H=3) (x/H=4) (x/H=5) (x/H=1) (x/H=2) (x/H=3) (x/H=4) (x/H=5) (3) Cpe1=1.7 (6) Cpe1=2.0

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**k is underestimated in this area by type B model**

Comparison of vertical profiles of k behind tree (Cpe1=1.8) measurement Type B model(Cpe1 =1.8) kの鉛直分布 k is underestimated in this area by type B model

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**In types C, Fk = Production(Pk) - Dissipation(Dk) **

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= ) Similar term also appears in Fe. Fi Fk Fe typeA typeB typeC Hiraoka： Cpe1=2.5 Yamada： Cpe1=1.0 Uno：Cpe1=1.5 Svensson： Cpe1=1.95 Green： Cpe1=Cpe2=1.5 Liu：Cpe1=1.5， Cpe2=0.6

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**Optimization of model coefficient Cpe2 for typeC**

Green ：Cpe1= Cpe2=1.5 Liu et al. : Cpe1=1.5, Cpe2= 0.6

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**Green ：Cpe1= Cpe2=1.5 Liu et al. : Cpe1=1.5, Cpe2= 0.6 : measurement**

: CFD with type C model (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) vertical velocity profiles behind tree vertical profiles of k behind tree Green ：Cpe1= Cpe2=1.5 (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) vertical velocity profiles behind tree vertical profiles of k behind tree Liu et al. : Cpe1=1.5, Cpe2= 0.6

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**Optimization of model coefficient Cpe2 for typeC**

Computed Cases Cpe1=1.8 ( optimized value for type B ) typeC

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**Comparison of numerically predicted drag coefficient CD**

■Pressure difference ⊿P V(z) Pf Pb ■Drag coefficient of tree CD

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**Comparison of numerically predicted drag coefficient CD ( Cpe1=1.8 )**

typeC

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**Comparison of streamwise profiles of k & e **

around tree ( type C, Cpe1=1.8 ) tree experiment Cpe2 =0.6 4.5 m Cpe2 =0.6 ε/ (UH3/H) Cpe2 =1.4 Cpe2 =1.4 Cpe2 =1.6 Cpe2 =1.8 X1/H k/UH2 X1/H

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**Comparison of vertical profiles of e behind tree ( type C, Cpe1=1.8 ) **

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**Comparison of vertical profiles of k behind tree ( type C, Cpe1=1.8 ) **

measurement Cpe2=1.6 Cpe2=1.4 Cpe2=1.8 Cpe2=0.6 Result with Cpe2=1.4 shows good agreement.

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**Comparison of vertical velocity profiles **

behind tree ( type C, Cpe1=1.8 ) measurement Cpe2=1.6 Cpe2=1.4 Cpe2=1.8 Cpe2=0.6 Result with Cpe2=1.4 shows good agreement.

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**Effects of Cpe2 When Cpe2 is decreased ･･･ within tree canopy**

behind tree e increase e decrease k decrease k decrease Mean wind velocity decrease Cpe2=1.4 was selected under the condition of Cpe1=1.8..

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**Comparison of vertical velocity profiles behind tree (Cpe2 =1.4)**

experiment Cpe1 =1.8 , Cpe2 =1.4 Comparison of vertical velocity profiles behind tree (Cpe2 =1.4) Comparison of vertical profiles of k behind tree (Cpe2 =1.4)

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**Comparison of vertical velocity profiles behind tree**

experiment type C model （Cpe1 =1.8 , Cpe2 =1.4） type B model （Cpe1 =1.8） (x1/H=1) (x1/H=2) (x1/H=3) (x1/H=4) (x1/H=5) Comparison of vertical velocity profiles behind tree (x1/H=1) (x1/H=2) (x1/H=3) (x1/H=4) (x1/H=5) Comparison of vertical profiles of k behind tree

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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

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**LAWEPS： Local Area Wind Energy Prediction System**

Developed by NEDO through the Four-Year Project ( ) 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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Outline of LAWEPS Five-stage Grid Nesting ( One-way) 500km 100km 1st Domain 2nd Domain 3rd Domain 10km 50km 10km 10km 3rd Domain 4th Domain 5km 5th Domain tree canopy model is incorporated into the model for 5th Domain 5th Domain Wind Turbines 0.5~1km 1~2km

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**Table : Five sub-domains in LAWEPS**

Domains Horizontal Area Horizontal Resolution ×500 km km ×100 km km ×50 km m ×10 km m ×1 km 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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Field observation Long term measurements of wind velocities at Shionomisaki Peninsula of Wakayama Prefecture, Japan.

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**Testing Area: Shionomisaki Peninsula, Japan**

1st-3rd Domain 4th Domain (a) (b) 11km 1st 9km N W E 2nd S 3rd 5th Domain B A A & B are Obs. Sites Doppler Sodar Observations are done at site B

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**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 ) Cpe1 = 1.8 Fi Fk Fe

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**Comparison of the 1st-5th Full Nesting Calculation with the Ground Observations**

Site A Site A Site B 2001 Dec. 15th 15JST Oct 28th 12JST Dec. 15th 15Jst 5th Domain Model Observation 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 m/s m/s % Site B m/s m/s % Frequency of the Occurrence of Wind Speed

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**Annual Mean Wind Speed Map 30m above the Ground**

4th Domain 0~8m/s 5th Domain(a) 5th Domain(b)

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**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.

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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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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.

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APPENDIX

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**Prediction of thermal effects of planted trees**

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**Following effects are considered :**

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）

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**Shading effects of solar and long-wave radiations**

The present model is based on the following assumptions: Only the effect of tree crown is modelled. The effects of stem and branches are assumed to be negligibly small. The ratio of absorbed radiations to the total incident radiation on the tree crown is given by the function 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] (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.

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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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**Higashi-Nibancho Street in Sendai City**

Prediction of thermal effects of trees planted on a main street in Sendai city sidewalk median strip roadway building 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

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**Computed cases building median strip roadway tree (2) Case 2**

Wind Wind tree (1) Case 1 (2) Case 2 sidewalk N S W E Table Computed cases Condition of Tree Planting Case 1 Not Planted Case 2 Present Situation Case 3 Densely Planted Wind (3) Case 3

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**Physical processes to be considered and model equations to be solved**

Momentum transfer by wind and turbulence diffusion Heat transfer by wind and turbulence 3 Contaminant diffusion by wind and turbulence 4 Moisture transfer by wind and turbulence Radiative heat transfer in outdoor space Heat conduction to underground and inside of building Heat energy balance at urban surface (ground surface and building surface ) →all processes listed here are considered

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**Flowchart for assessing outdoor human comfort**

based on CFD

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**All heat balance components to calculate the surface temperature**

To begin with, I’ll be speaking about outline of radiation calculation. Radiative transport is computed using the Monte – Carlo simulation. This figure shows all heat heat balance components to calculate wall and building surfaces temperature. In this figure, absorbed solar radiation Si and long-wave radiation Ri are calculated with Monte – Carlo simulation.

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**Distribution of surface temperature**

（August 4, 12:00） [C] Case 1 (Not Planted) (2) Case 2 (Present Situation ) (3) Case 3 (Densely Planted)

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**Lastly, I’d like to show the distribution of SET*.**

SET* is effected by wind, temperature, radiation, humidity, clothing, metabolism.

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**Horizontal Distributions of Velocity Vectors **

at the Height of 1.5m （August 4, 13:00） Wind Velocity is decreased by trees A’ A Case 1 (Not Planted) (2) Case 2 (Present Situation ) (3) Case 3 (Densely Planted)

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**Vertical Distribution of Wind Velocity Vectors at A-A’ sections （August 4, 13:00）**

Case 1 (Not Planted) (2) Case 2 (Present Situation ) Case 1 Case 2 (3) Case 3 (Densely Planted) Case 3

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**air temperature Vertical Distribution （August 4, 13:00）**

29.0 30.5 32.0 [C] Case 1 (Not Planted) Case 1 (Not Planted) (2) Case 2 (Present Situation ) (2) Case 2 (Present Situation ) Wind Velocity Vectors air temperature

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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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**Horizontal distribution of SET**

Horizontal distribution of SET* (Standard Effective Temperature) at the height of 1.5m 25.0 30.0 35.0 [℃] （August 4, 13:00） Case 1 (Not Planted) (2) Case 2 (Present Situation ) (3) Case 3 (Densely Planted)

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**(Present Situation ) －(Not Planted)**

Difference of SET* at the height of 1.5m (August 4, 13:00) -5.0 0.0 5.0 [℃] ① SET* is decreased by trees ② But SET* is increased by trees in these areas (Case 2) －(Case 1) (Present Situation ) －(Not Planted)

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**Horizontal Distributions of Velocity Vectors **

at the Height of 1.5m （August 4, 13:00） Wind Velocity is decreased by trees Case 1 (Not Planted) (2) Case 2 (Present Situation ) (3) Case 3 (Densely Planted)

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**Change of SET* by greening**

11 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. In this study, The effect of increasing grass area ratio is that SET* decrease and the thermal environment is improved. But, by planting trees, SET* increase and cause a rising discomfort in outdoor thermal environment. This is because a density of trees in planting area is too mach. Therefore, the following result is clarified. The effect of wind velocity on the outdoor thermal environment is significantly large. 2) Overly dense arrangement of plant canopies may not improve the outdoor environment. 3) It is necessary to clarify the suitable density arrangement of plant canopies.

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**Gas diffusion within street canyon**

• Gas is released from all roadway area (red area) at height of 0.15m Computed cases

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**Vertical Distribution of Wind Velocity**

Using these velocities, contaminant diffusion is predicted Case 1 (Not Planted) (2) Case 2 (Present Situation ) Case 1 Case 2 (3) Case 3 (Densely Planted) Case 3

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**Vertical distribution of gas concentration**

0.0 1.5 3.0 W E CV Average value in CV：0.84 CV Average value in CV ：0.74 Sidewalk Sidewalk Sidewalk Sidewalk Case 1(Not Planted) (2) Case 2 (Present Situation ) -> In case 1, Gas is convected to sidewalk area CV Average value in CV ：0.76 Sidewalk Sidewalk (3) Case 3 (Densely Planted) Gas is diffused to upper region in Cases 2 and 3

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**Averaged values in CV and PS**

PS : Pedestrian Space (from 0.3m to 1.8m height on sidewalk) PS Sidewalk Sidewalk Normalized values • Gas is not convected to sidewalk area so much in Case2 and Case3 by the effects of trees on flowfield

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