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1 Optimization of tree canopy model for CFD application to local area wind energy prediction Akashi Mochida Akashi Mochida LBEE ( Laboratory of Building Environment Engineering ) Tohoku University, Japan T. Iwata, A. Kimura, H. Yoshino, and S. Murakami NATO ASI, May 6

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2 Factors affecting the flow around a hilly terrain Separation Circulation Re-circulation Convex Concave RoughnessRecirculation 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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3 This study focuses on modelling of aerodynamic effects of tree canopy ( effects on wind flow and turbulence ) CFD prediction (revised k-εmodel) A birdview over the planted park and surroundings

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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

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5 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 – model was proposed by Hiraoka (1989 in Japanese, 1993 in English). several revisions (1990s

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6 Modelling of aerodynamic effects of tree canopy k – model with tree canopy model decreases in velocity increases in turbulence increases in dissipation [Continuity equation] [k transport equation] [ transport equation] [Average equation] F i F k ii Fu F kp FC k : fraction of the area covered with trees C f : drag coefficient for canopy a : leaf surface area density C p 1 : model coefficient for F F i : extra term added to the momentum equation + F k : extra term added to the transport equation of k + F : extra term added to the transport equation of

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7 Extra terms for incorporating aerodynamic effects of tree canopy a leaf surface area density C f drag coefficient for canopy fraction of the area covered with trees C p C p model coefficients in turbulence modeling FiFi FkFk F typeA typeB typeC Hiraoka C p 1 =2.5 Uno C p 1 =1.5 Yamada C p 1 =1.0 Green C p 1 =C p =1.5 Liu C p 1 =1.5 C p 2 =0.6 Svensson C p 1 =1.95

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8 Difference in F k (types A & B VS type C) In types A and B, F k = F i ( : ensemble-average ) So-called wake production term this form can be analytically derived (Hiraoka) FiFi FkFk F typeA typeB typeC Hiraoka C p 1 =2.5 Uno C p 1 =1.5 Yamada C p 1 =1.0 Green C p 1 =C p =1.5 Liu C p 1 =1.5 C p 2 =0.6 Svensson C p 1 =1.95

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9 Difference in F k (type A & B VS type C) In types C, Fk = Production(P k ) - Dissipation(D k ) P k : production of k within canopy (= F i ) D k : a sink term to express the turbulence energy loss within canopy (Green) (D k = ) This terms also appears in F FiFi FkFk F typeA typeB typeC Hiraoka C p 1 =2.5 Uno C p 1 =1.5 Yamada C p 1 =1.0 Green C p 1 =C p =1.5 Liu C p 1 =1.5 C p 2 =0.6 Svensson C p 1 =1.95

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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/ ) FiFi FkFk F typeA typeB typeC Hiraoka C p 1 =2.5 Uno C p 1 =1.5 Yamada C p 1 =1.0 Green C p 1 =C p =1.5 Liu C p 1 =1.5 C p 2 =0.6 Svensson C p 1 =1.95

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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) FiFi FkFk F typeA typeB typeC Hiraoka C p 1 =2.5 Uno C p 1 =1.5 Yamada C p 1 =1.0 Green C p 1 =C p =1.5 Liu C p 1 =1.5 C p 2 =0.6 Svensson C p 1 =1.95

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12 C p C p type Btype C FiFi FkFk F 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, C f Extra terms F i, F k, F

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13 1) revision of modelling of eddy viscosity Reynolds stress : Modifying eddy viscosity A mixed time scale, m, proposed by Nagano et al. Revised k- model adopted here -mixed time scale model-

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14 A harmonic balance of, i.e. and s (timescale of mean velocity gradient) 2) Introduction of the mixed time scale (Nagano et al.) C s =0.4 Mixed time scale s, time scale of mean velocity gradient, turbulence time scale Revised k- model based on mixed time scale concept

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15 Results of CFD computations with tree canopy models

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16 model 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

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17 Case No.typeC p 1-1 typeA typeB typeA Leaf surface area density a =17.98[m 2 /m 3 ] Drag coefficient C f =0.8[-] Expressions for F typeB (L=1/ a)

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18 Comparison between types A and B Distribution of mean wind velocity (at 0.6m height) Tree model experiment p 1 Tree model experiment p 1 Mean wind velocity [m/s] 0.6m TypeA TypeB x 1 [m]

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19 Distribution of mean wind velocity (at 0.8m height) 0.8m p 1 TypeA TypeB Mean wind velocity [m/s] x 1 [m] C p =4.0 Tree model experiment C p =1.0 C p =1.5 x 1 [m] C p =1.0 Effect of difference in C p 1 value is large compared to the difference of model type (types A or B) Type B model corresponds well with experiment in the range C p 1 = Type B was selected in this study More detailed optimizations for C p 1 were done

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20 Fi FkFk F Optimization of model coefficient C p for typeB Tsuijimatu Rectangular-cutted-pine-trees as wind-break By comparing CFD results with measurements, C p was optimized.

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21 Computational domain 100m(x 1 :streamwise)×100m (x 3 :vertical) CL 2D computation is carried out at the central section Comparison of flow behind pine trees

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22 (x/H=5)(x 1 /H=4)(x 1 /H=3)(x 1 /H=2)(x 1 /H=1) (x/H=5)(x/H=4)(x/H=3)(x/H=2)(x/H=1) (x 1 /H=5)(x 1 /H=4)(x 1 /H=3)(x 1 /H=2)(x 1 /H=1) (x/H=5)(x/H=4)(x/H=3)(x/H=2)(x/H=1) (x/H=5)(x 1 /H=4)(x 1 /H=3)(x 1 /H=2)(x 1 /H=1)(x 1 /H=5)(x 1 /H=4)(x 1 /H=3)(x 1 /H=2)(x 1 /H=1) Comparison of vertical velocity profiles behind tree : measurement: CFD with type B model (1) C p =1.5 (2) C p =1.6 (3) C p =1.7 (4) C p =1.8 (5) C p =1.9 (6) C p =2.0 a =1.17[m 2 /m 3 ] C f =0.8[-]

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23 Type B model(C p =1.8) measurement Comparison of vertical velocity profiles behind tree (C p =1.8)

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24 (1) C p =1.5 (2) C p =1.6 (3) C p =1.7 (4) C p =1.8 (5) C p =1.9 (6) C p =2.0 (x/H=5)(x 1 /H=4)(x 1 /H=3)(x 1 /H=2)(x 1 /H=1) (x/H=5)(x/H=4)(x/H=3)(x/H=2)(x/H=1) (x 1 /H=5)(x 1 /H=4)(x 1 /H=3)(x 1 /H=2)(x 1 /H=1) (x/H=5)(x/H=4)(x/H=3)(x/H=2)(x/H=1) (x/H=5)(x 1 /H=4)(x 1 /H=3)(x 1 /H=2)(x 1 /H=1)(x 1 /H=5)(x 1 /H=4)(x 1 /H=3)(x 1 /H=2)(x 1 /H=1) Comparison of vertical profiles of k behind tree : measurement: CFD with type B model a =1.17[m 2 /m 3 ] C f =0.8[-]

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25 Comparison of vertical profiles of k behind tree (C p =1.8) Type B model(C p =1.8) measurement k is underestimated in this area by type B model

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26 Performance of Type C model in which the energy loss in canopy is also considered In types C, Fk = Production(P k ) - Dissipation(D k ) P k : production of k within canopy (= F i ) D k : a sink term to express the turbulence energy loss within canopy (Green) (D k = ) Similar term also appears in F FiFi FkFk F typeA typeB typeC Hiraoka C p 1 =2.5 Uno C p 1 =1.5 Yamada C p 1 =1.0 Green C p 1 =C p =1.5 Liu C p 1 =1.5 C p 2 =0.6 Svensson C p 1 =1.95

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27 Optimization of model coefficient C p for typeC Green C p 1 = C p 2 =1.5 Liu et al. : C p 1 =1.5, C p 2 = 0.6 typeC

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28 : measurement: CFD with type C model (x 1 /H=5)(x 1 /H=4)(x 1 /H=3)(x 1 /H=2)(x 1 /H=1) (x 1 /H=5)(x 1 /H=4)(x 1 /H=3)(x 1 /H=2)(x 1 /H=1) (x 1 /H=5)(x 1 /H=4)(x 1 /H=3)(x 1 /H=2)(x 1 /H=1) (x 1 /H=5)(x 1 /H=4)(x 1 /H=3)(x 1 /H=2)(x 1 /H=1) Green C p 1 = C p 2 =1.5 Liu et al. : C p 1 =1.5, C p 2 = 0.6 vertical profiles of k behind tree vertical velocity profiles behind tree

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29 Computed Cases typeC C p 1 =1.8 ( optimized value for type B ) Optimization of model coefficient C p for typeC

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30 Comparison of numerically predicted drag coefficient C D PfPf PbPb V(z)V(z) Pressure difference P Drag coefficient of tree C D

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31 C p 2 C D Comparison of numerically predicted drag coefficient C D ( C p 1 =1.8 ) typeC

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32 experiment C p 2 =1.6 C p 2 =1.4 C p 2 =0.6 C p 2 =1.8 tree ε/ (U H 3 /H) k/U H 2 C p 2 =0.6 C pe2 =1.4 X 1 /H 4.5 m Comparison of streamwise profiles of k & around tree ( type C, C p 1 =1.8 )

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33 C p 2 =1.6 C p 2 =1.4 C p 2 =1.8C p 2 =0. 6 Comparison of vertical profiles of behind tree ( type C, C p 1 =1.8 )

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34 Comparison of vertical profiles of k behind tree ( type C, C p 1 =1.8 ) measurement C p 2 =1.6 C p 2 =1.4 C p 2 =1.8C p 2 =0.6 Result with C p 2 =1.4 shows good agreement.

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35 measurement C p 2 =1.6 C p 2 =1.4 C p 2 =1.8C p 2 =0. 6 Comparison of vertical velocity profiles behind tree ( type C, C p 1 =1.8 ) Result with C p 2 =1.4 shows good agreement.

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36 within tree canopy behind tree decrease k decrease increase k decrease Mean wind velocity decrease When C p 2 is decreased Effects of C p C p 2 =1.4 was selected under the condition of C p 1 =1.8..

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37 C p 1 =1.8, C p 2 =1.4 experiment Comparison of vertical velocity profiles behind tree (C p 2 =1.4) Comparison of vertical profiles of k behind tree (C p 2 =1.4)

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38 Comparison of vertical velocity profiles behind tree Comparison of vertical profiles of k behind tree type C model C p 1 =1.8, C p 2 =1.4 experiment type B model C p 1 =1.8 (x 1 /H=5)(x 1 /H=4) (x 1 /H=3)(x 1 /H=2) (x 1 /H=1) (x 1 /H=5)(x 1 /H=4) (x 1 /H=3)(x 1 /H=2) (x 1 /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 distribution Local Area Wind Energy Prediction System (LAWEPS) Prediction of local area wind distribution The tree canopy model ( type B ) optimized here was incorporated into Local Area Wind Energy Prediction System (LAWEPS)

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40 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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41 2 nd Domain 1 st Domain Five-stage Grid Nesting ( One-way) 3 rd Domain 3 rd Domain 4 th Domain 5 th Domain Wind Turbines 500km 100km 10km 1~2km 0.5~1km 5km 10km 50km Outline of LAWEPS tree canopy model is incorporated into the model for 5 th Domain

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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 )

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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 1 st 2 nd 3 rd 9km 11km A B 5 th Domain 4 th Domain A & B are Obs. Sites Doppler Sodar Observations are done at site B N WE 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) C f = 0.2 (typical value for plant community ( stands of tree ) C p = 1.8 Fi FkFk F

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46 Comparison of the 1 st -5 th Full Nesting Calculation with the Ground Observations 2001 Dec. 15 th 15JST 2000 Oct 28 th 12JST 2001 Dec. 15 th 15Jst Site A Site B 5 th Domain Model Observation Vertical distributions of the calculated wind speed are compared with the tower observations.

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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

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48 Annual Mean Wind Speed Map 30m above the Ground 4 th Domain 5 th Domain(a)5 th 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 C p 1 = ) The value of 1.8 was selected for C p 1 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 C p 1 =1.8 and C p 2 =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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52 APPENDIX

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53 Prediction of thermal effects of planted trees

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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

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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 (1) Distance through the tree crown [m] (2) Leaf area density a [m 2 /m 3 ] (3) Absorption coefficient k [-] (here, k=0.6) Tree crown=

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56 Generation (transpiration) of water vapor and heat balance at leaf surface The heat balance equation at leaves that compose the tree crown (1) S P : Absorbed solar radiation [W] R DP : Absorbed long-wave radiation [W] H P : Sensible heat [W] LE P : Latent heat [W] Using Eqs. (1), (2) and (3), leaf surface temperature T P is obtained. H P, LE P and T P are used as boundary conditions for CFD computation. (2) (3)

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57 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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58 2.5m Higashi-Nibancho Street in Sendai City (1) Plan (2) Section building sidewalk roadway tree median strip tree building roadway sidewalk 0.3m center Prediction of thermal effects of trees planted on a main street in Sendai city

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59 Computed cases N S WE (1) Case 1 (2) Case 2 (3) Case 3 Condition of Tree Planting Case 1Not Planted Case 2Present Situation Case 3Densely Planted N S WE N S WE Table Computed cases Wind building sidewalk roadway tree median strip

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60 Physical processes to be considered and model equations to be solved 1Momentum transfer by wind and turbulence diffusion 2Heat transfer by wind and turbulence 3 Contaminant diffusion by wind and turbulence 4 Moisture transfer by wind and turbulence 5Radiative heat transfer in outdoor space 6Heat conduction to underground and inside of building 7Heat energy balance at urban surface (ground surface and building surface ) all processes listed here are considered

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61 Flowchart for assessing outdoor human comfort based on CFD

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62 All heat balance components to calculate the surface temperature

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

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

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66 (1)Case 1 (Not Planted) (2) Case 2 (Present Situation ) (3) Case 3 (Densely Planted) Vertical Distribution of Wind Velocity Vectors at A-A sections August 4, 13:00 Case 3 Case 1Case 2

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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] Vertical Distribution August 4, 13:00

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68 Evaluation of Standard Effective Temperature (SET*) Velocity Temperature Humidity Mean Radiative Temperature (MRT) Index for thermal comfort SET*

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

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

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

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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.

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73 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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74 (1)Case 1 (Not Planted) (2) Case 2 (Present Situation ) (3) Case 3 (Densely Planted) Vertical Distribution of Wind Velocity Using these velocities, contaminant diffusion is predicted Case 3 Case 1Case 2

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75 (2) Case 2 (Present Situation ) (3) Case 3 (Densely Planted) Average value in CV 0.84 Average value in CV 0.74 Average value in CV 0.76 (1)Case 1 (Not Planted) Sidewalk 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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76 Averaged values in CV and PS Sidewalk CV PS PS : 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 Normalized values

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