Presentation on theme: "NATO ASI, May 6 Optimization of tree canopy model for CFD application to local area wind energy prediction Akashi Mochida LBEE ( Laboratory of Building."— Presentation transcript:
1 NATO ASI, May 6Optimization of tree canopy model for CFD application to local area wind energy prediction Akashi MochidaLBEE ( Laboratory of Building Environment Engineering )Tohoku University, JapanT. Iwata, A. Kimura, H. Yoshino, and S. Murakami
2 Factors affecting the flow around a hilly terrain SeparationCirculationRe-circulationConvexConcaveRoughnessRecirculationSea SurfaceInlet flowWake of windmillCollisionAcceleration way・Existence of trees changes wind speed at a windmill heightconsiderably.・So, the effects of trees should be considered carefully forthe selection of a site for wind power plantThe canopy model for reproducing the aerodynamic effects of trees was optimized for the use of local area wind energy prediction.
3 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 parkand surroundingsCFD prediction(revised k-εmodel)
4 Modelling of aerodynamic effects of trees In order to reproduce the aerodynamic effects of trees, i.e.1) decrease of wind velocity2) increase of turbulence,extra terms are added to model equations.Here, a revised k-e model is used as a base.
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 thebasic equations for DSM ( DifferentialStress Model ), ・ the expressions for Mellor-Yamada level2.5 model was proposed by Yamada(1982)・the expressions for k – e model wasproposed by Hiraoka (1989 in Japanese,1993 in English). ・several revisions (1990’s～）
6 Modelling of aerodynamic effects of tree canopy decreases in velocityincreases in turbulenceincreases in dissipationk – e model with tree canopy model[Continuity equation][Average equation][k transport equation][ transport equation]FiFkiFukpFCe1e×Fe: fraction of the area covered with treesCf: drag coefficient for canopya : leaf surface area densityCp1: 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
7 Extra terms for incorporating aerodynamic effects of tree canopy h：fraction of the area coveredwith treesCpe1, Cpe2 ： model coefficients in turbulence modelingCf：drag coefficient for canopya： leaf surface area densityFiFkFetypeAtypeBtypeCHiraoka： Cpe1=2.5Yamada： Cpe1=1.0Uno：Cpe1=1.5Svensson： Cpe1=1.95Green：Cpe1=Cpe2=1.5Liu：Cpe1=1.5， Cpe2=0.6
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)FiFkFetypeAtypeBtypeCHiraoka： Cpe1=2.5Yamada： Cpe1=1.0Uno：Cpe1=1.5Svensson： Cpe1=1.95Green：Cpe1=Cpe2=1.5Liu：Cpe1=1.5， Cpe2=0.6
9 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 losswithin canopy (Green)(Dk= )This terms also appears in Fe.FiFkFetypeAtypeBtypeCHiraoka： Cpe1=2.5Yamada： Cpe1=1.0Uno：Cpe1=1.5Svensson： Cpe1=1.95Green：Cpe1=Cpe2=1.5Liu：Cpe1=1.5， Cpe2=0.6
10 Difference in Fe (type A VS type B & C) In type A, length scale within canopyL=1/a (a： leaf surface area density )Fe∝(here t = k/e )FiFkFetypeAtypeBtypeCHiraoka： Cpe1=2.5Yamada： Cpe1=1.0Uno：Cpe1=1.5Svensson： Cpe1=1.95Green：Cpe1=Cpe2=1.5Liu：Cpe1=1.5， Cpe2=0.6
11 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 ∝FiFkFetypeAtypeBtypeCHiraoka： Cpe1=2.5Yamada： Cpe1=1.0Uno：Cpe1=1.5Svensson： Cpe1=1.95Green：Cpe1=Cpe2=1.5Liu：Cpe1=1.5， Cpe2=0.6
12 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 layerh, a, Cf ：parameters to be determined according to the real conditions of treestype Btype CFiFkFeまず、モデル係数Cpeの最適化について説明します。
13 Revised k-e model adopted here -mixed time scale model- 1) revision of modelling of eddy viscosityReynolds stress :Modifying eddy viscosityA mixed time scale, m , proposed by Nagano et al.
14 Revised k-e model based on mixed time scale concept 2) Introduction of the mixed time scale (Nagano et al.)Mixed time scalets , time scale of mean velocity gradientA harmonic balance of , i.e ands (timescale of mean velocity gradient)Cs=0.4t , turbulence time scale
15 Results of CFD computations with tree canopy models
16 Comparison between types A and B ・Results of wind velocity behind a model tree werecompared.・Wind tunnel experiment was carried out by Ohashi・Exact value of leaf area density “a” of the modeltree was given30cm30cmmodel tree
17 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 coefficientCf =0.8[-]Expressions for FeCase No.typeCpe11-1typeA1.01-21.51-34.02-1typeB2-22-32.02-43.02-5typeA (L=1/ a)typeB
18 Distribution of mean wind velocity (at 0.6m height) Comparison between types A and BDistribution of mean wind velocity (at 0.6m height)0.6mTree modelexperimentpe1Tree modelexperimentpe1Mean wind velocity [m/s]Mean wind velocity [m/s]x1 [m]x1 [m]TypeATypeB
19 Distribution of mean wind velocity (at 0.8m height) Tree modelTree modelpe1pe1experimentexperimentCpe1 =4.0Mean wind velocity [m/s]Mean wind velocity [m/s]Cpe1 =1.0Cpe1 =1.5Cpe1 =1.0x1 [m]x1 [m]TypeATypeB・Effect of difference in Cpe1 value is large compared to the differenceof model type (types A or B)・Type B model corresponds well with experiment in the rangeCpe1=1.5～2.0.・Type B was selected in this study・More detailed optimizations for Cpe1 were done
20 Optimization of model coefficient Cpe1 for typeB ・ By comparing CFD results with measurements,Cpe1 was optimized.FiFkFe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 ）
21 Computational domain：100m(x1:streamwise)×100m (x3:vertical) Comparison of flow behind pine treesCL2D 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)
22 Comparison of vertical velocity profiles behind tree a=1.17[m2/m3]: measurement: CFD with type B modelCf =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
23 Comparison of vertical velocity profiles behind tree (Cpe1=1.8)measurementType 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。
24 Comparison of vertical profiles of k behind tree a=1.17[m2/m3]: measurement: CFD with type B modelCf =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
25 k is underestimated in this area by type B model Comparison of vertical profiles of k behind tree (Cpe1=1.8)measurementType B model(Cpe1 =1.8)kの鉛直分布k is underestimated in this area by type B model
26 In types C, Fk = Production(Pk) - Dissipation(Dk) Performance of Type C model in which the energy loss in canopy is also consideredIn types C, Fk = Production(Pk) - Dissipation(Dk)Pk: production of k within canopy (=<ui >Fi)Dk: a sink term to express the turbulence energy losswithin canopy (Green) (Dk= )Similar term also appears in Fe.FiFkFetypeAtypeBtypeCHiraoka： Cpe1=2.5Yamada： Cpe1=1.0Uno：Cpe1=1.5Svensson： Cpe1=1.95Green：Cpe1=Cpe2=1.5Liu：Cpe1=1.5， Cpe2=0.6
27 Optimization of model coefficient Cpe2 for typeC Green ：Cpe1= Cpe2=1.5Liu et al. : Cpe1=1.5, Cpe2= 0.6
28 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 treevertical profiles of k behind treeGreen ：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 treevertical profiles of k behind treeLiu et al. : Cpe1=1.5, Cpe2= 0.6
29 Optimization of model coefficient Cpe2 for typeC Computed CasesCpe1=1.8( optimizedvalue for type B )typeC
30 Comparison of numerically predicted drag coefficient CD ■Pressure difference ⊿PV(z)PfPb■Drag coefficient of tree CD
31 Comparison of numerically predicted drag coefficient CD ( Cpe1=1.8 ) typeC
32 Comparison of streamwise profiles of k & e around tree ( type C, Cpe1=1.8 )treeexperimentCpe2 =0.64.5 mCpe2 =0.6ε/ (UH3/H)Cpe2 =1.4Cpe2 =1.4Cpe2 =1.6Cpe2 =1.8X1/Hk/UH2X1/H
33 Comparison of vertical profiles of e behind tree ( type C, Cpe1=1.8 )
34 Comparison of vertical profiles of k behind tree ( type C, Cpe1=1.8 ) measurementCpe2=1.6Cpe2=1.4Cpe2=1.8Cpe2=0.6Result with Cpe2=1.4 shows good agreement.
35 Comparison of vertical velocity profiles behind tree ( type C, Cpe1=1.8 )measurementCpe2=1.6Cpe2=1.4Cpe2=1.8Cpe2=0.6Result with Cpe2=1.4 shows good agreement.
36 Effects of Cpe2 When Cpe2 is decreased ･･･ within tree canopy behind treee increasee decreasek decreasek decreaseMean wind velocity decreaseCpe2=1.4 was selected under the condition of Cpe1=1.8..
37 Comparison of vertical velocity profiles behind tree (Cpe2 =1.4) experimentCpe1 =1.8 , Cpe2 =1.4Comparison of vertical velocity profiles behind tree (Cpe2 =1.4)Comparison of vertical profiles of k behind tree (Cpe2 =1.4)
38 Comparison of vertical velocity profiles behind tree experimenttype 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
39 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 surfaceEffect of surface roughness by plants
40 LAWEPS： Local Area Wind Energy Prediction System Developed by NEDO through the Four-Year Project( )New Energy and Industrial TechnologyDevelopment Organization of Japan ( Project Leader: S.MurakamiMembers: Y.Nagano, S.Kato, A.Mochida, M.Nakanishi, etc.)The Goal of the Project:To Develop a wind prediction Model which isApplicable to Complex Terrain including Steep Slopes, Able to Predict the Annual Mean Wind Speed withthe Prediction Error of less than10%.
41 Outline of LAWEPSFive-stage Grid Nesting ( One-way)500km100km1st Domain2ndDomain3rdDomain10km50km10km10km3rd Domain4th Domain5km5th Domaintree canopy model is incorporated into the model for 5th Domain5th DomainWind Turbines0.5~1km1~2km
42 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 mDomains 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 Field observationLong term measurements of wind velocities at Shionomisaki Peninsula of Wakayama Prefecture, Japan.
44 Testing Area: Shionomisaki Peninsula, Japan 1st-3rd Domain4th Domain(a)(b)11km1st9kmNWE2ndS3rd5th DomainBAA & B are Obs. SitesDoppler Sodar Observations are done at site B
45 Leaf surface area density a is given from a = LAI/HLAI : 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 = 1.8FiFkFe
46 Comparison of the 1st-5th Full Nesting Calculation with the Ground Observations Site ASite ASite B2001 Dec. 15th 15JST Oct 28th 12JST Dec. 15th 15Jst5th Domain ModelObservationVertical 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 m/s m/s %Site B m/s m/s %Frequency of the Occurrence of Wind Speed
48 Annual Mean Wind Speed Map 30m above the Ground 4th Domain0~8m/s5th Domain(a)5th Domain(b)
49 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.
50 Conclusions3) 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 Conclusions5) 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.
54 Following effects are considered : Model for tree canopyFollowing effects are considered :decrease of velocity and increase of turbulencegeneration of water vapor from leafshading effect on long-wave radiationshading effect on short-wave (solar) radiationTree crown （樹冠）
55 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 functionℓ(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](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.
57 Coupled simulation of radiation, conduction and convection Prediction of thermal effects of trees planted on a main street in Sendai city
58 Higashi-Nibancho Street in Sendai City Prediction of thermal effects of trees planted on a main street in Sendai citysidewalkmedian striproadwaybuilding2.5mtree(1) PlancentertreeHigashi-Nibancho Street in Sendai City（東二番丁通，仙台）0.3mbuildingsidewalkroadway(2) Section
59 Computed cases building median strip roadway tree (2) Case 2 WindWindtree(1) Case 1(2) Case 2sidewalkNSWETable Computed casesCondition of Tree PlantingCase 1Not PlantedCase 2Present SituationCase 3Densely PlantedWind(3) Case 3
60 Physical processes to be considered and model equations to be solved Momentum transfer by wind and turbulence diffusionHeat transfer by wind and turbulence3 Contaminant diffusion by wind and turbulence4 Moisture transfer by wind and turbulenceRadiative heat transfer in outdoor spaceHeat conduction to underground and inside of buildingHeat energy balance at urban surface (ground surface and building surface )→all processes listed here are considered
61 Flowchart for assessing outdoor human comfort based on CFD
62 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.
63 Distribution of surface temperature （August 4, 12:00）[C]Case 1(Not Planted)(2) Case 2(Present Situation )(3) Case 3(Densely Planted)
64 Lastly, I’d like to show the distribution of SET*. SET* is effected by wind, temperature, radiation, humidity, clothing, metabolism.
65 Horizontal Distributions of Velocity Vectors at the Height of 1.5m （August 4, 13:00）Wind Velocity is decreased by treesA’ACase 1(Not Planted)(2) Case 2(Present Situation )(3) Case 3(Densely Planted)
66 Vertical Distribution of Wind Velocity Vectors at A-A’ sections （August 4, 13:00） Case 1(Not Planted)(2) Case 2(Present Situation )Case 1Case 2(3) Case 3(Densely Planted)Case 3
67 air temperature Vertical Distribution （August 4, 13:00） 29.030.532.0[C]Case 1 (Not Planted)Case 1 (Not Planted)(2) Case 2 (Present Situation )(2) Case 2 (Present Situation )Wind Velocity Vectorsair temperature
68 Evaluation of Standard Effective Temperature (SET*) ・Velocity・Temperature・Humidity・Mean RadiativeTemperature (MRT)Index for thermal comfort（ SET*）
69 Horizontal distribution of SET Horizontal distribution of SET* (Standard Effective Temperature) at the height of 1.5m25.030.035.0[℃]（August 4, 13:00）Case 1(Not Planted)(2) Case 2(Present Situation )(3) Case 3(Densely Planted)
70 (Present Situation ) －(Not Planted) Difference of SET* at the height of 1.5m(August 4, 13:00)-5.00.05.0[℃]① SET* is decreased by trees② But SET* is increased by trees in these areas(Case 2) －(Case 1)(Present Situation ) －(Not Planted)
71 Horizontal Distributions of Velocity Vectors at the Height of 1.5m （August 4, 13:00）Wind Velocity is decreased by treesCase 1(Not Planted)(2) Case 2(Present Situation )(3) Case 3(Densely Planted)
72 Change of SET* by greening 11Change of SET* by greeningThe 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.
73 Gas diffusion within street canyon • Gas is released from allroadway area (red area)at height of 0.15mComputed cases
74 Vertical Distribution of Wind Velocity Using these velocities, contaminant diffusion is predictedCase 1(Not Planted)(2) Case 2(Present Situation )Case 1Case 2(3) Case 3(Densely Planted)Case 3
75 Vertical distribution of gas concentration 0.01.53.0WECVAverage value in CV：0.84CVAverage value in CV ：0.74SidewalkSidewalkSidewalkSidewalkCase 1(Not Planted)(2) Case 2 (Present Situation )-> In case 1,Gas is convectedto sidewalk areaCVAverage value in CV ：0.76SidewalkSidewalk(3) Case 3 (Densely Planted)Gas is diffused to upper region in Cases 2 and 3
76 Averaged values in CV and PS PS : Pedestrian Space(from 0.3m to 1.8m heighton sidewalk)PSSidewalkSidewalk Normalized values• Gas is not convected to sidewalk area so much in Case2 and Case3by the effects of trees on flowfield