LES ESTIMATION OF ENVIRONMENTAL DEGRADATION AT THE URBAN HEAT ISLAND DUE TO DENSELY-ARRAYED TALL BUILDINGS

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1 3.3 LES ESTIMATION OF ENVIRONMENTAL DEGRADATION AT THE URBAN HEAT ISLAND DUE TO DENSELY-ARRAYED TALL BUILDINGS Tetsuro Tamura* Junch Nagayama Kench Ohta Tetsuya Takem and Yasuo Okuda Tokyo Insttute of Technology Yokohama Japan Buldng Research Insttute Tukuba Japan. INTRODUCTION For the mtgaton of heat sland effects on coastal ctes t s sometmes expected that the sea breeze come nto the nland area of a cty where ts cold ar mngles wth the hotter ar over and nsde the urban canopes. In the downtown of Tokyo there exsts a coastlne at the southeast boundary so the sea breeze s observed to reach nto about 0 km nland. But recently several very tall buldngs have been constructed at Shodome near ths coast lne between the center of Tokyo and the Tokyo bay. We are concerned about that these tall buldngs block a passage of sea breeze nto the downtown of Tokyo. Of course t s generally thought that the sze of heat sland phenomenon tself ranges to several tens square klo-meters wth meso-scale behavor whch s ten tmes larger than the Shodome area of some square klo-meters. Such a large dscrepancy tends to ntroduce ths local effect to be not serous but trval. Therefore the treatment to aspect of the ground surface has been thus far very poor. But for the analyss of the heat sland the surface treatment and the area consdered should be selected by a sgnfcance of phenomenon that each ssue encompasses. In such a convecton-domnant phenomenon at Shodome t s mportant to focus on detals of the very local flow characterstcs nsde both of the roughness layer and the urban canopes and to clarfy the effect of cold ar contaned wthn the sea breeze on heat envronment n the downtown of Tokyo. To solve ths ssue we have to formulate the physcal model or the numercal model whch represents correctly aspect of the ground surface condton consstng of buldngs structures and vegetaton et al. In order to get the data for buldng shapes n a local area the electronc mappng nformaton s utlzed. The present study uses heght data of surface roughness and expresses drectly surface shapes of urban area for the numercal smulaton. The prevous numercal smulaton of the boundary layers usually has employed the log law model or sometmes a lttle sophstcated verson such as the wall layer model for the treatment of the ground surface condton. It means that the ntegral * Correspondng author address: Tetsuro Tamura Dept. of Envronmental Scence and Technology Tokyo Insttute of Technology G Nagatuda Mdor-ku Yokohama Japan; e-mal: tamura@depe.ttech.ac.p quanttes are utlzed for representng total boundary effects but not local effects. Recent data for buldng heght determnng the surface roughness are much mproved and have a horzontal resoluton wth about or.5 m so t mght be enough to smulate roughness shapes even an ndvdual resdental house placed on the ground surface n urban areas. Further n the case of the numercal smulatons for wnds n urban canopes whch need to deal wth detals of exstng flows throughout spaces between buldngs so the RANS (Reynolds averaged Naver-Stokes) technque mght have advantage to compute the flow feld hghly resolved by the grd from standponts for computer capacty. However n the case that we focus on the roughness layer or nsde the urban canopes the flow n ths near-wall regon s very complcated and unsteady due to separaton vortex-sheddng rapd flow contracton and extenson among roughness elements. Nevertheless the complete RANS modelng of turbulence has not been developed yet for such a complex flow. Also for the estmaton of mtgaton of heat sland effect by utlzng the local area crculaton the numercal model whch can predct tme sequental turbulence s approprate because the convecton by fluctuatng behavor of turbulent flows represents drectly and strctly a scale or a range of heat transport. Hence ths study employs the LES (large eddy smulaton) technque whch s appled to the wnd flow over actual roughened ground surface n Tokyo area. For the horzontal nflow boundary condton of the computatonal doman at the Shodome area of km by.5 km turbulent flow data such as wnd velocty or temperature are mposed by takng nto consderaton exstence of the sea upstream. For the generaton of nflow turbulence we addtonally set up the drver doman of km by.5 km and solve a spatally developng turbulent boundary layer over smooth sea surface by applyng the quas-perodc condton based on the rescalng technque for smooth wall wthout any surface deformaton. Accordng to the prevous study the feld measurement around the Shodome area showed that the extreme reducton of wnd velocty behnd a group of tall buldngs. We compare the LES results wth these feld measurement data and valdate the LES model. Next we show the wnd flow characterstcs around tall buldngs at the Shodome area. Especally

2 we brng nto focus the turbulence structures n the roughness layer and the urban canopes. Fnally based on these results at the Shodome area we nvestgate the envronmental aspects at the urban heat sland due to densely-arrayed tall buldngs.. PROBLEM FORMULATION. Governng Equatons In ths study we carry out large-eddy smulaton (LES) analyss of spatally-developng turbulent boundary layers. Under the Boussnesq approxmaton the fltered governng equatons consst of the Naver-Stokes equatons the contnuty equaton and the temperature equaton for three dmensonal ncompressble stratfed flow as follows: coeffcents C and C θ are evaluated dynamcally usng the Germano dentty..3 Numercal Model Fgure llustrates a numercal model for the smulaton of urban boundary layers at Shodome area where the south-southeast nflow correspondng to the sea breeze s gven. A large eddy smulaton of the spatally developng smooth-wall turbulent boundary layer whch has no pressure gradent s formulated Re-scaled Re-ntroduced Recycle Staton Inflow Sodome Area u u u p u u τ + = + + Rbθδ 3 t x ρ x Re x + z x x τ Drver Regon Man Regon x () u θ u θ θ h + = y Fg. Numercal Model t Reτ Pr x where t u p θ Re τ =u τ δ/ν R b =vβ θδ/u τ and Pr=ν/α denote tme velocty pressure temperature the Reynolds number the bulk Rchardson number and Prandtl number (u τ : frcton velocty δ : boundary layer depth β : thermal expanson coeffcent ν : eddy vscosty α :coeffcent of thermal dffusvty g : gravty acceleraton) respectvely. u = ( u v w) are the fltered components of the velocty vector. The quanttes τ and h are the subgrd-scale (SGS) stress and heat flux respectvely as follows: τ = u u u u h = u θ u θ. (). Sub-grd Scale Modelng In ths study the SGS closure s performed by a Smagornsky-type concept for eddy vscosty (ν t : turbulent vscosty α t : turbulent thermal dffusvty) as follows: τ 3 δτkk = νt S = C S S (3) θ h = αt θ = Cθ S (4) where C and C θ denote the model coeffcents for SGS modelng of velocty and temperature felds respe ctvely S the stran rate tensor and = ( ) 3 x y z grd-flter wdth respectvely. Ths Smagornsky-type model can be extended to the dynamc Smagornsky model n whch the model Bottom: Smooth Wall utlzng the technque of the quas-perodc boundary condton (Lund et al. 998 [] ). In ths model we set up the computatonal doman whch conssts of two parts: one s a man regon for the smulaton of the flow feld over the Sodome area where many hgh-rse buldngs densely locate at the center of the man regon; and the other s a drver regon for the auxlary smulaton for generatng nflow turbulence for the man regon. In the drver regon the varables at a sngle y-z secton are rescaled accordng to the development rato of the boundary layer thckness and frcton velocty along the streamwse drecton and rentroduced at the nflow boundary. The velocty profle at the nflow boundary s reset based on the law of the wall n the nner regon or defect law n the outer regon. Ths process allows the generaton of spatally developng neutral turbulent boundary layer wth a small computatonal doman. The drver computatonal regon s set to be 5δ 0 *.6δ 0 *δ 0 (δ 0 =500[m] s the boundary layer thckness at the nflow boundary.) wth correspondng grd numbers of and 400 n the streamwse (x) wall-normal (z) and spanwse (y) drectons respectvely. The mesh wdths are ( x + z + y + ) = ( ~ ). The man computatonal regon s set to be 3δ 0.6δ 0 δ 0 n x z and y drectons wth the same resolutons as those for the drver regon except for x + =.95. As a frst step we assume that temperature s dealt wth a passve scalar and hence buoyancy effects are neglected. It s because we fnd out how the heat generated from the buldng group moves by the sea breeze at the Sodome area. In the man regon the passve scalar wth a value of unty s gven at the surfaces of a group of hgh-rse buldngs as a

3 boundary condton. Accordngly we set R b to be zero and Pr=0.5. Also we set Re τ to be Numercal Method The numercal method used s based on a MAC method for the man regon and a fractonal step method for the drver regon. For a tme advancng the Adams-Bashforth method for convecton terms and the Crank-Ncolson method for dffuson terms are employed. The spatal dervatves are approxmated by the second-order central dfference for the drver regon and fourth-order central dfference for the man regon. The boundary condtons for velocty and passve scalar are shown n Table. south locaton where the nfluence of the buldng group on the wake flow s nsgnfcant the west where the nfluence s consdered to be sgnfcant and the north where the nfluence s so strong and wnd feld s much changed. To compare our computed result wth ths observatonal data we also calculated the traectory of the balloon accordng to the followng moton equatons and obtaned the nstantaneous velocty at each heght where balloon exsts: m x = ρ( u x ) v r ACD m y = ρ( v y ) v r ACD m z = mg + ρ( w z ) v AC B r D + (5) Table Boundary condtons where x y z mg ρ v r = ( u x ) + ( v y ) + ( w z ) A C D =0.4 B=mg-W t ρac D / denote the balloon Velocty Drver Man Bottom Top No-slp u / z w=u δ*/dx No-slp Free-slp Spanwse Perodc Perodc Inflow Outflow Passve Scalar All of Boundary Rescaled velocty Velocty at x/δ = 4.8 n the drver regon / t + c / / t + c / Neumann Condton where δ* s the dsplacement thckness c s taken to be the bulk velocty. 3. COMPARISON WITH OBSERVATION DATA Here there s the observatonal data [] [3] obtaned by castng up the plot balloon at three observaton ponts (see Fg.). Wnd velocty was measured by traectory of the ascendng plot balloon n daytme sunny July The surface aspect of the Sodome area has dfferent type at three locatons: the heght [m] SE SSE S SSW SW WSW south (Present LES) west (Present LES) north (Present LES) south (Tanaka and Mkam) west (Tanaka and Mkam) north (Tanaka and Mkam) max buldng heght wnd drecon [deg.] Fg. 3 Vertcal profle of wnd drecton south (Present LES) west (Present LES) north (Present LES) south (Tanaka and Mkam) west (Tanaka and Mkam) north (Tanaka and Mkam) South West North Smulaton Observaton Fg. Traectory of plot balloon n the man regon heght [m] horzontal velocty [m/s] Fg. 4 Vertcal profle of horzontal velocty max buldng heght 8

4 poston the gravty force the ar densty relatve velocty of the balloon to the wnd velocty the cross secton area of the balloon the drag coeffcent and buoyant force. W t s assumed to be.5 [m/s] as the constant ascendng (or termnal) velocty. Fgures 3 and 4 show the profle for the wnd drecton and horzontal velocty respectvely together wth the observatonal result. In spte of the dfference of the nflow between the observaton and the smulaton the vertcal profles of the smulated wnd drectons and horzontal velocty are reasonably consstent wth the observaton results at the south of the buldng group. On the LES results at the west sde and the north sde both velocty and drecton of the wnd are much decreasng around a top of tall buldngs lke the observaton data. But below the maxmum buldng heght both of the LES and the observaton data are relatvely dfferent from each other. Especally n the LES results the nflow s completely shelded by the buldngs and the velocty extremely decreases to about 8 % and s almost constant below the buldngs heght at the leeward regon. On the other hand the observaton data shows a rapd ncrease of velocty n the lmted locaton. At the west sde the horzontal velocty fluctuates more unsteadly than LES results. Streamwse dr. Fg. 6 Instantaneous streamwse velocty n a vertcal cross secton of tall buldngs 4. WIND FLOW CHARACTERISTICS Based on the flow vsualzaton t can be seen that very complcated but specfed wnd flow patterns are formed n the wake of a group of tall buldngs and these patterns vary n the vertcal drecton. These flow patterns may be thought to strongly affect the formaton of thermal envronment. Fgure 5 llustrates the LES results for nstantaneous streamwse velocty feld n varous cross-sectons. We can fnd that all buldngs at Sodome are completely embedded n the turbulent boundary layer. Fgure 6 and 7 llustrate nstantaneous streamwse velocty n a vertcal (shown Fg. 7 Instantaneous streamwse velocty n a horzontal cross secton of tall buldngs by a broken lne n Fgure 7) and horzontal cross secton of a group of tall buldngs at the alttude of 90 meters. It can be recognzed that the streamwse velocty entrely decreases on the leeward of buldngs. But we also fnd a path wth strong wnd among the buldng group. So ths means nstantaneous strong wnd sometmes happens n the wake. It can be seen n the horzontal secton that there s a wdely extendng regon wth a low velocty nsde of the buldng group and hgh velocty regon among a complex arrangement of buldngs. Fg. 5 Turbulent boundary layer over Shodome area 5. CONVECTION AND DIFFUSION OF HEAT In vew of accurate estmaton for Heat Island degradaton t s necessary to dscuss the convecton and dffuson of heat. As the frst stage we used a passve scalar n whch the buoyancy s not consdered and set t on the surface of the buldng group as heat sources. Fgure 8 shows a locaton of the settng passve scalar at ntal stage. Fgure 9 depcts the heat (passve scalar) transfer. It can be seen that the passve scalar s convected far away at a hgher poston. Whle a below the buldngs passve scalar s not transported so much by the effect of the blockng sea breeze. Also we can see that a passve scalar

5 the detaled analyss for example the buoyancy effect ncorporated. Fg. 8 Intal stage of passve scalar on the surface of tall buldngs Streamwse dr. 7. REFERENCES [] Lund T.S. Wu X. and Squres K.D. 998; Generaton of turbulent nflow data for spatally developng boundary layer smulatons J. comput. Phys [] Tanaka H. and T. Mkam 005; Evaluaton of the effects of the buldngs n the Shodome dstrct on the downstream of sea breeze Proc. Fall Conf. Meteo. Soc. Japan 88 Kobe Hyogo Japan P34. [3] Mkam T. 006; Feld Measument at Shodome and Shnbash areas Feld Measurement Report on March 6 th Mnstry of Land Infrastructure and Transport hou/ hou-3.pdf) Fg. 9 Aspect of the heat (passve scalar) transfer has stagnated n the buldng group because the cavty regon s formed among the buldng group. In spte of no effect of the buoyancy passve scalar dffuses largely n the upward as well as the streamwse drecton. 6. CONCLUSIONS In ths study for the estmaton of envronmental degradaton at the urban heat sland due to densely arrayed tall buldngs we conducted LES for turbulent flow and temperature felds around a group of tall buldngs near the sea. The followng results are obtaned. In comparson wth feld measurement data we have valdated that the reasonably good results can be obtaned by the present LES method. Accordng to the LES results for turbulent flows n the roughness layer over a cty and the urban canopes t s recognzed that the flow velocty extremely decreased behnd the buldng blocks. Accordngly we can easly magne the occurrence of the envronmental degradaton for the thermal condton due to densely arrayed tall buldngs. Also we can fnd the very specal aspect such as the steady patterns of a path wth strong wnd n the wake of a group of tall buldng. By the passve scalar (temperature) analyss from the heat sources on the surface of the buldng blocks we can fnd the heat has been convected and dffused largely behnd a group of tall buldngs. For the accurate estmaton of thermal envronment we need