Ming-Chung Chan and Chun-Ho Liu

Transcription

1 Large-eddy smulaton of turbulent flows and pollutant transport nsde and above dealzed urban street canyons under dfferent unstable thermal stratfcaton Mng-Chung Chan and Chun-Ho Lu Department of Mechancal Engneerng, The Unversty of Hong Kong 7/F Hakng Wong Buldng, Pokfulam Road, Hong Kong. Abstract Large-eddy smulaton (LES) s employed to study the behavours of flows and pollutant transport nsde and over dealzed urban street canyons under dfferent unstable thermal stratfcaton. Three confguratons of dealzed street canyon, consstng of buldng-heght-to-street-wdth (aspect) ratos,.5, 1 and, are consdered. Under unstable stratfcaton, the vertcal profles of streamwse velocty and temperature over the bottom rough surface are more unform and the turbulent transport of momentum and heat are enhanced. Insde the street canyons, the ventlaton performance, whch are characterzed by the ar exchange rate (ACH), pollutant exchange rate (PCH), pollutant retenton tme and average pollutant concentraton, s found mproved n unstable stratfcaton. 1 Introducton Apart from wnd speed, wnd drecton, buldng geometry and buldng sze, thermal stratfcaton s another maor factor affectng the flows and pollutant transport over urban areas and nsde street canyons. Ths stuaton s not rare that s usually found n daytme when the solar radaton s strong and the wnd s calm,.e. an envronment of unstable thermal stratfcaton. It can be observed from the feld measurements that the temperature on a buldng facade s up to 5 o C n a summer afternoon (Bourba and Awb, 4) and the temperature gradent n the near-wall regon s as large as 5 o C cm -1, resultng n an over-1- o C temperature dfference between buldng facade and ar (Louka et al., ). It was also observed that unstable stratfcaton n the urban boundary layer accounted for 85% n daytme and stll 64% n nght-tme (Nachou et al. 8). Therefore, the effects of unstable thermal stratfcaton on the wnd flows and ventlaton n urban envronments should not be overlooked. Under unstable thermal stratfcaton, the (negatve) vertcal temperature gradent nduces an upward buoyancy force to the wnd felds that substantally changes the mean flows, and the turbulent transport of momentum, heat and pollutants both nsde and above urban street canyons. Numerous computatonal flud dynamcs (CFD) studes have been performed to nvestgate the turbulent flows and pollutant transport nsde a street canyon under dfferent thermal confguratons, such as wall heatng, ground heatng and all-urban-surface heatng (Xe et al., 7, L et al., 1, Cheng and Lu, 11). These studes generally showed that the turbulence s more energetc and the ventlaton s promoted n unstable stratfcaton. The changes n turbulence structure due to unstable stratfcaton affect the ground-level ventlaton performance of a street canyon, especally the narrow one, n whch the mean wnd s relatvely calm and the pollutant removal manly reles on roof-level turbulence. Therefore, an n-depth understandng of how unstable thermal stratfcaton affects the behavours of 1

2 6 th European and Afrcan Conference on Wnd Engneerng turbulent flows and pollutant transport nsde and above street canyons could facltate sophstcated urban plannng towards better ar qualty. For example, the thermal envronment of a street canyon can be controlled by buldng materals of proper thermal propertes or orentaton of buldng facades wth respect to ncomng solar radaton such that the ground-level pollutant concentratons are reduced. In ths study, large-eddy smulaton (LES) senstvty tests, ncludng urban geometry confguratons of three aspect ratos (.5, 1 and ) and dfferent ntenstes of unstable thermal stratfcaton, are performed wth the neutral case for each urban confguraton as the respectve reference. The LES results are compared to the wnd tunnel results by Uehara et al. (). For the free-stream regon above the buldng roughness elements, the vertcal profles of mean streamwse velocty, mean temperature, velocty fluctuatons, and turbulent momentum and heat fluxes are dscussed. Insde the (frst) street canyon wth the ground-level pollutant source, the pollutant concentratons, ventlaton performance (measured by ar (ACH) and pollutant (PCH) exchange rates), pollutant retenton tme and average pollutant concentraton under dfferent unstable thermal stratfcaton are also reported. Methodology Fgure 1: Computatonal doman and boundary condtons LES equpped wth the one-equaton subgrd-scale () turbulent knetc energy (TKE) model and the box flter (flow varables are fltered accordng to the grd sze) s employed n ths study. A threedmensonal (3D) doman, whch s homogeneous n the spanwse drecton, s constructed by a seres of dealzed (rectangular) urban street canyons and a free-stream regon aloft (Fgure 1). Three values of buldng-heght-to-street-wdth (aspect) ratos, h/b =.5, 1 and, are examned and the number of street canyons s 8, 1 and 16, respectvely, where h (kept constant) s the buldng heght and b (vared) s the street wdth. The rato between the heght of free-stream regon and the buldng heght H/h equals 7. A unform background pressure gradent P x s appled n the streamwse drecton to drve the prevalng flow n the free-stream regon. Hence, the free-stream wnd s perpendcular to the street axes so that the worst scenaro of street canyon ventlaton s examned. A free-slp boundary

3 6 th European and Afrcan Conference on Wnd Engneerng 3 condton (BC) s assgned to the doman top whle no-slp BCs are assgned to all urban surfaces. To smulate the unstable thermal stratfcaton, the top boundary s kept at constant temperature θ f whle the urban surfaces are kept at a hgher constant temperature θ f + θ. Perodc BCs for flows and temperature are assgned to the spanwse and streamwse doman extents smulatng nfntely repeatng, nfntely long street canyons. Buoyancy force s modelled by the Boussnesq approxmaton so that the effects of densty varaton are neglected except n the buoyancy force n the governng equatons. The ntensty of unstable thermal stratfcaton s controlled by the value of gravtatonal acceleraton g, wth g = for the reference cases n neutral stratfcaton. An area source of constant concentraton C s used to release pollutant contnuously on the ground surface of the frst street canyon. A zero-pollutant BC s assgned to the doman nlet, a symmetry BC to the doman top and the urban surfaces, an open BC to the doman outlet, hence, the pollutant s removed from the doman by prevalng flow wthout reflecton. Perodc BCs are assgned to the spanwse extent. Consequently, n the frst street canyon, the ground-level pollutant emsson rate equals the vertcal pollutant flux across the roof area that determnes the streamwse pollutant flux movng out through the doman outlet n pseudo steady-state. In the LES models, the flud (ar) s assumed to be dry and ncompressble whle the pollutant s assumed to be passve (flow s ndependent from pollutant concentraton) and nert (no chemcal reacton). The resolved-scale parts of wnd velocty, temperature, knematc pressure and pollutant concentraton are calculated numercally from the fltered governng equatons, namely, the contnuty (1), momentum transport (), thermal energy transport (3) and pollutant transport (4): u = (1) u t + u u p = + u ( ν + ν ) + λ Px δ 1 + αg( θ θ) δ 3 () θ t + u θ ( ν + ν = Pr ) θ (3) c + u t c ( ν + ν = Sc ) c The over-bar denotes the resolved-scale varables. Tensor notaton and summaton conventon on repeated ndces are used (, = 1, and 3 denote streamwse x, spanwse y, and vertcal z drectons, respectvely). u s the velocty vector, p s the knematc pressure, λ = 1 for the free-stream regon and λ = nsde the street canyons, δ s the Kronecker delta, ν s the knematc vscosty, α s the thermal expanson coeffcent, θ s the temperature, θ s the reference temperature (a nomnal mean temperature n the doman), c s the pollutant concentraton. The Prandtl number Pr and the Schmdt number Sc are both set to.7. The Smagornsky model (Smagornsky, 1963) s used and the knematc eddy vscosty ν s calculated by: 1/ ν = C k (5) k where C k (=.7) s a modellng constant and (= [ x y z] 1/3 ) s the flter wdth. By the oneequaton model (Schumann, 1975), the turbulent knetc energy (TKE) k s calculated by ts transport equaton: (4)

4 6 th European and Afrcan Conference on Wnd Engneerng 4 k t + u k = k αgν 3/ ν SS Cε + ( ν + ν ) + δ 3 Pr k θ (6) where the stran rate tensor S s calculated by: S 1 u = and C ε (= 1.5) s another modellng constant. u + The spatal doman for each model s dscretzed nto over 4,5, rectangular elements. The grd s refned near all the no-slp surfaces to capture the rapdly changng flow varables. The smallest grd szes n the street canyon and the free-stream regon are, respectvely, h 3 and h 3. The tme step ncrement for each model s.5h/u f Δt.3h/U f, where U f s the free-stream velocty (streamwse velocty at top boundary) dependng on the thermal stratfcaton. To acheve the pseudo steady-state, an ntalzaton perod of at least 1h/U f s processed n a coarser mesh (around 5, to 6, rectangular elements). Afterwards, another development tme of at least 5h/U f s processed n the aforementoned (refned) mesh confguraton. The data are then collected for another duraton of at least 5h/U f that are averaged n the spanwse drecton and over the samplng tme. As the smulaton tme goes on, the felds of turbulent flow, temperature and pollutant are selfdeveloped. The LES data n pseudo steady-state flows, n whch the mean and fluctuatng statstcs are unchanged wth tme, are ensemble averaged n tme and spanwse domans. The calculated statstcs are subsequently analysed n dfferent non-dmensonal forms. (7) 3 Results and Dscusson The smulaton condtons are characterzed by the Reynolds number Re and the bulk Rchardson number R (Table 1). The free-stream velocty U f and the overall doman temperature dfference θ are the velocty and temperature scales, respectvely. The subscrpts h and H denote whch length scale s used. Buldng heght h s used as the length scale when descrbng the flow condtons nsde a street canyon whle the free-stream heght H s used for flow condtons n the free-steam regon. Table 1: Smulaton condtons of LES models. h/b Re H R H Re h R h.5 74, 3, ,6 4, , 4, 94, 4, ,7 6, 13,5 6,

5 6 th European and Afrcan Conference on Wnd Engneerng 5 a) b) c) d) Fgure : Vertcal profles of a) streamwse mean velocty, b) standard devatons of streamwse velocty, c) standard devatons of vertcal velocty and d) Reynolds stress at the mddle of street canyon. The LES and wnd tunnel results are shown n the left and rght panels, respectvely

6 6 th European and Afrcan Conference on Wnd Engneerng 6 The LES results are compared to those of the wnd tunnel experments of Uehara et al. () at h/b = 1. The vertcal profles of mean streamwse wnd velocty, the standard devatons of streamwse and vertcal wnd veloctes and the Reynolds stress along the vertcal lne at the mddle of a street canyon are shown n Fgure. In the wnd tunnel experments, 3D cubcal blocks, whch were dfferent from the D square rbs n the current LES, were used as the buldng elements. Shorter roughness elements were used to develop an ncomng turbulent flow that entered the test secton contanng the buldng elements. The vertcal profles were taken at the ffth (sample) street canyon. The Reynolds number Re based on buldng heght and ncomng flow velocty was about 3,5. The bottom ground surface was heated to nduce the unstable stratfcaton and the buldng elements are thermally nsulted. The bulk Rchardson number R, whch s used to descrbe the wnd tunnel results, was based on the temperature dfference between the ground and the roof-level openng of street canyons. The velocty scale used to normalze the wnd tunnel results s the mean streamwse velocty at 7 mm above the ground level and the overall heght of wnd tunnel test secton s 1 m. Both the LES and wnd tunnel results show a smlar trend for the mean and fluctuatng propertes of the flows wth respect to the ncrease n unstable stratfcaton. The mean wnd relatve to the freestream wnd and the turbulence ntenstes are enhanced both nsde the street canyons and n the freestream regon as the unstable stratfcaton are strengthened. However, the mean wnd and turbulence ntenstes nsde the street canyons measured n the wnd tunnel experments are several tmes hgher n magntudes than those n the LES. The dscrepancy s manly due to the 3D geometry of buldng elements so addtonal momentum entranment s transferred from the street ntersectons around cubcal buldngs nto the street canyons. Fgure 3: Vertcal Profles of normalzed (a) mean streamwse velocty and (b) mean temperature n free-stream regon over street canyons of aspect rato h/b =.5 In the free-stream regon of the models of street canyons of aspect rato h/b =.5, by further averagng the LES data n the entre streamwse drecton, the vertcal profles of mean flow varables are shown n Fgure 3 whle the vertcal profles of flow fluctuatons, turbulent momentum flux and turbulent heat flux are shown n Fgure 4. It s found that, wth the ncrease n buoyancy, the profles of mean velocty and temperature over urban roughness are more unform. It s because the turbulent mxng enhances wth the level of unstable stratfcaton. The local maxmum of turbulence ntensty ust above the buldng roof-level rses as the unstable stratfcaton s enhanced. For the LES models of h/b = 1 and, the trends of results wth respectve to the level of stratfcaton n the free-stream regon are smlar to those of h/b =.5 (whch wll also be reported n the conference).

7 6 th European and Afrcan Conference on Wnd Engneerng 7 Fgure 4: Vertcal profles of normalzed (a) streamwse velocty fluctuaton, (b) spanwse velocty fluctuaton, (c) vertcal velocty fluctuaton, (d) vertcal turbulent momentum flux and (e) vertcal turbulent heat flux n free-stream regon over street canyons of aspect rato h/b =.5 a) b) c) d) Fgure 5. Varaton of a) ACHmean, b) ACHturb, c) ACHsgs and d) ACH of street canyons wth Rh for all ARs

8 6 th European and Afrcan Conference on Wnd Engneerng 8 Ar exchange rate ACH s defned as the temporal average of the volumetrc outflux of ar attrbuted to upward flows at the roof level. ACH s decomposed nto ACH mean, ACH turb and ACH sgs, denotng the ar volumetrc outfluxes drven by upward mean wnd velocty, resolved-scale turbulence and turbulence, respectvely (Fgure 5). The roof-level openng area plus buldng roof area A roof and the free-stream velocty U f are used to normalze all the ACH components and ACH. It s shown that the street-canyon ventlaton s domnated by turbulence n all the cases (dfferent h/b and R h) and the overall ventlaton performance s generally mproved wth stronger unstable stratfcaton. Apart from ACH, pollutant exchange rate (PCH), pollutant retenton tme and average pollutant concentraton consstently show that the street-level ventlaton performance s mproved wth stronger unstable thermal stratfcaton (these wll also be explaned n detals n the conference). 4 Conclusons Wth unstable thermal stratfcaton, the vertcal profles of mean velocty and temperature n the freestream regon over the roughness elements of hypothetcal urban areas are more unform. Moreover, the velocty fluctuatons, turbulent momentum flux and turbulent heat flux are enhanced. Insde the street canyons, ACH, PCH, pollutant retenton tme and average pollutant concentraton all consstently show that the street-level ar qualty s mproved n unstable thermal stratfcaton. References Bourba, F. & Awb, H.B. 4. Buldng cluster and shadng n urban canyon for hot dry clmate Part 1: ar and surface temperature measurements. Renewable Energy, 9, Louka, P., Vachon, G., Sn, J.-F., Mestayer, P.G. & Rosane, J.-M.. Thermal effects on the ar flow n a street canyon - Nantess'99 expermental results and model smulatons. Water, Ar and Sol Polluton: Focus, Nachou, K., Lvada, L. & Santamours, M., 8. Expermental study of temperature and ar flow dstrbuton nsde an urban street canyon durng hot summer weather condtons part I: ar and surface temperatures. Buld. Envron. 43, Xe, X., Lu, C.-H. & Leung, D.Y.C. 7. Impact of buldng facades and ground heatng on wnd flow and pollutant transport n street canyons. Atmos. Envron. 41, L, X.-X., Brtter, R.E., Koh, T.Y., Norford, L.K., Lu, C.-H., Entekhab, D. & Leung, D.Y.C. 1. Large-eddy smulaton of flow and pollutant transport n urban street canyons wth ground heatng. Boundary-Layer Meteorol. 137, Cheng, W.C., & Lu, C.-H. 11. Large-eddy smulaton of turbulent transports n urban street canyons n dfferent thermal stabltes. J. Wnd Eng. Ind. Aerodyne. 99, Uehara, K., Murakam, S., Okawa, S. & Wakamatsu, S.,. Wnd tunnel experments on how thermal stratfcaton affects flow n and above urban street canyons. Atmos. Envron. 34, Schumann U., Subgrd scale model for fnte dfference smulatons of turbulent flows n plane channels and annul. J. Comput. Phys. 18: Smagornsky, J., General crculaton experments wth the prmtve equatons I: the basc experment. Mon. Weather Rev. 91: