11.2 ESTIMATES OF AIR AND POLLUTANT EXCHANGE FOR STREET CANYONS IN COMBINED WIND- BUOYANCY DRIVEN FLOW USING THE RANS RENORMALIZATION GROUP

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1 11.2 ESTIMATES OF AIR AND POLLUTANT EXCHANGE FOR STREET CANYONS IN COMBINED WIND- BUOYANCY DRIVEN FLOW USING THE RANS RENORMALIZATION GROUP k-ε TURBULENCE MODEL Chun-Ho Lu *, Wa Ch Cheng and Denns Y.C. Leung Deparmen of Mechancal Engneerng, The Unversy of Hong Kong, Pokfulam Road, Hong Kong 1. INTRODUCTION Cy-scale ar polluon s a wdely concerned problem because of s adverse mpacs on he healh of cy nhabans and he assocaed medcal burden on he communy. In a cy, one of he maor sources of ar polluans s vehcular exhaus whch ems more han 5% of nrogen doxde (NO 2 ), carbon monoxde (CO) and oher organc ar polluans. Vehcular polluans are mosly emed on he ground level. I follows he mcroscale wnd flow nsde he sree canyon movng upward o he roof level and evenually beng removed o he shear layer. Ths ranspor process s complcaed by he buldng confguraons and meeorologcal condons ha has araced he neress of numerous research sudes ncludng feld measuremens, laboraory expermens and mahemacal modelng. More dealed leraure revews are dscussed elsewhere (e.g. Vardoulaks e al. 23; L e al. 26). Cheng e al. (28) focused on an dealzed wodmensonal (2D) sree canyon of buldng-hegh-osree wde (aspec) rao h/b 1 n whch hey revealed he mechansms of ar (ACH) and polluan (PCH) exchange raes usng seady-sae compuaonal flud dynamcs (CFD) soluons under sohermal condons. In fac, buoyancy, manly due o he hea dsspaon from solar radaon on facades and road surfaces, subsanally modfes he srucures of wnd flow and polluan ranspor nsde a sree canyon (Km and Bak 1999, 21; Xe e al. 26, 27). In hs paper, we are neresed n he unseady-sae behavors, f any, of venlaon and polluan removal n a sree canyon under unsable srafcaons. An dealzed sree canyon of h/b 1 a Reynolds number (Re U h/ν, where U s he reference wnd speed scale and ν he molecular knemac vscosy) equal o 12, serves as a demonsraon n hs paper o llusrae he unseadysae naure of ACH and PCH a Rchardson number (R -gh/u 2 ΔΘ/Θ, where g s he gravaonal acceleraon, ΔΘ he emperaure dfference and Θ he characersc emperaure scale) equal o -8 and METHODOLOGY 2.1 Mahemacal Model Unlke our prevous sudy (Cheng e al. 28), he unseady-sae ncompressble Reynolds-averaged Naver-Sokes (RANS) equaons equpped wh he Renormalzaon Group (RNG) k-ε urbulence model (Yakho e al. 1986) was used. The governng equaons conss of he connuy and he momenum conservaon Here, u p ' u ' δ s he me, Caresan coordnae, 2 θ Θ Θ g (1). (2) u he velocy ensor, x he p he knemac pressure, δ he Kronecker dela and θ he ar emperaure. The ensor u ' u ' represens he Reynolds sress whch s modeled by he eddy-vscosy model u ' u ' u ν 2 δk 3, (3) where ν ( C ν k 2 /ε) s he urbulen knemac vscosy, C ν (.845) he modelng consan, k ( u ' u ' 2 ) he urbulen knec energy (TKE) and ε he TKE dsspaon rae. Boussnesq approxmaon s used n Equaon (2) o handle he effecs of buoyancy. Equaons (1) and (2) are expressed n ensor noaon and he usual summaon convenon on repeaed ndces (, 1, 2) apples. A varable wh an overlne represens he ensemble average whle wh a prme represens he flucuang quany. To accoun for he hermal effecs, he energy conservaon θ θ θ κ s consdered, where κ ( ν /Pr, where Pr.72 s he urbulen Prandl number) s he urbulen dffusvy of hea. For a passve and ner ar polluan wh ensemble averaged concenraon φ, s ranspor s represened by he mass conservaon φ φ D φ where D ( ν /Sc, where Sc.72 s he urbulen Schmd number) s he urbulen dffusvy of polluan. (4) (5) * Correspondng auhor address: Chun-Ho Lu, Deparmen of Mechancal Engneerng, 7/F Hakng Wong Buldng, The Unversy of Hong Kong, Pokfulam Road, Hong Kong; e-mal: luchunho@graduae.hku.hk

2 Turbulence of he sysem s modeled by he RNG k- ε urbulence model whch ncludes he ranspor of TKE k k and he ranspor of ε k α ν k Pk G ε ε ε x x αεν x ε C1 ε ( Pk C3 εgb ) k 3 2 Cνη ( 1 η η ) ε C2ε 3 1 γη k b ε (6). (7) Here, α k and α ε are he nverse effecve Prandl number for k and ε, respecvely. In hs paper, a flow a hgh Re s assumed ha yelds α k α ε The source erms P k and G b represen, respecvely, he TKE producon due o wnd shear k ν (8) P and buoyancy G b g ν θ δ2 Θ Pr The las erm on he rgh-hand sde of Equaon (7) s k ε (9) η. (1) The modelng consans for he RNG k-ε urbulence model are η 4.38, γ.12, C 1ε 1.42, C 2ε 1.68 and C 3ε anh w/v, where w s he vercal and v he horzonal velocy componens. 2.2 Compuaonal Doman & Boundary Condons The 2D compuaonal doman consss of 13 dencal sree canyons of h/b 1 regularly placed under he shear layer (Fgure 1). Only he wnd flow and polluan ranspor n he cener sree canyon s examned whle he res of he sree canyons are used o faclae fully developed urbulence n he core of he compuaonal doman (Meroney e al. 1996). A he op of he shear layer, h f 3h measurng from he roof of he sree canopy, s prescrbed as symmery boundary a consan emperaure Θ. The prevalen wnd n he shear layer s drven by an nflow boundary a he upsream nle and an ouflow boundary a he downsream ouflow. The nflow (vercal) wnd profle s α U ( z) h z h U, (11) f also known as he power law, where α (.28) s he wnd profle exponen and z he ground-normal dsance. To accoun for he effecs of (unsable) srafcaon, all he srees are heaed a a unform emperaure (ΘΔΘ) o acvae unsable srafcaons. In addon, a lnear (decreasng) emperaure profle Θ ΘΔΘ h ( z) 1 z (12) s prescrbed a all he buldng facades. No-slp boundares are used on all he sold boundares (roofs, facades and srees). A unform area polluan source wh consan polluan concenraon C s placed on he ground surface of he cener sree canyon. The wnd flow s characerzed by he dmensonless parameers Prandl number (Pr), Re and R. In hs paper, Pr and Re are kep consan a.72 and 12,, respecvely, ha are hgh enough for flow ndependen from molecular vscosy (Pavageau and Schazmann 1999). Whls, R measures he relave drvng forces of wnd and buoyancy o he flow ha s conrolled by adusng g. The aspec rao of he sree canyon s kep consan a h/b 1. Over 2 mllon rangular elemens were used o dscreze he 2D compuaonal doman. Gven h 2 he cross-seconal area of he sree canyon of h/b 1, he mnmum and maxmum szes of he elemen are approxmaely 1-7 h 2 and 1-3 h 2, respecvely. The 3 rd - order-accurae monoone upsream-cenered scheme for conservaon law (MUSCL) was used n he spaal doman whle he mplc 1 s -order-accurae PISO scheme was used n he emporal doman. 3. FORMULATIONS OF ACH & PCH Fgure 1. Compuaonal doman and boundary condons for he combned wnd-buoyancy drven wnd flow and polluan ranspor n sree canyons. The shaded regon s he volume Ω of cener sree canyon. Cheng e al. (28) developed he mahemacal formulaons of ACH and PCH based on he eddyvscosy and -dffusvy models for a sysemac comparson of venlaon and ar qualy n sree canyons. Ths secon summarzes hose formulaons.

3 where wc s he vercal polluan flux normal o he roof of sree canyon. Analogously, PCH can be dvded no s mean ( PCH ) and urbulen ( ) componens PCH PCH. (18) PCH s calculaed by he mean vercal polluan flux whle PCH wc dx (19) s calculaed by he eddy-dffusvy model c w'c' dx D dx. (2) z Fgure 2. Sreamlnes of he sree canyon a R Ar Exchange Rae (ACH) ACH represens he rae of ar removal from a sree canyon hrough he roof level. I s defned as 1 ACH w dxd. (13) Here, w s he vercal velocy componen, Γ roof he roof area of he sree canyon and he samplng me. The subscrp sgnfes ha only he upward wnd flow w > s aken no accoun. The ACH n Equaon (13) can be furher paroned no s mean ( ACH ) and urbulence ( ACH' ) componens n he form ACH ACH ACH'. (14) ACH can be calculaed by he mean flow ACH w (15) whle ACH' can be calculaed by assumng soropc urbulence and usng he eddy-vscosy model ACH' Γ roof Γ roof 1 2 dx w' w' dx k 1 w ν 6 2 z dx. (16) 4. RESULTS & DISCUSSIONS In hs secon, we repor he CFD resuls for he venlaon and polluan removal for he sree canyon of h/b 1 a Re 12,. In parcular, he perodc behavors a R -8 and -16 are conrased. 3.2 Polluan Exchange Rae (PCH) PCH, whch represens he rae of polluan removal from a sree canyon hrough he roof level, can be defned n a manner smlar o ACH 1 PCH wc dxd (17) Γ roof Fgure 3. Tme races of ACH and R -8. ACH' a

4 4.1 R -8 Fgure 2 shows he snapsho of sreamlnes nsde he sree canyon a R -8 (slghly unsable). For prevalen wnd flows from he lef-hand sde o he rghhand sde, a large clockwse-roang prmary recrculaon ogeher wh anoher small counerclockwse-roang secondary recrculaon are formed, respecvely, a he cener core and he ground-level wndward corner of he sree canyon. Moreover, buoyancy promoes boh he mean and flucuang wnds nsde he sree canyons. No shown n hs paper are he sreamlnes under sohermal condons n whch he prmary recrculaon cenered n he sree canyon domnaes he flow. In hs paper, one of he maor fndngs of he venlaon and polluan ranspor nsde a sree canyon under unsable srafcaons s he perurbed wnd flow. A suffcenly hgh R ( -8 as deermned n hs sudy), he wnd flow s no longer seady-sae, Insead, he venlaon exhbs perodc ACH n whch he perod s abou 2,2 sec. We decompose he me race of ACH no he mean ( ACH ; Fgure 3a) and urbulen ( ACH' ; Fgure 3b) componens. Boh ACHs are posve so ha no large-scale fresh ar enry s calculaed by he CFD. ACH' (.4531) s larger han ACH (.1915) by more han 2 mes ha s n lne wh our prevous fndng under sohermal condons. The amplude of he perodc ACH ( ) s larger han ha of he perodc ACH' ( ) by almos hree mes. Ths fndng sgnfes he predomnan conrbuon of buoyancy o he mean flow. I s also worh menonng ha a me lag (abou 2 sec) s observed n-beween he peaks of ACH and. ACH' Fgure 4 depcs he snapsho of he spaal conours of polluan concenraon nsde he sree canyon a R -8. Because of he unform ground-level area polluan source, he polluan s dsrbued que evenly n he near-ground regon. Hgher polluan concenraons are observed on boh he leeward and wndward facades ha are caused by he characersc recrculang wnd. Because of he clockwse-roang prmary recrculaon, he polluan s carred oward he leeward facades once emed from he source. Nex, ravels upward along he leeward facade o he roof level resulng n he (slghly) elevaed polluan concenraon near he roof-level leeward corner. The aged ar and polluan are hen removed from he sree canyon o he shear layer (manly on he leeward sde). Smulaneously, he fresh ar from he shear layer eners he sree canyon ha leads o a lower polluan concenraon on he wndward sde of he sree canyon. Indeed, he polluan concenraon nsde he couner-clockwse-roang secondary recrculaon s hgher (comparable o ha on he ground-level) due o s solaed naure (from he prevalen wnd n he shear layer) and he weaker urbulen ranspor n-beween he recrculaons. The polluan hus accumulaes on he wndward façade leadng o prolonged reenon me. Fgure 4. Polluan dsrbuon a R -8. Fgure 5. Tme races of PCH and -8. a R

5 Because he wnd s he carrer of he polluan, he polluan ranspor and removal are unseady-sae n naure. PCH and are calculaed by Equaons (19) and (2), respecvely, a R -8. Fgure 5 shows he me races of he PCHs. Smlar o he venlaon a he same R, he polluan removal arbued o he mean componen ( PCH. 1; Fgure 5a) s much smaller (> 2 mes) han ha of he urbulen componen ( ; Fgure 5b). On he conrary, he.2685 magnude of he perodc PCH ( ) s larger han s ( ) counerpar by wo folds. ACH and ACH' are, respecvely, and Hence, buoyancy has predomnan effec on mean wnd. Fgure 8 shows he spaal dsrbuon of polluan nsde he sree canyon a R -16. I s smlar o ha a R -8 because of he smlar recrculang srucures. Owng o he larger values of ACH and PCH a R -16, he roof-level polluan concenraon s slghly lower. I s hus suggesed ha buoyancy favors venlaon and polluan removal. Perodc behavors are also observed n he PCHs of sree canyon a R -16 (Fgure 9). PCH ( ) lags slghly behnds ( ). Smlar o oher ACHs and PCHs repored prevously, he amplude of perodc PCH ( ) s larger han ha of ( ) by more han wo mes ha agan suggess he predomnan conrbuon of buoyancy o he mean flow. Fgure 6. Sreamlnes of he sree canyon a R R -16 Nex, we double he R o -16 for mldly unsable srafcaons. Heang up he sree canyon o R -16 makes he srafcaon more unsable. Fgure 6 depcs he sreamlnes nsde he sree canyon a R -16. Smlar o s R -8 counerpar, wo couner-roang recrculaons are developed. The prmary one leans slghly o he leeward sde connecng o he prevalen wnd n he shear layer. The secondary recrculaon s an solaed one resded a he ground-level wndward corner. As expeced, buoyancy promoes boh he mean and flucuang wnds n he sree canyon whch can be refleced from he larger sreamfuncon (and graden). The me races of ACHs a R -16 also exhb perodc behavors whose perod s abou 1,8 sec (Fgure 7). Buoyancy no only acvaes he perodc venlaon bu decreasng R (ncreasng ΔΘ) also shorens he perod of oscllaon. ACH has no well developed ye bu he average value s abou.393 (Fgure 7a). Whereas, he urbulen componen ACH' has developed almos fully n whch he mean value s abou.672 (Fgure 7b). The ampludes of perodc Fgure 7. Tme races of ACH and R -16. ACH' a

6 5. CONCLUSIONS The mechansms of venlaon and polluan Pavageau, M. and Schazmann, M., 1999: Wnd unnel measuremens of concenraon flucuaons n an urban sree canyon. Amo. Envron., 33, removal for 2D sree canyons of h/b 1 under unsable srafcaon (R -8 and -16) wh all he buldng roofs, facades and srees beng heang up were suded usng he RNG k-ε urbulence model. In parcular, we focused on he perodc behavors of venlaon and polluan removal nduced by buoyancy. CFD resuls shows ha wo couner-roang recrculaons are developed nsde he sree canyon. Buoyancy favors venlaon and so does polluan removal a large. Vardoulaks, S., Fsher, B.E.A., Percleous, K. and Gonzalez-Flesca, N., 23: Modellng ar qualy n sree canyons: a revew, Amo. Envron., 37, Xe, X., Lu, C.-H., Leung, D.Y.C. and Leung, M.K.H., 26: Characerscs of ar exchange n a sree canyon wh ground heang. Amo. Envron., 4, Xe, X., Lu, C.-H. and Leung, D.Y.C., 27: Impac of However, he solaed naure of he secondary buldng facades and ground heang on wnd flow recrculaon leads o an locally elevaed polluan concenraon on he wndward façade. Buoyancy promoes he unseady-sae ACHs and PCHs as well n and polluan ranspor n sree canyons. Amo. Envron., 41, Yakho, V., Orszag, S.A., Thangam, S., Gask, T.B. and whch he ampludes of he perodc ACHs and PCHs Spezale, C.G., 1986: Renormalzaon group are found o ncrease wh ncreasng R. analyss of urbulence. J. Sc. Compu., 1, Fgure 8. Polluan dsrbuon a R REFERENCES Cheng, W.C., Lu, C.-H. and Leung, D.Y.C., 28: Compuaonal formulaon for he evaluaon of sree canyon venlaon and polluan removal performance. Amo. Envron., 42, Km, J.-J. and Bak, J.-J., 1999: A numercal sudy of hermal effecs on flow and polluan dsperson n urban sree canyon. J. Appl. Meeorol., 38, Km, J.-J. and Bak, J.-J., 21: Urban sree-canyon flows wh boom heang. Amo Envron., 35, L, X.-X., Lu, C.-H., Leung, D.Y.C. and Lam, K.M., 26: Recen progress n CFD modellng of wnd feld and polluan ranspor n sree canyons. Amo. Envron., 4, Meroney, R.N., Pavageau, M., Rafalds, S. and Schazmann, M., 1996: Sudy of lne source characerscs for 2-D physcal modelng of polluan dsperson n sree canyons. J. Wnd Eng. Ind. Aerodyn., 62, Fgure 9. Tme races of PCH and -16. a R