Large-Eddy Simulation of Plume Dispersion within a Regular Array of Cubic Buildings

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1 Progre n NUCLEAR SCIENCE and TECHNOLOGY, Vol., pp () ARTICLE Large-Eddy Smulaton of Plume Dperon wthn a Regular Array of Cubc Buldng Hromaa NAKAYAMA * and Haruyau NAGAI Japan Atomc Energy Agency, -4 Shrakata, Toka-mura, Naka-gun, Ibarak-ken, 39-95, Japan There a potental problem that the ntentonal releae of radoactve materal by terror attack and the accdental pllage from the tranportaton or torage of flammable and toxc ga occur wthn populated urban area. For the aement of human health hazard or the afety analy of the hazardou ga, not only mean but alo fluctuatng concentraton hould be etmated. Therefore, we perform Large-Eddy Smulaton () of turbulent flow and plume dperon wthn a regular array of cubc buldng a dealzed urban canopy and nvetgate the charactertc of mean and fluctuatng concentraton. The geometry of the buldng array 5 7 wth λ f =.5. Here, λ f the buldng frontal area ndex and defned a the rato of the total frontal area of buldng to the plan area of the tudy te. The plume ource located at the ground urface behnd the buldng n the 7th row of the buldng array. We can capture the unteady behavor of turbulent flow and plume dperon wthn the buldng array and how the patal dtrbuton of mean and fluctuatng concentraton. KEYWORDS:, turbulent flow, dperon, fluctuatng concentraton, buldng array I. Introducton An accurate analy of plume dperon mportant for emergency repone agant accdental or ntentonal releae of hazardou and flammable materal wthn populated urban area. For the aement of human health hazard or the afety analy of the hazardou ga, not only mean but alo fluctuatng concentraton hould be etmated. Therefore, the dperon charactertc of a plume through obtacle array have been examned manly by feld and wnd tunnel experment. For example, Macdonald et al. ) and Sato et al. ) nvetgated the effect of buldng array on averaged charactertc of plume dperon by a feld experment. Bezpalcova and Ohba, 3) and Okawa and Meng 4) conducted wnd tunnel experment of plume dperon wthn buldng array and nvetgated the effect of the buldng arrangement and obtacle denty on the charactertc of mean and root mean quare (r.m..) concentraton. In th tudy, we perform a numercal mulaton of plume dperon wthn a regular array of cubc buldng a dealzed urban canopy by Large-Eddy Smulaton () that can gve detaled nformaton on a concentraton feld. The obectve of th tudy to valdate our model n comparon wth the expermental data of Bezpalcova and Ohba 3) and nvetgate the dtrbuton pattern of mean and fluctuatng concentraton, and the charactertc of peak concentraton wthn the buldng array. II. Numercal Model The governng equaton for of atmopherc flow are the fltered contnuty equaton, the Naver-Stoke equaton *Correpondng author, E-mal: nakayama.hromaa@aea.go.p c Atomc Energy Socety of Japan, All Rght Reerved. 463 a follow; and u, u u u t uu uu, p u () u f, () (3) C f S S kk S 3, (4) S u u /, (5) 3 x y z, where u, t, p,,, and f are the wnd velocty, tme, preure, denty, knetc vcoty, ubgrd-cale Reynold tre and external force term, repectvely. The ubcrpt tand for coordnate (: treamwe, : panwe, and 3: vertcal drecton). Upper bar, ( ) denote applcaton of the patal flter.,, C and f are the Kronecker delta, the eddy vcoty coeffcent, the model contant of flow feld and Van Dret dampng functon, 5) repectvely. denote grd-flter wdth. In th model, the external force term propoed by Goldten et al. 6) appled for t computatonal tablty for turbulent flow around bluff body. Th force term, f ncorporated nto the Naver-Stoke equaton to conder the buldng effect and can be aumed a the followng expreon; t (6) f ( ) u t dt u ( t),,, (7)

2 464 Hromaa NAKAYAMA et al. where and are negatve contant. The tandard Smagornky model 7) wth Van Dret dampng functon 3) ued becaue of t mplcty and low computatonal cot. C et to.. 8) of plume dperon alo computed by ung the tandard Smagornky model. 7) The patally fltered calar conervaton equaton are preented by and c u t c, (8) u c u c, (9) Sc c, () where the ubgrd-cale calar flux, whch alo parameterzed by an eddy vcoty model. The model contant, Sc, the turbulent Schmdt number and et to a g contant value,.5. 9) Each equaton dcretzed ung a fnte-dfference method baed on taggered grd ytem where velocty component are defned at the boundary of a cell, whle preure and concentraton are defned at the center of a cell. The couplng algorthm of velocty and preure feld baed on the MAC method wth the Adam-Bahforth cheme for tme ntegraton. ) The Poon equaton olved by the SOR method. For the patal dcretzaton n the governng equaton of flow and the tracer tranport, a econd-order accurate central dfference ued. For only advecton term n a concentraton feld, Cubc Interpolated Peudo-partcle,) mpoed. Reynold number baed on the cubcal buldng heght almot 5,. III. Tet Calculaton. The Wnd Tunnel Experment for Evaluatng the Model Performance The experment wa carred out by Bezpalcova and Ohba 3) n the Boundary Layer Wnd Tunnel at Wnd Engneerng Center of Tokyo Polytechnc Unverty, Japan. The expermental et-up cont of buldng wth dmenon: 7 mm (wdth), 7 mm (length), and 7 mm (heght). They are arranged n the regularly algned array wth =.5. Here, f roughne denty defned a the buldng frontal area f ndex and defned a the rato of the total frontal area of buldng to the plan area of the tudy te. There are 8 row of buldng, each cont of 9 buldng. The ground-level pont ource located at the center ut behnd the buldng of the 8th row and the 5th column of the array a how n Fg.. Here, the row are numbered n ncreang order n the treamwe drecton from the leadng edge of the array and the column are numbered n ncreang order n the panwe drecton from the rght-hand de of the array when lookng n the flow drecton. The approachng flow generated by pre et up at the entrance of the wnd tunnel ecton and roughne block. The profle of mean wnd velocty can be approxmated by a power law exponent of.5. Concentraton meaured by a Ar flow 8 row n total y fat-repone flame onzaton detector. The vertcal and panwe profle of mean and r.m.. concentraton are hown by ther expermental tudy. In th tudy, to evaluate the model performance, we compare our reult wth thee wnd tunnel expermental data.. Computatonal Settng In conductng of turbulent flow n the atmophere, an approachng flow wth turbulent fluctuaton a the nlet of the model doman hould be generated. Fgure how a chematc llutraton of numercal model. Two computatonal doman are et up: The man regon for a mulaton of plume dperon wthn a buldng array and the drver regon for generatng a patally-developng turbulent boundary layer flow. Frt, a thck turbulent boundary layer flow generated by ncorporatng the extng nflow turbulence generaton method,.e., Kataoka and Mzuno method 3) nto an uptream mall fracton of the drver regon a hown n Fg.. Then, a trong wnd velocty fluctuaton produced by a trppng fence and roughne block placed at the downtream of the recycle taton a hown n Fg.. The fluctuatng part of the velocty at the recycle taton recycled and added to the pecfed mean wnd velocty at each tme tep by aumng that boundary layer thckne contant wthn a drver ecton. Calculaton of both drver and man regon are conducted by the ame model wth dfferent computatonal ettng. A the boundary condton, Sommerfeld radaton condton 4) mpoed at the ext, a free-lp condton for treamwe and panwe velocty component mpoed and vertcal velocty component at the top, a perodc condton mpoed at the de, and a non-lp condton for each velocty component mpoed at the ground urface. The ze and the number of grd pont for the drver regon 3.8δ 3.8δ 5.δ (δ: the heght of a turbulent boundary layer thckne) and 46 5 n treamwe, panwe and vertcal drecton, repectvely. The ze and the number of grd pont for the man regon are.δ 3.8δ 5.δ and 5 n treamwe, panwe and vertcal drecton, repectvely. In the man regon, there are 5 row of buldng and each cont of 8 buldng. The pont ource located ut behnd the 8th row and the 4th column of the buldng array z o Source Fg. Coordnate ytem and plume ource locaton. Thee buldng depct the 5th column of the array. The orgn the ground-level pont ource. x PROGRESS IN NUCLEAR SCIENCE AND TECHNOLOGY

3 Large-Eddy Smulaton of Plume Dperon wthn a Regular Array of Cubc Buldng 465 Inlet Recycle Staton Turbulent Flow Turbulent Inflow Fully Developed Turbulent Boundary Layer Trppng Fence Spatally-Developng Turbulent Boundary Layer Roughne Block Buldng Array Fg. Schematc of numercal model: drver regon for generatng turbulent boundary layer flow and man regon for turbulent flow and plume dperon wthn a buldng array z/δ..8.6 PowerLaw(α=.5) WT(Bezpalcova,8) z/δ..8.6 WT(Bezpalcova,8) Ar flow Plume ource locaton Poton of vertcal profle (central treet canyon poton) Poton of tme ere of concentraton (central treet canyon poton) Poton of tme ere of concentraton (crong poton) Poton of panwe profle.4. and at the ground urface. Each buldng of the array reolved by grd n the treamwe, panwe and vertcal drecton, repectvely. At the nlet of the man regon, the nflow turbulence data obtaned near the ext of the drver regon mpoed at each tme tep. In a concentraton feld, zero gradent mpoed at all the boundare. A hown n Fg., aumng that the locaton of a plume ource pont n the wnd tunnel experment x/h=., y/h=. and z/h=. (H: a buldng heght), that of a plume ource pont n th model x/h=., y/h=-.3 and z/h=.. Becaue the number of grd pont for ndvdual cubc buldng even number, the plume ource poton n the y/h coordnate lghtly dfferent from that n the expermental condton. Mean and r.m.. concentraton of a plume are normalzed by H and the ource trength (Q). IV. Reult U/U. Approachng Flow Fgure 3 compare the reult for mean wnd velocty (U) and turbulence knetc energy (k) wth the expermental data of Bezpalcova and Ohba. 3) Mean wnd velocty and turbulence knetc energy are normalzed by a free-tream velocty (U ), repectvely. The heght n the k/u Fg. 3 Charactertc of approachng flow: mean wnd velocty and turbulence knetc energy Fg. 4 Poton of the meaurement of concentraton for comparon of wth the experment. The crcle depct a ource locaton. The trangle depct the poton of the vertcal profle. The quare and tar ymbol depct poton of tme ere of concentraton. The blue lne depct the poton of the panwe profle. plot normalzed wth repect to δ. δ correpond to about 4.H. It found that mean wnd velocty of content wth both wnd velocty profle wth a power law exponent of.5 and the expermental data. Turbulence knetc energy by how a peak near the ground urface by the nfluence of roughne block and then gradually decreae wth heght, whle that of the experment how a contant n the range of.-.7δ by the nfluence of pre et up at the wnd tunnel entrance. Intead of th dcrepancy turbulence knetc energy by mlar n magntude to that of the experment. Becaue turbulent boundary layer flow fully developed n th model, th lght dcrepancy neglgble. Therefore, t condered that approachng flow correpondng to the wnd tunnel flow uccefully mulated n the drver regon.. Dperon Charactertc Fgure 4 how poton of the meaurement of concentraton for comparon of wth the expermental data. Fgure 5 how the reult for panwe profle of normalzed mean (C ave ) and r.m.. (C r.m.. ) concentraton. The locaton of the buldng alo hown. Mean concentraton profle of the wnd tunnel experment how a peak at the plume ax, thu, y/h=.. On the other hand, a peak of mean concentraton profle of located at y/h=-.5. VOL., OCTOBER

4 466 Hromaa NAKAYAMA et al...9 WT(Bezpalcova,8) 3 WT(Bezpalcova,8) 3 WT(Bezpalcova,8) C ave C r.m y/h y/h WT(Bezpalcova,8) Fg. 5 Spanwe profle of concentraton: mean concentraton and r.m.. concentraton However, mean concentraton value of are generally mlar n magntude to thoe of the experment. R.m.. concentraton profle of the experment how the local mnmum at y/h=. and the local maxmum at y/h=-. and.. R.m.. concentraton profle of alo how uch a tendency, but the value of the local maxmum at y/h=-. overetmated. However, except the poton where data are overetmated, r.m.. concentraton value of are generally mlar n magntude to that of the experment. Both mean and r.m.. concentraton how an aymmetrc pattern for data. The maxmum value can be found at the left hand de (y/h<). Th due to even number of the computatonal cell and aymmetrc placement of the ource decrbed n Secton III.. However, the dtrbuton rapdly become ymmetrc wth downtream dtance. The nfluence of thee dagreement on the downward dperon n the center ax condered to be mall. Fgure 6 how the reult for vertcal profle of normalzed mean and r.m.. concentraton by H and Q at the central treet canyon poton (y/h=) between t and nd row behnd the ource (ee the trangle n Fg. 4). Mean concentraton profle of how almot a contant wthn buldng canopy (at heght le than.h) and gradually decreae above buldng canopy wth heght. Such a tendency quanttatvely content wth the experment. R.m.. concentraton profle of alo how a contant wthn buldng canopy, but ncreae ut above buldng canopy and then decreae wth heght. Such a tendency mlar to the experment. z/h..4.6 C ave z/h Although peak locaton of the panwe of mean and r.m.. concentraton are a lttle dfferent from thoe of the experment and the peak value of r.m.. concentraton overetmated, reult are generally mlar n magntude to the expermental reult. Furthermore, vertcal profle of mean and r.m.. concentraton of are content wth thoe of the experment. Therefore, t condered that the charactertc of mean and r.m.. concentraton of a plume wthn a buldng array are uccefully mulated by th model. 3. Spatal Dtrbuton of Concentraton Fgure 7 how the patal dtrbuton of mean and r.m.. concentraton at the heght of.h. It found that mean concentraton dtrbuted around the pont ource wth wder pread by the nfluence of the buldng and then the pread gradually gettng narrower due to the helterng effect of the buldng array. Th dtrbuton pattern of mean concentraton the ame a Macdonald feld experment. R.m.. concentraton alo dtrbuted around the pont ource wth wder pread, but t value found to rapdly decreae wth downwnd dtance. Fgure 8 how the treamwe varaton of mean and r.m.. concentraton at the heght of.h at the plume ax (y/h=.). It found that mean concentraton gradually decreae wth downwnd dtance. R.m.. concentraton found to rapdly decreae although t value ncreae wthn each central treet canyon. 4. Charactertc of Peak Concentraton In cae of releae of toxc or flammable gae nto the atmophere, t mportant to etmate ntantaneou hgh concentraton. For th purpoe, theoretcal probablty dtrbuton of concentraton fluctuaton have been tuded by many reearcher. For example, Canady 5) and Hanna 6) propoed theoretcal model of the lognormal and exponental dtrbuton for predctng concentraton fluctuaton of a plume, repectvely, a follow C r.m.. Fg. 6 Vertcal profle of concentraton: mean concentraton and r.m.. concentraton PROGRESS IN NUCLEAR SCIENCE AND TECHNOLOGY

$I tand for ntermttency factor defned a a fracton of tme, when no concentraton gnal appear and can be expreed ung C a follow. 6)... I, (3) C where C concentraton fluctuaton ntenty defned a the rato of r.$ m.. concentraton to mean concentraton, C r.m.. C. ave Thee theoretcal model cannot predct the patal dtrbuton of concentraton but can etmate peak concentraton at a tatonary pont. Sato et al.

m.. concentraton to mean concentraton, C r.m.. C. ave Thee theoretcal model cannot predct the patal dtrbuton of concentraton but can etmate peak concentraton at a tatonary pont. Sato et al.

5 Large-Eddy Smulaton of Plume Dperon wthn a Regular Array of Cubc Buldng 467 Fg. 7 Spatal dtrbuton of concentraton at the heght of.h: mean concentraton and r.m.. concentraton. C ave, C r.m.. ln c n Lognormal type: P c erf c () l c Exponental type: P c I exp I () C where erf, n and c l are error functon, the medan concentraton and the logarthmc tandard devaton. I tand for ntermttency factor defned a a fracton of tme, when no concentraton gnal appear and can be expreed ung C a follow. 6)... I, (3) C where C concentraton fluctuaton ntenty defned a the rato of r.m.. concentraton to mean concentraton, C r.m.. C. ave Thee theoretcal model cannot predct the patal dtrbuton of concentraton but can etmate peak concentraton at a tatonary pont. Sato et al. 7) examned the lognormal and exponental type of probablty dtrbuton of concentraton fluctuaton behnd an olated cubcal buldng wth thoe for the wnd tunnel experment by ung concentraton tattc of nc, l and C obtaned by the experment. They howed that the probablty dtrbuton of concentraton fluctuaton can be evaluated by the lognormal type for.3< C <., the lognormal or the exponental type for.< C <.5 and the exponental type for C >.5. In th tudy, we compare to the wnd tunnel expermental data of the probablty dtrbuton dependng on the value of C n Mean concentraton R.m.. concentraton. x/h Fg. 8 Streamwe varaton of mean and r.m.. concentraton at the heght of.h order to examne our model performance. Fgure 9 how tme ere of concentraton at the central treet canyon and crong poton (ee Fgure 4). The red lne ndcate the averaged value. At the poton of central treet canyon, concentraton fluctuate moothly and contnuouly. On the other hand, at the crong poton, ntantaneou hgh concentraton frequently occur. Thee pattern of concentraton fluctuaton nde and outde of the cavty regon of a buldng are mlar to the wnd tunnel experment of Mavrod and Grffth. 8) Fgure how a comparon of probablty dtrbuton Pc of concentraton fluctuaton of at the central treet canyon and crong poton at the heght of z/h=.. Concentraton normalzed by C ave. c 99, c 95 and c 9 are defned a the value determned from Pc =.99,.95 and.9, repectvely. Concentraton fluctuaton ntenty, C, how.34 and. at the central treet canyon and crong poton, repectvely. For evaluatng probablty dtrbuton of concentraton fluctuaton of each theoretcal model, concentraton tattc of nc, and l C obtaned by are ued. At the poton of central treet canyon, the probablty dtrbuton of content wth that of the lognormal type, whle that of much maller than the exponental one n the range of.< Pc<.. At the crong poton, the probablty dtrbuton of content wth both lognormal and exponental type. It hown from thee reult that the charactertc of probablty dtrbuton obtaned by dependng on the value of C are content wth thoe reported by Sato et al. 7) Focung on varou peak concentraton, c 99, c 95 and c 9 of at the central treet canyon are found to how.,.8 and.5, repectvely. On the other hand, thoe of at crong poton how 4.5, 3.8 and.7, repectvely, and qualtatvely much dfferent from thoe at the central treet canyon. Th ndcate that t mportant to evaluate peak concentraton baed on a buldng cale for the aement of human health hazard or the afety analy of the hazardou ga wthn populated urban area. V. Concluon In th tudy, we perform Large-Eddy Smulaton of plume dperon wthn a regular array of cubc buldng a dealzed urban canopy and nvetgate the charactertc of VOL., OCTOBER

6 468 Hromaa NAKAYAMA et al. Fg. 9 Tme ere of concentraton: the central treet canyon poton and the crong poton data Log normal type Exponental type data Log normal type Exponental type -p(c). -p(c) c/c ave c/c ave Fg. Probablty dtrbuton functon of concentraton: the central treet canyon poton and the crong poton. mean and fluctuatng concentraton. The obtaned reult are a follow:. A patally-developng turbulent boundary layer flow n the drver regon generated by ncorporatng extng nflow turbulence generaton method nto an uptream mall fracton of the drver regon wth a trppng fence placed at the ground urface and roughne block. By th cheme, we have uccefully mulated a turbulent boundary layer flow correpondng to the wnd tunnel experment of Bezpalcova and Ohba 3) n the drver ecton.. When compared to the expermental data 3) of the panwe and vertcal profle of mean and r.m.. concentraton, t hown that th model uccefully mulate plume dperon wthn a buldng array. Furthermore, t found that r.m.. concentraton rapdly decreae n the treamwe drecton, whle mean concentraton gradually decreae wth downwnd dtance. 3. It hown that peak concentraton value at the central treet canyon are much dfferent from thoe at crong pont. Th ndcate that t mportant to evaluate peak concentraton baed on a buldng cale for the aement of human health hazard or the afety analy of the hazardou ga wthn populated urban area. Acknowledgment The author thank Dr. Klara Bezpalcova who provded the wnd tunnel expermental data. Reference ) R. Macdonald, R. Grffth, S. Cheah, Feld experment of dperon through regular array of cubc tructure, Atmo. Envron., 3[6], (997). ) A. Sato, H. Takmoto, T. Mchoka, M. Kanda, Feld Experment of Flow and Dperon wthn a Buldng Canyon of the Comprehenve Outdoor Scale Model, Ann. J. Hydraul. Eng., 53, 47-5 (7), [n Japanee]. 3) K. Bezpalcova, M.Ohba, Advectve and turbulent vertcal fluxe of the pave contamnant nde an urban canopy, Proc. of th Natonal Sympoum on Wnd Eng., Tokyo, Japan,, 9-4 (8). 4) S. Okawa, Y. Meng, A Wnd-tunnel Study of the Flow and Dffuon wthn Model Urban Canope, J. Jpn. Soc. Atmo. Envron., 3, (997). 5) E. R. Van Dret, On turbulent flow near a wall, J. Aero. Sc., 3, 7- (956). 6) D. Goldten, R. Handler, L. Srovch, Modelng a no-lp flow boundary wth an external force feld, J. Comput. Phy., 5, (993). 7) J. Smagornky, General crculaton experment wth the prmtve equaton, Mon. Wea. Rev., 9[3] (963). 8) T. Shraawa, Y. Endo, R. Yohe, A. Mochda, H. Tanaka, Comparon of and Durbn type k-ε model for ga dffuon n weak wnd regon behnd a buldng, J. Envron. Eng., 73[67], 65-6 (8), [n Japanee]. PROGRESS IN NUCLEAR SCIENCE AND TECHNOLOGY

7 Large-Eddy Smulaton of Plume Dperon wthn a Regular Array of Cubc Buldng 469 9) K. Sada, A. Sato, Numercal calculaton of flow and tack-ga concentraton fluctuaton around a cubcal buldng, Atmo. Envron., 36, (). ) A. J. Chorn, A numercal method for olvng ncompreble vcou flow problem, J. Comp. Phy.,, -6 (967). ) H. Takewak, A. Nhguch, T. Yabe, Cubc Interpolated Peudo-partcle method (CIP) for olvng hyperbolc-type equaton, J. Comput. Phy., 6, 6-68 (985). ) T. Yabe, E. Take, A new hgher-order Godunov method for general hyperbolc equaton, J. Phy. Soc, Japan, 57[8], (988). 3) H. Kataoka, M. Mzuno, Numercal flow computaton around aeroelatc 3D quare cylnder ung nflow turbulence, Wnd Struc., 5, (). 4) P. M, Greho, Some nteretng ue n ncompreble flud dynamc, both n the contnuum and n numercal mulaton, Adv. Appl. Mech., 8, 45 4 (99). 5) G. T. Canady, Turbulent dffuon n the envronment, D. Redel Publ., Dordrecht, Holland, -48 (973). 6) S. R. Hanna, The exponental probablty denty functon and concentraton fluctuaton n moke plume, Bound-Layer Meteorol., 9, (984). 7) A. Sato, K. Sada, A wnd tunnel experment on tracer ga concentraton fluctuaton near a cubcal model buldng, Proc. Japan Soc. Cvl Eng., 76, 4-49 (), [n Japanee]. 8) I. Mavrod, R. Grffth, Local charactertc of atmopherc dperon wthn buldng array, Atmo. Envron., 35, (). VOL., OCTOBER

Coupling of WRF and building-resolving urban CFD models for analysis of strong winds over an urban area

Coupling of WRF and building-resolving urban CFD models for analysis of strong winds over an urban area .6 Couplng of WRF and buldng-reolvng urban CFD model for analy of trong wnd over an urban area Hromaa Nakayama *, Tetuya Takem 2 and Haruyau Naga Japan Atomc Energy Agency, Ibarak, Japan 2 Dater Preventon