Mitsubishi Heavy Industries Technical Review Vol. 49 No. 1 (March 2012)

Transcription

1 Mtsubsh Heavy Industres Techncal Revew Vl. 49 N. (March 0) Develment f Numercal Smulatn Technque fr Unsteady Turbulent Dsersn ver Cmlcated Terran - As an Alternatve t Wnd Tunnel Exerments - 98 Kazuk Okabayash * Yshnr Nagayama * Tmhr Hara * Ech Hr *3 Yu Ohya *4 Takanr Uchda *5 The Standards Cmmttee f the Atmc Energy Scety f Jaan has recently launched effrts t frm the bass f standards amng t substtute numercal smulatns fr cnventnal wnd tunnel exerments t evaluate radatn exsure arund nuclear facltes n safety assessments. As such, Mtsubsh Heavy Industres (MHI) aled an unsteady numercal smulatn technque t dsersn felds ver cmlcated terran usng a Large-Eddy Smulatn (LES) mdel and cmared the smulatn results wth the crresndng wnd tunnel exerment. Ths smulatn mdel assures hghly-accurate redctns wthn ractcal cmutatn tmes, shwng that ths analytcal methd s an unsteady turbulent flw and dsersn smulatn mdel that can becme an alternatve t wnd tunnel exerments.. Intrductn Large-scale unsteady turbulent flw smulatns have requred very lng cmutatnal tmes, but recent advancements n cmuter erfrmance and fast cmutatn technlgy have made t mre ssble t cmlete the smulatns wthn ractcal tmes. Meantme, the Atmc Energy Scety f Jaan has launched a standardzatn f numercal smulatns as an alternatve arach t cnventnal wnd tunnel exerments t evaluate exsure arund nuclear facltes. Currently, the mst wdely and cmmnly used turbulent mdel s the Reynlds Averaged Naver-Stkes Smulatn (RANS) due t ts lwer cmutatnal tme. RANS fcusng n rather flat terran and smle buldngs has started t be valdated wth the am f substtutng RANS fr wnd tunnel exerments, 3 but there are few valdatn studes fr cmlcated terran. Mrever, f RANS s aled t cmlcated flws and dsersn felds, t requres smulatn accuracy valdatn and there are accuracy lmtatns n RANS. 4,5 In ths study, we tred t aly a Large-Eddy Smulatn (LES) turbulent mdel t an unsteady dsersn feld ver cmlcated terran. LES drectly slve turbulent structures larger than the cmutatnal grd by mdelng the structures smaller than the grd, requrng lnger cmutatnal tmes than RANS. There are many studes n LES, but mst are fcused n smle structures n the fundamental research f atmsherc dsersn, 6 and there s a lack f ractcal large-scale smulatn cases targetng cmlcated terran. As such, we cnducted an unsteady dsersn smulatn usng LES targetng cmlcated terran, and we valdated the mdel by cmarng the smulatn results wth the crresndng exermental data, whch have been carred ut by us and ther research facltes.. Outlne f atmsherc dsersn mdel. Arflw smulatn mdel The gvernng equatns f arflw are the cntnuty equatn and Naver-Stkes equatn f the ncmressble flw, as shwn n Equatns () and (). In ths study, we used the RIAM-COMPACT 7 cde,.e. arflw mdel develed by the Research Insttute fr Aled Mechancs, Kyushu Unversty. * Reasearch Manager, Nagasak Research & Develment Center * Nagasak Research & Develment Center *3 Reactr Safety Engneerng Deartment, Nuclear Plant Engneerng Dvsn, Nuclear Energy Systems *4 Prfessr, (Wnd Engneerng Sectn, Dvsn f Renewable Energy Dynamcs,) Reaserch Insttute fr Aled Mechancs, Kyushu Unversty *5 Asscate Prfessr, (Wnd Engneerng Sectn, Dvsn f Renewable Energy Dynamcs,) Reaserch Insttute fr Aled Mechancs, Kyushu Unversty

2 Mtsubsh Heavy Industres Techncal Revew Vl. 49 N. (March 0) 99 u x 0 u u t u x x Re u x x 3 x u u uk uk SGS S, C f S, SGS s s S S S u x 0 u x S, f s ex z 5, h h h 3 x y z () () where, A : flterng eratn fr each quantty A (averaged by the cmutatnal grd wdth n ths case) x : -drectn crdnate (x = x, x = y and x 3 = z dente the dwnwnd, crsswnd and vertcal drectns, resectvely) u : velcty cmnent n the -drectn u ': varatn f velcty cmnent n the -drectn : ressure Re: Reynlds number v SGS : eddy vscsty f sub-grd scale (equal r smaller than the cmutatnal grd wdth) C s : Smagrnsky cnstant(= 0.) f s : damng functn z + : wall crdnate h x, h y, h z : flterng wdth f each drectn (the cmutatnal grd wdth n ths case) Here, the standard Smagrnsky mdel s used t reresent the stress f the sub-grd scale eddes. The sum rules can be aled t the dulcated suffxes n the abve equatns,.e., the a b 3 means a b. Sl cndtns are aled t the sde and uer bundary surfaces, a cnvectve utflw cndtn t the utflw bundary surface and a nn-sl cndtn t the grund surface.. Dsersn mdel The fllwng equatn s used as the atmsherc dsersn mdel. C C C C C u v w K t x y z x x K Re Sc Sc SGS turb C K y y C K q z z (3) where, C: cncentratn K: dsersn ceffcent Sc: Schmdt number Sc turb : turbulent Schmdt number q: surce strength f emssn The turbulent Schmdt number Sc turb s set as lw as ssble fr the subsequent cmarsn wth exermental data because Sc turb des nt have a large effect n the smulatn results. The Schmdt number Sc s set t 0.7. In ths mdel, 3rd-rder uwnd dfference and nd-rder central dfference schemes are used fr the advectn and dffusn terms resectvely, the same as n RIAM-COMPACT. Euler's exlct methd s used as the tme dfference scheme. The cncentratn s set t 0 at the nflw

3 Mtsubsh Heavy Industres Techncal Revew Vl. 49 N. (March 0) bundary, and the Neumann bundary cndtn s used fr the ther bundares ncludng the grund surface. 3. Valdatn methd In nt EU research (SMEDIS rect), 8 sme research grus cnducted numercal smulatns usng CFD mdels (STAR-CD, FLUENT, CFX, etc.) t rerduce wnd tunnel exermental data. Based n these effrts, mdel accuracy valdatn gudelnes were establshed (COST 73). 9 We used COST 73 t verfy the erfrmance f ur mdel descrbed n Chater. The arrateness f the COST 73 crtera fr mdel erfrmance s defned based n the best erfrmance cases n gas cncentratn evaluatns where the gas s emtted frm a dwnwnd grund-level surce behnd a rectangular buldng. In ths valdatn rcess, the fllwng 3 standard metrcs are used n cmlance wth the basc valdatn rtcl shwn n COST 73. () FAC (Fractn f X wthn a factr f tw f X ) FAC s defned as the fllwng equatn and means a fractn whch has the rat f the redcted value X t the bserved (exermental) value X wthn FAC N n n n N fr 0.5 N else 0 X X.0 () FB (Fractnal Mean Bas) FB s defned as the fllwng equatn where A s the average f the quantty A. It s equvalent t the average f dfferences (errrs) between the bserved value X and the redcted value X, whch s value t evaluate the verall bas. FB ( X X ) /( X X ) (3) NMSE (Nrmalzed Mean Square Errr) NMSE s defned as the fllwng equatn, meanng the range f the mean square errr. NMSE (( X X ) ) /( X X 4. Valdatn f numercal mdel ) T valdate the atmsherc dsersn mdel descrbed n Chater, we cmared the smulatn results wth the crresndng wnd tunnel exermental data frm a safety assessment f nuclear facltes that we revusly cnducted, etc., usng the COST 73-based erfrmance crtera 9 descrbed n Chater Cmarsn wth exerment fr flat terran Frst, the rerducblty f ths numercal mdel was valdated by cmarng arflw and cncentratn felds at several smke surce heghts at a flat-late cndtn between the smulatn and the exerment. In ths calculatn, we rerduced a smlar sre (an ssceles trangle wth a heght f 50 mm) as the exerment was used as a surface rughness t cntrl the bundary layer and the turbulence bundary layers develng n the dwnwnd drectn ver the flat late were smulated. The gas dsersns frm dfferent heghts wthn the bundary layers were als calculated. The cmutatnal grd wdths are 3-6 mm n the flw drectn, 6.5 mm fxed n the crsswnd drectn and.5-30 mm n the vertcal drectn. The vertcal mesh sze becmes narrwer as t araches the grund surface, ttalng abut 9M meshes. The cmbnatn f bth 6-CPU arallel cmuters and an arflw database t be descrbed hereafter makes t ssble t cmlete the smulatn wthn 50 hurs. Fgure shws a cmarsn f vertcal rfles f the average wnd velcty n the dwnwnd drectn and the 3-turbulent ntensty cmnent at the lcatn f the surce f emssn between the smulatn and the exerment. The smulated values were averaged by a 6.5 sec duratn tme and n advance, t was cnfrmed that the values were unaffected by the dfference f averagng tme. Fgure als shws the gd agreement between the smulatn and exerment. The smulatn results are dented at actual scale by the same scale f /000 as the wnd tunnel exerment.

4 Mtsubsh Heavy Industres Techncal Revew Vl. 49 N. (March 0) 0 Fgure Arflw rfle n flat-late cndtn These are cmarsns f average wnd velcty and vertcal dstrbutn f 3-turbulent ntensty cmnents between the exerment and calculatn. (The values are at an actual scale changed by a mdel scale f :000 n a wnd tunnel exerment.) Fgure shws a cmarsn f the maxmum grund-level cncentratn dstrbutns (grund-level cncentratn dstrbutn alng the lume axs) n the dwnwnd drectn at dfferent surce heghts between the exermental and smulatn data. The cncentratn C s dented by the nrmalzed cncentratn UC/Q (m ), where U s the unfrm wnd velcty and Q s the surce strength. Fgure ndcates the grund-level cncentratn dstrbutns alng the lume axs at each surce heght s n a gd agreement between the exerment and smulatn. Fgure 3 s a cmarsn f the dsersn wdth n the vertcal drectn (equvalent t the standard devatn f the cncentratn dstrbutn) frm a grund nt surce between the exerment and smulatn. The dsersn wdths were determned frm the wnd tunnel data by the least-square methd assumng that the cncentratn s nrmally-dstrbuted. The dsersn wdths are ltted n Fgure 3 wth the Pasqull-Gffrd chart, n whch a dsersn wdth s defned fr each atmsherc stablty class. Frm Fgure 3, t s fund that the dsersn wdth s n a gd agreement between calculatn and exerment and are ltted nearby the targeted neutral atmsherc stablty zne (between Class-C and D). Fgure Dwnwnd dstrbutns f grund-level cncentratn at dfferent surce heghts Ths s a cmarsn f grund-level cncentratn alng the lume axs at dfferent surce heghts (0, 0, 40, 60, 80, 00 and 00 m) at a flat-late cndtn. (The values are at an actual scale changed by a mdel scale f :000 n a wnd tunnel exerment.) Fgure 3 Prfle f vertcal lume wdth Ths s a cmarsn f vertcal lume wdth between the smulatn and the exerment. (The values are at an actual scale changed by a mdel scale f :000 n a wnd tunnel exerment.) In the calculatn regardng cmlcated terran t be descrbed n Sectn 4., the smulatn tme can be dramatcally reduced by mttng arachng flw regn A frm the whle calculatn dman. The detals are as fllws. Frst, ar flw n regn A s calculated t make a database at a dwnwnd bundary f regn A. Next, the arflw database f regn A s used as the nflw bundary cndtn nt dman B, as shwn n Fgure 4.

5 Mtsubsh Heavy Industres Techncal Revew Vl. 49 N. (March 0) 0 Fgure 4 Reductn f calculatn dman The arflw data f the dwnwnd sectn n entrance sectn A s used as the nflw cndtn f calculatn dman B wth cmlcated terran. 4. Cmarsn wth wnd tunnel exerment fr cmlcated terran Next, the alcablty f ths smulatn mdel t cmlcated terran was valdated by cmarng the exermental and smulatn data targetng cmlcated terran shwn n Fgure 5. In ths smulatn, surce lcatns are at A and B and 5 wnd drectns I t V shwn n Fgure 5 are chsen. Table s a lst f all 7 smulatn cases n ths study, 0 whch have dfferent surce lcatns, wnd drectns and surce heghts. Fgure 6 shws the grund-level cncentratns alng the lume axs n the reresentatve cases; wth a breeze ver flat terran frm the sea (Wnd drectn I) and a cmlcated flw frm uwnd terran (Wnd drectn V). As shwn n Fgure 6, bth cases ndcate the gd agreement between the exerment and smulatn. Fgure 5 Cmlcated terran n the calculatn Ths ma llustrates wnd drectns (I - V), smke surce lcatns (A and B) and the cntur lnes f the targeted area s gemetry. Table Case N. Lst f calculatn cases Wnd drectn Surce lcatn Surce heght (m) A 44 I A 58 3 B 63 4 II A 58 5 III A 44 6 IV B 63 7 V B 63 Ths table ndcates the wnd drectn, surce lcatn and heght n each case. Fgure 6 Cmarsn f dwnwnd grund-level cncentratn rfle These are cmarsns f the grund-level cncentratns alng the lume axs vs. the dwnwnd dstance between the exerment and calculatn. (The values are at an actual scale changed by a mdel scale f :500 n a wnd tunnel exerment.)

6 Mtsubsh Heavy Industres Techncal Revew Vl. 49 N. (March 0) Table s a lst f the 3 standard metrcs (FAC, FB and NMSE) fr mdel erfrmance f all 7 cases evaluated n cmlance wth the COST 73 rtcl descrbed n Chater 3. Table shws that all cases meet the crtera f each metrc, ndcatng the adequate redctn accuracy f ths smulatn mdel. Case N. Table Fr lume axs data (Crtern = 0.89 and abve) Perfrmance evaluatn f ths calculatn mdel FAC FB NMSE Fr ttal Fr lume axs Fr ttal surface surface data data data (Crtern = (Crtern = 0.5 (Crtern = and abve) and belw) and belw) Fr ttal surface data (Crtern= 4.0 and belw) Ths s a cmarsn between the exerment and calculatn data fr the 3-standard metrcs (FAC, FB and NMSE) based n the grund-level cncentratns alng the lume axs and the ttal surface cncentratns. The crtern f FAC s frm COST 73 and thse f FB and NMS are frm Chang et al. cted n COST Cmarsn wth smle buldng exerment Fnally, we valdated ths smulatn mdel by usng wnd tunnel exerment data ublshed by the Unversty f Hamburg, whch s exermental data arund a smle buldng (L =00 mm, W = 50 mm, H = 5 mm). The ublshed data lack the nfrmatn fr LES smulatn n the uwnd rughness cndtns t make turbulent bundary layer devel at the frnt-sde f the buldng, and therefre t s dffcult t set frnt-sde arflw cndtns strctly n an unsteady numercal smulatn. Hwever, t s cnsdered that the turbulence generated by the buldng s a dmnant factr t the henmenn behnd the back-sde f a buldng, and the effects f the rughness cndtn are small. Hence n ths valdatn, a dffusn structure arund a smle buldng was calculated under turbulent bundary layer develed by -D blcks as dummes f the rughness n the exerment. Fgure 7 llustrates the gd agreement f dwnwnd dstrbutn f grund-level cncentratns alng the lume axs behnd the buldng between ths smulatn and the exerment. The FAC f the grund-level cncentratn alng the lume axs s.0 (the crtern: mre than 0.89), shwng accetable redctn accuracy. The FAC f the ttal grund-level cncentratn and satal cncentratn (ttal cncentratn) s 0.57, whch s slghtly hgher than the crtern The reasn seems t be that the smulatn culd nt fully rerduce the turbulent bundary layer develed n the wnd tunnel exerment due t the lack f the nfrmatn n the rughness cndtns f the database, as descrbed abve. 03 Data fr cmarsn Grund-level cncentratn alng the lume axs Cncentratn at all measurement nts FAC (Crtern).00 (0.89) 0.57 (0.54) Fgure 7 Prfle f grund-level cncentratns alng lume axs Ths s a cmarsn f dmensnless cncentratn (K = UCH b /Q) at a certan dmensnless dwnwnd dstance (X/H b ), where U s the wnd velcty, C the grund-level cncentratn alng the lume axs, H b the buldng heght and Q the surce strength.

7 Mtsubsh Heavy Industres Techncal Revew Vl. 49 N. (March 0) Cnclusns We cnducted an unsteady flw dsersn smulatn targetng cmlcated terran usng a knd f turbulent mdel, Large Eddy Smulatn (LES), and valdated the redctn accuracy based n the COST 73 rtcl, whch are mdel evaluatn gudelnes develed n the EU. Frst, we cnfrmed that ths smulatn mdel well rerduced wnd tunnel exerment results at flat terran cndtns. Next, we cnfrmed that ths smulatn mdel rerduced wnd tunnel exerment results at cmlcated terran cndtns t a satsfactry level. The 3 standard metrcs (FAC, FB and NMSE) f ths smulatn suffcently meet the crtera suggested n COST 73. The metrcs determned n anther smulatn usng anther research faclty s exermental data als met the references. Frm these results, we have cnfrmed that ths newly develed numercal mdel has suffcent redctn accuracy and we wuld exect t substtute ths mdel fr wnd tunnel exerments. Ths mdel wuld becme an alternatve arach that ensures sgnfcant reductn n examnatn duratns cmared wth cnventnal wnd tunnel exerments. Acknwledgements We wuld lke t exress ur arecatn t the Jaan Atmc Pwer Cmany fr rvdng us wth the wnd tunnel exermental data. References. Atmc Energy Scety f Jaan(AESJ), Cde fr Wnd Tunnel Exerments t Calculate the Effectve Heght f Emttng Surce fr Nuclear Pwer Facltes Safety Analyss: 009 (00), n Jaanese. Atmc Energy Scety f Jaan(AESJ), Cde fr Numercal Mdel t Calculate the Effectve Surce Heght fr Nuclear Pwer Facltes Safety Analyss: 0 (0), n Jaanese 3. Sada et al., Numercal Mdel fr Atmsherc Dffusn Analyss and Evaluatn f Effectve Dse fr Safety Analyss : Effectve Stack Heght and Effectve Dse Estmated by Wnd Tunnel and Numercal Mdel, Transactn f the Atmc Energy Scety f Jaan, vl.8 N.(009).84-96, n Jaanese 4. Sat et al., Exermental and numercal smulatn f llutant dsersn n a hgh densty resdental area : () RANS smulatn f llutant dsersn, Prceedngs f the 49th Annual Meetng f Jaan Scety fr Atmsherc Envrnment (008), n Jaanese 5. Mchka et al., Exermental and numercal smulatn f llutant dsersn n a hgh densty resdental area (N. 3) : LES smulatn f llutant dsersn, Prceedngs f the 49th Annual Meetng f Jaan Scety fr Atmsherc Envrnment (008), n Jaanese 6. Nakayama,H. et al., Develment f Lcal-scale Hgh-Reslutn Atmsherc Dsersn Mdel Usng Large-Eddy Smulatn Part: Turbulent Flw and Plume Dsersn arund a Cubcal Buldng,Jurnal f Nuclear Scence and Technlgy,vl.48 N.3 (0).374~ Uchda, T. et al.,large-eddy Smulatn f Turbulent Arflw ver Cmlex Terran, Jurnal f Wnd Engneerng Industral Aerdynamcs, vl.9 (003).9~9 8. Carssm, B. et al., The SMEDIS Database and Valdatn Exercse, Internatnal Jurnal f Envrnment and Pllutn, vl.6 (00) Brtter, R. et al., Mdel Evaluatn Gudance and Prtcl Dcument, COST Actn 73, (007), htt:// 0. Nagayama, Y et al., Valdatn f Numercal Smulatn wth LES Aled t Atmsherc Dsersn ver Cmlex Terran by Usng Wnd Tunnel Exermental Data, Prceedngs f the 0 Meetng f the Jaan Scety fr Aernautcal and Sace Scences Western Branch(0).39-4, n Jaanese. Chang, J. et al., Ar qualty mdel erfrmance evaluatn, Meterlgy and Atmsherc Physcs, vl.87(007) Hamburg Unversty, Publc database, htt://