Computer modelling of technogenic thermal pollution zones in large water bodies

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1 Journal of Physcs: Conference Seres PAPER OPEN ACCESS Compuer modellng of echnogenc hermal polluon zones n large waer bodes To ce hs arcle: Ya N Parshakova and T P Lyubmova 218 J. Phys.: Conf. Ser Vew he arcle onlne for updaes and enhancemens. Ths conen was downloaded from IP address on 3/5/218 a 3:48

2 Compuer Smulaons n Physcs and beyond (CSP217) IOP Conf. Seres: Journal of Physcs: Conf. Seres (218) 1217 do :1.188/ /955/1/1217 Compuer modellng of echnogenc hermal polluon zones n large waer bodes Ya N Parshakova 1, T P Lyubmova 1, 2 1 Insue of Connuous Meda Mechancs UB RAS, Acade. Koroleva 1, Perm 61413, Russa 2 Perm Sae Unversy, Bukreva 15, Perm 61499, Russa E-mal: parshakova@cmm.ru Absrac. In he presen work, he hermal polluon zones creaed due o dscharge of heaed waer from hermal power plans are nvesgaed usng he example of he Permskaya Thermal Power Plan (Permskaya TPP or Permskaya GRES), whch s one of he larges hermal power plans n Europe. The sudy s performed for dfferen echnologcal and hydromeeorologcal condons. Snce he vercal emperaure dsrbuon n such wasewaer reservors s hghly nhomogeneous, he compuaons are performed n he framework of 3D model. 1. Inroducon The densy srafcaon ecs caused by nhomogenees of emperaure and mneralzaon felds can play an mporan role n he formaon of boh hydrologcal and hydrochemcal regmes of surface waer bodes. However, hey can no be descrbed n he framework of hydrodynamcal models based on he shallow waer approxmaon. Such ecs can be accuraely descrbed only usng he hydrodynamc models n hree-dmensonal formulaon. The sgnfcance of he problem under consderaon s confrmed by he fac ha came no he vew of researchers as early as n 3-es of he XX cenury whch gave an mpeus o he developmen of he frs appled models of plane hydrodynamcs for s soluon [1,2]. There are a number of facors why fndng soluons o hese problems s a challengng ask. Among hese are he fracaly of morphomery of naural waer bodes, consderable dfference n he scales of naural and echnologcal parameers, essenal varably of hydromeereologcal facors. Earler, he resrced cency of he compuaonal means was one of he bgges lmng facors. Tha s why, sarng from he poneerng works of N.M Bernadsk [1,2] and unl recenly, he mos wdely used approach o hese problems was 2D modellng based on he shallow waer approxmaon (see, for example [3-7]). In [3], he auhors oulne he mehods of compuaonal hydrodynamcs whch are based on 1- and 2-D approaches. The compac fne dfference mehods are descrbed n в [4]. In [5], a model of sea ce moon akng no accoun he amospherc and waer flows due o emperaure nhomogenees s consruced based on he daa of Arcc and Anarcc regons. A 2Dnumercal smulaon of he spread of hermal polluon n he coasal area of he Red Sea s performed n [6]. An ec of hermal polluon produced by Iran hermal power plan s numercally nvesgaed n [7] wh he use of 2D approach. The soluon s consruced for hree dfferen scales - 25 km х 25 km, 12 km х 12 km, 7 km х 7 km. Consderaon s gven o dfferen scenaros of meeorologcal and season condons. However, numerous daa of feld observaons srongly sugges he need for revsng he formulaon whch s based on he wo-dmensonal represenaon of he examned felds Conen from hs work may be used under he erms of he Creave Commons Arbuon 3. lcence. Any furher dsrbuon of hs work mus manan arbuon o he auhor(s) and he le of he work, journal caon and DOI. Publshed under lcence by Ld 1

3 Compuer Smulaons n Physcs and beyond (CSP217) IOP Conf. Seres: Journal of Physcs: Conf. Seres (218) 1217 do :1.188/ /955/1/1217 and homogeney of he deph dsrbuon of waer emperaure. Therefore, o oban more adequae resuls, s necessary o change o 3D models. In works [8-1], a hree dmensonal numercal smulaon of urbulen mxng of waer masses of dfferen emperaures was carred ou based on he soluon of he Naver-Sokes equaons and LES model of urbulence. Compuaons were done wh he use of a hree sage scheme wh parallelzaon. A dependence of he compung me on he number of grd nodes and processors was obaned. The compuaonal aspecs of he LES model of urbulence were dscussed n [11]. The auhors of he presen paper developed hydrodynamcal models of surface waer bodes, whch are based on 3D numercal smulaons [13-15]. In he presen paper, wh reference o he Permskaya hermal power plan (TPP) (Permskaya GRES), we nvesgaed he emperaure felds generaed due o dscharge of heaed waers dependng on echnologcal and hydromeeorologcal parameers. I s consruced 3D model for he doman of 1 km whch ncludes he nake and dscharge channels of he Permskaya TPP. 2. Compuaonal echnque. The 3D hydrodynamcal model was bul for he reservor par of lnear dmensons of 1 m adjacen o he Perm TPP and ncludng he pons of waer nake and waer dscharge. Sofware package ANSYS Fluen was used for he 3D smulaons a he compuer cluser URAN of he IMM UB RAS. The problem was solved n he framework of a non-saonary non-sohermal approach on he bass of he k ε model descrbng urbulen pulsaons. We mplemen he Reynolds-averaged Naver-Sokes equaons: ρ + ( ρu) = (1) x p u u j 2 u l ( ρu) + ( ρ uu j ) = + µ + δj + x j x x j x j x 3 x l u u j 2 u l + µ + ρ k + µ δj + ρ g x j x j x 3 xl Here, ρ s he densy, x are coordnaes (we use Caresan coordnae sysem), u are he velocy componens, µ s he knemac vscosy, µ s he urbulen vscosy. The urbulence knec energy k and rae of s dsspaon ε are obaned from he followng ranspor equaons: µ k ( ρk) + ( ρ ku ) = µ + + Gk + Gb ρε (3) x x j σ k x j 2 µ ε ε ε ( ρε ) + ( ρε u) = µ + + C1 ε ( Gk + C3 εgb ) C2ε ρ (4) x x j σ ε x j k k In equaons (3)-(4), G represens he generaon of urbulence knec energy due o he mean velocy gradens S 2SS j j G k k 2 S = µ where S s he modulus of he mean sran rae ensor, defned as =, Sj.5 ( uj / x u / u ) = +, G b s he urbulence knec energy due o buoyancy, whch s calculaed as µ T Gb = g β Pr x where µ s he urbulen vscosy deermned as: µ = ρc k 2 / ε, where C µ s a consan. µ (2) (5) 2

4 Compuer Smulaons n Physcs and beyond (CSP217) IOP Conf. Seres: Journal of Physcs: Conf. Seres (218) 1217 do :1.188/ /955/1/1217 Smulaon of urbulen hea ransfer s performed usng he Reynolds model smlarly o ha of urbulen momenum ransfer. Hence, he equaon of energy s expressed as where T ( ρe) + [ u( ρe + p) ] = k + u ( τ j ) (6) x x j x j p E = ch + denoes oal energy, h= C pt denoes sysem enhalpy, k denoes ecve ρ hermal conducvy, and ( τ ) s he sress ensor devaor defned as j u j u 2 uk ( τ j ) = µ + µ δj (7) x x j 3 xk The model consans Pr, G1 ε, C2 ε, C µ, σ k and σ ε were aken o have he followng values [16]: Pr=.85, C1 ε = 1.44, C2 ε = 1.92, C µ =.9, σ k= 1., σ ε= 1.3. The spaal dscrezaon scheme of second-order accuracy was appled. Smulaon of emporal evoluon was carred ou usng an explc second-order scheme. Boundary condons mposed on he edges of he compuaon doman were as follows. A he boom and a he banks he no-slp condons and fxed emperaure were mposed: u1= u2= u3=, T= T, A he nle o he compuaonal doman he man flow velocy was assumed o have one nonzero componen whch was aken o be consan over he nle cross-secon, and he emperaure was assumed o be equal o he background emperaure of he reservor waer: u= V, T= T, A waer nake and waer dscharge pons, he waer velocy and emperaure were aken o be consan: u= Vnake, T= T a he npu channel enrance and u= Venrance, T= T enrance a s oule. The upper boundary of he flud was assumed o be free and non-deformable, and he ec of wnd s aken no accoun by specfyng he angenal sresses accordng o Ekman formula [17], he lnear hermal ransfer law was appled accounng for he surface heang from he surroundng ar, he hea ransfer cocen was chosen from he analyss of he obaned n-su measuremen daa. A compuaonal grd was generaed wh Gamb 2.4 package of ANSYS Fluen. The number of nodes hrough he deph of he compuaonal doman was aken o be 21. The non-unform mesh was consruced usng he boom morphomerc daa obaned from n-su measuremens n 214. In a horzonal drecon, he compuaonal mesh conssed of eragonal elemens dsrbued unformly along he enre lengh, wh he characersc lnear sze of 2m. The mesh ncluded 4 hundred housands of nodes. To adap he morphologcal daa avalable n a coordnae-deph forma o he capables of he mesh generaor Gamb, he reservor boom morphology was represened as a se of smple geomercal objecs of some specfed resoluon, whch were hen nroduced no he fle. A code has been wren o produce a bach fle for he Gamb grd generaor of he ANSYS Fluen package from he daa array descrbng he reservor boom morphology. Thus, he complex geomery of he compuaonal doman s realzed. The proposed code s of general characer and s applcable o he consrucon of smlar geomeres and n oher asks. Some prelmnary sudes have been conduced o ge a numercal soluon o he problem of neres usng ANSYS Fluen. Frs, we obaned a saonary soluon o he examned problem gnorng wnd ecs. Ths soluon akes several hundreds of eraons o rapdly converge. Then, he problem was solved usng a non-saonary approach wh he me sep of 2 seconds n he presence of wnd ecs. 3

5 Compuer Smulaons n Physcs and beyond (CSP217) IOP Conf. Seres: Journal of Physcs: Conf. Seres (218) 1217 do :1.188/ /955/1/ Resuls of calculaons 3D numercal modelng was conduced for dfferen scenaro condons of he mpac of he Perm TPP on he Kamsk reservor. The calculaon resuls for wo of hese crcal scenaros whch are of mos neres from he ecologcal and echnologcal pons of vew are gven below. Accordng o he curren regulaory documens deermnng he permssble loads on fshery facles and he Kama Reservor, s no allowed o ncrease he waer emperaure o more han 28 o C n summer. Fgure 1. Map wh he conrol pons locaon. Each pon s denoed by wo numbers, of whch he frs corresponds o he number of a conrol lne, and he second o he pon number along he lne. 3.1 Frs scenaro The goal of hs sudy s o assess he zone of hermal polluon n he "normal" mode of operaon of Permskaya GRES and for he mos probable meeorologcal and hydrologcal condons. Technologcal parameers: 3 operang power uns (2 sream-power uns and 1 combned-cycle un under consrucon), flow rae of dscharged waer m 3 /sec, and dscharge waer emperaure 32.4 С. Under hese condons, he formaon of he flow srucure n he surface layer s governed by he wnd acon and he dscharge of heaed waers from he Permskaya GRES. In general, he flow acqures a undreconal srucure raher quckly. When approachng he mxng zone, he surface flow veloces are m/s. The flows formed by he dscharge of heaed waers have a velocy of abou.2-.4 m/sec (Fg. 2a). The wnd praccally does no shf he sream o he bank of he rver, nensve propagaon of he heaed waers all over he reservor akes place, due o whch here s nensve mxng of waers up o he deph of 3 meers s observed (Fgure 3). Fgures 3a-d show he deph-dsrbuon of he waer emperaure n he conrol pons 1, 2, 3 and 11 for he frs scenaro 1. As one can see from Fgures 11a, b, c, n he conrol secons 1, 2, 3, he flow of warm waer s dreced downsream, here s a sgnfcan heerogeney of he deph-dsrbuon of emperaure. A he enrance o he workng channel (Fg. 11 g, conrol pon 11), emperaure nhomogenees n deph and wdh of he reservor are no observed. However, along he lef bank, were he ouflow channel s locaed, here s a sgnfcan ncrease n emperaure downsream. The area a whch he emperaure ncreases wh respec o background values by 3 degrees or more s abou 1.2 km Second scenaro The goal of calculaons for hs waer dscharge varan s o deermne he zone of hermal mpac n he presence of souhern wnds a mos probable meeorologcal and echnologcal parameers. Technologcal parameers are he same as n varan 1. Hydrologcal and meeorologcal parameers are he same as n varan 1 excep for he wnd drecon. Sourh-eas wnd of velocy of 3 m/s and 8 m/s. 4

6 Compuer Smulaons n Physcs and beyond (CSP217) IOP Conf. Seres: Journal of Physcs: Conf. Seres (218) 1217 do :1.188/ /955/1/1217 (а) (b) Fgure 2. Numercal daa for he frs scenaro: (a) velocy vecor feld n he surface layer of he Kama reservor, (b) emperaure feld ( C) n he surface layer of he Kama reservor (he lnes denoe he boundares of emperaure rse by 3 and by 5 C relave o he background emperaure) Under hese condons, a raher complex flow srucure s formed, boh near he surface and a he deph. Ths s due o he fac ha he runoff, wnd and he dscharge flows (formed due o he dscharges of he Permskaya GRES) have nearly he same veloces, bu hey are muldreconal. In addon, here are he densy ecs due o he dfferen emperaures of he sreams. Therefore, here s no any dsngushed flow drecon a dephs of up o 5-6 meers. H, m H, m H, m H, m (а) (b) (c) (d) Fgure 3. Deph-dsrbuons of waer emperaure n he conrol pons for he frs scenaro: a) he frs conrol pon seres, b) he second, c) he hrd, d) he elevenh In he case of souheasern wnds, he mos unfavorable suaon wh he arrval of warm waer n he supply channel of Permskaya GRES s observed (Fgure 4). In hs case, he ncrease n wnd velocy reduces he me-perod needed for warm waer o reach he supply channel and ncreases he nensy of he arrval of warm waer and he ncrease n he flow rae exers he oppose ec on hese processes. Decrease n he flow rae ncreases he probably of warm waer arrval o he waer nake facles. As follows from he resuls of calculaons, he reverse flows from he oule channel o he supply channel are observed only n he upper layer of hckness, as a rule, no more han 2-3 m. In general, when he second scenaro s mplemened, he maxmum hermal polluon ec s observed: he ncrease n emperaure wh respec o he background values by 3 and 5 C occurs, respecvely, n he waer area of 2.8 and 1.5 km 2. In he case of sgnfcan wnd n he drecon oppose o he drecon of he flow n he rver, a hree-dmensonal vorex s formed whn a few hours, he horzonal dmenson of whch s equal o he dsance beween he nerfaces of he supply and reurn channels wh he reservor, and he vercal dmenson s equal o he deph of he rver. The presence of hs vorex leads o he moon of warm waer agans he flow n he rver. In hs case, less han n a day, warm waer reaches he se of he nake of he coolng channel, whch s exremely undesrable from a echnologcal pon of vew. There s also a sgnfcan emperaure nhomogeney n deph, and he emperaure graden s greaes near he boom of he rver. 5

7 Compuer Smulaons n Physcs and beyond (CSP217) IOP Conf. Seres: Journal of Physcs: Conf. Seres (218) 1217 do :1.188/ /955/1/1217 (а) (b) Fgure 4. Temperaure feld ( C) n he surface layer of he Kama reservor (he lnes ndcae he boundares of emperaure ncrease by 3 and by 5 C relave o he background emperaure), (a) SE wnd 3 m/s, (b) SE wnd 8 m/s 4. Concluson The sudy of hydrodynamc characerscs and he calculaon of he propagaon of hermal polluon zone n he rver basn has been carred ou usng he example of Permskaya GRES. Numercal modellng based on he hree-dmensonal model yelded hydrodynamc characerscs of drecons and veloces of flow. Calculaon of he propagaon of hermal polluon zone due o he dscharge of heaed waer from Permskaya GRES were performed for dfferen wnd drecons. I was found ha he arrval of warm waer no he supply channel durng he ce-free perod can be observed when he followng condons are realzed: here s farly srong souh-easern wnd (W> 3 m / sec) durng he long enough me (> hours); he flow rae of he waer dscharge n he Kama HPP secon s low, Q <1 m3 / sec; he emperaure of he dscharged waer from he Permskaya GRES waer s a leas 3 C; he dscharge rae s greaer han 4 m3/s. Acknowledgmens The work was suppored by Russan Scenfc Foundaon (gran No ). References [1] Bernadks N M 1933 Maer. on hydrology, hydrography and waer resource. of he USSR, 2 [2] Bernadks N, Proskuryakov B 1933 Theory and Pracce of Calc.s of he Coolng Pond. 1 [3] Flecher C A 1988 Specal Technques for Dfferenal Flow Caegores [4] Tolsykh A I 199 Compac Dfference Scheme and Ther Applcaons o Flud D. Problems [5] Parknson C L 1979 J. Geophys. Res [6] Cheh S H 1987 J. Hydraulc Engneer. 113 (8) 132 [7] Abbaspour M, Javd A H, Moghm P, Kayhan K 25 J. of Envr. Scence and Techn. 2 (1) 13 [8] Issakhov A 211 J. of Physcs 318 (4) 4251 [9] Issakhov A 213 Power, Conrol and Opmzaon [1] Issakhov A 214 Scenfc World J. do /214/67895 [11] Tennekes H, Lumley J L 1972 The MIT Press [12] Leseur M, Meas O, Come P 25 Large Eddy Smulaon of Turbulence [13] Lepkhn A P, Lyubmova T P, Parshakova Y N, Tunov A A 212 J. of Mn. Scence 48 (2) 39 [14] Lyubmova T, Lepkhn A, Konovalov V, Parshakova Ya, Tunov A 214 J. Hydrology [15] Lyubmova T, Lepkhn A, Parshakova Ya, Tunov A 216 J. of Hydrology [16] Launder B E, Spaldng D B 1972 Lecures n Mahemacal Models of Turbulence [17] Welander P 1968 Tellus XX 1 1 6