Partial Similarity in Solar Tower Modeling

Transcription

1 Te 0t Cofeee of Meaial Eieei Netwok of Tailad 8-0 Otobe 006, Nako Ratasima, Tailad Patial Similaity i Sola Towe Modeli Atit Koosisuk ad Tawit Citsomboo Sool of Meaial Eieei, Istitute of Eieei, Suaaee Uivesity of Teoloy, Nako Ratasima 0000, Tailad, Tel: , Fax: , atit@mat.sut.a.t Abstat Dimesioal aalysis is emloyed to detemie te similaity oditio fo ysial models of a sola towe (a sola owe lat fo eeati eletiity). I a evious study, full eometial similaity ad led to usi diffeet sola eat fluxes fo ea model i ode to aieve dyami similaity: a oditio diffiult to ealize i a atual atie. Tis study aims to eate dyami similaity wile usi te same sola flux fo all models. Te study eveals tat, to aieve te desiable oditio, te models aot be fully eometial simila, ee atial similaity. Te futioal elatiosi tat ovides te oditio fo tis atial similaity is oosed ad its validity is oved by usi umeial solutios of flows i sola towes. Keywods: Sola towe, Dimesioal aalysis, Patial similaity, Dyami similaity, Natual ovetio. Nomelatue A flow aea, m A oof aea, m seifi eat at ostat essue, J/(k.K) avitatioal aeleatio, m/s towe eit, m oof eit above te oud, m m& mass flow ate, k/s q isolatio, W/m q sola eat absotio e uit volume, W/m R as ostat, J/k K towe adius, m oof adius, m S soue tem i CFX T absolute temeatue, K flow veloity, m/s Geek symbols oeffiiet of volumeti temal exasio, /K γ seifi eats atio Π dimesioless aamete ρ desity of woki fluid, k/m Subsits ositio at oof ilet (Fiue ) ositio at towe ilet (Fiue ) towe m model ototye oof. Itodutio Sola towe is a sola owe lat oosed to eeate eletiity i lae sale, by tasfomi sola eey ito meaial eey. I ote wods, it is a atifiial wid eeato, albeit a ot oe. Te semati of a tyial sola towe owe lat is sketed i Fiue. Sola adiatio stikes te tasaet oof sufae, eati te ai udeeat as a esult of te eeouse effet. Due to buoyay effet, te eated ai flows u te towe ad idues a otiuous flow fom te eimete towads te middle of te oof wee te towe is loated. Saft eey a be extated fom te temal ad kieti eeies of te flowi ai to tu a eletial eeato []. Fiue Semati of a sola-towe owe lat Tyial size of a sola-towe owe lat is quite lae. Te 00 MW lat oosed i Austalia is km tall wit a oof diamete of km []. Exeimetal study i sola towe a teefoe best be efomed i a small sale model, but a similaity oditio fo te small sale model must fist be establised. I te evious study [], it was foud tat fo a eometial simila model to be dyamial simila to te ototye te sola eat fluxes (isolatio) must be diffeet fom tat of te ototye s.

2 Tis is vey ioveiet i a exeimetal setu sie it suests te use of a tited lass oof of diffeet sade ta te oe used i te ototye. It is teefoe efeable tat te same isolatio be used i all models. Hee, tis is te mai aim of te ivestiatio of tis ae. Afte te ivestiatio it is foud tat te same isolatio ould ideed be used, but at a ie of ot bei able to use te full eometial similaity; oly a atial eometial similaity is allowed.. Dimesioal Aalysis I tis study, te atio of towe eit to towe diamete is ot vey lae. Teefoe, te flow ould be aoximated as a ivisid flow witout saifii mu i auay [4]. I tis study, a sola towe witout a tubie is ivestiated. Aodi to te evious wok of Citsomboo [], te matematial model of te flow i a sola towe was oosed as, m & da A da ρa ρ ρa + + A T RT A γ ρ = T da da A Tis matematial model was a esult of te sytesizi of te osevatio equatios of mass, mometum ad eey, toete wit te ideal as elatio. Due to its eliable editios i omaiso wit CFD, te foms of te tems aea i tis equatio ould eas be used as a uide to fom te list of vaiables i te dimesioal aalysis. To tis ed, te deedee of owe, ( ) ρa, o te ideedet aametes was oosed, i [], as ρa () = f ( ρ,,,, ) () By usi,,, ad as eeati vaiables, a staitfowad dimesioal aalysis ives te dimesioless vaiables as ρa 4 = f o = f ) ( ρ ( ) q () Te validity of Eq.() was oved by sali te umeial esults of te vaious models []. Howeve, te oosed seme also equied, fo dyami similaity, tat qm = (4) m q tus fo a small sale model te oditio i (4) stiulates a lesse isolatio fo te small-sale model ta tat of te ototye s, a ioveiet oditio as metioed ealie. Tis leads to a idea to sea fo a simila oditio tat equies te same isolatio fo diffeet models. It is oted tat te udesiable simila oditio of te evious study mit be due to te use of q ( = ) istead of q. Teefoe, i tis study te diet use of q is oosed. By examii Eq.() it is see tat tis tem always aea i ombiatio as q A, wi is te total eat flux stiki te etie oof. Tis quatity, ate tat just q, will be oosed i tis study sie it eeset te well defied divi eey of te system. Te oedual stes i fidi te dimesioless vaiables ae listed as follows: Ste Poosi te imitive-vaiable futioal elatiosi: ρa A = f ( ρ,,,, ) () Ste Usi mass (M), let (L), time (t), ad temeatue (Θ) as te fudametal dimesios. Te dimesios of vaious tems ae listed i Table. ( Note: Te metodoloy used ee is oosed i [6, ]; it yields te same esult as te familia Bukiam s i teoem wit a little moe oveiee i aleba omlexity.) Table : Pimitive vaiable s dimesios i tems of owes of te fudametal dimesios q A ρa ρ M L t Θ Ste Coose ρ,,, ad as te sali vaiables. Te fudametal dimesios a ow be extated as, L = (6) Θ = ()

3 t = (8) M = ρ (9) Ste 4 Sale te emaii vaiables aodi to tei dimesios i te owes of te fudametal dimesios, tus: m & Π = (0) ad Π = ρ ρ A ( () Fially, te futioal elatiosi is, = f ), o m & ρ = f A ρ (). Eieei Iteetatio of te Dimesioless aiables Eieei iteetatio ofte els i a deee udestadi of te ysial eomeo, wi is bei eeseted by te matematis. Te sali vaiable of, ρ, ould be iteeted as te owe equied to lift te ai u te towe eit. To laify tis, fist ote tat is a time sale fo te flow to limb fom te base to te to of te towe. Aodily, ρ = ρ A 4 4 ρ = ρ = = ρa t = m& t Te last tem is eadily evealed as te owe equied to lift te ai u te towe. So, ould be iteeted as te kieti owe of te system measued i te sali uit tat is ootioal to te owe equied to lift te ai u te towe. Futemoe, ould be iteeted as te buoyat foe e uit weit. Note tat A = m& T, ad tat te sali vaiable ρ = ρ = ρ A m = = & t ρ. ow beomes T ρ ρ iteeted as te buoyat foe (eated by, wi ould be ρ ) saled by te weit of te fluid of te same volume. Te etie elatio of = f ( ) a be summaized as tyi to fid te elatio of aateisti kieti eey (te ituitive outut) as a futio of te iial aateisti divi foe of te system (te ituitive iut). 4. Similaity Requiemets To obtai similaity fo te models, te stiulatio equied by betwee ototye ad model is, π π = m Substituti te oditios tat te eat flux values ae te same, it is obtaied, () m = m (4) 4 It is sow i Eq. (4) tat te oof adius does ot saled i a liea fasio wit te towe eit; tis suests a distoted model. I ote wods, tis suests a atial eometi similaity. Te dimesios of atially eometial simila models equied fo esui dyami similaity amo models ae eseted i Table. Table Seifiatio of ototye ad distoted model lats. Case Towe Heit sale fato Towe eit Roof eit Towe adius Roof adius Pototye Model Model Model Model Model CFD Modeli Numeial alulatios ave bee efomed usi CFX, oe of te widely-aeted ommeial CFD odes. Fo tis uose, CFX solves te osevatio equatios fo mass, mometa, ad eey usi a fiite volume metod. Adative ustutued tetaedal meses wee used i te eset study. Te lats studied wee modeled as axis-symmety wee te etelie of te towe is te axis of symmety. To simulate axis-

4 symmety, a deee setio of te lat is ut out fom te etie eiey as sow i Fiue. To make etai tat similaity (o te lak teeof) was ot affeted by id-tooloy ieulaity, id similaity fo all te test ases was efoed. Gid similaity meas tat we te model is saled to be te same size as te ototye, its id is exatly te same as tat of te ototye. Moeove, id oveee was also esued by vayi te umbes of id util o ae i outut aamete was otied. Te CFD esults of te ototye ad all distoted models ae sow i fiue -. All lots to be subsequetly eseted ae dislayed alo te saled flow at, equali zeo at oof ilet ad oe at towe to). Fiue sows te aveae veloity alo te flow at; it a be see tat te veloities of te flow ude te oof iease alo te flow at ad emais ostat alo te towe. Te temeatue ofiles, sow i Fiue 4, also demostate simila beavios as te veloity ofiles. I Fiue, te essue distibutios ae see to be omially ostat ude te oof befoe falli liealy i te towe otio, to meet te ydostati essue distibutio at te towe to. Note tat te odiate is te aue essue saled su tat essues at te to of towe ae always zeo. Fiue Ustutued id used fo te deee axissymmeti omutatioal domai. Fiue Numeial editio of veloity ofiles fo isolatio = 800 W/m Poe bouday oditios ae eeded fo a suessful omutatioal wok. At te oof ilet, te total essue ad temeatue ae seified; weeas at te towe exit te outlet oditio wit zeo stati essue is esibed. Te symmety bouday oditios ae alied at te two sides of te seto wile te adiabati fee-sli oditios ae esibed to te emaii boudaies, osistet wit te fitioless flow tat ae bei modeled. All test ases ad bee omuted util esiduals of all equatios eaed tei esetive miima. Moeove, lobal osevatio of mass ad bee eeked to fute asetai te oveee of te test ases. 6. Results ad Disussio Te isolatios of te ototye ae set at 600, 800,,000, ad,00 W/m wi ive Π, esetively, at.0 0-4,.4 0-4,.8 0-4, ad Te equality of Π wee te used to omute te oof adiuses of te models equied fo te esetive isolatios (aodi to Eq.(4)). Fiue 4 Numeial editio of temeatue ofiles fo isolatio = 800 W/m

5 By usi te above equatio, te maximum eetae diffeee of Π betwee te atial eometial simila models ad te ototye is eseted i Table. Fiue Numeial editio of essue ofiles fo isolatio = 800 W/m Fiues - sowed te ue diseaies of te imitive flow vaiables betwee te ototye ad te diffeet-size models, wi ae atially eometially simila ad Π -simila to te ototye. If dyami similaity existed as oosed, saled data of te vaious ases, aodi to te foms of te dimesioless vaiables, must ollase. To tis ed, Fiue 6 esets te distibutios of te values of te dimesioless vaiable, Π, omuted fom te ivolved imitive vaiables. Te fiue dislays te lustes of values of Π aodi to vaious values of Π tat wee used i te omutatios. It is lealy see tat te widely satteed data ow almost ollase, suesti similaity o so it aeas. Fiue 6 Π -Π aateistis. To quatify similaity, te eetae diffeee of Π betwee te ototye ad all te distoted models is defied as follows: Peetae diffeee of Π Π Π model ototye = Πototye 00 Table Te maximum eetae diffeee of Π (MPDP) betwee ototye ad all distoted models. Case MPDP (%) m Pototye N/A Model 0..8 Model Model Model 4. Model Table sows iteesti esults i tat we te size is made 4 folds smalle, te eo is 0.6%; but we it is made folds lae, te eo is mu ie at.%. It seems, te, tat we te ysial sizes ae lae te eetae eos ae ie, ad vie vesa. I ote wods, te eos ae ot saled liealy. Tis mit be attibutable to te effet of atifiial visosity, wi is a iteal at of most umeial semes. Noted tat similaity ee is oosed o a ivisid latfom. Te atifiial visosity edes te ivisid flow to be visous-liked. Te lae (tus talle) lats ted to eate ie flow veloities, esulti i mu ie atifiial Reyolds umbes ta te smalle lats. Te elative diffeees i atifiial Reyolds umbes ae tus believed to be te easo beid te diseaies i te ivisid similaity fo all tese ases. Pysial exeimetatio is te oly way to ove te validity of te ivisid similaity oditio as oosed i tis study.. Colusios Dimesioless vaiables ae oosed to uide a exeimetal study of te flow i a ysial sola towe model. Distoted eomety (atial similaity) is equied fo te model i ode to be dyamial simila to te ototye wile oldi te isolatio to be te same fo all ases. Comutatioal fluid dyamis (CFD) is emloyed to obtai umeial esults tat ae used to ove te similaity of te oosed dimesioless vaiables. Aalyses of te esults fom CFD sow tat te atially eometial simila models ae dyamially simila to te ototye, to witi a, eas aetable, eo bad wi is still uetai as to wat auses it. Akowledmets Te autos ae takful to te Royal Golde Jubilee (RGJ) P.D. Poam of te Tailad Resea Fud (TRF): te soso of tis esea ojet. Refeees [] Slai, J. 99. Te Sola Cimey: Eletiity fom te Su. Axel Mees, Stuttat, Gemay.

6 [] Eviomissio, 006. Te Sola Towe Pojet. tt:// (aessed o Auust 006). [] Koosisuk, A. ad Citsomboo, T., 004. Similaity Aalysis i Sale Modeli of a sola towe, Poeedis of te 8t Natioal Meaial Eieei Cofeee, Ko Kae, Tailad. [4] Koosisuk, A., Citsomboo, T., 00. Fitioal effet o te flow i a sola imey. I: Poeedis of te 4 t Natioal Symosium o Gaduate Resea. [] Citsomboo, T., 00. A validated aalytial model fo flow i sola imey. Iteatioal Joual of Reewable Eey Eieei. (), [6] Citsomboo, T., 00. Costutio ad iteetatio of dimesioless vaiables i a ew way. I: Poeedis of te t Natioal Meaial Eieei Cofeee, ol.,. TF9-TF4. [] Citsomboo, T., 00. Fluid Meais. MGaw- Hill/To, Tailad. (i Tai)