Mist/air Cooling in a Two-Pass Rectangular Rotating Channel with 45-deg Angled Rib Turbulators

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1 Proceedngs of Turbo Expo 11 GT11 June -1, 11, Vancouver, DC, Canada Ms/ar Coolng n a Two-Pass Recangular Roang Channel wh -deg Angled Rb Turbulaors GT11-9 T. S. Dhanasearan and Tng Wang Energy Converson and Conservaon Cener Unversy of New Orleans New Orleans, LA 18-, USA E-mals: sdhana@gmal.com; wang@uno.edu ABSTRACT Increasng he urbne nle emperaure can ncrease he gas urbne cycle effcency. In order o ncrease he urbne nle emperaure sgnfcanly, an advanced coolng sysem has o be essenally developed. Injecon of ms o he coolan flud s consdered a promsng echnque o proec he ho componens such as combusor lners, combusor ranson peces, and urbne vanes and blades. A seres of expermens conduced n he pas proved he success of ms coolng echnology n he laboraory envronmen. Favorable resuls from he numercal smulaon furher encourage connuous exploraon of employng ms-coolng echnology n he acual gas urbne worng envronmen n varous applcaons. The presen sudy focuses on applyng ms coolng o he roang ms/ar nernal coolng passage wh rb urbulaors usng numercal smulaon. In he frs par, he compuaonal flud dynamcs (CFD) models of smooh and rbbed channels whou ms and roaon are valdaed wh he expermenal resuls avalable n leraure. The agreemen beween he predced and expermenal values n he lower Reynolds number (Re) range s whn % devaon, and, a hgher Re range, he devaon s abou 1%. For he smooh channel, he agreemen wh expermenal resul s good for he enre range of Re values. In he second par, he roaonal effec on he smooh and rbbed channels s predced and analyzed. In he las par, he ms coolng enhancemen on he rbbed channel wh roaon s smulaed. The secondary flows creaed due o channel bend and roaon are specfcally analyzed. The resuls show ha he ms coolng enhancemen s abou % a he ralng surface and abou % a he leadng surface of he frs passage wh % ms njecon. In he second passage, % enhancemen s predced for boh he surfaces. NOMENCLATURE A p surface area of drople b slo wdh (m) C concenraon (g/m ) D h Channel hydraulc dameer GT gas urbne h convecve hea ransfer coeffcen (W/m -K) H hegh of channel (m) urbulen nec energy (m /s ) K hermophorec coeffcen Local ssel number, hd h /c m mass (g) q wall hea flux (W/m ) Re Reynolds number (ρ V j d / μ ) Ro roaonal number, Ω D h / V T w wall emperaure ( o C) V nle bul velocy (m/s) W wdh of channel (m) Gree ε urbulence dsspaon (m /s ) λ hermal conducvy (W/m-K) Ω roaonal speed (rad/s) Subscrp p, d parcle or drople r rble s smooh. 1. INTRODUCTION Increasng he urbne nle emperaure s one of he major means o ncrease he gas urbne (GT) effcency. The ncreased ho gas emperaure ypcally exceeds he allowable maeral lm for he blades and vanes. Hence, here s always demand for connuously developng new advanced coolng echnologes o cool he ho componens n hgh-performance gas urbnes. One of he promsng echnologes o sgnfcanly enhance he hea ransfer s o njec waer ms no he coolan flow. Each drople acs as a coolng sn and fles over a dsance before compleely vaporzes. Ths dsrbued coolng characersc allows conrolled coolng by manpulang dfferen szes of njeced waer droples. The ms/seam coolng scheme applcable o an Advanced Turbne Sysem (ATS) was nroduced and verfed wh exensve basc expermens under laboraory worng condons, n a horzonal ube [1,], a 18-degree curved ube [], mpngemen jes on a fla surface [], and mpngemen jes on a curved surface []. Typcally, an average coolng enhancemen of - % was acheved by njecng 1-% (w.) ms no he seam flow. A very hgh local coolng enhancemen of - % was observed n he ube and on a fla surface, and local coolng enhancemen 1

2 above % was observed when he seam flow passed he 18-degree bend. The ms/ar flm coolng sysem appled o modern gas urbnes was smulaed by L and Wang [-] and showed ha a small amoun of ms njecon (% of he coolan mass flow rae) could ncrease he adabac flm coolng effecveness by abou % % under low emperaure, velocy and pressure condons smlar o hose n he laboraory. They also nvesgaed he effecs of dfferen flow parameers, njecon hole confguraon, and coolan supply plenum on he coolng effecveness. In order o smulae he acual GT operang condons more closely, L and Wang [8] presened he ms/ar flm coolng hea ransfer coeffcen under a conjugae wall condon by employng nernal channel coolng beneah he blade surface. The resul of conjugaed - D cases ndcaed ha reverse hea conducon from downsream o upsream along he sold wall was srong whn a dsance of slo wdhs. L and Wang [9] suded he curvaure effec on ms flm coolng, as well. They found ha he magnude of he ms coolng enhancemen was ordered as follows: fla surface > pressure surface > sucon surface > leadng edge. Ther smulaon showed ha he flm coolng effecveness ncreases approxmaely % a he leadng edge, % on he concave surface, and % on he convex surface wh % ms concenraon. Ther sudes [-9] on ms/ar flm coolng were conduced wh he urbne n a saonary condon. Recenly, Dhanasearan and Wang [1] smulaed he ms/ar flm coolng enhancemen over a roang blade under gas urbne worng condons wh elevaed pressure, hea flux, and Reynolds number. They predced an average of % ms coolng enhancemen wh an equvalen blade surface emperaure reducon of -1 K. As a connuaon of ms coolng echnology developmens, he presen sudy employs compuaonal flud dynamcs (CFD) smulaons o nvesgae he coolng performance of applyng ms n a gas urbne nernal blade wh rbles under boh saonary and roang condons. The early nvesgaons of enhancng urbne arfol nernal coolng under roang condons were performed wh sragh, smooh, crcular ubes [11-1]. Han e al. (for example Ref. [1] and [1]) have conduced several expermenal sudes on sragh rb-roughened, non-roang and roang channels o nvesgae he effec of urbulaor confguraons (such as rb hegh, spacng and angle), he flow channel aspec rao, and he flow Reynolds number on he dsrbuons of he local hea ransfer and pressure drop. Recenly, as CFD schemes became more sophscaed and powerful, numercal sudes of hea ransfer n rbbed channels have become popular. Chang and Mlls [1] employed a low Reynolds number urbulence model for a wo-dmensonal suaon nvolvng flow n a saonary crcular ube wh repeaed recangular rbs. Arman and Rabas [1] subsequenly predced he flow feld and hea ransfer n a saonary crcular ube wh repeaed rbs usng a wo-layer model. Praash and Zerle [18] have used he sandard -ε model wh wall funcons o predc he hea ransfer n roang rb ducs wh he assumpon of perodc, fully developed flow suaons. In he presen sudy, a ms/ar compuaonal model s developed o predc he ms coolng enhancemen on he roang, rbbed, recangular channel. Inally, he ar-only compuaonal model s valdaed wh he expermenal resuls avalable n open leraure. The effecs of roaonal force on he flow physcs and hea ransfer n he channel wh rbles are nvesgaed. Fnally, he ms coolng enhancemen s smulaed usng he valdaed compuaonal model.. mercal Mehod A feasble mehod o smulae he ar/ms flow s o consder he droples as a dscree phase snce he volume fracon of he lqud s small (less han.1%) n hs sudy. The rajecores of he dspersed phase (droples) are calculaed by he Lagrangan mehod. The mpacs of he droples on he connuous phase are consdered as source erms o he governng equaons of mass, momenum, energy, and speces. The connuous phase, ncludng ar and waer vapor, s formulaed wh he Euleran mehod. The ms coolng compuaonal model has been esablshed and valdaed whn % o 1% devaon from he expermenal daa for varous confguraons ncludng: ms/seam mpngemen on a fla surface [19], on a curved surface [], n a horzonal ube [1], and n a 18 degree bend ube []. The dealed descrpon of CFD ms flow modelng s referred o Dhanasearan and Wang s oher sudes [19,1] and s no repeaed here. A summary of he CFD model s presened below. Connuous Phase The me-averaged governng equaons of mass, momenum, energy, and speces are: ( ρu ) = S m (1) x x x x v P ( ρu u j ) = ρg j + ( τj - ρu' u' j ) + Fj x j x T ( ρc p u T) = λ - ρc p u' T' + μφ + Sh x x j ( ρu C j ) = ρd j - ρu' C' j + S j x C x where τ j s he symmerc sress ensor. The source erms (S m, F j and S h ) are used o nclude he conrbuons from he dspersed phase. μφ s he vscous dsspaon and λ s he hermal conducvy. C j s he mass fracon of speces j n he mxure, and S j s he source erm for hs speces. D j s he dffuson coeffcen. The dffuson erm s used for bdffuson beween he waer vapor and ar mass. When he lqud evaporaes, he vapor produced surrounds he lqud drople. Then, hs vapor wll be ranspored away hrough convecon and mass dffuson. Three speces (oxygen, nrogen and waer vapor) are smulaed n he paper. The erms of ρu' u' j, ρc p u' T' and ρ u' C' j n he equaons above represen he Reynolds sresses, urbulen hea fluxes, and urbulen concenraon (or mass) fluxes, whch should be modeled properly for a urbulen flow. More dealed nvesgaons and dscussons on urbulence models and her effecs on he smulaon of ms coolng can be found elsewhere [19, 1-]. The equaons for he urbulen nec energy () and s dsspaon rae (ε) are: x μ σ x ( ρu ) = μ + + G ρε x σ ε x. () μ ε ε ε ( ρu ε) = μ + + C G C ρ. () x x 1ε ε () () ()

3 The erm G s he generaon of urbulence nec energy due o he mean velocy gradens. The urbulen vscosy, μ, s calculaed from he equaon: μ = ρcμ ε () The effecve hermal conducvy (λ eff ) and he effecve dffuson coeffcen are calculaed by he followng wo equaons, respecvely: λ = λ + c μ / Pr, (8) eff eff p D = D + μ / Sc. (9) The consans C 1ε, C ε, C μ, σ, and σ ε are assgned he followng : C 1ε = 1., C ε = 1.9, C μ =.9, σ = 1., σ ε =1. []. In addon, he urbulence Prandl number, Pr, s se o.8, and he urbulence Schmd number, Sc, s se o.. For he near wall regon, he enhanced wall reamen s used, n whch he sandard wo-layer model s combned wh wall funcons. To apply he wo-layer approach, he compuaonal doman s separaed no a vscosy-affeced regon and a fully-urbulen regon by defnng a urbulen Reynolds number, Re y, whch s based on he dsance from he wall. Re μ y = y 1/ / ν, enhanced = θμ + (1 θ)μ,l (1) where s he urbulence nec energy and y s he dsance from he wall. The flow s assumed o be n he fully urbulen regon f Re y >, and he -ε model s used. Oherwse, he flow s n he vscosy-affeced regon, and he one-equaon model of Wolfsen [] s used. The urbulen vscoses calculaed from he wo regons are blended wh a blendng funcon (θ) o mae he ranson smooh. (11) where μ s he vscosy from he -ε model of hgh Reynolds number, and μ,l s he vscosy from he near-wall oneequaon model. The blendng funcon s defned so s a he wall and 1 n he fully-urbulen regon. The wall funcons are also enhanced by blendng lnear (lamnar) and logarhmc (urbulen) laws-of-he-wall o mae he blended wall funcon applcable hroughou he enre near-wall regon. Dscree Phase Based on Newon s nd law, he drople moon can be formulaed by m p dv p / d = F (11) where v p s he drople velocy (vecor). The rgh-hand sde s he combned force acng on he drople, whch normally ncludes he hydrodynamc drag, gravy, and oher forces such as Saffman's lf force, he hermophorec and Brownan forces, ec. In hs sudy, Saffman's lf force s ncluded. To nclude radaon hea ransfer, he P1 model [] was used. The P1 model deermnes he local radaon nensy by solvng he ranspor equaon for ncden radaon, G as follows:. (Ψ G) a G + aσt = S g (1) where Ψ = 1/((a+ σ s ) (Cσ s )), a = absorpon coeffcen, σ s = scaerng coeffcen, σ = Sefan-Bolzmann consan, S g = radaon source, C = lnear-ansoropc phase funcon. The hea source due o radaon n he followng form s drecly subsued no he energy equaon. -. q r = aσt (1) The drople s hea ransfer s gven n he followng equaon. dt dmp mpcp = A ph(t - T) + h fg + A pε pσ ( θ R T ) d d (1) where h fg s he laen hea, ε p = parcle emssvy, θ R = radaon emperaure. The convecve hea ransfer coeffcen (h) can be obaned wh an emprcal correlaon [ and 8]: hd.. d = =. +.Red Pr (1) λ where d s he ssel number, and Pr s he Prandl number. The mass change rae or vaporzaon rae n Eq. (1) s governed by concenraon dfference beween drople surface and he ar sream, dmp = πd c(cs C ) (1) d where c s he mass ransfer coeffcen, and C s s he vapor concenraon a he drople surface, whch s evaluaed by assumng he flow over he surface s sauraed. C s he vapor concenraon of he bul flow, and s obaned by solvng he speces ranspor equaons. The values of c can be gven from a correlaon smlar o Eq. (1). cd.. Sh p = =. +.Rep Sc (1) D where Sh s he Sherwood number, Sc s he Schmd number (defned as ν/d), and D s he dffuson coeffcen of vapor n he bul flow. When he drople emperaure reaches he bolng pon, he followng equaon (18) can be used o evaluae s evaporaon rae: dm p λ. = πd (. +.Rep )ln( 1+ c p (T T) / h fg )/ c (18) p d d where λ s he gas/ar hea conducvy and c p s he specfc hea of he bul flow. Theorecally, evaporaon can occur a wo sages: (a) when he emperaure s hgher han he sauraon emperaure (based on local waer vapor concenraon), waer evaporaes, and he evaporaon s conrolled by he waer vapor paral pressure unl % relave humdy s acheved; (b) when he bolng emperaure (deermned by he ar-waer mxure pressure) s reached, waer connues o evaporae. The sochasc mehod [] s used o consder he urbulence dsperson effec on drople racng. The drople rajecores are calculaed wh he nsananeous flow velocy ( u + u' ), and he velocy flucuaons are hen gven as:. ( /). u' = ς u' = ς (19) where ς s a normally dsrbued random number. Ths velocy wll apply durng he characersc lfeme of he eddy ( e ), a me scale calculaed from he urbulence nec energy and dsspaon rae. Afer hs me perod, he nsananeous velocy wll be updaed wh a new ς value unl a full rajecory s obaned. To consder he neracons beween he ny lqud droples around he rbles and he effec of he roaon and channel bend, he Taylor Analogy Breaup (TAB) model [9] and O Roure coalescence model [] are employed n hs

4 sudy. The TAB model s a classc mehod based upon Taylor's analogy beween an oscllang and dsorng drople and a sprng mass sysem, where he surface enson forces, drople drag force and drople vscosy forces are analogzed wh resorng, exernal, and dampng forces. O'Roure's coalescence model consders coalescence as an oucome of collson. O'Roure's algorhm assumes ha wo droples may collde only f hey are n he same connuous-phase cell. Ths assumpon can preven droples ha are que close o each oher bu no n he same cell from colldng, alhough he effec of hs error s lessened by allowng some droples ha are farher apar o collde. The overall accuracy of he scheme s second-order n space. Once s deermned ha wo parcles collde, he oucome of he collson s coalescence f he droples collde head on, and bouncng f he collson s more oblque. Drople breaup and coalescence models mprove dscree phase calculaon when srong local acceleraon or deceleraon s presen n he flow feld such as over he rble surface or around he channel bend wh roaon..1 Boundary Condons.1.1 Arflow The approach adoped n hs sudy s o frs valdae he CFD model for ar-only flows wh expermenal resuls avalable n open leraure, and hen o smulae he ar/ms flow n order o predc he coolng enhancemen. The expermenal resuls of Fu e al. [1] are used for hs purpose. The geomery of a wo-pass channel wh a -deg rbbed wall consdered for hs sudy s shown n Fg. 1a. The dmensons are exacly he same as used n he expermenal sudy [1]. The channel cross secon s 1. x 1. mm mang he aspec rao of 1:1 (W:H) hroughou he lengh excep he bend poron. The rb hegh, e = 1.9 mm, he channel hydraulc dameer, D h = 1. mm, and he rb pch-o-hegh rao, p/e = 1. Each pass has a 1. mm long heang secon (Fg. 1a). The compuaonal doman conans a mm unheaed enrance lengh o provde he fully-developed flow condon. The clearance of he 18-deg sharp urn s 1. mm from p o end wall. The dvder wall has a hcness of 19.1 mm wh a 9. mm radus a he p. The rbs wh a cross secon of 1.9 mm 1.9 mm are placed on he op and boom of he channel. As n he expermenal se-up, a gap of.9 mm s mananed beween he rbs and he sdewall. The rao of rb pch-o-rb hegh s 1. The ar nflows wh Reynolds numbers of,, 1,,,, and, wh a emperaure of K and he roaonal speed of rpm are consdered. The consan hea flux of,8 W/m s assgned o he heang poron of he compuaonal doman. A urbulence nensy of 1% s assgned a he mansream nle. The pressure a he flow ex s assumed o be mananed a a consan value of 1 am. All of he walls n he compuaonal doman are adabac and have a no-slp velocy boundary condon..1. Drople njecon A unform drople sze of μm s consdered, hen he effec of dsrbued drople dameers s smulaed for comparson. The mass rao of lqud droples over arflow s % (abou 1.1 x 1 - g/s for ms) for boh cases. The number of ms njecon pons a he coolan nle depends on he number of compuaonal meshes a he nle surface. In he presen case, abou njecon pons are placed. The rajecory number for sochasc racng s chosen o be 1 for each njecon. The boundary condon of droples a he walls s assgned as reflec, meanng he droples elascally rebound off once reachng he wall. Deals abou he model are documened n a prevous sudy by Dhanasearan and Wang [1]. A he oule, he droples jus smply escape from he compuaonal doman. (a) R = 8.8 Unheaed poron (b) Leadng Rbbed (c) Y Heaed poron X Z All dmensons are n mm Tralng Rbbed Regon 1 Man flow drecon Fgure 1 (a) Plane vew of he channel geomery (b) compuaonal elemens on he surfaces and (c) -D schemacs and coordnaes, modeled followng expermenal wor of Fu e al. [1].. Meshng and smulaon procedure The compuaonal doman s consruced by srucured hexahedral elemens as shown n Fg. 1b. More nensve meshes are used near he wall and rbbed area. A oal of 1 mllon cells are used for hs confguraon. In he roang channel case, he coordnae sysem shown n Fg. 1c roaes wh he channel. In hs sysem, he flow s seady, bu he cenrfugal and Corols forces are accouned for va he addonal source erms n he equaon of moon (Eq.). The droples wll be affeced by he roang effec ndrecly because he drople races are aached o he coordnaes of he connuous phase. Therefore, here s no need o add he cenrfugal force n he force balance equaon (Eq. 11). The compuaon s carred ou usng he commercal CFD sofware FLUENT (Verson..1) from Ansys, Inc. The smulaon uses he segregaed solver ha employs an mplc pressure-correcon scheme and decouples he momenum and energy equaons. The SIMPLE algorhm s used o couple he pressure and velocy. A second order upwnd scheme s seleced for spaal dscrezaon of he convecve erms and

5 speces. The compuaon s conduced for he connuous phase (ar) frs. Afer obanng an approxmae converged flow feld of he ar, he dspersed phase of drople rajecores are calculaed. A he same me, drag, hea and mass ransfer beween he droples and he ar are calculaed. Varable propery values are calculaed usng polynomal equaons for ar and a pecewse approxmaon for waer droples. The mxure properes are calculaed by he mass-weghed mehod. I was dscovered ha he propery daabases for waer vapor and seam n FLUENT are no suffcen. A dealed daabase has been ncorporaed hrough he use of a Funcon saemen. Ieraons proceed alernaely beween he connuous and dscree phases. Ten eraons n he connuous phase are conduced for every wo eraons n he dscree phase. Converged resuls are obaned afer he mass resdual reaches 1 -, he energy resdual reaches 1 -, and he momenum and urbulence nec energy resduals reach 1 - each. These resduals are he summaon of he mbalance for each cell. The compuaon was carred ou n parallel processng on wo dual-core Penum clusers wh 1 nodes and nodes, respecvely.. RESULTS AND DISCUSSION.1 Valdaon of CFD Model The compuaonal model for ar-only flow s valdaed agans he expermenal resuls of Fu e al. [1]. The grd ndependence sudy s carred ou wh mesh szes of. mllon, 1 mllon, and 1. mllon cells usng he sandard -ε urbulence model. Fg. shows he ssul number dsrbuon for nle flow condons for Re =,, 1,,, and,. The ploed here are averaged values from he leadng and ralng rbbed walls. The hea ransfer coeffcen (h) and ssel number are calculaed as follows: h = q /(T w T b,x ) () = hd h /λ (1) Where T w s he wall emperaure, T b,x s he bul emperaure a he x locaon, and λ s he hermal conducvy of he coolan. To mprove he accuracy of he compuaonal model, apar from he sandard -ε urbulence model, he oher four urbulence models ncludng RNG -ε, Realzable -ε, sandard -ω, and he Reynolds Sress Model (RSM) are employed for comparson, and he resuls are shown n Fg.. The predced resuls from all he models are almos he same for he lower Re numbers and vary whn + 1% a he hgher Re numbers. Comparavely, he sandard -ε model provdes he closes mach wh he expermenal resuls; herefore, he sandard -ε model wh enhanced-wall funcon s employed for cases n hs sudy. 1 Re Exp, rbbed -e ε Sd -e ε RNG -e ε Rea -w ω sd RSM Fgure Effec of fve urbulence models on dsrbuon n a smooh channel. The comparsons beween he CFD and he expermenal daa of boh he rbbed and smooh channels are shown n Fg.. The agreemen of he ssel numbers s very good for he enre Re range for he smooh channel. I clearly shows ha he flow becomes complex wh rbles, and, n he hgh Re range, he CFD model's accuracy drops noceably. 1 Exp, rbbed CFD, rbbed Exp,smooh CFD, smooh 1 Exp, rbbed -e ε sd (. mllon elemens) -e ε sd (1 mllon elemens) -e ε sd (1. mllon elemens) Re Fgure Grd ndependence analyss In general, he predced resul does no vary oo much for he hree dfferen mesh numbers, and specfcally, he resul of 1 mllon elemens almos concdes wh ha of 1. mllon meshes. Therefore, he res of compuaonal analyss s conduced wh 1 mllon meshes. The predcon s abou % lower han he expermenal resul n he lower Reynolds number range and abou 1% lower n he hgher Reynolds number range. r/s Exp CFD 1 Re (1 ) Fgure CFD Model valdaon (-ε model). Fgure b shows he hea ransfer enhancemen ( r / s ) due o rbles. for rbles and smooh surfaces are

6 ndvdually calculaed usng Eq. 1. Hgher hea ransfer enhancemens are seen a low Re values. An average of abou 1% under-predcon of he enhancemen rao ( r / s ) s noced for hs smulaon wh a hgher local devaon of % a a low Re, bu a lower local devaon of 8% a a hgh Re. Ths rend of error s he oppose of he acual ssel number predcon due o he sensvy of he coolng enhancemen rao calculaon. For example, a Re =,, he ssel numbers are 8% off for he smooh channel and.% for he rbbed channel, bu he rao of r / s gves a hgher percenage devaon of 1% r/s (a) (b) 18 urn Rbs, non-roang Smooh, non-roang non-roang Axal locaons Fgure Effec of rbles on perpheral averaged ssel number a Re =, whou roaon. The Effec of Roaon on Smooh and Rbbed Channels wh Ar-only Flow To nvesgae he effec of rbles over a smooh surface on he hea ransfer enhancemen under non-roang condons, he ssel number dsrbuons are ploed n Fg.. The values are regonally averaged hroughou he heaed secon for Re =,. The locaon of each regon s shown n Fg. 1c. The dsrbuons over he leadng and ralng edges are smlar whou roaon, so only he averaged values over he leadng surface s shown n Fg. o smplfy he analyss. In he acual measuremen, here were slgh devaons beween hese surfaces a he second pass, whch was observed by Fu e al. [1]. In he smooh channel, he value decreases once he flow eners he channel, bu ncreases n he bend secon o a maxmum value a he end of bend. Wh rbles, he value ncreases o a maxmum value a locaon and reaches a local maxmum downsream of he bend. The ssel number rao dsrbuon n Fg. b clearly shows he hea ransfer enhancemen wh rbs a varous axal locaons. The flow physcs responsble for hs hea ransfer paern wll be dscussed n he laer secons. Please noe ha no local hea ransfer daa s avalable from Fu e al. [1], so no expermenal daa s shown n Fg.. The effecs due o he roaon on smooh and rbbed channels are nvesgaed and explaned n Fg.. Whou roaon, he dsrbuon along he sreamwse drecon on leadng and ralng surfaces s almos he same for smooh and rbbed channels. In he frs pass, wh roaon on he smooh channel, Fg. a shows ha he values ncrease on he ralng surface compared o he non-roaonal case and decrease on he leadng surface. The rend s reversed n he second pass,.e., values ncrease a he leadng surface and decrease a he ralng edge. On he oher hand, Fg. b shows ha he effec of roaon on he rbbed surface s manly capured n he frs pass. In he second pass, he effec s comparavely mnmal. The expermenal resuls [1] showed he same effec and confrmed he accuracy of predcng he correc rend of he roang effec of he presen smulaon Smooh, ralng, non-roang Smooh, leadng, non-roang Smooh, ralng, roang Smooh, leadng, roang (a) (b) Rbs, ralng, non-roang Rbs, leadng, non roang Rbs, ralng, roang Rbs, leadng, roang Axal locaons Fgure Effecs of roaon on (a) smooh and (b) rbbed channels a Re=,. o K (a) Smooh () Non-roang, Leadng () Non-roang, Tralng () Roang, Leadng (v) Roang, Tralng (b) Rbbed () Non-roang, Leadng () Non-roang, Tralng () Roang, Leadng (v) Roang, Tralng Fgure Temperaure conours a leadng and ralng surfaces (Re =,)

7 Fgure shows he local emperaure dsrbuons, whch conssenly reflec he ssel resuls n Fg., ndcang ha lower emperaure areas correspond o hgher coolng raes and, hus, hgher ssel numbers. (a) non-roang Leadng surface flow feld a Saon 9 of Fg. 8b. More upwellng flow can be seen movng oward he leadng surface. Ths resuls n hgher hea ransfer on he leadng surface n he second pass as shown n Fg. a. There are several papers (for example Al- Qahan e al. []) explanng he flow srucure of roang channels wh varous aspec raos of channel wdh over hegh and roaonal numbers. (a) non-roang Tralng surface (b) roang (b) roang Fgure 8 Velocy conours a seleced cross-secons of smooh channel wh and whou roaon a Re =,. Roaon s n he posve z-drecon or ou of he paper. To explan he flow physcs, he velocy conours a seleced normal cross-secons n he frs and second passes for boh he roang and non-roang cases are shown n Fg. 8. I s clearly seen from Fg. 8a ha he core flow s locaed a he mdsecon of he channel for he non-roang case. For he roang case (Fg. 8b), he core flow s pushed oward he ralng surface by he Corols force ( ω V) rgh from he axal locaon 1, mposng a hgher velocy graden, and, hence, a hgher hea ransfer on he ralng surface. In he second pass, he flow s almos symmerc wh an organzed secondary flow movng from he nner surface oward he ouer surface whou roaon (Fg. 8a). However, n he roang case, he core flow urns oward he leadng edge due o he Corols force. The maxmum hea ransfer aes place mmedaely afer he bend near regon 8 for all condons and surfaces; mplyng ha he hea ransfer enhancemen s no caused by roaon. Raher, s domnaed by he flow behavor nduced by he channel bend. The nsered crossseconal flow vecor plo a saon 9 n Fg.8a for he nonroang case shows formaon of he secondary flow as he couner roang vorces under he nfluence of cenrfugal force nduced by he channel bend. In he roang case (Fg. 8b), hs par of couner-roang vorces are nerfered wh by he Corols force. The op vorex grows and he he boom vorex dmnshes as shown n he nsered cross-seconal Fgure 9 Velocy conours a seleced laeral cross secons of rbbed channel wh and whou roaon (Re =,). The velocy conour plo for he rbbed case (Fg. 9) shows more complex flow felds. I s neresng o see ha he large srucure of he secondary flow conssng of a par of couner-roang vorces s sll vsble, bu he vorces only locally dsurbed by he rbles n second pass of he nonroang channel. Smlar o he suaon n he roang smooh channel, he core flow of he roang rbbed channel s pushed and mposed upon he ralng edge n he frs pass by he Corols force. Bu, dfferen from he roang smooh channel, he couner-roang vorces dsappear n he second pass for he roang rbbed channel case. Fgure 1 shows he velocy vecor plos on he vercal md-plane n he rbbed channel for boh non-roang and roang cases.

8 (a) Non-roang, frs pass m/s Rbs, ralng, roang, % ms Rbs, leadng, roang, % ms Rbs, ralng, roang, ar-only Rbs, leadng, roang, ar-only 8 (b) Non-roang, second pass (a) (c) Roang, frs pass (d) Roang, second pass Fgure 1 Velocy vecor plo a normal cross secon of rbbed channel n he frs and second passes (Re =,).. Ms/ar coolng enhancemen wh roaon on Rbbed Channels To predc he ms/ar coolng enhancemen, % ms (1.1 x 1 - g/s) was njeced a he nle of he rbbed channel. The unform mcron dameer droples are consdered nally o nvesgae he drople sze varaon and drople dynamcs. The drople breaup and coalescence are found o have a neglgble effec on hs sudy. A ypcal hea ransfer resul predced for Re =, s shown n Fg. 11. In general, he ms coolng acheves a hgher value n he frs pass han n he second pass due o he roaonal effec. In he frs pass, ms coolng enhancemen on he ralng surface s hgher han ha on he leadng surface. In he second pass, he coolng enhancemen s almos he same for boh he surfaces. I can be noed ha n he enry regon (regon 1, Fg. 11a) of he ralng surface, he hea ransfer s very hgh compared o he ar-only case. In he frs pass, he average ms coolng enhancemen rao s abou % on he ralng surface and abou % on he leadng surface. In he second pass, a relavely unform, % coolng enhancemen rao s predced for boh of he surfaces. Fgure 1 shows he drople races n he roang rbbed channel. Some droples move wh spral pahs, suggesng ha he droples are subjec o he effec of cenrfugal and Corols forces. Fgure 1 shows he lqud drople concenraon (g/m ) dsrbuons on hree cuaway planes wh one near he leadng surface, one near he ralng surface, and one n he cener of he channel. I s neresng o see more lqud concenraon near he upsream surface of each rble and low lqud concenraon behnd he rble, ndcang accumulaon of lqud droples when hey h he rble surface. No clear correlaon can be drawn beween he lqud concenraon level n Fg. 1 and he hea ransfer level n Fg.. ums/ar N (b) Rbs, ralng, % ms.9 Rbs, leadng, % ms Axal locaons Fgure 11 Ms coolng enhancemen on rbbed channel a Re =,. s Leadng surface (a) Frs pass Tralng surface (b) Second pass Fgure 1 Drople races colored by resdence me n he vcny of rb gaps for roang case a Re =,. 8

9 g/m 11 1 (a) 9 8 ms Rbs, ralng, % ms, mcrons Rbs, ralng, % ms, dsr Rbs, leadng, % ms, mcrons Rbs, leadng, % ms, dsr Axal locaons g/m Fgure 1 Effec of drople dsrbuon. (b) Plane a 1 mm from leadng surface. CONCLUSIONS A CFD model was developed o predc ms/ar coolng enhancemen n a roang rbbed recangular channel. The resuls are concluded below: (c) Md plane from leadng and ralng surfaces (d) Plane a 1 mm from ralng surface Fgure 1 Lqud concenraon a varous planes for roang rble case a Re =,. To smulae he acual non-unform dsrbuon of lqud drople szes more closely, he Rosn-Rammler dsrbuon funcon s used based on he assumpon ha an exponenal relaonshp exs beween he drople dameer, d d, and he mass fracon of droples wh dameer greaer han d. Ths relaonshp s expressed n he followng equaon: n ( d / d Y m ) d = e () where d m refers o he mean dameer (μm) and n refers o he spread parameer. From he relaonshp, he spread parameer (.) s calculaed and used o f he expermenal sze dsrbuon of Guo e al [] no he CFD model. The dfference beween usng he unform μm droples and non-unform droples can only be observed n he enrance regon of he channel, as shown n Fg. 1. Ths can be explaned by he fas evaporaon of droples smaller han μm n he case wh dsrbued droples n he enrance regon. The mpac o downsream hea ransfer s neglgble. More deals abou drople dsrbuon can be found n Dhanasearan and Wang s sudy [1]. The CFD model for ar-only flow on a rbbed channel was valdaed wh he expermenal resuls and acheved good agreemen a lower Re values. A hgher Re values, he devaon s abou 1%. For he smooh channel, he agreemen s whn % for he enre range of Re values. For he smooh channel, roaon mposes cenrfugal force upon he ralng surface n he frs pass and enhances s coolng; whereas n he second pass, he Corols force pushes he flow oward he leadng surface and resuls n more effecve coolng on he leadng surface. For he rbbed channel, he effec of roaon s only realzed n he frs pass wh enhanced coolng on he ralng surface and suppressed coolng on he leadng surface. The effec of he roaon n he second pass s neglgble. Wh % (w.) ms njecon, he average ms coolng enhancemen s abou % on he ralng surface and abou % on he leadng surface n he frs pass under roang condons. In he second pass, abou % ms coolng enhancemen s predced for boh he surfaces. When subjeced o he cenrfugal and Corols forces, some of he waer droples are seen o move n spral pahs. More lqud concenraon s seen on he upsream surface of rbles and much lower lqud concenraon behnd he rble. ACKNOWLEDGMENTS Ths sudy was suppored by he Lousana Governor's Energy Inave va he Clean Power and Energy Research Consorum (CPERC) and admnsered by he Lousana Board of Regens.. REFERENCES [1] Guo, T., Wang, T., and Gadds, J. L.,, Ms/Seam Coolng n a Heaed Horzonal Tube: Par 1: Expermenal Sysem, ASME J. Turbomachnery, 1, pp. -. [] Guo, T., Wang, T., and Gadds, J.L.,, Ms/Seam Coolng n a Heaed Horzonal Tube: Par : Resuls and Modellng, ASME J. Turbomachnery, 1, pp. -. 9

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