Forced flow heat transfer from a round wire in a vertically- mounted pipe to supercritical hydrogen

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1 IOP Confrnc Sris: Matrials Scinc and Enginring PAPER OPEN ACCESS Forcd flow hat transfr from a round wir in a vrtically- mountd pip to suprcritical hydrogn To cit this articl: Y Hori t al 2015 IOP Conf. Sr.: Matr. Sci. Eng Viw th articl onlin for updats and nhancmnts. Rlatd contnt - Transint hat transfr from a wir to a forcd flow of subcoold liquid hydrogn passing through a vrtically- mountd pip H Tatsumoto, Y Shirai, M Shiotsu t al. - A ring cyclotron with a vrtically incrasing magntic fild A P Fatv and B N Yablokov - Build-up of macroscopic ignstats in a mmory-basd constraind systm M Labouss, S Prrard, Y Coudr t al. This contnt was downloadd from IP addrss on 23/01/2018 at 12:19

2 Forcd flow hat transfr from a round wir in a vrticallymountd pip to suprcritical hydrogn Y. Hori 1 M. Shiotsu 1 Y. Shirai 1 D. Higa 1 H.Shigta 1 H. Tatsumoto 2 Y. Naruo 3 S. Nonaka 3 H. Kobayashi 3 and Y. Inatani 3 1 Dpt. of Enrgy Sci. & Tch., Kyoto Univrsity, Sakyo-ku, Kyoto , Japan 2 J-PARC Cntr, Japan Atomic Enrgy Agncy, Tokai, Ibaraki, , Japan 3 Inst. of Spac and Astronautical Scinc, JAXA, Kanagawa, , Japan shiotsu@p.nrgy.kyoto-u.ac.jp Abstract. Forcd flow hat transfr of hydrogn from a round wir in a vrtically-mountd pip was masurd at prssur of 1.5 MPa and tmpratur of 21 K by applying lctrical currnt to giv an xponntial hat input (Q=Q 0xp(t/τ),τ=10 s) to th round wir. Two round wir hatrs, which wr mad of Pt-Co alloy, with a diamtr of 1.2 mm and lngths of 54.5 and 120 mm wr st on th cntral axis of a flow channl mad of FRP with innr diamtr of 5.7 and 8.0 mm, rspctivly. Suprcritical hydrogn flowd upward in th channl. Flow vlocitis wr varid from 1 to 12.5 m/s. Th hat transfr cofficints of suprcritical hydrogn wr compard with th convntional corrlation prsntd by Shiotsu t al. It was confirmd that th hat transfr cofficints for a round wir wr xprssd wll by th corrlation using th hydraulic quivalnt diamtr. 1. Introduction Whn a suprconducting coil wound by cabl in conduit conductor (CICC) is coold by hydrogn undr a suprcritical prssur, an xtraordinary hat at a qunch will b coold down smoothly without a jump to film boiling. For a dsign and safty valuation of such a suprconducting coil, xprimntal rsults of forcd flow hat transfr undr suprcritical prssur with an inlt fluid tmpratur lowr than th critical tmpratur is ncssary. Forcd flow hat transfr of low tmpratur hydrogn undr suprcritical condition has bn studid for a cooling dsign of rockt ngins [1, 2]. Howvr, ths studis wr mainly aimd for cooling systms oprating nar th tmpratur limitation of mtals. Shiotsu t al [3] studid th hat transfr from innr wall of a vrtical tub to forcd flow of low tmpratur hydrogn undr suprcritical prssurs for th tst tubs with various innr diamtrs and lngths. Thir xprimntal rsults wr compard with an quation of forcd flow hat transfr undr suprcritical prssurs prsntd bforhand [4] basd on xprimntal data of hlium and convntional data for non-cryognic fluids. It was confirmd that th quation can b applicabl to forcd flow of hydrogn in hatd tubs with wid rangs of diamtr and lngth. In cas of CICC, hat is transfrrd not from innr sid of a tub but from a round wir to outr flowing fluid. Th purpos of this study is firstly to obtain th xprimntal data of forcd convction hat transfr from a round wir to suprcritical hydrogn, and scondly to confirm th applicability of Contnt from this work may b usd undr th trms of th Crativ Commons Attribution 3.0 licnc. Any furthr distribution of this work must maintain attribution to th author(s) and th titl of th work, journal citation and DOI. Publishd undr licnc by Ltd 1

3 th quation with th us of quivalnt diamtr. 2. Apparatus and mthod Figur 1 shows a schmatic of th xprimntal systm, whos dtail has bn alrady prsntd in othr papr [3]. It compriss of a main cryostat, a sub tank (rcivr tank), a conncting transfr tub with a control valv, a fd hydrogn gas lin from clustrd cylindrs and vnt lins. Two tst hatr blocks ar locatd in sris at on nd of th transfr tub in th main tank. Thy ar usd on by on. Liquid hydrogn in th main tank is forcd to flow into th transfr tub by th prssur diffrnc btwn th cryostat and sub tank. Th mass flow rat is st by th prssur diffrnc and th valv opning (CV001). Liquid hydrogn flows upward through th concntric conduit of th tst hatr blocks. Th main tank is prssurizd to a dsird prssur by pur hydrogn gas ( %) controlld by a dom-loadd gas rgulator, whil th sub tank is maintaind to b atmosphric prssur by opning th rlas valv (PV105).Th mass flow rat is stimatd by th wight chang of th main tank, which is put on a scal (MttlrToldo WMHC 300s) that can masur up to 400 kg within kg rsolution. Th fd hydrogn gas is controlld so that th prssur is kpt constant during th tst. Th mass flow rat stimatd abov is calibratd with th flow rat of th fding gas. Flow masurmnt rror is stimatd to b within 0.1 g/s, if th flow rat is assumd to b constant during th tst priod of 60 s, for xampl. Th liquid tmpratur of th main tank and th inlt tmpratur T in of th conduit ar masurd by Crnox tmpratur snsor. Th bath tmpratur is controlld by a shathd hatr coil with th maximum powr of 500 W which is st at th bottom of th main tank. Tst Hatr FIGURE 1. Schmatic of th xprimntal apparatus. Two typs of tst hatr block ar usd. Figur 2 shows schmatic of th hatr blocks. Typ A has a tst wir mad of PtCo (0.5 wt. %) alloy, 1.2 mm in diamtr D 2, 54.5 mm in lngth L supportd at th cntr of D = 5.7 mm conduit in a block mad of fibr rinforcd plastic (FRP). Hydraulic quivalnt diamtr D ( ) D D2 and th ratio of LD for th hatr block ar 4.5 mm and 13.3, 1 2

(a) (b) FIGURE 2. Schmatic of th tst hatr blocks (a) Typ A and (b) Typ B. rspctivly. Typ B has th tst wir mad of PtCo alloy, D 2 = 1.2 mm, L = 120 mm supportd at th 1 cntr of D = 8 mm conduit.

Each hatr has an ntranc lngth corrsponding to ovr tn tims its diamtr. Th hating currnt to th tst wir is supplid by a powr amplifir (max. 400 A at a powr lvl of 4.8 kw).

4 (a) (b) FIGURE 2. Schmatic of th tst hatr blocks (a) Typ A and (b) Typ B. rspctivly. Typ B has th tst wir mad of PtCo alloy, D 2 = 1.2 mm, L = 120 mm supportd at th 1 cntr of D = 8 mm conduit. Th valus of D and LD for th hatr block ar 6.8 mm and Both nds of ach hatr wir ar lctrically insulatd from th hydrogn transfr lin by th FRP channl, whos diamtr is qual to D. Each hatr has an ntranc lngth corrsponding to ovr tn tims its diamtr. Th hating currnt to th tst wir is supplid by a powr amplifir (max. 400 A at a powr lvl of 4.8 kw). Th lctric rsistanc of th hatr was masurd using a doubl-bridg circuit. Th output voltag of th bridg circuit togthr with th voltag across a standard rsistanc was amplifid and passd to a 16 bit digital mmory systm (Yokogawa WE7000). Th voltag drops across th potntial taps of th tst hatr and th output signal of a strain gaug prssur snsor wr also masurd. Ths signals ar simultanously sampld at an intrval of 30 ms. Th avrag tmpratur of th hatd wir, T av, was stimatd using its lctrical rsistanc. Tmpratur charactristics of th rsistanc had bn obtaind prviously. Th surfac hat flux q was givn as th diffrnc btwn th hat gnration rat Q and th tim rat of nrgy storag. Th avrag tmpratur on th hatd surfac T w was calculatd by solving stady-stat conduction quation in a radial dirction of th wir using T av and Q (that is T w is givn as th boundary condition that satisfis masurd T av for Q). Th doubl-bridg circuit for masurmnt of th wir hatr rsistanc has an accuracy of , and a tmpratur dviation of about 0.1 K can b masurd by th bridg. Th inlt tmpratur was masurd by a Crnox snsor with an accuracy of 10 mk and amplifid by a prcision amplifir (Yokogawa 3131). Calibration of th masurmnt circuit is prformd bfor a sris of xprimnt by using a standard volatag-currnt gnrator and an approvd prssur gaug. Exprimntal rror is stimatd to b within 0.2 K for T w and 3 % for q, and 0.1 K for T in. Forcd convction hat transfr from th vrtically-mountd hatd wir was masurd with a quasistady incras of th hat gnration rat of Q 0 t/ with 10.0 s at a prssur P of 1.5 MPa. It had bn alrady confirmd that th hat transfr phnomna could b rgardd as a continuous sris of stady-stats with =10 s. Th inlt tmpraturs T in is 21 K and th flow vlocity is incrasd to 12.6 m/s. Th para-hydrogn is considrd to b mor than 99% although th liquid hydrogn tmpratur is 3

5 tmporarily incrasd in th xprimnt. This is bcaus it was liqufid using an ortho-para hydrogn convrtr and it taks a long tim to chang from para-hydrogn to ortho-hydrogn [5]. 3. Rsults and discussion 3.1 Boiling curv undr suprcritical prssur Typical boiling curvs for th hatrs of Typ A and Typ B undr a suprcritical prssur of 1.5 MPa ar shown in figur 3 and figur 4 rspctivly. Thy ar shown with flow vlocity as a paramtr on th hat flux q vrsus wall tmpratur incras from th inlt tmpratur T L graph. Th hat transfr curvs on ach figur shift upward with th incras in th flow vlocity. Th nuclat boiling and transition to film boiling do not occur as shown in ths figurs. Th hat transfr curv for ach flow vlocity consists of a rgion with a highr gradint and that with a lowr gradint. Th highst tmpratur limit of th formr rgion is slightly highr than th psudo-critical tmpratur T cr at which th spcific hat taks a maximum pak at th prssur. Whn T L xcd that point, th hat transfr cofficint h starts to dcras with an incras of TL. It is wll known that thrmo-physical proprtis of fluids rmarkably chang for th fluid tmpratur highr than T cr. Low dnsity (gas-lik) flow xists in thrmal boundary layr surrounding th hatr wir and high dnsity (liquid-lik) fluid is flowing in th gap btwn th surfac of th boundary layr and th innr surfac of th conduit. Th boundary layr would grow along th innr surfac of th tst wir with th incras in th wall tmpratur byond T cr. Th growth of th boundary layr would b th caus of th dgradation of hat transfr from th formr rgion. Thicknss of th boundary layr would bcom thickr and mutual action btwn th main flow and th boundary layr would bcom significant with th incras in th wall tmpratur. W can s in figurs 3 and 4 that hat transfr for ach flow vlocity tnds to oscillat and bcoms bttr at th T L of approximatly 100 K. This may b du to th partial collaps of th boundary layr by th mutual action btwn thm. q [ W/m 2 ] 10 6 Typ A Hatr P = 1500 kpa T in = 21 K 10 5 T cr ' Authors' Eq T L [ K ] Flow Vlocity 12.6 m/s 6.2 m/s 2.3 m/s 1.8 m/s FIGURE 3. Hat transfr curvs for Typ A hatr with flow vlocity as a paramtr. 4

q [ W/m 2 ] 10 6 10 5 Typ B Hatr P = 1500 kpa T in = 21 K 10 4 Flow Vlocity 8.67 m/s 3.82 m/s 1.01 m/s 10 3 Authors' Eq. 0.73 m/s 10 0 10 1 10 2 T L [ K ] FIGURE 4.

2 Comparison of hat transfr undr suprcritical prssur with that undr a prssur lowr than P cr Th boiling curv with th sam flow vlocity at a prssur of 1.

In th rgion whr T L is lowr than th psudo-critical tmpratur T cr, th hat flux undr suprcritical prssur incrass with an incras of hat input along with th curv prdictd by Dittus- Boltr quation [6], whr

6 q [ W/m 2 ] Typ B Hatr P = 1500 kpa T in = 21 K 10 4 Flow Vlocity 8.67 m/s 3.82 m/s 1.01 m/s 10 3 Authors' Eq m/s T L [ K ] FIGURE 4. Hat transfr curvs for th Typ B hatr with flow vlocity as a paramtr. 3.2 Comparison of hat transfr undr suprcritical prssur with that undr a prssur lowr than P cr Th boiling curv with th sam flow vlocity at a prssur of 1.1 MPa, which is slightly lowr than th critical prssur, ar shown in figur 5 and figur 6 for th Typ A and Typ B hatrs rspctivly. In th rgion whr T L is lowr than th psudo-critical tmpratur T cr, th hat flux undr suprcritical prssur incrass with an incras of hat input along with th curv prdictd by Dittus- Boltr quation [6], whr hydraulic quivalnt diamtr D ( D ) 1 D2 was usd as a typical lngth. Th hat transfr at suprcritical prssur agrs wll with that at blow critical prssur. Thn, in th rgions whr TL is highr than T cr, th hat flux at th suprcritical prssur is highr than that at blow critical prssur. T cr ' FIGURE 5. Typical hat transfr curv of suprcritical hydrogn for th Typ A hatr in comparison with that blow critical prssur. FIGURE 6. Typical hat transfr curv of suprcritical hydrogn for th Typ B hatr in comparison with that blow critical prssur. 5

7 4. Hat transfr corrlation Shiotsu t al. [4] prsntd th following corrlation for forcd flow hat transfr to suprcritical hlium basd on thir xprimntal data for a flat plat hatr pastd on innr sid of a rctangular duct. This corrlation consists of th Dittus-Boltr quation with a corrction factor F c to xprss th dgradation of hat transfr du to th growth of thrmal boundary layr D D c Nu R Pr F (1) F [ ( L / D ) ] [ ( T / T )]( / ) ( / ) (2) ' c L cr w in in w whr Nu D and R D ar Nusslt and Rynolds numbrs, Pr c /, c ( h h ) / ( T T ), p in in p w in w in h is th nthalpy and suffixs w and in man wall and inlt. Th D is quivalnt diamtr, L is th hatd lngth, th, ar dnsity and viscosity. Thn w studid th hat transfr from innr wall of a vrtical tub to forcd flow of hydrogn undr a suprcritical prssur for th tst tubs with various innr diamtrs and lngths [3]. W compard th xprimntal rsults with th quation (1). Th thrmophysical proprtis of para-hydrogn ar givn using th computr softwar GASPACK. It was confirmd that th quation can b applicabl for wid rangs of tub diamtr and lngth. Th curvs prdictd by th quation (1) ar shown in figurs 3 and 4 for comparison.th xprimntal data almost agr with th prdictd curvs although fluctuation around th curvs can b sn. Th fluctuation may b du to th growth and collaps of th boundary layr mntiond abov and liquid-lik fluid outsid is comprssibl. This would b th charactristic of th undvlopd suprcritical forcd flow hat transfr. To s th applicability of our corrlation in mor dtail, all th xprimntal data ar shown on NuD Pr Fc vs. R D graph in figur 7 in comparison with th quation (1). Ths data ar for th 4 5 Rynolds numbrs ranging from about to Most of th data ar within +35 % and - 30 % of th quation. Though th rror band is rlativly wid du to th fluctuation, this corrlation would b usful for a cooling dsign of HTC systms whr rlativly low tmpratur rang is important. Nu D Pr -0.4 F c P=1.5 MPa T in =21 K Authors' Eq.(1) R D +35% -30% Typ A Hatr Typ B Hatr FIGURE 7. Comparison of th corrlation with th xprimntal data. 6

8 5. Conclusions Hat transfr from a PtCo wir in a vrtically-mountd conduit to flowing suprcritical hydrogn was masurd for two diffrnt sizd hatr blocks. Th masurmnt was mad at a prssur of 1.5 MPa for an inlt fluid tmpratur of 21 K and flow vlocitis from 0.5 to 12 m/s. Exprimntal rsults lad to th following conclusions: Th hat transfr cofficints ar highr for highr flow vlocity. Th hat transfr curv for ach flow vlocity consists of a rgion with a highr gradint and that with a lowr gradint. Th highst tmpratur limit of th formr rgion is slightly highr than T cr of th fluid at th prssur. Th hat transfr in th formr rgion agrs wll with th Dittus-Boltr quation and bcoms lowr than th quation with furthr incras in wall tmpratur. Th xprimntal rsults wr compard with th authors quation of forcd flow hat transfr 4 5 undr suprcritical prssur. Most of th data for R D from to ar within +35 % and - 30 % of th quation. It was confirmd that th quation can b applicabl for a cntral wir hatr in a conduit. This would b usful for a cooling dsign of HTC systms whr rlativly low tmpratur rang is important. 6. Acknowldgmnts This rsarch was supportd in part by JST, ALCA. Th authors thank th tchnical staffs of JAXA for thir tchnical assistanc. 7. Rfrncs [1] Niino M t al 1979 Hat transfr charactristics of liquid hydrogn at suprcritical prssur, (in Japans) Tchnical Rport of National Arospac Laboratory NAL TR-583. [2] Thompson W R and Gry E L 1960 Hat transfr to cryognic hydrogn at suprcritical prssurs Arojt Rport, No [3] Shiotsu M t al 2014 Forcd flow hat transfr of suprcritical hydrogn for suprconductor cooling AIP Conf. Proc. 1573, 36 [4] Shiotsu M t al 2009 Forcd convction hat transfr to suprcritical fluids Proc. of ICEC 22- ICMC [5] Tatsumoto H t al 2014 Oprational charactristics of th J-PARK cryognic hydrogn systm for a spallation nutron sourc AIP Conf Proc [6] Van Scivr S W 1986 Hlium Cryognics (Nw York, Plnum Prss) Nomnclatur 1 c : ( ( h h )( T T ) ), spcific hat (Jkg -1 K) p w in w in D :innr diamtr of conduit (m) D : ( D D2 ), quivalnt diamtr, (m) D :hatr diamtr (m) 2 h : ( q/ T L ), hat transfr cofficint (Wm -2 K -1 ) h :nthalpy (Jkg -1 ) L :tst hatr lngth (m) Nu D : ( hd / m), avrag Nusslt numbr P :prssur (kpa) P :critical prssur (kpa) cr Pr : ( c / ), Prandtl numbr p in in Q :hat gnration rat (Wm -3 ) q :hat flux (Wm -2 ) 7

9 R : ( ud / ), Rynolds numbr D in T av :avrag hatr tmpratur (K) T in :inlt liquid tmpratur (K) T cr ' :psudo-critical tmpratur (K) T w :hatr surfac tmpratur (K) u :vlocity (ms -1 ) T L : ( Tw Tin ) (K) :thrmal conductivity (Wm -1 K -1 ) :viscosity (kg s -1 m -1 ) :dnsity (kgm -3 ) :xponntial priod (s) Subscripts in: at inlt tmpratur, w: at wall tmpratur 8

is an appropriate single phase forced convection heat transfer coefficient (e.g. Weisman), and h

is an appropriate single phase forced convection heat transfer coefficient (e.g. Weisman), and h For t BWR oprating paramtrs givn blow, comput and plot: a) T clad surfac tmpratur assuming t Jns-Lotts Corrlation b) T clad surfac tmpratur assuming t Tom Corrlation c) T clad surfac tmpratur assuming