Transcription

1 Titl Film boiling hat transfr from a w hydrogn and liquid nitrogn Shiotsu, M.; Shirai, Y.; Hori, Y.; Author(s) Tatsumoto, H.; Hata, K.; Kobayashi, Y.; Inatani, Y. Citation IOP Confrnc Sris: Matrials Sc (2015), 101 Issu Dat URL Contnt from this work may b usd Right Crativ Commons Attribution 3.0 li distribution of this work must main author(s) and th titl of th work Typ Confrnc Papr Txtvrsion publishr Kyoto Univrsity

2 IOP Confrnc Sris: Matrials Scinc and Enginring PAPER OPEN ACCESS Film boiling hat transfr from a wir to upward flow of liquid hydrogn and liquid nitrogn To cit this articl: M Shiotsu t al 2015 IOP Conf. Sr.: Matr. Sci. Eng Viw th articl onlin for updats and nhancmnts. Rlatd contnt - Ground oprations dmonstration unit for liquid hydrogn initial tst rsults W U Notardonato, W L Johnson, A M Swangr t al K liquid hydrogn thrmal Enrgy Storag Unit for futur ESA scinc missions P Borgs d Sousa, D Martins, G Tomás t al. - Suprfluidity in liquid hydrogn? Ptr McClintock This contnt was downloadd from IP addrss on 05/01/2018 at 07:08

3 Film boiling hat transfr from a wir to upward flow of liquid hydrogn and liquid nitrogn M Shiotsu 1 Y Shirai 1 Y Hori 1 H Shigta 1 D Higa 1 H Tatsumoto 2 K Hata 3 H Kobayashi 4 S Nonaka 4 Y Naruo 4 and Y Inatani 4 1 Dpt. of Enrgy Sci. & Tch., Kyoto Univ., Sakyo-ku, Kyoto , Japan 2 J-PARC Cntr, Japan Atomic Enrgy Agncy, Tokai, Ibaraki, , Japan 3 Inst. of Advancd Enrgy, Kyoto Univ., Uji, Kyoto , Japan 4 Inst. of Spac and Astronautical Scinc, JAXA, Kanagawa, , Japan shiotsu@p.nrgy.kyoto-u.ac.jp Abstract. Film boiling hat transfr cofficints in liquid hydrogn wr masurd for th hatr surfac suprhats to 300 K undr prssurs from 0.4 to 1.1 MPa, liquid subcoolings to 11 K and flow vlocitis to 8 m/s. Two tst wirs wr both 1.2 mm in diamtr, 120 mm and 200 mm in lngths and wr mad of PtCo alloy. Th tst wirs wr locatd on th cntr of 8 mm and 5 mm diamtr conduits of FRP (Fibr Rinforcd Plastics). Furthrmor film boiling hat transfr cofficints in liquid nitrogn wr masurd only for th 200 mm long wir. Th film boiling hat transfr cofficints ar highr for highr prssur, highr subcooling, and highr flow vlocity. Th xprimntal data wr compard with a convntional quation for forcd flow film boiling in a wid channl. Th data for th 8 mm diamtr conduit wr about 1.7 tims and thos for th 5 mm conduit wr about 1.9 tims highr than th prdictd valus by th quation. A nw quation was prsntd modifying th convntional quation basd on th liquid hydrogn and liquid nitrogn data. Th xprimntal data wr xprssd wll by th quation. 1. Introduction Knowldg of film boiling hat transfr from a hatd wir to forcd flow of liquid hydrogn or liquid nitrogn in a narrow gap is important for conductor dsign and qunch analysis of suprconducting magnts wound with high-tc cabl in conduit conductor (CICC). Howvr thr hav bn fw xprimntal data as far as w know. Shiotsu and Hama [1] studid th film boiling hat transfr from a vrtical cylindr in forcd flow of watr and R113 in 40 mm dia. cylindrical conduit to mak clar th hat transfr of rflooding procss in a loss of coolant accidnt of a nuclar ractor. Thy drivd a corrlation of forcd convction hat transfr. Rcntly, Shiotsu t al. [2] hav masurd th forcd convction film boiling hat transfr from a round wir to liquid hydrogn flowing upward in concntric annulus with a narrow gap. Thy rportd that th xprimntal data wr about 1.7 tims highr than th valus prdictd by th Shiotsu-Hama quation, although th trnd of dpndnc on flow vlocity was similar to that prdictd by th quation. Thy suggstd that vapour film layr around th wir hatr may b mad thinnr by a narrow gap. 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

4 Th purpos of this study is firstly to obtain th xprimntal data of film boiling hat transfr from a hatr wir to forcd flow of liquid hydrogn and liquid nitrogn in round conduits with diffrnt gaps and scondly to prsnt th film boiling hat transfr quation basd on th xprimntal data. 2. Apparatus and mthod Figur 1 shows a schmatic of th xprimntal systm, whos dtail has bn alrady prsntd in othr papr [3]. It consists of a main cryostat, a sub tank (rcivr tank), a conncting transfr tub with a control valv. 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 conduit of tst hatr blocks. Th main tank is prssurizd to a dsird prssur by pur hydrogn gas ( %) controlld by a gas rgulator, whil th sub tank is maintaind to b atmosphric prssur. 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. Flow masurmnt rror is stimatd to b within 0.1 g/s. Th inlt tmpratur T B is masurd by Crnox tmpratur snsor and controlld by a shathd hatr coil which is st at th bottom of th main tank. Two typs of tst hatr block ar usd. Typ 1 has a tst wir mad of PtCo (0.5 wt. %) alloy, 1.2 mm in diamtr, 120 mm in lngth supportd at th cntr of 8 mm diamtr conduit in a block mad of fibr rinforcd plastic (FRP). Typ 2 has a similar construction as shown in Figur 2. It has th tst wir mad of PtCo alloy, 1.2 mm in diamtr, mm in lngth supportd at th cntr of 5 mm diamtr conduit. 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 input signal of th powr amplifir is controlld so that th hat gnration rat in th tst wir agrd with a dsird valu. In this study, xponntial hat gnration rat of Q = Q 0 t/ ( m )/ with = 10.0 s up to a crtain valu Q m at t = t m (at point E in figur 3), and t t Q Qm for t > t m ar applid to th tst wir. It was confirmd xprimntally that th hat transfr phnomnon by Tst Hatr FIGURE 1. Schmatic of th xprimntal apparatus. 2

5 this hat gnration rat could b rgardd as a continuous squnc of stady-stat. Th lctric rsistanc of th hatr was masurd. Th voltag drops across th potntial taps of th tst wir and across a standard rsistanc and th output signal of a strain gaug prssur snsor wr amplifid and passd to a 16 bit digital mmory systm (Yokogawa WE7000). Ths signals ar simultanously sampld at 30 ms-intrvals. 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 hatr wir using T av and Q (that is T w is givn as th boundary condition that satisfis masurd T av for Q). 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 voltag-currnt gnrator and an approvd prssur gaug. Exprimntal rror is stimatd to b within 1.0 K for T w and 5 % for q, and 0.1 K for T. 3. Rsults and discussion B Figur 2 Typ 2 tst hatr block. 3.1 Typical hat transfr procsss Film boiling hat transfr cofficints wr masurd for th hatr surfac suprhats up to 300 K undr prssurs from 0.4 to 1.1 MPa, liquid subcoolings to 11 K, and flow vlocitis to 8 m/s. Figur 3 shows a typical procss of a masurd film boiling hat transfr without too much thrmal shock to th tst hatr. Vrtical axis is hat flux q and horizontal on is wall tmpratur incras from 10 6 T sat E q [ W/m 2 ] q DNB Non-boiling B A F Minimum Film Boiling Point Film Boiling for 5.83 m/s P=409 kpa T B: =20.75 K T sat =26.08 K T sub =5.33 K D C Film Boiling for 0.9 m/s 10 3 Dittus-Boltr Eq. v=5.83 m/s T L [ K ] Figur 3 Hat transfr procss to masur film boiling hat transfr. 3

6 inlt tmpratur. Firstly th hat gnration rat was gradually incrasd for a low flow rat (0.9 m/s). Boiling initiats at point A. Th procss from A to B is nuclat boiling rgim. Whn th hat flux rachs th DNB (Dpartur from Nuclat Boiling) hat flux (point B), hatr tmpratur jumps to film boiling for 0.9 m/s (point C). Transint hat transfr procss during th jump is shown in th figur. Th procss from B to th bottom of hat flux is th transition boiling and th bottom to th point C is film boiling. Thn flow vlocity is incrasd to a dsird valu (hr 5.83 m/s) whil hating currnt is continuously incrasd to th hatr tmpratur around 300 K. Thn th hating currnt is dcrasd xponntially and film boiling hat transfr cofficints ar masurd. 3.2 Rsults of film boiling hat transfr in liquid hydrogn Figur 4 and figur 5 show th rlations btwn film boiling hat transfr cofficint h q / Tsat vrsus wall suprhat Tsat at P = 0.4 MPa undr saturatd condition with flow vlocity as a paramtr for th Typ 1 and Typ 2 hatrs, rspctivly. Brokn lins in ths figurs ar th prdictd curvs by our corrlation shown latr. As th hat input is rducd from high T sat (th fully dvlopd film boiling rgim) down to about 80 K, th cofficint h dcrass gradually, howvr, for furthr dcras of wall suprhat T sat, that is hat input, th cofficint h incrass stply, sinc th vapor film bcoms thinnr drastically. Th film boiling hat transfr cofficints ar highr for highr flow vlocity. Th lngth z and th quivalnt diamtr D of th Typ 2 hatr ar about 1.63 tims and 0.56 tims as long as thos of Typ 1, rspctivly. It can b sn from th comparison of th hat transfr cofficints for th Typ 1 and Typ 2 hatrs for narly th sam vlocitis such as 1.6 m/s and 1.98 m/s, and 4.1 m/s and 4.71 m/s that thy ar almost sam. This would b du to combind ffcts of hatr lngth and quivalnt diamtr. Th hat transfr cofficints would b lowr for longr hatr lngth du to th growth of vapor film along th hatr. Th hat transfr cofficints would b highr for smallr quivalnt diamtr bcaus vapour film layr around th wir hatr would b mad thinnr by a narrowr gap. Th xprimntal data for th lowst vlocitis of 0.77 m/s and 1.98 m/s in figurs 4 and 5, rspctivly, could not b obtaind for Tsat highr than approximatly 180 K. Th flow vlocity was so small that th hydrogn flow could not kp th dsignatd vlocity in highr wall suprhat. Figurs 6 and 7 show th rlations btwn film boiling hat transfr cofficint and Tsat for th Typ 2 hatr at P = 0.7 MPa undr saturatd condition and liquid subcooling of 8 K with flow vlocity as a paramtr. Trnd of th dpndnc on T and flow vlocity is similar to that for saturatd sat Typ 1 Hatr P =0.4 MPa Saturatd Condition 4.1 m/s 3.2 m/s 1.6 m/s 0.77m/s T sat [ K ] Figur 4 Film boiling hat transfr cofficints for Typ 1 hatr at P=0.4MPa undr saturatd condition Typ 2 Hatr P =0.4 MPa Saturatd Condition 9.72 m/s 4.71 m/s 1.98 m/s T sat [ K ] Figur 5 Film boiling hat transfr cofficints for Typ 2 hatr at P=0.4MPa undr saturatd condition. 4

7 Typ 2 Hatr P =0.7 MPa Saturatd Condition 10.49m/s 3.31 m/s 1.35 m/s 0.88 m/s T sat [ K ] T sat [ K ] Figur 6. Film boiling hat transfr Figur 7. Film boiling hat transfr cofficints for Typ 2 hatr at P=0.7 MPa cofficints for Typ 2 hatr at P=0.7 MPa undr saturatd condition. for T sub=8 K. condition mntiond abov. By comparing th data for 9.72 m/s in figur 5 with that for m/s in figur 6 and th data for 3.31 m/s in figur 6 with that for 3.76 m/s in figur 7, w can s that th hat transfr cofficints ar highr for highr prssur and liquid subcooling. 3.3 Rsults of film boiling hat transfr in liquid nitrogn Forcd flow film boiling hat transfr cofficints of liquid nitrogn wr masurd for P = 0.55 and 1.0 MPa using th sam apparatus and xprimntal procdur. Figurs 8 and 9 show th rsults for th Typ 2 hatr in forcd flow of liquid nitrogn. Th hat transfr curvs in th figurs ar for th inlt tmpratur of 78 K ( Tsub 16 K) at P = 0.55 MPa and at 1.0 MPa ( Tsub 25 K), rspctivly. Brokn lins in th figurs ar th prdictd valus by our corrlation dscribd latr. As th viscosity of liquid nitrogn is about 15 tims highr than liquid hydrogn, maximum flow vlocity attaind for th Typ 2 tst hatr is far lowr than that for liquid hydrogn. Though in a narrow rang, ffct of flow vlocity is clarly sn in ths figurs; film boiling hat transfr cofficints ar highr for highr flow vlocity Typ 2 Hatr P =0.7 MPa T B =21.0 K T sub =8 K 7.23 m/s 3.76 m/s 2.06 m/s 1.65 m/s Typ 1 Hatr P = 0.55 MPa T sub = 16 K 2.4 m/s 1.4 m/s 1.3 m/s 0.50 m/s 0.16 m/s 2.4 m/s 1.4 m/s 1.3 m/s 0.5 m/s 0 m/s T sat [ K ] Figur 8 Film boiling hat transfr in liquid nitrogn for Typ 1 hatr at 0.55 MPa. h [ W/m 2 /K ] Typ 1 Hatr P = 1.0 MPa T sub =25 K 1.9 m/s 1.6 m/s 0.77 m/s 0.35 m/s 1.9 m/s 1.6 m/s 0.77 m/s 0.35 m/s T sat [ K ] Figur 9 Film boiling hat transfr in liquid nitrogn for Typ 1 hatr at 1.0 MPa. 5

8 4. Film boiling corrlation 4.1 Drivation of th corrlation Rcntly, w [2] hav masurd th forcd convction film boiling hat transfr from a round wir to liquid hydrogn flowing upward in concntric annulus with a narrow gap. W found that th xprimntal data wr about 1.7 tims highr than th valus prdictd by th Shiotsu-Hama quation [1], although th trnd of dpndnc on flow vlocity was similar to that by th quation. Shiotsu-Hama quation was basd on th xprimntal data for a wid conduit. W hav assumd that th vapour film layr around th wir hatr would b mad thinnr by a vry narrow gap. By introducing th quivalnt diamtr D to xprss th gap ffct, w hav drivd th following quation by xtnding th Shiotsu-Hama quation basd on th xprimntal data of hydrogn and nitrogn obtaind in this work. whr 1/4 Nu zd R M F R F (1) /3 D 0.63 ( ) for D l v p D v M ( SpR )[1 { E (2Pr Sp) }][1 0.7 ScE ] (2) F l p ( PP cr ) (3) E 2 is a positiv root of th following cubic quation E (5Pr S S ) E 5Pr S S E 7.5Pr S R 0 (4) 2 l p c 2 l p c 2 l p Th film boiling hat transfr cofficints prdictd by Eq. (1) dcras with th dcras in flow vlocity but do not bcom lowr than th cofficints of pool film boiling hat transfr from a vrtical surfac givn by th following quation [4]. whr 1 1 1/2 1/4 1/4 D 0.52 { ( ) } for l v z D v Nu z D z g M R F z z 1 Prl Prl M Gr Sp E E Sp R Sp (6) 1/2 1/3 1/2 1/3 E A CB A CB 1/ 3 Sc * (7) A 1/ 27 Sc * 1/ 3R Sp Pr lsc * 1/ 4R Sp Prl (8) B 4 / 27 Sc * 2 / 3 Sp Pr Sc* 32 / 27 Sp Pr R 1/ 4 Sp Pr 2 / 27 Sc* / R (9) l l l C (10) 2 0.5R SpPrl Sc* 0.93Pr l Sc (11) Th lowr limit, F v, of R numbr for quation (1) is givn as follows by quating quation.(1) with quation (2) / ( ) { ( ) } v l v z v l p 0.22 F z D z g M M F (12) 4.2 Comparison with th xprimntal data Th film boiling hat transfr cofficints prdictd by quations (1) and (5) ar compard with th data of liquid hydrogn in figurs 4 to 7 and with th data of liquid nitrogn in figurs 8 and 9. W can s that th trnd of dpndnc on wall suprhat and flow vlocity at ach prssur and subcooling ar xprssd wll by th quation. In cas of liquid nitrogn, th prdiction accuracy is not as good as that for liquid hydrogn. Th quation undrstimats th xprimntal data spcially for th flow vlocitis lowr than 1 m/s. (5) 6

9 To s th applicability of th corrlation in mor dtail, all th xprimntal data of liquid hydrogn undr saturatd and subcoold conditions at prssurs for th Typ 1 and Typ 2 hatrs xcpt thos 1/3 1/4 1 for RD F c ar shown on NuD ( / ) ( / ) v l M z D F p vs. RD graph in figur 10. Th curv of quation (1) is shown in th figur as a straight lin. Th rror bands of 20 % ar shown as dottd lins. W can s that most of th xprimntal data ar within 20 % of th valus prdictd by th quation Nu D ( v / l ) M 1/3 (z/d ) 1/4 Fp Liquid Hydrogn Typ 1 Hatr 10 2 Prssur T sub Typ 2 Hatr 0.4 MPa 5 K Prssur T sub 0.4 MPa 0 K 0.4 MPa 5 K 0.7 MPa 8 K 0.4 MPa 0 K 0.7MPa 0K 0.7MPa 8 K 1.1MPa 11 K 0.7MPa 0 K MPa 0 K R D y=0.63*x % FIGURE 10. Comparison of th corrlation with th xprimntal data of liquid hydrogn -20% 4.3 Comparison with th convntional non-cryognic data Th xprimntal data of watr undr saturatd condition and R113 undr subcoold condition by Shiotsu and Hama [1] ar shown in Figurs 11 and 12. Th curvs of quations (1) and (5) ar also shown in ths figurs. Th valus prdictd by our quation for ach flow vlocity agr with th xprimntal data of watr and R113 with ±10 % rror. It is xpctd that our corrlation can xprss film boiling hat transfr in forcd flow of cryognic and non-cryognic liquids for a round wir in conduits with various gaps, although furthr study is ncssary for confirmation Watr d 1 =40 mm d 2 = 3 mm z=180 mm P= MPa Saturatd Condition Flow 2.65 m/s 2.32 m/s 1.66 m/s 1.01 m/s 0.36 m/s 0 m/s 2.65 m.s 2.32 m/s 1.66 m/s 1.01m/s 0 m/s T sat [ K ] Figur 11. Comparison of our corrlation with watr data [1] for 40 mm-dia. conduit R113 d 1 =40 mm d 2 = 3 mm z=180 mm P=0.49 MPa T sub = 20 K Flow 1.99 m/s 1.66 m/s 1.33 m/s 1.01 m/s 0.68 m/s 0.36 m/s 0 m/s 1.99 m/s 1.66 m/s 1.33 m/s 0 m/s T sat [ K ] Figur 12. Comparison of our corrlation with R113 data [1] for 40 mm-dia. conduit. 5. Conclusions Film boiling hat transfr cofficints wr masurd for th two typs of hatr blocks with th sam diamtr of th hatr wir and diffrnt hatr lngths and gaps of th conduit. Th xprimntal rsults ld to th following conclusions. Th hat transfr cofficints ar highr for highr prssur, highr subcooling and highr flow 7

10 vlocity. Th hat transfr cofficints for th Typ 1 and Typ 2 hatrs for narly th sam vlocitis ar almost th sam, though th lngth z and th quivalnt diamtr D of th Typ 2 hatr ar about 1.6 tims and 0.56 tims as long as thos of Typ 1, rspctivly. A nw corrlation was prsntd modifying th Shiotsu-Hama quation by introducing th quivalnt diamtr D to xprss th gap ffct. Th xprimntal data of liquid hydrogn and liquid nitrogn ar xprssd wll by th nw corrlation. Th xprimntal data of watr and R113 by Shiotsu and Hama [1] ar also xprssd wll by th nw corrlation. It is xpctd that our corrlation can xprss film boiling hat transfr in forcd flow of cryognic and non-cryognic liquids for a round wir in conduits with various gaps, although furthr study is ncssary for confirmation. 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] Shiotsu M and Hama K 2000 Nucl. Eng. & Ds [2] Shiotsu M t al 2015 Physics Procdia [3] Tatsumoto H t al 2010 J. Physics Confrnc Sris 234. [4] Sakurai A t al 1992 Pool Film Boiling Hat Transfr and Minimum Film Boiling Tmpratur in Pool and Extrnal Flow Boiling d by V K Dhir and A E Brgls ASME pp Nomnclatur D : ( d1 d2), quivalnt diamtr, (m) d :innr diamtr of conduit (m) 1 d :hatr diamtr (m) Gr z : ( g( l v) v z l ), Grashof numbr h : ( q/ T sat ), boiling hat transfr cofficint (Wm -2 K -1 ) h :latnt hat (Jkg -1 ) fg h : ( h 0.5 c T ), modifid latnt ' fg fg pv sat hat (Jkg -1 ) Nu D : ( hd / v ), avrag Nusslt numbr P :prssur (kpa) P :critical prssur (kpa) cr Pr : ( c / ), Prandtl numbr of liquid l v pl l l Pr : ( c / ), Prandtl numbr of vapor pv v v Q :hat gnration rat (Wm -3 ) q :hat flux (Wm -2 ) 1/2 R : ( { / ( )} ) D v v l l R : ( ud / ), Rynolds numbr l ' Sc : ( c T / h ), non-dimnsional pl sub fg subcooing ' Sp : ( c T / h / Pr ), non-dimnsional pv sat fg v suprhat T av :avrag hatr tmpratur (K) T B :inlt liquid tmpratur (K) T sat ;saturation tmpratur (K) T w :hatr surfac tmpratur (K) u :flow vlocity (ms -1 ) z :tst hatr lngth (m) : ( T T ), surfac suprhat (K) T sat w sat T sub ( Tsat TB ), subcooling (K) :thrmal conductivity (Wm -1 K -1 ) :viscosity (kg s -1 m -1 ) :kinmatic viscosity (m 2 s -1 ) :dnsity (kgm -3 ) :surfac tnsion (Nm -1 ) :xponntial priod (s) Subscripts l : liquid, v:vapor 8