A PWR operates under the conditions given below. Problem Data. Core Thermal Output. Gap Conductance 1000 Btu/hr-ft 2 -F

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1 A PWR oprats undr th onditions givn blow. Problm Data Cor hrmal Output 34 Mw Ful ight 44 inhs Rod Pith.49 inhs Outr Clad Diamtr.374 inhs Clad hiknss.5 inhs Pllt Diamtr.35 inhs Gap Condutan Btu/hr-t -F Clad hrmal Condutivity 9. Btu/hr-t-F Systm Prssur 5 psia Cor Mass Flu.48 lbm/hr-t Cor Inlt mpratur 55 F Powr Paking Fator.5 Aial Pak to Avrag Ratio F.5 Numbr o Ful Rods 5,95 Enrgy Dpositd in Ful 97.4 % a For hannls having th sam hat input, imum hat lu and pak to avrag ratio, th position and valu o th Minimum DNB ratio is a untion o th hat lu proil. Assuming th W3 orrlation is valid, dtrmin th loation and th valu o th Minimum DNB ratio in th hot hannl. Assum aial hat lu proils o th orm i Nominal hoppd o ii Bottom Pakd - - = iii op Pakd = b Assuming th nominal hat lu proil, dtrmin th hang in th magnitud and position o MDNBR or a % inras in th or thrmal output. What would b th hang in th imum ul ntrlin tmpratur orrsponding to this inras in or powr lvl? For th nominal hat lu proil, dtrmin th hang in th MDNBR or a % rdution in th or mass lu. What would b th nssary rdution in primary sid prssur to ahiv th sam MDNBR? Critial at Flu 34

2 SOLUION h DNB ratio is dind to b DNBR h minimum DNB ratio is most asily ound by omputing th DNB ratio ovr th hannl hight and sarhing or th minimum. at Flu h hat lu proil is in trms o two unknown paramtrs, th trapolation distan and th amplitud. h trapolation distan is dtrmind by th aial pak to avrag ratio. h amplitud sts th magnitud o th hat lu. Rod Sura at Flus Avrag Channl Q n R o 89,4 Btu/hr-t ot Channl F 473,5 Btu/hr-t Etrapolation Distan h aial pak to avrag ratio is dind to b F whr is th position o imum hat lu in a partiular hannl, and is th aially avragd hat lu in th sam hannl. Not, that or any givn hannl and both ontain th amplitud, this paramtr anls and th aial pak to avrag ratio is only a untion o shap. h position o imum hat lu is that loation suh that d d Nominal at Flu Proil For this hat lu proil, th imum hat lu ours at,suh that 473,5 Btu/hr-t. Critial at Flu 34

3 h aially avragd hat lu is dind to b. d d os os h aial paking ator is thn F os os For.3 t., this prssion is transndntal in and must b solvd itrativly. Itrating on givs Bottom Pakd Proil For this hat lu proil, th imum hat lu dos not our at, nor is th untion valuatd at th position o imum hat lu ual to on, suh that. Dtrmination o is urthr ompliatd by th at that th solution or ontains th trapolation distan whih is as o yt unknown. W an avoid this problm by dining a nw variabl suh that and imiing with rspt to d d os whih is transndntal in and must b solvd itrativly. Not, that Itrating on yilds th solution. 9. h aially avragd hat lu is dind to b [, ], or Critial at Flu 34 3

4 Critial at Flu 34 4 d d os os h aial paking ator an thn b writtn in trms o and as F os os For, this prssion is transndntal in and must b solvd itrativly. Itrating on givs.77 t. h imum hat lu orrsponds to or in trms o th paramtr suh that For th data givn hr, Btu/hr-t op Pakd Proil h top pakd proil has th sam trapolation distan and magnitud as th bottom pakd proil, i...77 t and, Btu/hr-t

5 Critial at Flu h ritial hat lu is dpndnt on th loal uilibrium uality, whih in turn is a untion o th loal nthalpy. h luid nthalpy distribution is givn by h h Dd m For th hat lu proils givn hr, th nthalpy distributions ar a Nominal Proil D h h os os m b Bottom Pakd Proil D h h os os m op Pakd Proil D h h os os m h hannl mass low rat is m GA A S D m / 4 4 / t / lbm hr h W-3 orrlation is givn in Euation. whr: EU,.. 43P P p[ P ] [ G/ 37. ] [ p 35. D ] [ h h ] in EU, = Critial hat lu in a uniormly hat hannl Btu/hr-t P = Prssur to 3 psia = Quality at th ritial loation -.5 < <.5 Critial at Flu 34 5

6 G = Mass Flu to 5 lbm/hr-t D = Euivalnt diamtr. -.7 inhs h = Saturatd liuid nthalpy Btu/lbm h in = Inlt nthalpy > 4 Btu/lbm h orrlation givn abov is or ritial hat lu in uniormly hatd hannls. o aount or non-uniorm hat lus, w mploy th ollowing orrtion ator, N, F EU N, C F p[ C N ] d [ p, C ] N, EU, 3 whr: C 44. inhs - 4 G/ N, = Critial hat lu in th non-uniormly hatd hannl Btu/hr-t N, = Aial loation at whih DNB ours in th non-uniormly hatd hannl inhs EU, = Aial loation at whih DNB ours in a uniormly hatd hannl inhs h DNB Ratio DNBR is dind to b th ritial hat lu at a spii loation dividd by th oprating hat lu at that loation, or N, DNBR h Minimum DNB Ratio MDNBR ours at th loation whr th ritial hat lu and th oprating hat lu ar th losst. o utili th W-3 orrlation or a givn st o oprating onditions, i.. prssur, low, hat lu, t. Slt a loation N, starting in th viinity o th or midplan at whih you wish to omput th ritial hat lu. Comput th loal nthalpy and uality at this loation. For a gl hannl modl th nthalpy at N, is N, h h in m, N Dd and th uality is thn h h h g 3 Comput EU, rom th W-3 orrlation or a uniormly hatd hannl. Not, EU, is th hat lu in a uniormly hatd hannl nssary to produ DNB or th givn loal luid onditions. Critial at Flu 34

7 4 Comput th lngth EU, that must b hatd at EU, to giv th sam loal onditions. h h in m,, EU EU Dd h hin, EUD, EU m, EU m h hin D, EU whr h is th sam loal nthalpy as alulatd in stp. 5 Comput F this gnrally ruirs numrial intgration and thn Inras N, and rpat., N, F his produr is rpatd ovr th ntir hannl lngth, and th minimum DNB ratio omputd. For th givn hat lu proils, th aial loation and valu o th MDNBR or th thr dirnt hat lu proils ar givn in th ollowing tabl EU at Flu Proil Position o MDNBR inhs MDNBR Bottom Pakd Nominal 5.8 op Pakd I th imum hat lu or th nominal hat lu proil is inrasd by % 58,9, th MDNBR and its loation ar MDNBR =.9 at = 3 inhs. Ful Cntrlin mpratur Channl Eit Conditions For th givn problm paramtrs, and a hannl inlt nthalpy o h Btu/lbm, th hannl it nthalpy in th hot hannl is h 7.9 Btu/lbm. h nthalpy o a saturatd liuid at 5 psia is 7.95 Btu/lbm suh that th oolant lavs th hannl as a saturatd mitur. h luid proprtis ar valuatd at th avrag luid tmpratur in th suboold rgion o th hannl av giving sat inlt Critial at Flu 34 7

8 C p =.435 =.979 k =.35 h hannl saturation proprtis ar takn at 5 psia sat = 5.74 h = 7.95 h g = 45. From th Wisman Corrlation h k D C R Pr 8. / 3 Convtiv at ransr Coiint whr C.4 S / D / =.37. Euivalnt Diamtr S D / 4. t 4A 4 D 38 D D Rynolds Numbr GD R 484,.979 Prandtl Numbr C p Pr.99 k.35 From whih th onvtiv hat transr oiint an b ound to b h k D C R Pr 8. / 3 = ,.8.99 /3 8,3.38 Btu/hr-t -F ransition rom Singl Phas Ford Convtion to Nulat Boiling Inipint Boiling Point nulation point h transition rom gl phas ord onvtion to mid boiling is assumd to our whr th wall tmpratur prditd by th gl phas ord onvtion orrlation is ual to that prditd by an inipint boiling orrlation. h wall tmpratur undr gl phas ord onvtion is o h and assuming th inipint boiling orrlation Critial at Flu 34 8

9 n 5. [ o n sat] P P th solution or n is itrativ. For th givn data, n 5.8 t. Fully Dvlopd Nulat Boiling Point h transition rom mid boiling to ully dvlopd nulat boiling is assumd to our whr th wall tmpratur prditd by th mid boiling orrlation is ual to that prditd by th ully dvlopd nulat boiling orrlation. Assuming th Brgls and Rohsnow orrlation is valid in th mid boiling rgion, thn th transition point to ully dvlopd nulat is th loation B whih satisis B NB n B FC B FC B B / whr: is th oprating hat lu proil FC B h[ w B B ] w B sat B / m Wall tmpratur rom th ully dvlopd nulat boiling orrlation [ ] m NB n w n sat n w n n h h D h h os os m h hom Corrlation givs P p 7 m h solution or B givs Ful Cntrlin mpratur t. Nulat boiling is assumd or all lvations abov this point. B h ul ntrlin tmpratur or a uniorm radial volumtri hat gnration rat is givn by solution o th transndntal uation Critial at Flu 34 9

10 9. s ln R 4 s o whr th volumtri hat gnration rat is givn in trms o th hat lu by R o R o. R R h ul pllt sura tmpratur is rlatd to th lad sura tmpratur and th aial hat lu through Ro Ro Ro s o ln R i G k Ri h pak ul ntrlin tmpratur lis in th viinity o th pak hat gnration rat. For this problm, th pak hat gnration rat ours at /, suh that th pak ul ntrlin tmpratur will our in th mid boiling rgion whr th wall tmpratur is obtaind rom whr: NB NB n FC FC NB / is th oprating hat lu proil h [ ] FC o [ ] m NB o sat [ ] m NB n o n sat n o n n h h Solution or th outr lad tmpratur, ul pllt sura tmpratur and ul ntrlin tmpratur in th viinity o / is givn in th tabl blow inhs o h imum ul ntrlin tmpratur is 3774 F and ours btwn 7 and 73 inhs in th hannl. I th imum hat lu is inrasd by %, thn 473,5. 58, 9 Btu/hr-t. h solution or imum ul ntrlin tmpratur is idntial to that abov, with th inipint boiling point n 4. t and th transition point to ully dvlopd nulat boiling 7.5 t. B s o Critial at Flu 34

11 Solution or th outr lad tmpratur, ul pllt sura tmpratur and ul ntrlin tmpratur in th viinity o / is givn in th tabl blow or th inrasd hat lu inhs o h imum ul ntrlin tmpratur is 4478 F and ours btwn 7 and 73 inhs in th hannl. It should b notd, that th ul mlt tmpratur or unirradiatd UO is around 47 F. s o Rdution in Mass Flu I th mass lu is rdud by %, i. G and th powr lvl stays th sam, th MDNBR is rdud to.745. h t o Prssur on MDNBR is illustratd in th ollowing tabl. Prssur h h g sat MDNBR Intrpolating th tabl givs a prssur o approimatly 3 psia to produ a MDNBR o.745. Critial at Flu 34

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