Opratin paramtrs r rprsntativ BWR an PWR sins ar ivn blw. Fr t PWR t cannl an t BWR avra cannl cmput an plt: 1) t vi an quality istributins ) Dtrmin t iniviual cmpnnts an t ttal prssur rp Cmpar t rsults btain usin bt quilibrium an nn quilibrium mls. Yu may assum t saturatin prprtis ar cnstant aln t lnt t cannl an may b valuat at t inlt prssur. Assum t Dix crrlatin r Cncntratin Paramtr an Drit Vlcity PRESSURIZED WATER REACTOR PARAMETERS Prssur 50 psia Clant Mass Flux.48 x 10 6 lbm/r-t Cr Inlt Tmpratur 55.5 F Maximum Cr Hat Flux 474,500 Btu/r-t R Pitc 0.496 incs R Diamtr 0.374 incs Ful Hit 144 incs Axial Pakin Factr 1.5 Fractin Enry Dpsit in Ful 0.974 Numbr Spacr ris 10 Spacr lss cicint 0.5 Cr Inlt Lss Cicint 1.5 Cr Exit Lss Cicint 1.5 T axial at lux may b takn t b ( z ) q() z = q 0 sin H BOILING WATER REACTOR PARAMETERS Cr Avra Hat Flux 144,03 Btu/r-t Prssur 1000 psia Clant Flw Rat 77 x 10 6 lbm/r Numbr Ful Assmblis 560 Can Dimnsins 5.78 x 5.78 incs R lcatins pr Assmbly 64 Cr Inlt Tmpratur 53 F R Pitc 0.640 incs R Diamtr 0.493 incs Ful Hit 146 incs Axial Pakin Factr 1.4 Fractin Enry Dpsit in Ful 0.97 Uppr an Lwr Ti Plat Lss Cicint 1.5 Numbr ris 8 Gri Lss Cicint 0.5 T axial at lux may b takn t b 1
( H - z ) ( H - z ) q() z = q0 sin H H Nt: q0 is nt t maximum at lux r tis istributin. Yu may assum t tw-pas rictin multiplir is ivn by t xprssin 0 1 1 (1 x) wr is t turbulnt Martinlli paramtr an ivn by 0. 1 x x 18. 1.75 an tat t Hmnus Multiplir riv in class is vali r t lcal lsss.
SOLUTION Hat Flux Prils PWR T at lux pril r t PWR cas is ivn as ( z ) q() z = q 0 sin wr r tis pril t maximum at lux ccurs at H / an is qual t q0. Fr t t cannl, tn 0 qmax 474,500 Btu/r - t q. T xtraplatin istanc assciat wit tis at lux pril is 0.301 t. BWR T at lux pril r t BWR cas is ivn as T avra cannl is in suc tat Fr t at lux pril ivn r q av H ( H - z ) ( H - z ) q() z = q0 sin H H q av H 1 q ( z H 0 q ( H ) H H ( H cs ( H )cs sin sin H H H H H 0 wic r q av 144, 03 may b slv irctly r q0 ivin ) q 0 1.108 10 Btu/r-t. T xtraplatin istanc assciat wit tis pril is 3.055 t. Entalpy Distributins T ntalpy istributin is ivn by t simpl nry balanc z 1 z ( ) (0) q( Dz m 0 5 wr t mass lw rat is ivn by trmin rm m GAx an A x S D / 4. Fr t BWR cas, t mass lux is 3
6 m m 7710 G 1.6610 A n S n D 60.83 cr asssmblis ( can rs /4) 6 lbm/r-t PWR z 1 ( H 0 m 0 H z ( ) (0) qsin Dz qdh 0 ( z ) z () (0) cs cs m H H Wr: BWR A x S D / 4 0.496 m GA x 0.374 / 4 0.136 in 6 4.48 10 9.46 10 344.9 lbm/r 9.46 10 4 t z 1 ( H ( H z ( ) (0) q 0 sin Dz m 0 H H qdh 0 ( H H ( H ( H ) H ) ( H ) z ( ) (0) cs sin cs sin m H H H H H H Wr: A x S D / 4 0.640 m GA x 0.493 / 4 0.187 in 6 4 1.66 10 15.19 10 19.8 lbm/r 15.19 10 4 t Bubbl Dpartur Pint T Bubbl Dpartur Pint can b btain rm t Saa-Zubr Crrlatin DC 0.00 q( z ) k q( z ) 154 G p P 70,000 P 70,000 wr GD C P k p R Pr is t Pclt Numbr an t ntalpy at t bubbl partur pint is ivn by z 1 in q ( Dz. m 0 Fr t quilibrium ml, t bubbl partur pint is takn t b t nnbilin it in by In itr cas, slutin is itrativ. ( H ) 4
PWR Takin t trmynamic prprtis at t mipint btwn t inlt tmpratur an t saturatin tmpratur ivs C p 1.4336 Btu/lbm-F k 0.3051 Btu/r-t-F T quivalnt iamtr is ivin r t Pclt numbr D 4Ax D 4 0.136 0.4637 incs 0.0386 t 0.374 6 GDC p.4810 0.03861.4336 P 4.501 10 k 0.3051 5 T bubbl partur pint is tn t slutin t transcnntal quatin q( z ) 154 G wr an t nn bilin it is t slutin qdh 0 ( z ) (0) cs cs m H H qdh 0 ( H ) (0) cs cs m H H Fr t PWR t cannl, z 8.319 t an H 10.07 t. BWR T subclin is suicintly small, tat t trmynamic prprtis can b apprximat as ts at t saturatin pint r valuatin t Pclt numbr. At 1000 psia, t saturatin tmpratur is T 544.58 F. C p 1.85 Btu/lbm - F k 0.3314 Btu/r - t - F T quivalnt iamtr is sat D 4Ax D 4 0.187 0.5648 incs 0.0471t 0.493 ivin r t Pclt numbr 5
6 GDC p 1.6610 0.04711.85 P.311 10 k 0.3314 5 T bubbl partur pint is tn t slutin t transcnntal quatin q( z ) 154 G wr qdh 0 ( Hz ) H ( H ( H ) H ) ( H ) (0) cs sin cs sin m H H H H H H an t nn bilin it is t slutin qdh 0 ( HH) HH) ( HH) ( H ) H ) ( H ) (0) cs sin cs sin m H H H H H H Fr t BWR avra cannl, z 0.118 t z 0 an H 1.399 t. Quality Distributins T lw quality as a unctin psitin is ivn by t Lvy pril it ml x x ( x) 0 x xp ( x ) 1 z z z z wr x is t lcal quilibrium quality an ( x ) is t quilibrium quality at t bubbl partur pint, i.. ( x ) Fr t quilibrium ml, t lw quality is ivn by 0 x x z H z H wr t lcal quilibrium quality is ivn by ( x ( PWR 6
T quality istributins assumin quilibrium an nn quilibrium lws ar illustrat blw. T cannl xit quality assumin quilibrium lws is x ( H) 0.09, an assumin nn quilibrium lw is xh ( ) 0.043. PWR Quality Distributins 0.05 0.04 Equilibrium Ml Nn Equilibrium Ml Quality 0.03 0.0 0.01 0.00 0 4 6 8 10 1 Axial Psitin (t) BWR T quality istributins assumin quilibrium an nn quilibrium lws ar illustrat blw. T cannl xit quality assumin quilibrium an nn quilibrium lws ar t sam an qual t xh ( ) 0.16. 7
BWR Quality Distributins 0.16 0.14 Equilibrium ml Nn quilibrium ml 0.1 Quality 0.10 0.08 0.06 0.04 0.0 0.00 0 4 6 8 10 1 Axial Psitin (t) Vi Distributin T Zubr-Finlay Crrlatin r vi ractin is 1 1 x V C 1 x Gx j wic r a iv cannl mass lux an prssur is nly a unctin t quality an t liqui pas nsity. T liqui pas nsity can b it t a lw rr plynmial as a unctin t liqui pas ntalpy. Assumin an quilibrium lw ml, t liqui pas nsity is ivn by ( ) z H z H Fr t nn quilibrium ml, t quality is btain rm t pril it ml an t liqui pas nsity is ivn by ( ) wr t liqui pas ntalpy is ivn by 8
( x( ( 1 x( PWR T Vi istributins assumin quilibrium an nn quilibrium lws ar illustrat blw. T cannl xit vi assumin quilibrium lws is ( H ) 0.179, an assumin nn quilibrium lw is ( H ) 0.35. q PWR Vi Distributins 0.5 0.0 Equilibrium Ml Nn Equilibrium Ml Vi Fractin 0.15 0.10 0.05 0.00 0 4 6 8 10 1 Axial Psitin (t) BWR T vi istributins assumin quilibrium an nn quilibrium lws ar illustrat blw. T cannl xit vi ractin assumin quilibrium an nn quilibrium lws ar t sam an qual t ( H ) 0.711. 9
BWR Vi Distributins 0.7 0.6 Equilibrium ml Nn quilibrium ml Vi Fractin 0.5 0.4 0.3 0. 0.1 0.0 0 4 6 8 10 1 Axial Psitin (t) Prssur Drp T prssur rp in t cannl is t sum t acclratin, rictin, lcal an lvatin lsss. Acclratin Lsss T acclratin lss in t cannl is P acc G ( c 1 x( H ) ( H ) x( H ) ( H ) 1 (0) Frictin Prssur Drp T rictinal lss is z z G G P rictin( ( z D D c c H wr aain r t quilibrium cas, t bubbl partur pint is takn as t nn bilin it Fr smt tubin, t rictin actr can b takn t b H. 0.184 R 0. Lcal Lsss 10
W can writ t lcal lsss witin t cannl as P lcal G j j c z j [0, z] K ( z ) j wr in t tw pas multiplir is takn t b n in t sinl pas rin. Fr t PWR cas, t ri lcatins (in incs) ar z j [0,16, 3, 48, 64, 80, 96, 11,18, 144] In t BWR cas, t ris ar plac unirmly aln t lnt t bunl, but nt at t bunl inlt an xit suc tat t ri lcatins (in incs) ar z j [16., 3.44, 48.66, 64.88, 81.11, 97.33,113.56,19.78] Elvatin Lsss T lvatin lsss ar btain by intratin t nsity istributin vr t cannl lnt, i.. P lv 0 H ( c z wr t nsity is ivn by ( ( ( ( ( z z z z Prir t racin quilibrium, t liqui nsity is a unctin ntalpy an can b btain by a simpl parablic it nsity t ntalpy rm t stam tabls. T ttal prssur rp is t sum t iniviual rps P P acc P rictin P lcal P lv T intrals in t prssur rp quatins ar valuat numrically. T iniviual prssur rps ar PWR Equilibrium 1.0 psi P acc 6.06 psi P rictin 10.4 psi P lcal 3.4 psi P lv 0.87 P ttal 11
Nn Equilibrium 1.17 psi P acc 7.37 psi P rictin 10.63 psi P lcal 3.35 psi P lv P ttal.5 BWR Equilibrium 1.76 psi P acc 9.73 psi P rictin 5.38 psi P lcal.035 psi P lv 18.4 P ttal Nn Equilibrium 1.76 psi P acc 9.876 psi P rictin 5.4 psi P lcal 1.97 psi P lv 18.54 P ttal 1