SOLUTION. The reactor thermal output is related to the maximum heat flux in the hot channel by. Z( z ). The position of maximum heat flux ( z max
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1 Te verpwer trip set pit i PWRs is desiged t isure te iu fuel eterlie teperature reais belw a give value T, ad te iiu rati reais abve a give value MR. Fr te give ifrati give a step by step predure, iludig all equatis, fr deteriig te trip set pit wi satisfies tese liits. Fr te purpses f tis prble, yu a assue te lat eters te re igly subled ad a steady state aalysis is valid. Itegrals wi d t ave lsed fr slutis a be left i itegral fr. Fr slutis ivlvig iterati, it is suffiiet t state wi equati(s are t be slved iteratively ad te variable(s t be iterated. Yu ay assue te fllwig ifrati is kw. Yu ay als assue ay eessary fluid ad/r terdyai prperties/relatis are available. Te eat flux prfile i te ael a be assued t be f te fr q q Z were te sape futi Z( is arbitrary but kw. Prble Paraeters Frati f Eergy epsited i Fuel Pwer Peakig Fatr Axial Peak t Average Rati Pressure Nuber f fuel rds Fuel Heigt Rd iaeter Rd Pit (square lattie Cre Ilet Etalpy Cre Mass Flux Gap Cdutae Clad Teral Cdutivity Clad Tikess Pellet iaeter f F q F P rds H S i G H G k t SOLUTION Reatr Teral Pwer Te reatr teral utput is related t te iu eat flux i te ael by Q F H q Q q H f q ffq were q q Z(. Te psiti f iu eat flux ( satisfies dz d, is idepedet f te eat flux agitude ad a be fud fr ay Z(. Give, te prble redues t fidig q tat satisfies te ad fuel teperature liits. Liit
2 Te R at ay lati witi te ael is were q q ( x (, G, P,, rit rit e e i ( xe fg f ( i q d GAx f q rit R q A S x /4 e 4[ S / 4] Te iiu R is te i[r(]. T deterie te value f = (MR TARGET, te fllwig predure a be fllwed. q wi satisfies te liit a Guess a value f q q ( q Z( b At speified ireets fr [ H /, H], pute ( x( q ( R ( ad rit e rit rit rit rit rit MR = i[r(] If MR > (MR TARGET irease q MR < (MR TARGET derease q d Retur t b ad repeat util MR = (MR TARGET q Fuel Ceterlie Liit Te fuel eterlie teperature ( T ( at ay lati is te iterative sluti f
3 69.6 Ts q R l Ts 46 T T 4 4 were te fuel surfae teperature a be writte i ters f te lad surfae teperature i te ael by R R R Ts T q l. RH i G k Ri Te vluetri eat geerati rate is related t te eat flux by q R q. ( ( Te lad teperature is a futi f te lal eat trasfer regie. Sie it is give tat te fluid eters igly subled, te pssible eat trasfer regies are sigle pase fre veti, ixed bilig ad fully develped uleate bilig. Fr a give eat flux, te first step ivlves deteriig te bilig budaries. Trasiti fr Sigle Pase Fred Cveti t Mixed ilig At te Iipiet ilig Pit (,.56 q ( q ( 5.6 P T ( T sat.34.3/ P were is te sigle-pase fred veti eat trasfer effiiet ad a be btaied fr te Weisa Crrelati.8 k Ge C p C( S / e k /3. T ( is te lal fluid teperature ad a be btaied fr te etalpy at ay lati by T T (, P, were ( i q d GAx f Fr a give ass flux, ilet ditis ad eat flux prfile, te ly ukw is, wi ay be slved fr iteratively. Trasiti fr Mixed t Fully evelped Nuleate ilig At te trasiti pit betwee ixed ad fully develped uleate bilig (
4 / q ( q ( q q q q were q ( [ T ( T ] 6 sat q ( T ( T ( q [ T T ] q ( ( sat 6 T T T T (, P Fr a give eat flux prfile ad ael peratig ditis, tese equati redue t a sigle liear equati i te bilig trasiti pit ad ay be slved iteratively T T(, P. Oe te bilig budaries are kw, te lad teperature at ay lati a be deteried. Clad Teperature istributi Give te bilig budaries, te lad teperature is Sigle Pase Fred Cveti Regi [, ] q T T Mixed ilig Regi [, ] Te wall teperature at ay lati i te ixed bilig regi is te sluti f q q ( q q q q were: q ( [ T T ] / q ( 6 [ T ] T sat
5 ad te ly ukw at ay lati is T ( wi ay be slved fr iteratively. 3 Fully evelped Nuleate ilig Regi I te Fully evelped Nuleate ilig Regi, te lad teperature a be deteried diretly fr q T Tsat 6 Predure fr deteriig te eat flux wi satisfies te fuel eterlie liit a Guess q q ( q Z( q( b Cpute te bilig budaries ad At speified ireets fr [, H] pute T (, T ( ad T ( d if [ T ( ] > T derease q s [ T ( ] < T irease q e Retur t b ad repeat util T = T q [ ( ] T Te eat flux wi satisfies bt liits is q i q, q T. Te trip set pit is te H Q TRIP q Z( F f q
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