SUPPLEMENT TO CHAPTER 12 OF REACTOR PHYSICS FUNDAMENTALS This supplement summrizes some key physics principles in the text nd expnds on the mthemticl tretment. You should be milir with the text mteril beore you study this supplement. Fst Feedbck Rectivity Eects Physicl Eects o Temperture: therml expnsion moleculr speeds Eects on Rectivity Fctors: h,, p, e,(lt & L) Fuel Temperture Eect Modertor Temperture Eect Coolnt Temperture Eect Core Voiding: eects on e &p possible eect on eect on h John L Groh 1
PHYSICAL EFFECTS OF TEMPERATURE Incresing the temperture in the rector core hs two physicl eects, cusing three types o chnge in nucler processes (in bold print below): Therml expnsion, Reduced DensityotheHetedMterils Atoms/molecules push urtherprtromonenother, so density decreses, (THE DENSITY EFFECT). Increse is Moleculr Speeds Asmterilsre heted, the kinetic energy o the toms nd molecules increses. The increse in moleculr speedshstwo nucler eects, cused becuse: the U-238 nucler trgets move ster, (DOPPLER BROADENING), the thermlized neutrons move ster, (THE NEUTRON SPECTRUM EFFECT). Chpter 12 is bout rectivity chnges cused by temperture chnges in the uel, coolnt nd modertor. This supplement looks t how ech o the ctors in the six ctor ormul, k = ephl L t,chnges with temperture becuse o these three eects. First, consider these processes one t time: 1. THE DENSITY EFFECT Lower density ects mcroscopic cross sections. Recll the ormule or rection rte (R), mcroscopic cross section (S), nd men ree pth(mp): R=S S =Ns mp = 1/S Density nd N, (the number o nucler trgets per unit volume) decreses s temperture increses. Mcroscopic cross sections o the heted mteril decrese nd neutron pth lengths increse. Rection rtes (rections per cm 3 per second) decrese, but this is not lwys importnt. For exmple, i uel bundle expnds, the rte o rection per bundle stys the sme. For exmple, nincrese in neutronpth lengths, prticulrly with modertor heting, increses neutron lekge nd resonnce cpture in djcent uel chnnels, but decreses modertor bsorption.
2. DOPPLER BROADENING The nucler trgets inhotter mterils move t higher speeds. This hs one importnt eect; U-238 resonnce cpture o slowing neutrons increses drmticlly. Only uel temperture increse cn increse the U-238 vibrtion, nd only epitherml neutrons (neutrons in the resonnce energy rnge) re ected. This eect is explined in the text. The net eect is to reduce resonnce pek height nd to brodenits energy rnge. In igure 12.13 (or 3.3)theshrpnrrow peks re mde lower s temperture increses, but the vlleys betweenthe peks re illed in. This increses the probbility o cpture in U-238 throughout the resonnce energy rnge. 3. THE NEUTRON SPECTRUM EFFECT Therml neutrons interct with hotter mterils, shre the energy o their surroundings, nd move ster. Microscopic cross sections decrese t higher neutron speeds. This my hve two seprte eects: neutron pth lengths increse becuse o the energy dependence o the microscopic cross section, s. Recll tht most cross-sections behve pproximtely s s µ 1/v. Since S =Ns nd mp = 1/S, S decreses nd mp increses. The rection rte orninducedrection,r=s, myormynot chnge. Recll tht =nvnd S =Ns. Anincresein verge neutron speed, v, increses the therml lux,, while the cross section, s, decreses with incresed neutron speed. In simple words, shiting the neutron spectrum to higher speeds increses the number o therml neutrons crisscrossing region,buttthesmetimedecresesthesize o the trgets in tht region. These two eects tend to oset one nother. 3
For 1/v cross section the decrese in s exctly osets the increse in so the temperture chnge hs no eect on the rection rte. Fissile mterils such s Pu-239 do not hve idel 1/v cross sections, so rection rtes in these mterils chnge with temperture. While neutrons re slowing down the energy loss per collision is not ected by the temperture o the toms the neutrons collide with. Rector core temperture chnges cnnot ect st nd epitherml neutrons. Reproduction Fctor, h. Spectrum Eects on h nd The CANDU temperture coeicients re dierent or resh uel nd equilibrium uel. The dierence is minly cused by h. Consider how h chnges or resh CANDU uel s the temperture o the core increses. One physicl eect is tht wrmer neutronsenter the uel. The ission nd bsorption cross sections o substnces in the uel re dierent or dierent neutron energies. h CANDU resh = S U -235 U -235 U -235 U -235 ns ns / S ns / s h 235 U 238 = U U = U U = U + + -238-235 + -238-235 S 1 S / S 1 S / S 1 + S / S U - - -238 U -235 For pureu-235, h U-235,islmostconstntinthetherml neutron energy rnge. (It decreses very slightly with energy. However, the denomintor o h CANDU increses or wrmer neutrons, so the spectrum eect cuses h CANDU to decrese. The rte o bsorption in U-235, S,decreses or wrm neutrons, while the bsorption rte in the other mterils in the uel is independent o temperture. For pure Pu-239, h 239 decreses slightly with incresing neutron energy in the therml neutron energy rnge. Both s & s decrese much less thn 1/v, giving very strong increse in rection rtes. The rte o bsorption in Pu-239 CANDU is so strong tht it domintes U-235 in equilibrium uel, so h equilibrium increses s neutron temperture increses.
Therml Utiliztion Fctor,. The therml utiliztion ctor,, is deined in terms o cross section rtios, so one lso expects it to chnge with neutron temperture, much s h does. There is, however, n interesting osetting eect clled the therml disdvntge ctor. uel S uel S = uel S uel + ertors mod 1 = 1 + ( / ) ( S / S ) non- uel mod ertor uel uel = non- uel uel non- uel S + ( ertor / ) S mod uel uel where the rtio (modertor/uel)isthe therml disdvntge ctor. The eect o neutron spectrum chnge cused by temperture chnge in the surroundings is, gin, ccounted or by compring the rection rtes. In resh uel (no Pu-239) S(uel) decreses s neutron temperture increses. With signiicnt Pu-239present, S(uel) increses sneutron temperture increses. The correction is much lrger or Pu-239 thn or U-235, so Pu-239 domintes the behviour o equilibriumuel. An increse in neutron bsorption in the uel depresses lux in the uel, i.e. when S(non-uel)/S(uel) decreses, modertor/uel increses nd prtly osets the chnge. The result is tht prt o the chnge in is similr to the chnge in h,butnotslrge. Therml utiliztion,, is lso ected by density chnges, so its behviour is more complicted thn the behviour o h. With poison in the modertor, or with low modertor isotopic, the density dependence (e.g. with modertor temperture chnge) is likely to be the dominnt eect. 5
k e h e p L L t PHYSICAL REASONS FOR CORE TEMPERATURE AND VOID REACTIVITY FEEDBACKEFFECTS FUEL TEMPERATURE spectrum eect neutrons re hotter Ø or U-235, or Pu- 239 lrge eect, but lwys dominted by peect no signiicnt eect depends on U-238 content & st lux These don't chnge. Doppler Brodening vibrtionou-238 trgets increseso bsorption o epitherml neutrons increses. pø mjor eect spectrumeect chngeslike h,but reduced becuse o the therml disdvntge ctor ( m / ) nosigniicnt eect depends on slowing down pth length nd geometry spectrumeect increse in therml neutron pth length becuse cross sections decrese. MODERATOR TEMPERATURE spectrum eect neutrons re hotter Ø or U-235, or Pu- 239 no signiicnt eect depends on U-238 content & st lux These don't chnge. density eect longer pth lengths increse epitherml neutron popultion in djcent chnnels. pø density eect lessmodertor bsorption. Spectrum eect my dds to or prtly osets thiseect density eect incresespth length so st neutrons trvel urther pth length increses due to both density eect smller cross sections COOLANT TEMPERATURE spectrum eect neutrons re hotter Ø or U-235, or Pu-239 density eect decrese in density -slightincresein st lux in the chnnel - smll eect. density eect Epitherml lux reduces little in chnnel o birth, so there isless resonnce cpture. p -smlleect spectrum &density eect slightly ewer sctters rom hotter molecules some reduced bsorption becuse o density eect density eect insigniicnt increse in pth length pth length increseslittle due to smller cross sections 100% VOID spectrum eect(loss o re-wrming by the coolnt) neutrons re cooler lrge eect or U-235, Ø or Pu-239 density eect lux o st neutrons in the chnnel increses mjor eect density eect lux o epitherml neutrons in the chnnel decreses mjor eect density eect reduces bsorption. Lrge eect; limited by keeping coolnt isotopichigh. Also spectrum eect. density eect smll incresein pth length smll incresein pth length density eect slightly oset by lrger cross sections
COOLANT VOIDING Void Coeicient is oten deined s the rectivity chnge per%void. The void chrcteristics o CANDU core re givenby reporting the rectivity chnge tht occurs or 100% voiding o the chnnels. Most CANDUs hve two het trnsport system loops tht isolte on loss o coolnt. The rectivity chnge or hl core voiding is much smller thn or ull core voiding. For the CANDU core, the biggest contributor to void rectivity is cused by the loss o modertion in the coolnt chnnel. With voiding, st neutrons rom ission, escping rom the uel, do not begin slowing down in the coolnt. Thisincreses the number o very st neutrons ner the uel, nd decreses the number o resonnce energy neutrons. As result, both e &p increse shrply. Thermlized neutrons entering the uel rom the modertor do not undergo spectrumwrming by interctions with the coolnt. This hs lrge eect too: h increses or resh uel nd decreses or equilibrium uel. Neutron bsorptioninthe coolnt decreses whenthe chnnels void. This cuses to increse. This increse in therml utiliztion is potentilly bigger eect thnny o the others, but is kept rom being dominnt by keeping the coolnt isotopic higher thn speciied minimum. Lekge is ected only little with voiding. Neutrons do not begin slowing down until they rech the modertor so, on verge, they trvel bit urther rom their strting point, incresing lekge. 7
Typicl Components othe Fuel Temperture Coeicient or CANDU (Nominl Operting Conditions. Units re mk/ C * ) TERM FRESH FUEL EQUILIBRIUM FUEL (1/e)de/dT 0.0 0.0 (1/p)dp/dT -9.3-9.3 (1/)d/dT -0.8 +0.3 (1/h)dh/dT -4.0 +5.3 (1/L )dl /dt 0.0 0.0 (1/Lt)dLt/dT -0.8-0.4 TOTAL -15-4 * e.g. uel temperture increse o 500 C(typiclorchngeromzeropower hot to ull power) or equilibrium uel resultsin decrese in rectivity o bout 2 mk. Component o the Rectivity Chnge in mk due to Full Core Totl Loss o Coolnt t FullPower-Typicl CANDU vlues TERM FRESH FUEL EQUILIBRIUM FUEL De/e 5.0 5.0 Dp/p 6.0 6.0 D/ 3.0 2.5 Dh/h 2.3-2.5 DL /L -0.8-0.8 DLt/Lt -0.3-0.3 TOTAL 15 10