1.Vật lý Neutron và Lò PƯ

N.Z. Cho Introduction to Nuclear Reactor Physics 1Vt l neutron v l phn ngNeutron and Reactor PhysicsVt l Ht nhnHUS 9/20092Vt l neutron v l phn ng1. Ging vin:PGS. TS Phm Quc HngThS. V Thanh Mai2. Thi lng: 45 tit3. Khung tnh im: Bi tp: 30%Gia k: 20%Cui k: 50%V.T.MaiVt l neutron v l phn ng3Ti liu1. Gio trnh:Vt l l phn ng ht nhn Ng Quang Huy -NXB. HQG HNIntroduction to nuclear reactor theory Lamarsh2. Ti liu tham kho:Nuclear reactor physics DuderstadtL phn ng ht nhn Phm Quc Hng NXB. HQG HNV.T.MaiVt l neutron v l phn ng41. Gii thiu chung1.1 Nh my in ht nhn1.2 Vt l l v l thuyt l P2. Tng tc ca neutron vi vt cht v nguyn tc cu to l P2.1 Neutron 2.2 Tn x v hp th2.3 Phn hch ht nhn2.4 Phn ng dy chuyn 2.5 Phn loi l P 3. Lm chm v khuch tn neutron3.1 C ch lm chm3.2 Khuch tn neutron3.3 PT khuch tn 1 nhm neutron3.4 PT khuch tn 2 nhm neutron3.5 PT vn chuyn neutronNi dungV.T.MaiVt l neutron v l phn ng5Ni dung4. Trng thi ti hn ca l P4.1 H s nhn hiu dng4.2 Cng thc 4 tha s4.3 Cng sut l P5. ng hc l P5.1 P5.2 Vai tr ca neutron tc thi v neutron tr trong P dy chuyn5.3 PT ng hc l P6. S thay i P trong qu trnh lm vic ca l6.1 S nhim c Xenon v Samari6.2 S chy nhin liu v to x trong l P6.3 Hiu ng nhit 6.4 Hiu ng cng sut6.5 hiu dng ca cc thanh nhin liuV.T.MaiVt l neutron v l phn ng61.1 Nh my in ht nhn1 Gii thiu chung< Gin cu hnh ca nh my in PWR >V.T.MaiVt l neutron v l phn ng7< Gin cu hnh li l P PWR>V.T.MaiVt l neutron v l phn ng8 V.T.MaiVt l neutron v l phn ng91. Thanh nhin liu (Fuel rod)2. Vnhinliu(Fuelcladding)lmtng Zircaloy-4 dy 0.025 inch (0.635 mm).3. VinUO2 (UO2pellet)cnnlmc2 uiuchnh thch hpchos dn n v nhit v s phng ln ca nhin liu. SPRINGUO2 PELLETSFUEL CLADDINGAl2O3SPACERDISCLONG LOWER END CAPUPPEREND CAP< Gin thanh nhin liu>V.T.MaiVt l neutron v l phn ng10 V d : Li l VHTRCoolantGraphite BlockC-matrixFuel kernelREPLACEABLE CENTRAL& SIDE REFLECTORSCORE BARRELACTIVE CORE102 COLUMNS10 BLOCKS HIGHPERMANENTSIDEREFLECTOR36 X OPERATINGCONTROL RODSBORATED PINS (TYP)REFUELINGPENETRATIONS12 X START-UPCONTROL RODS18 X RESERVE SHUTDOWNCHANNELSREPLACEABLE CENTRAL& SIDE REFLECTORSCORE BARRELACTIVE CORE102 COLUMNS10 BLOCKS HIGHPERMANENTSIDEREFLECTOR36 X OPERATINGCONTROL RODSBORATED PINS (TYP)REFUELINGPENETRATIONS12 X START-UPCONTROL RODS18 X RESERVE SHUTDOWNCHANNELSFuel KernelBuffer LayerInner PyrocarbonSilicon CarbideOuter PyrocarbonTRISO ParticlesV.T.MaiVt l neutron v l phn ng111.2 L phn ng ht nhn v vt l l L phn ng ht nhn l mt thit b k thut, trong nhin liu ht nhn v cc vt liu cu trc c sp t sao cho phn ng dy chuyn t duy tr c th iu khin c. Nng lng ht nhn (di dng ng nng ca cc mnh phn hch, neutron, tia gamma) gii phng trong qu trnh phn ng dy chuyn c s dng. Vt l l hay phn tch l phn ng l s xc nh v nguyn l ca phn b neutron trong l phn ng di cc cu hnh v iu kin vn hnh cn bng khc nhau:- neutron sinh ra do phn hch v- neutron mt i do phn ng bt (capture) hoc d d neutron (leakage). Kt qu ca phn tch l P:- S phn b nng lng (Power distributions)-H s nhn hiu dng (Effective multiplication factors) - keffV.T.MaiVt l neutron v l phn ng122 Tng tc ca neutron vi vt cht v nguyn tc cu to l P Ht nhn:do cc proton v neutron, cc ht c khi lng gn bng nhau v c cng mmen gc (spin) bng 1/2. Proton l ht mang mt n v in tch dng trong khi neutron khng c in tch. Thut ng nucleon c s dng cho c proton v neutron. Mt ht nhn c nhn dng bi nguyn t s, Z (ngha l s proton), s neutron, N v s khi, A, trong A=Z+N.2.1 Neutron V.T.MaiVt l neutron v l phn ng142 Tng tc ca neutron vi vt cht v nguyn tc cu to l P2.1 Neutron V.T.MaiVt l neutron v l phn ng152 Tng tc ca neutron vi vt cht v nguyn tc cu to l P2.1 Neutron 1. Neutron c to ln bi 1 quark up v 2 quark down. 2. 1 trong 2 quark down chuyn thnh 1 quark up. V quark down c in tch bng -1/3 v quark up c in tch bng 2/3, qu trnh ny c trung gian bi 1 ht o W-, ht ny mang in tch -1 ( in tch c bo ton).3. Quark up mi bt ra khi ht W-. Neutron gi tr thnh 1 proton.4. Mt electron v 1 phn ht neutrino hnh thnh t ht o W- 5. Proton, electron v ht phn neutrino tch khi nhau.Phn r beta ca neutron:V.T.MaiVt l neutron v l phn ng162 Tng tc ca neutron vi vt cht v nguyn tc cu to l P2.1 Neutron Phn loineutron: 3 loi theo 3 min nng lng1. Neutron nhit (thermal neutron): 0 ZA+1 -> n+ZA+ P (n, ) and (n, f) : S hp th neutron (absorption of neutron)Bt bc x (radiative capture): n+ZA -> ZA+1 -> ZA+1Phn hch (fission): n+ZA -> ZA+1 -> ZB+ ZC (B+C=A+1)V.T.MaiVt l neutron v l phn ng18Ht nhn hp phn (Compound Nucleus)10n+AZX10n+AZX:Tn x th (potential scattering)- phn x sng neutron t b mt ht nhnTn x n hi (elastic scattering)Tn x khng n hi (inelastic scattering)P bt (capture)Phn hch (fission)( )A+1ZXHt nhn hp phn14~10 sec10n+AZXV d: Neutron tng tc vi U-2351 2350 92n U +1 21 21 2350 922369210: scattering: (radiative) capture: fission+++ +A AZ Zn UUX X n(2.4)(2.5)(2.6)V.T.MaiVt l neutron v l phn ng19 V.T.MaiVt l neutron v l phn ng202 Tng tc ca neutron vi vt cht v nguyn tc cu to l P2.3 P phn hch ht nhn235U + 1n -> fission products + neutrons + energy (~200 MeV)V.T.MaiVt l neutron v l phn ng212 Tng tc ca neutron vi vt cht v nguyn tc cu to l P2.3 P phn hch ht nhnC ch v nng lng Mu git Nng lng ti hn (Critical energy) ,critical qE E Q 21 21 2qZZeER R+trong (2.7): Th nng CoulombV.T.MaiVt l neutron v l phn ng22 Nng lng kch thch (excitation energy) ca ht nhn hp phn: A-1A-1Ifwith10 : Z , fissionableIf: Z , fissileexcitation c critical ccriticalE B E E E MeVB E + > ,excitation cE B E +B Nng lng lin kt (binding energy) ca neutron cui cng trong ht nhn hp phn (ZA)*,cEng nng (kinetic energy) ca neutron.(2.8)trong :NuNuvicth phn hch phn hchV.T.MaiVt l neutron v l phn ng23 V.T.MaiVt l neutron v l phn ng24Phn loi ht nhn nhin liu: Ht nhn phn hch (Fissile nuclides) Ht nhn c ngng (Fissionable nuclides) Nguyn liu ht nhn (Fertile nuclides) phn hch bi cc neutron chm U233, U235, Pu239, Pu241 phn hch bi ccneutron nhanh Th232, U233, U235, U238, Pu239, Pu241, ...c chuyn ha thnh ht nhn phn hch nu mt neutron c hp th Th232, U238V.T.MaiVt l neutron v l phn ng25V d 1 phn ng phn hch -RaysA AZ Zn U X X n + + + +1 21 21 235 10 92 0Fig. 3-7.Fission product yields: thermal and 14-MeV fission of U235.Cc mnh phn hchCc tia tc thi2 nhm khi lng 80110 v 125155 c sut ra ln nht. Giu neutron: hot tnh beta ( -decay) Cc sn phm phn hch: cc mnh phn hch+ con chu( ),A AZ ZX X1 21 2V.T.MaiVt l neutron v l phn ng26Phn ng phn hch U235 gii phng nng lng c 200 MevV.T.MaiVt l neutron v l phn ng27 Neutron tc thi v neutron tr: Neutron tc thi (prompt neutrons) : sinh ra ti thi im phn hch :Neutron tr (delayed neutrons) : sinh ra t nhm cc con chu phn r beta (=ht nhn tin t Ci), do b tr li bng vi thi gian bn r beta: ) 1 ( , 6 , , 2 , 1 , ii .61ii Cc neutron phn hch gm 2 loi: V.T.MaiVt l neutron v l phn ng28 V.T.MaiVt l neutron v l phn ng29S liu ca neutron tr trong P nhit hch ca 235UNhm Thi gian bn r(sec)Hng s bn r(i,sec-1)Nng lng(keV)Sut ra, Neutron/ phn hchi 1 (Br87) 55.72 0.0124 250 0.00052 0.000215 2 (I137) 22.72 0.0305 560 0.00346 0.001424 3 6.22 0.111 405 0.00310 0.001274 4 2.30 0.301 450 0.00624 0.002568 5 0.610 1.14 - 0.00182 0.000748 6 0.230 3.01 - 0.00066 0.000273Tng sut ra:0.0158 : 0.0065Trung bnh s neutron/phn hch ( ) : 2.43V.T.MaiVt l neutron v l phn ng30Cc neutron to thnh t P phn hch Tnh trung bnh, (>2) neutron c sinh ra trong 1 P phn hchS trung bnh cc neutron phn hch Nng lng neutron gy ra P phn hch3.04 2.93 Pu2392.51 2.42 U2352.58 2.49 U2331 MeV 0.025 eVHt nhnV.T.MaiVt l neutron v l phn ng31Tit din phn ng (cross section) v tc phn ng (reaction rate) (xc sut) ca phn ng ht nhn xy ra gia 1 neutron v mt ht nhn no . Hm ph thuc rt ln vo:i) nng lng neutronii) ht nhniii) loi phn ngTit din vi m (Microscopic cross section), : n v tit din: cm2, barn (1 barn = 10-24 cm2) Tit din v m (Macroscopic cross section), : = N, N = mt ht nhn, n v : cm-1g R2V.T.MaiVt l neutron v l phn ng32 Tc phn ng (Reaction rates) : S cc phn ng loi /cm3.sec(E) =n(E) (E)= S cc neutron i qua 1 n v din tch trn 1 n vthi gian, c vn tc (hoc nng lng E=1/2m2)n(E)dE = S neutron/cm3 c nng lng nm gia E v E+dE Trong : V.T.MaiVt l neutron v l phn ng33Tra cu s liu tit din ht nhn:V.T.MaiVt l neutron v l phn ng34V d: Tit din phn hch ca U-235Energy (eV) Cross section (barns) V.T.MaiVt l neutron v l phn ng35V d: Tit din hp th (bt) ca U-238Energy (eV) Cross section (barns) V.T.MaiVt l neutron v l phn ng36V d : Tit din n hi/tit din tng ca HydrogenV.T.MaiVt l neutron v l phn ng37V d : Tit din n hi/tit din tng ca OxygenV.T.MaiVt l neutron v l phn ng382 Tng tc ca neutron vi vt cht v nguyn tc cu to l P2.4 P dy chuyn v nguyn tc lm vic ca l P ht nhnV.T.MaiVt l neutron v l phn ng392 Tng tc ca neutron vi vt cht v nguyn tc cu to l P2.4 P dy chuyn v nguyn tc lm vic ca l P ht nhnV.T.MaiVt l neutron v l phn ng402 Tng tc ca neutron vi vt cht v nguyn tc cu to l P2.4 P dy chuyn v nguyn tc lm vic ca l P ht nhnV.T.MaiVt l neutron v l phn ng412 Tng tc ca neutron vi vt cht v nguyn tc cu to l P2.4 P dy chuyn v nguyn tc lm vic ca l P ht nhnV.T.MaiVt l neutron v l phn ngH s nhn k:k= n2/n1Trong : n1 v n2 l cc mt neutron trong hai th h k tip nhauk=1: Trng thi ti hnk1: Trng thi trn ti hn, P dy chuyn pht trin422 Tng tc ca neutron vi vt cht v nguyn tc cu to l PV.T.MaiVt l neutron v l phn ngTn Chc nng c im yu cu Vt liuNhin liu ht nhnPhn hch ht nhn bi cc neutron Cc c tnh ht nhn tt dn nhit caoBn ha hc v bc xUO2, UO2/PuO2, U-Zr, Cht lm chmGim nng lng neutron bng tn x v cc neutron khng b bt ng k Tit din tn x ln Tit din hp th nhS khi nhH2O, D2O, Be, CCht ti nhit Chuyn nhit t cc ngun nhit chnh nhue l l hoc v ti sinh Sc bm cn thit nh Bn bc x Di do & gi thnh rH2O, D2O, CO2, He, Na lng, Pb-Bi lngCht iu chnh hot iu chnh thng lng neutron trong l bng P hp th neutron Thanh iu khin: B, B4C, Cd, Cht dp tt (Burnable poision): Eu2O3, Gd2O3Vt liu cu trcDuy tr hnh hc l cng v tnh mm do cao Tit din hp th nh Bn nhit v phng x t b bo mnZicarloy, Al v hp kim Cc thnh phn chnh ca l P432 Tng tc ca neutron vi vt cht v nguyn tc cu to l P2.5 Phn loi l PV.T.MaiVt l neutron v l phn ngNng lng neutronNhanh/Trung gian/NhitHu ht cc l P ang vn hnh l l neutron nhitng dngNng lng/Nghin cu/Cht ti nhit, cht lm chm hoc nhin liuTi nhit bng nc, kh hoc kim loi lngLm chm bng graphite, nc nng, Cht ti nhit l yu t du tin phn loi l PH s ti sinht nhin liu, nhn nhin liu442 Tng tc ca neutron vi vt cht v nguyn tc cu to l PCc loi l P chnhV.T.MaiVt l neutron v l phn ng452 Tng tc ca neutron vi vt cht v nguyn tc cu to l PCc loi l P chnhV.T.MaiVt l neutron v l phn ng462 Tng tc ca neutron vi vt cht v nguyn tc cu to l PCc loi l P chnhV.T.MaiVt l neutron v l phn ng472 Tng tc ca neutron vi vt cht v nguyn tc cu to l PCc loi l P chnhV.T.MaiVt l neutron v l phn ng482 Tng tc ca neutron vi vt cht v nguyn tc cu to l PCc loi l P chnhV.T.MaiVt l neutron v l phn ng492 Tng tc ca neutron vi vt cht v nguyn tc cu to l PCc loi l P chnhV.T.MaiVt l neutron v l phn ng502 Tng tc ca neutron vi vt cht v nguyn tc cu to l PCc loi l P chnhV.T.MaiVt l neutron v l phn ng512 Tng tc ca neutron vi vt cht v nguyn tc cu to l PV.T.MaiVt l neutron v l phn ng522 Tng tc ca neutron vi vt cht v nguyn tc cu to l PV.T.MaiVt l neutron v l phn ng532 Tng tc ca neutron vi vt cht v nguyn tc cu to l PV.T.MaiVt l neutron v l phn ng542 Tng tc ca neutron vi vt cht v nguyn tc cu to l PV.T.MaiVt l neutron v l phn ng553. Lm chm v khuch tn neutronV.T.MaiVt l neutron v l phn ng3.1 C ch lm chm neutron Neutron sinh ra do phn hch ch yu l neutron nhanh (~2MeV), nhng tit din phn hch th cao i vi neutron nhit (~0.1 eV). Do , chng ta cn lm chm neutron thit k l P ti hn vi mt lng nhin liu ti thiu. C ch lm chm: Tn x neutron trong mi trng cht lm chm Tn x khng n hi vi cc ht nhn nng Tn x n hi vi cc ht nhn nh56Cc neutron phn hch (c MeV)( Hp th cng hnghoc r r)Cc neutron nhit di-eV(r hoc bt) Phn hchE : Lm chm thng qua tn xV.T.MaiVt l neutron v l phn ng57, urEE uurT l tn x n :, urE ( , ) ( , ) uur uur ur uurgsdE d E E E T l tn x ra khi : , uurE ( , ) ( , ) ( ) ( , ) ur uur ur uur uurgs sdE d E E E E E Trong ( ) ( , )( ) ( , ) ur uur urguur uurs sE dE d E EE d E T l tn x ra khi: E ( ) ( , ) ( ) ( ), uur uurs sd E E E E V.T.MaiVt l neutron v l phn ng58Tn x n hi (Elastic Scattering) H quy chiu phng TN -Laboratory System (LS) :NeutronmHt nhn biaMCME v,CMv0 VE v ,LV(3.1)V.T.MaiVt l neutron v l phn ng( )222 cos 11CA A EEA _ + + + ,59 H khi tm - Center of Mass System (CMS) :21 1 1cos , where2 2 1CE AE A + _ +

+ ,NeutronmHt nhn biaMCMCMCvCVCVCvC(3.2)( )( )( )( )( )2 sin2 sin 4 (1 )s L L Lss C C C s Cs sdP E E dEdP E EE V.T.MaiVt l neutron v l phn ng60 Nu l tn x ng hng trong h quy chiu tm qun tnh,-- Nng lng trung bnh ca neutron tn x n hi:- Nng lng trung bnh mt i sau 1 va chm:-: tng trung bnh ca lethargy (u) trn 1 va chm, : mt nng lng theo thang logarit trn 1 va chm.(1 )2EE + (1 )2EE E E ln lnEuE +111,(1 ) ( )0, , E E EE PE EE E E E < < ' < >1(1 ) E ( ) P E E E EE(2.11)(3.3)(3.4)(3.5)V.T.MaiVt l neutron v l phn ng61 Lethargy: Mc lm chm ca neutronLethargy tng khi E gim: tng trung bnh ca lethargy (u) trn 1 va chm, : mt nng lng theo thang logarit trn 1 va chm.ln lnEuE +11(3.6)V.T.MaiVt l neutron v l phn ng( ) ln EuEE(3.7)62 Thng s va chm ca mt s ht nhn Kh nng lm chm = ,s H s lm chm=asHt nhn H1D2He4Be9C12O16Na23U2380 0.111 0.357 0.640 0.716 0.779 0.840 0.9831 0.726 0.425 0.207 0.158 0.120 0.0825 0.0083S va chm(2MeV 1eV)14.5 20 43 70 92 121 171 1747Cht lm chm H2O D2O He Be C U2381.53 0.170 0.176 0.06471 5670 83 143 192 0.0092] [1 cmsas510 6 . 1V.T.MaiVt l neutron v l phn ng63Tn x khng n hi (Inelastic Scattering)V.T.MaiVt l neutron v l phn ng64Tn x khng n hiV.T.MaiVt l neutron v l phn ng Nu nng lng ca neutron ti c ng nng ch kch thch mt vi mc trong ht nhn: cc neutron khng n hi xut hin trong mt vi nhm nng lng ri rc. Nu nng lng ca neutron ti cao kch thch nhiu mcXc sut neutron khng n hi s c pht ra vi nng lng trong khong t E n E+dE:( )/2E TEP E E dE e dET Trong , T l nhit ca ht nhn3.2 / T E A (3.8)(3.9)65Tn x khng n hiV.T.MaiVt l neutron v l phn ng Nng lng trung bnh ca neutron khng n hi:( )02E E P E E dET V d: U238 b p bi cc neutron 10 MeV, T= 0.66 MeV, nng lng trung bnhca neutron tn x khng n hi:1.32 E MeW (3.10)66V d : U-238V.T.MaiVt l neutron v l phn ng67 V.T.MaiVt l neutron v l phn ng68Mt lm chm (Slowingdown density)-Mt va chm:-Mt lm chm: q(E) s neutron/cm3 trn ton vng nng lng chuyn xung di Etrn 1 sec do tn x( ) ( ) ( )tFE E E (3.11)V.T.MaiVt l neutron v l phn ng69Cht lm chm khng hp (Slowingdown in hydrogen (A=1))30neutrons/cm sec of energyS E ( ) ( ) ( ),tFE E E (3.12)(3.13)0000( ) ( ) ( )( )EsEEES dE dEFEdE E E dEE ES dE dEFE dEE E + +00( )( ) :EES FEFE dEE E +Phng trnh lm chmTrng thi n nh (v khng hp th):Trit tiu , dEV.T.MaiVt l neutron v l phn ng70-Nghim ca (2.17),( ) ,( ) ( )sSFEESEE E(3.14)(3.15)-S dng khi nim mt lm chm,-So snh(2.20) vi (2.17),(3.16)(3.17)00( ) ( )EES E EqE FE dEE E +( ) ( ) qE E FE V t (2.18),( ) qE S ngha l,(3.18)V.T.MaiVt l neutron v l phn ng71Hp th cng hng (Resonance Absorption) Trong biu tit din hp th cng hng ca U-238 c mt dy hp th cng hng i vi neutron c nng lng. 10 1 keV E eV < < Trong thit k l phn ng, cn phi gii hn s hp th cng hng, tuy nhin, khng nn qu nh: hp th cng hngphn hi theo nhit ca hot l m Nhin liu ma trn trong (Inert-matrix fuel) : rt kh c th thit k nhin liu khng bao gm U-238.V.T.MaiVt l neutron v l phn ng72-M hnh l tng:-Ngun phn b ng nht S neutron/cm3.sec vi nng lng E0-Hn hp ng nht, v hn,-Phng trnh lm chm cho mt lm chmCht lm chm c cht hp thi) hydrogen (A=1); tn x n hi, khng hp th vii) Cht hp th U-238; khng lm chm0, 00001( ) ( ) ( )( )( )( ) ( )EsEEsEs aSFEdE dE E E dE dEE EE S dE dEFE dEE E E E + + + (3.20)Do :00( ) ( )( )( ) ( )EsEs aE S FE dEFEE E E E + + ( ) ( ) ( )tFE E E V.T.MaiVt l neutron v l phn ng73-Nghim ca (2.23),-Vit li theo nh ngha ca mt lm chm,Ngha l:0 ( )( ) exp : (2.18)( ) ( )EaEs aE S dEFEE E E E 1 1 + ](3.21)0 ( )( ) exp : (2.19)( ) ( ) ( )EaEt s aE S dEEEE E E E 1 1 + ](3.22)So snh (2.26) vi (2.23),(3.23)( ) ( ): (2.21) qE E FE V bi (2.24),0( ) expEaEs adEqE SE 1 1 + ]( ) qES0 ( )( ) expEaEs aqE dEpES E 1 1 + ](3.24)(3.25)(3.26)00( )( ) ( )( ) ( )EsEs aE S E EqE FE dEE E E E + + : Xc sut neutron ngun khng b hp th khi b lm chm t E0 xung E0: xc sut trnh hp th cng hng p(E) bi thng hp th l hp th cng hng:V.T.MaiVt l neutron v l phn ng74< Thng lng neutron sau 1 hp th cng hng >-PT. (3.22) : thng lng gim ti vng cng hng (hiu ng t che chn - energy self-shielding)aEV.T.MaiVt l neutron v l phn ng75- : nh cng hng thp hn v rng rng hnHiu ng Doppler i vi hp th cng hng( ) ( , ) E E T rurVneutronnucleus Khi nhit mi trng tng,0 at 00 at 0 ururV TV TV.T.MaiVt l neutron v l phn ng76-Thng lng gim t hn (t che chn gim)-Hp th cng hng tng (p gim)

a1 2< T T11TE121T 2TV.T.MaiVt l neutron v l phn ng77Hiu ng t che chnNhin liu + cht lm chmNhin liu (U235+U238)Cht lm chmL ng nht khng ng nht(H2O)-Nu nhin liu l mt khi, s hp th cng hng gim (p tng).( , )fissionrE ( , )resrE ( , )thrE V.T.MaiVt l neutron v l phn ng783.1 Tng quan Trong thc t , l phn ng thng bao gm cc cu trc khng ng nht, do yu cu phn tch bng l thuyt vn chuyn (transport theory) L thuyt vn chuyn:- Xem xt thng lng gc ca neutron thu c chnh xc hn gi tr v hng, trong :- Phng trnh ch yu cho: phng tnh vn chuyn Boltzmann- Phng trnh vn chuyn Boltzmann th chnh xc nhng kh khn v tn thi gian gii Mt l phn ng trong thc t thng c hnh hc achiu.3 Khuch tn neutron( )rr ( ) ( , ). r uur r urr d r (3.1)( , ) r urr ( , ) r urr V.T.MaiVt l neutron v l phn ng79 Tnh ton thit k l phn ng theo 3 tng: FkM1Global diffusion calculation : AB 12AB 12AB 12AAAA CC 12CCC 12CCB 12B 12AA AAB 8B 8B 8Diffusion calculationHomogenizedCondensedLocal transport calculationMultigroup librarygenerationAB 12AB 12AB 12AAAA CC 12CCC 12CCB 12B 12AA AAB 8B 8B 8CoreAssemblyCellLi l B nhin liu,V.T.MaiVt l neutron v l phn ng803.2 Phng trnh lin tc ca neutron (Neutron Continuity Equation) Cc qu trnh quan trng khi 1 neutron tng tc vi vt liu l: - Tn x (dn ti khuch tn v lm chm neutron) - Phn ng bt- Phn hch D liu ca cc phn ng c bn (s, , f ) c o c, nh gi v lu gi trong th vin ht nhn. Tc phn ng: S mt loi phn ng nht nh trn 1 n v th tch, trong 1 giy.V d :a Trong ( )a f + : macroscopic absorption cross section: neutron fluxa a Nn V.T.MaiVt l neutron v l phn ng81 S cn bng ca neutron n nng trong mt th tch bt k: A( , ) ( , ) ( , ) ( , ) ( , )aV V V Adn r t dV S r t dV r t r t dV J r t ndAdt r r r r r rrV( , ) : neutron currentJ d r ur ur r ur raV V V VndV SdV dV JdVt r:anS Jt r(3.2)(3.3)(3.4)(3.1b)( , ) : n r trMt neutron ti im r, thi gian tTrong :Phng trnh lin tc ca neutronV.T.MaiVt l neutron v l phn ng823.3 L thuyt khuch tn (Diffusion Theory) If we use the Ficks lawt, coefficien diffusion , D D J Eq.(3.3) becomesequation diffusion :1 + D St va(3.6)(3.5)D : i) measured in early days of reactor physicsii) now calculated from the transport theory that uses only basic nuclear dataS : neutron source For steady state, ; Boundary Conditions on aD S + 0 g (3.7) The Ficks law is not valid in highly absorbing media or near the boundary.V.T.MaiVt l neutron v l phn ngN.Z. Cho Introduction to Nuclear Reactor Theory 83 If the neutron source is from fission, then and Eq. (3.7) becomes an eigenvalue problem,,fS (3.8); Boundary conditions on, + ga fDk 10 multiplication factor, k-1 = : reactivitykkN.Z. Cho Introduction to Nuclear Reactor Theory 84 Vacuum boundary conditions(3.8a)1 1 i),to represent( ) ,from approximation,with .from a higher transport theory ii)102230 71sttdJ xdn dd D Pd '( ) iii)( )00ssx dx+ (3.8b)(3.8c)N.Z. Cho Introduction to Nuclear Reactor Theory 85Solutions of Diffusion EquationsExample 1 : Infinite planar source in homogeneous medium: S isotropic neutrons/cm2secFrom Eq. (3.7),( )22adD S xdx (3.9)Eq. (3.9) is equivalent to, , wheread Dx Ldx L 222 210 0(3.10a)[ ]lim ( ) :source conditionxJ x S02(3.10b)The solution is( )xLSLx eD2(3.11)N.Z. Cho Introduction to Nuclear Reactor Theory 86Example 2 : Point source in an infinite medium: S isotropic neutrons/secFrom Eq. (3.7),( )22 22aDd d Sr rr dr dr r (3.12)Eq. (3.12) is equivalent to,d dr rr dr dr L 22 21 10 0(3.13a)lim ( ) :source conditionrrJr S 1 ]204(3.13b)The solution is( )rLS erDr4(3.14)N.Z. Cho Introduction to Nuclear Reactor Theory 87Example 3 : Infinite planar source in a bare slab: slab thickness 2a, extrapolation distance d, planar source at center, S isotropic neutrons/cm2sec,dxdx L 22 210 0(3.15a)[ ]lim ( ) :source conditionxJ x S02(3.15b)The solution is( )( )( )a d xSinhLSLxa d DCoshL 1+ 1 ]+ 1 1 ]2(3.16)( ) ( ) :boundary conditions a d a d + 0(3.15c)N.Z. Cho Introduction to Nuclear Reactor Theory 88Example 4 : Bare slab reactor (thickness a, extrapolation distance neglected),where f adBdxBD k+ _ ,222201 1(3.18)From Eq. (3.8),a,B.C.: 2a fdDdx k _ + t ,2210 0(3.17)Eq. (3.17) is rewitten as(3.19)N.Z. Cho Introduction to Nuclear Reactor Theory 89To find the solution to Eq. (3.18), consider the following eigenfunction expansion method:a,B.C.:.2GdBdx _+ t ,2220 0(3.20)( )cos sincos ,Gn GnGnx A B x C B xA B x +(3.21)Therefore, the positive solution to Eq. (3.18) can be taken asThe solution can be represented bywith ,, , ,GnnB na 1 3 5 L(3.22)( )cos : fundamental eigenfunction,Gx A B x 1(3.23a)where: materials buckling = geometrical bucklingGB B 2 21(3.23b)N.Z. Cho Introduction to Nuclear Reactor Theory 90From Eq. (3.23b),ff aakD k aDa _ _ , , _+ ,221 1(3.23c)( ),R fP E dV r rwhere fission joules 10 2 . 3 fission 20011 MeV ERThe constant A in Eq.(3.23a) is determined from the power level of the reactor,If k=1, critical; k>1, supercritical;k( ) E N.Z. Cho Introduction to Nuclear Reactor Theory 96N.Z. Cho Introduction to Nuclear Reactor Theory 97 Then, we generate multigroup cross sections as( ) : evaluated nuclear data for nuclide for reaction type with neutrons of energy,( ) :scattering cross section for nuclideof ne jjsE jEE E jutrons from energy to energy,( ):neutron flux spectrum in the medium,:energy group index. E EEg( ) ( ) ( ) ( ), ,( ) ( ) g g gg g gg gg gE E Ej jsE E Ej jg sg gE EE EdE E E dE dE E E EdE E dE E 1 1 11 1(3.34)where Macroscopic multigroup cross sections are thenj j jg gN (3.35)N.Z. Cho Introduction to Nuclear Reactor Theory 98 We can write multigroup diffusion equations discretizing the energy variable into a number of groups.For water reactors, two-group approximation is usually used :( ) , 0 ) (12 2 1 1 1 2 1 1 1 1 + + + f f s akD(3.36a), 01 2 1 2 2 2 2 + s aD(3.36b)with appropriate boundary conditions.MeV 10eV 1 ~00E1E2E))F 1T 2WR : 2~4 groupsHTGR : 5~10FBR : 20~30N.Z. Cho Introduction to Nuclear Reactor Theory 99Example : Two-group flux distributions of a reflected slab reactorcore reflector reflector( ) b a + 2 2 a 2 a b a + 2Core region :( ) , 0 ) (12 2 1 1 1 2 1 1 121 + + + c c f c c f c c s c a c ckD (3.37a), 01 2 1 2 2 222 + c c s c c a c cD (3.37b)Reflector region :( )21 1 1 1 2 10,r r a r s r rD + (3.37c), 01 2 1 2 2 222 + r r s r r a r rD (3.37d)withi) BC:ii) Flux and current continuity conditions at ( ) [ ] ( ) [ ] 0 2 22 1 + t + t b a b ar r 2 a x t 2 a b a + 212N.Z. Cho Introduction to Nuclear Reactor Theory 100Table : Representative two-group data for LWRsD1(cm)a1(cm-1)s12(cm-1)f1(cm-1)D2(cm)a2(cm-1)f2(cm-1)UO2 fuel cell 1.2 0.010 0.020 0.0050 0.4 0.100 0.125MOX fuel cell 1.2 0.015 0.015 0.0075 0.4 0.250 0.375Water reflector 1.2 0.001 0.050 0 0.2 0.040 0Control rod cell 1.2 0.040 0.010 0 0.4 0.800 0N.Z. Cho Introduction to Nuclear Reactor Theory 101 In multi-region reactors, we resort to numerical methods to solve two-group diffusion equations; rewriting Eq. (3.36) in an iterative form as( ) ( ) ( )( )( ) ( ) ( ),,21 11 1 1 111 1 12 2 2 2 1 2 11t t tr fg gtgt t tr sDkD + ++ + + + + (3.38a)( )( )( ) ( )( ) ( )( ) ( ),,21 11 1211 : power method,t tfg g fg gg t tt tfg g fg ggk k + + ++ (3.38b)(3.40)withEqs. (3.38a) and (3.38b) are in a same form of.rD Q + Eq. (3.40) can be discretized by a finite difference method (FDM) for numerical solution.(3.39)where is iteration index, t , , , , . 0 1 2 3 L t N.Z. Cho Introduction to Nuclear Reactor Theory 102Example : Cell-centered FDM for a one-dimensional slab problem( ) , + +i i i i iii id dxd d 1 112(3.41)By balancing neutrons in a cell ( integrating Eq. (3.24) over cell i ) and enforcing continuities of flux and current at the cell interface, we have in terms of cell-average flux,1iNi00 d 1d114Nd+NdiiiDd reflectiveB.C.vacuumB.C.( )( ) +i i ii i ii id dJ xd d 11122(3.42)N.Z. Cho Introduction to Nuclear Reactor Theory 103, , ,,1 1 1 1 i i i i i i i i i i ia a a Q + ++ + (3.43)and Eq. (3.24) becomes, where, ,, ,,,,.11 1111 111 11 120202 20i ii i i ii ii ii i i ii ii i i ii i ri ii i i id da ad ddda ad dd d ddad d d d ++ ++ + +