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Reactor Physics

Reactor Physics
Prepared by D. Hummel David Novog (Ph.D., P.Eng.) Associate Professor McMaster University (Canada) 1 m • Nucleus consists of: protons (positive charge) neutrons (no charge) • Surrounded by cloud of electrons negative charge memp,mn • of protons (Z) define the element • of protons + of neutrons (N) define the isotope (A) • Notation: X chemical symbol International Atomic Energy Agency .,) 2 efrici • The observed mass of a nucleus is smaller than the sum of its parts: L1 = zmP +(A Z)mn Amz • The mass deficit() has an equivalent energy (from E =mc2) called the binding energy ( 8 == 11 c2) • Nuclear reactions that result in a net release of energy (B) include: fusion of two small nuclei fission of a large nucleus International Atomic Energy Agency .,) 3 clear ergy 9 U25 Fess • .,..u2a E released from 1:: 0 6 fission ID (j =:1 1:: .. 5 Q) c.. 4 ID E released from ;:;: a;. C) fusion 3 1:: H3 =c , He .5 ..0 2 a C) H:2 ()); 1 H1 0 90 0 .30 60 1:20 150 190 :210 :240 270 Number of nucleons In nucleus Original Image Source: Adriaan Buijs, EP704 Advanced Reactor Physics, Course Notes, McMaster Univetkf009. International Atomic Energy Agency 4 • • ce I I • It is possible for a heavy nucleus to fission on its own, but it is very rare (low probability of occurrence) • Many elements fission readily when the nucleus absorbs an additional neutron • Classify these materials as: fissile: fissions readily with a low energy neutron e.g.: 233l/ 235ll 239JJL/ 92 92 94 fissionable: fissions with a high energy neutron e.g.: 238l/ 92 fertile: absorbs a neutron to become a fissile material e.g.: 232Th233ll 23sl/239fJll 90 92 92 94 International Atomic Energy Agency .,) 5 ele n • A neutron may undergo several different reactions with a nucleus, including: Scattering (elastic or inelastic): there is a transfer of energy between the neutron and the nucleus Absorption: the neutron is absorbed into the nucleus and lost Fission: the neutron causes the nucleus to fission, releasing additional neutrons and fission products • The likelihood of an interaction occurring is represented 28 2 with a microscopic cross section (a) 1 barn (b)== l0 m Dependent on the isotope of the interacting material (and its temperature) Dependent on the incident neutron energy International Atomic Energy Agency ) 6 • • I I n I I .. I f ® f I n .. n.. International Atomic Energy Agency .,) 7 ergy • Neutron energies cover 10 orders of magnitude: Fission spectrum Delayed spectrum Moderation • Interaction cross sections may change by 5+ orders of magnitude over this range of energy. • Need to solve neutron evolution over these ranges. • OPTIONS 7 Full transport (absorption, moderation, fission) at each "point" in the reactor (i.e., continuous energy solution). Transport over "Groupwise" energies (i.e., "multigroup cross sections). Diffusion over "Few" groups (i.e., 2group diffusion solvers such as SCALE) What is the relative calculation times for these approaches International Atomic Energy Agency ) 8 • the energies range up to several MeV, with a 0.4 maximum around 0.7 MeV. • The fissionneutron spectrum 0.2 has the form 0.1 036 x( E)== 0.453e1. £ sinh .J2.29 E (1) 2 4 6 8 10 Energy (MeV) (a) where E is in MeV Energy Distribution of Fission Neutrons (Note: this is a distribution in Note Illustration copyright: number of neutrons, not flux) Copyright 1985 by American Nuclear Society, La Grange Park, Illinois International Atomic Energy Agency .,) 9 • e erg1e • Neutronic energy distribution can be classified as: the fission spectrum at energies above about 50100 keV the slowingdown spectrum to about 1 eV the Maxwellian spectrum at thermal energies, below about 1 eV International Atomic Energy Agency ) 10 • • 235 I I r n E:HDF Request 92309. 2009Jul17.1l :S1:11 5 to ao 10 1 Fast range Epithermal energy range Thermal energy range to 1 1. 1 Incident Energy ( IMeU) Original Image Source: Adriaan Buijs, EP704Advanced Reactor Physics, Course Notes, McMaster Univl 2009. International Atomic Energy Agency 11 • erma I I Fast Neutrons Thermal Neutron 1 eV 3 10 m/s Heat 1 MeV Fission 7 10 m/s Products Original Image Source: Jeremy Whitlock, Powering Ontario: The Nuclear Solution, Presentation to the UofT Nuclear Power Group, 2005. . International Atomic Energy Agency (y) 12 e KEVCQ • Most neutrons born from fission are in the fast range (high energy) • To sustain a fission chain reaction, the fast neutrons must be brought down to a lower energy (where a fission is higher) via interaction with a moderator • Thermal reactor • Neutrons transfer their "excess" energy to the moderator through series of scattering interactions I collisions • Good moderators have: Low absorption cross sections cr absorption Low atomic masses (to maximize E in a single interaction) International Atomic Energy Agency ) 13 Fast Thermal Neutrons Neutrons 235U Fission Products Original Image Source: Jeremy Whitlock, Powering Ontario: The Nuclear Solution, Presentation to the UofT Nuclear Power Group, 2005. ) International Atomic Energy Agency 14 e ergy N tl\fJ1,wJ.t""' r"c.K 1\.A."" N'\,0"' F £ p:., k...w. c..l (A A,:.. l'ie........kiV''"') ) I 1 IO . 0 International Atomic Energy Agency ) 15 • The reactor is critical when the number of neutrons produced in each generation is equal to the number lost • The multiplication factor is defined as: k= rateot neutron production rate of neutron loss k 1 : the reactor is subcritical k = 1 : the reactor is critical k 1 : the reactor is supercritical International Atomic Energy Agency .,) 16 an elaye e • Neutrons that are released immediately after the fission occurs are referred to as prompt neutrons • Most fission products are unstable nuclei that undergo radioactive decay • Following radioactive decay, some daughter nuclei may have sufficient energy to release additional neutrons called delayed neutrons Time constants for release of delayed neutrons are dominated by the half life of the unstable fission product • Delayed neutrons must be included in analysis International Atomic Energy Agency ) 17 ce e • Direct fission neutrons have a "lifetime" Neutrons born in fission interact with • moderator (scatter/absorption) • core materials (absorption). • Fast fission materials Their "lifetime" is very short. Control of such a system is very difficult (mechanical and IC systems cannot respond on this timeframe). • Delayed neutrons have time scales much longer (order of seconds) . A thermal reactor is designed such that the reactor is slightly "subcritical" based on direct fission neutrons alone. The delayed neutrons provide the remaining neutrons to make the core critical. • Therefore control of the reactor can be achieved through changes in the delayed neutron absorption. International Atomic Energy Agency ) 18 • Define reactivity as the relative distance from criticality: 1 p==l k p 0 : the reactor is subcritical p = 0 : the reactor is critical p 0 : the reactor is supercritical • Units of reactivity 1 mk == 0.001, or 1 pcm == 0.01 mk are typically viewed as being added or removed from the reactor International Atomic Energy Agency .,) 19 • IC The goal of reactor physics calculations is to track neutrons as they evolve in space, energy and time. This allows redictions of ower, radiation levels, decay heat. ... etc .. • Fundamental assumptions of most reactor physics analysis: The average behaviour of neutrons is descriptive Neutrons do not interact with one another International Atomic Energy Agency ) 20 ac rr • To study the fission process, many physical features can be understood by examining the 4factor formula: kif) = cpflJ • Which can be derived form the diffusion equation. 1 vl: 1 + vl: 1 total fission rate f = 2: ; D = rate of thermal absorption in fuel 2 1 2 11 12 B = 2: n '1 D , total rate of thermal absorption s vl: . , thermal .fission rate f L a2D2 2.:slt212 p = L al Dl + 2.:sl211 l.: alDl + Ls12Ql rate of ,s :lovving dovvn rate of neutron production through thermal fission rate of slowing down + absorptions rate of thermal absorption International Atomic Energy Agency .,) 21 I e • Fundamental quantity is the z angular neutron flux density . 1n CD( r, E, n, f) Space (position r) Energy (E) Direction (solid angle Q) y Time (t) .. .. .. .. .. .. • Also expressible in terms of the neutron density Image Source: Daniel Rozon, "Chapter 2: The Diffusion Equation and the Steady State" in Introduction to Nuclear Reactor Kinetics, Ecole Polytechnique de Montreal, 1998 CD( r, E, n, f) == v n( r, E, n, f) neutro:::locity V= IT m: International Atomic Energy Agency .,) 22 • acr IC r n • Define the macroscopic cross section as: L(r,E,t) = N(r,t)CY(EJ cm1 density of nuclei microscopic cross section in a volume • L represents the probability of a reaction taking place • The reaction rate for any given reaction is simply: R==LcD International Atomic Energy Agency .,) 23 e • Posit that the rate of change of the neutron density in a volume is the sum of all neutron sources and sinks/losses Neutrons changing energy Neutrons lost via scattering/collision from leakage Neutrons born 0 in fission 0 Neutrons lost from absorption D ==Vn (£,0,0 (£,0,0 International Atomic Energy Agency .,) 24 e rr n neutrons lost via neutrons lost via angular neutron scattering and absorption leakage flux density ':V ==L...( Etl O·Vl V 0 f (r, E,D.,t) r, ' ) ( r, E,D.,t) (r, E,D.,t) 00 neutrons gained + f L s,(r, E'+E,t) P (r,E,fl,t) d f' via scattering 0 00 + V' f v L l dE' neutrons born in fission A/( f) Pc f') f(r,E',t) (r, E,D.,f) 0 + s(r,E,f) I delayed neutron other sources source International Atomic Energy Agency .,) 25 g e n e • The neutron transport equation can be solved with appropriate selection of initial and boundary conditions Some initial neutron flux distribution Vacuum, reflective, white or periodic boundaries • Typical approaches to solution are: Deterministic: discretization in space and energy with direct numerical solution (e.g. WIMSD, DRAGON) Stochastic: solution via Monte Carlo methods (e.g. MCNP, KENO, SERPENT) • Often looking for steady state flux distributions isotope depletion (burn up) evolved separately in time Used an initial condition for kinetics calculations. £J..) International Atomic Energy Agency 26 a ell PWR MOX fuel assembly 0 00 00 00 0 00 00 00 00 0 Neutron transport solutions are • 0 00 00 00 0 00 00 00 00 0 0 00 00 00 0 0 00 00 0 0 00 0 00 0 000 00 00 0 computationally intensive 0 00 00 00 0 00 00 00 00 0 0 0 00 00 00 00 00 0 00 00 00 0 00 00 00 00 0 0 00 00 000 00 00 00 00 0 0 0 00 00 00 00 00 • Solution normally constrained to 0 00 00 00 0 00 00 00 00 0 00 00 00 0 000 00 00 00 0 0 0 00 00 00 00 00 two dimensional models of single 0 00 00 000 000 00 00 00 0 00 0 00 00 0 00 QO Q 0 00 00 00 00 0 00 00 fuel assemblies or lattice cells 0 00 00 00 0 000 00 00 00 0 00 00 00 0 000 00 00 00 Image Source: SERPENT 1.1.7, VTT Technical • Can also create three Research Centre of Finland, 2010. Typical CANDU Supercell dimensional models of several lattice cells (called supercells) Useful for finding reactivity worth of control devices in the reactor ' . Image Source: Ben Rouben, "CANDU Fuel Management" in EP6003: Course Notes, McMaster University, 2009. (s.O...) International AtOmic Energy Agency 27 • I r • The quantity necessary to calculate the actual reactor power is the scalar neutron flux density 4;r ¢( r, E, ) = f I( r, E, 0, t)tfQ = vr( r, E, ) 0 • To solve the new equation we approximate the leakage term as a diffusion process 4;r f ( Q · VI( r, E, 0,) fn+ +V. D( r, E)V ¢( r, E,) 0 International Atomic Energy Agency .,) 28 • e I a neutrons lost via neutrons lost via scalar neutron scattering and absorption leakage flux density 1 a ¢(r, E, f)== 'L(r, E, t)¢(r, E, f)+ \7 · D(r, E)\7 ¢(r, E, f) vat 00 neutrons gained J ( f' E f)( E f) dE' via scattering + LJ s r, ' (j/ r, ' 0 00 neutrons born in tission + X p( E) J v p( E' )L , ( r, E', )¢( r, E, f) dE' 0 + Sd( r, E, f)+ S( r, E, f) I I delayed neutron other sources source International Atomic Energy Agency .,) 29 n • By assuming that leakage out of the unit cell is describable by diffusion, we've assumed a high level of isotropy in the neutron flux • This assumption breaks down: At material boundaries and the external boundary of the domain Near localized sources In highly absorbing materials • The high fidelity of a neutron transport solution is lost Must use unit cells much larger than the mean free path of a neutron with homogenized properties within the cell. Homogenization + "representative" properties for a "large cell" that give similar results as a more detailed calculation. .At International Atomic Energy Agency (y) 30 • e ifrl I a 3D Neutron Flux Map for CANDU • Codes that solve the diffusion equation allow three dimensional ) ) I 1 1 1 I 1 I 1 1 1 1 1 1 1 I I .) 0 J l I 1 i 1 1 I I I 1 1 1 1 I I I I I simulation of entire reactor cores I' J 1 I 1 i 1 1 1 1 1 I 1 1 I 1 I I I I 1 J 1 F J J 3: I 1 1 1 1 1 1 1 I 1 1 1 1 1 I I I 1 J J l J I J ) I 1 1 1 1 t 1 1 1 1 1 1 I 1 I I I 1 I J J H l l l I I 1 1 1 t 1 1 1 1 1 1 1 1 I I I 1 l l l J 1 J 3 I I I I 1 1 1 1 1 I 1 1 1 1 1 I I 1 3 1 3 e.g. PARCS, DONJON K I J 3 I I 1 1 1 I 1 I I 1 1 I 1 1 I I I 1 J J l L l J J I 1 I 1 1 I 1 1 I 1 1 I I 1 I I I 1 l l l It l l ) I 1 1 1 1 1 1 1 1 1 1 1 1 1 I I I 1 ) l l r.1 l l S I I 1 1 1 1 1 1 I I I I I I I I I 1 l l l Suitable for accident analysis and 0 J l I 1 I 1 1 I 1 I 1 1 1 I 1 1 I I I 1 l l P J l S I I 1 1 1 1 1 1 1 1 1 1 1 I I I 3 l l Q l l 1 I 1 1 1 1 1 1 1 I I 1 1 I I I l J refuelling calculations , 3: l 1 1 1 1 1 1 I 1 1 1 I 1 I I l l , l l l , 1 1 1 1 1 1 1 1 1 ) ) l l l 3 J l • Typically neutron energy is collapsed into few characteristic groups e.g. fast/thermal or more • Neutron transport codes are used to supply the collapsed few group homogenized cross sections in unit cells suitable for the diffusion Image Source: D. Sekki et al, A User Guide for solution DONJON Version 4, Ecole Polytechnique de Montreal, 2011. International Atomic Energy Agency ) 31 e • • Kinetics calculations are used to: Assess the neutron (power) behaviour in space and time over relatively shorter time scales Linkage to thermalhydraulics changes Safety and stability analyses. Point vs. 3D reactor kinetics. • Depletion calculations: Determine the slower evolution of physics 7 determine the change in composition of the fuel with burnup. International Atomic Energy Agency ) 32 • In "point kinetics", only the behaviour of the reactor as a whole (i.e. a "point") is considered • Furthermore, only "short time" phenomena are relevant Neither the core composition or flux "shape" are expected to change quickly relative to the total power or "amplitude" The flux and macroscopic crosssections over the entire reactor are thus homogenized or averaged as: ¢( r, E, f) = ¢(f) == n( f) v "L(r, E, f)= "L (constant International Atomic Energy Agency .,) 33 e • Again, express the rate of change of the neutron density as the sum of all neutron sources and sinks/losses Neutrons lost from leakage (diffusion: Dlf¢ Neutrons born in fission 0 " 0 0 v'L,¢ Neutrons lost " from absorptionL a¢ " 1 d¢ ( Q)¢ == VL L DB 1 V df a International Atomic Energy Agency .,) 34 • • e I I • The delayed neutron precursors are homogenized into a finite number of "groups" with characteristic yields and decay constants: " 1 d¢ ( \1 === vp'L,'LaD9JP+LAkCk v dt k • The concentration flf:k each group evlves over time as: == AkCk + vdk'L ,¢ dt International Atomic Energy Agency .,) 35 • • elaye e 1n I 235 • For the thermal fission of U typically use k== 6 0.0380 0.0133 0.1918 0.0325 vd=0.0166 0.1638 0.1219 0.3431 0.3169 0.1744 0.9886 fJ = 0.00682 0.0890 2.9544 International Atomic Energy Agency ) 36 • Effective multiplication factor V==Vp+Vd k neutrons created vL, ett neutrons lost La+ Dlf • Reactivity (or "distance from criticality") kef l VL La D If 1 p== kef VL 1 • Prompt neutron generation time A== 1 VvL 1 • Delayed neutron fraction K vdkL t f3k == f3 == LPk VL t ·Al k=I International Atomic Energy Agency (y) 37 e n • With some rearrangement, we get the classical form of the point kinetics equations: d(/J = (p f3) ;;, + "A, c . dCk ==A C + f3k :A dt k k A 'f/ dt A 'f/ k k' International Atomic Energy Agency .,) 38 • 1ng • The point kinetics equations are relatively easily solved as a system of k+ 1 equations • Point kinetics is typically used to easily determine the relative change in reactor power from insertions of reactivity • Many heat transport system thermalhydraulic codes (e.g. RELAP5, TRACE) contain point kinetics solvers International Atomic Energy Agency ) 39 3 • Often in Safety Analysis, the flux distribution can evolve very quickly (e.g. rod ejection event), and hence the neutronic behaviour may show "local" effects. • In such cases treating the core as a "point" in point kinetics may not be sufficiently accurate. • Need for 30 kinetics calculations Solve the diffusion equations in space and time. • See Lecture of THRP coupling International Atomic Energy Agency ) 40 T / r .. : 21£1.M.5D•C 11 Core Design Ccrslnl Power Rrrtili Low avera ge density· in the core .... . , o l na an Zl't Fast core is The rmal core needs possible dedicated moderator O:d•nl mm cf,.j. I I I .,rru:l: (D 57 · I I I :ir I "" c m I Fuol I :i2.11Mm r From Danielyan, 2003. International Atomic Energy Agency .,) 41 • w e n1c • A majority of work on SCWR is centered around a THERMAL DESIGN. • Important features: Fuel Moderator Structures • The SCWR coolant can be classified as either Gas like Liquid like The differences greatly affect the absorption/moderation characteristics. • Main difference in physics issues Doppler broadening of resonances Coolantdensity effects "Harder" Neutronic spectrum as compared to typical thermal reactors. Moderation International Atomic Energy Agency ) 42 w 1 • In many designs (e.g., HPLWR), the coolant enters the core in its "liquid" like state. Part of this "liquid like" coolant is first directed through "water boxes". The water boxes provide moderation to the surrounding assemblies • After passing through the water boxes, the coolant then travels through the fuel assemblies to remove heat. As its enthalpy rises in the fuel region 7 transitions to the "gas like" state. Rapid change in moderation/absorption cross section due to the rapid change in the density. Density feedback effects 7 Need for coupled neutronics­ thermalhydraulics. International Atomic Energy Agency ) 43 assembly box fuel p1 ins w1 re wrap from feedwater tank Koehly, 2009 J . Starflinger, FZK, Presentation at McMaster University, June 9, 2009 International Atomic Energy Agency .,) 44 e Control rod Honeycomb structures Water box wall Fuel rods with wire wraps Assembly box wall with holes Herbell, EnBW, Himmel, FZK, 2007 International Atomic Energy Agency .,) 45 2 • The heavy water type thermal reactors utilize separate moderator coolant systems (e.g., CANDU­ SCWR) Allows for moderator to be in a fuei subcritical fluid regime. ohannls No mixing of coolant and moderator Control and safety devices are not inserted into the high pressure region fttetliflj manlflima of the core. Cold moderator (60C) • Pressure tube isolates the coolant/fuel region from the International Atomic Energy Agency .,) 46 moderator tank. era I e • Insulate pressure tube on the ins1 ide. • Remove calandria tub· e. • Insulator thickn.ess \IOOii..l'tU OR. optimiz ed to obtain Usual heat oss by conduction/convec .ion to IN5ilh ;\TOll: PlRJ'O \. niD r.1 iii'. It the .moderator under normal operat·on. Sufficient heat reje·c.t1 ion by radia ion/conduction/ con·vection under accident conditions. International Atomic Energy Agency () 47 • e e li S) Cell Bo tundary ..1 Moderator Pressure Tube Insulator Coolant 21 fuell element ring 14 fuell element ring 7 fue ll ellement ring Dysprosium central ning ==================================== 48====•ncy(. ce el el: •Eliminate the calandria tube •Insulate the inside of the pressure tube Heavy Water Moderator coolant moderator temperature temperature / Calandria Tube Fuel Bundle Porous Insulator Heat deposited in moderator 5 (neutron/gamma Heat deposited in moderator 5 (neutron/gamma heating); 0.1 through gas gap heating + 1 through insulator International Atomic Energy Agency nc g em ark • SCWR neutronics has no "new" or unique physics to be modelled. • Rather the geometry, temperatures, properties are different. • While many physics code can perform calculations under these conditions 7 the accuracy and validity of the results has not been rigorously demonstrated. Higher fuel and moderator temperatures Harder neutronic spectrums • In addition to more calculations, there is a need for validation. International Atomic Energy Agency ) 50
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