核能發(fā)電物理

1、1OverviewHow a Fission Reactor works: Avoiding Chernobyl 2Energy from fissionNuclear energy can be released from any reaction (e.g. fusion, fission etc) if it yields an increase in total binding energy (same as) a decrease in total mass Thus: mass converted to energy (E=mc2)Number of nucleons, ABind

2、ing Energy per nucleon (MeV)Energy from fissionEnergy from fusion3Energy from fissionE.g. one 238U nucleus (Z=92) splits into two 119Pd nuclei (Z=46): apply conservation of mass-energyWhere Q = energy released. 21192382119223822cQPdMUMQcPdMcUMuPdMuUM922705.118 ,050785.238119238so Q/c2 = 0.20538u, 1u

3、= 931.5 MeV/c2, so Q = 191 MeVNote: Q is positive i.e. energy is released (mass is reduced) Enormous energy released mostly in KE of fission fragments4Energy from fissionQuestion: Why doesnt 238U simply fission spontaneously? It obviously wants to!In fact, Q +ve for most nuclei over A=100, so why do

4、nt they ALL fission?Consider pot energy of two “separating” 119Pd fragmentsEnergyQ MeVSeparationCoulomb potentialNuclear PotentialFission barrier, D5Neutron-induced fissionSo, nucleus needs to be given energy (D) before it can fission. Where can you get it from?Consider “firing” a neutron at a 235U

5、nucleus to make it fission(this is a typical fission reaction from 235U). For this fission event, D D=6.2 MeV. Now, look at the first stepFrom the masses, we find that Q = 6.54 MeV 236235QUnUfQnCsRbQUnU2Simply absorbing the neutron provides enough energy to cause fission Thus, 235U is F

6、ISSILE How many naturally-occurring fissile nuclides are there? 238U, however, is FISSIONABLE. Q is not quite enough, needs a bit more energy6Neutron-induced chain reactionNow a chain reaction is feasiblefQnCsRbnU2 14193235Energy released = 178 MeVOne of these (on average) needs to go on to cause an

7、other fission eventLooks easy ! Put a large lump of 235U together, and relax to enjoy fireworks !However. other things can happen to neutrons natural U is 0.715% 235U (fissile) and 99.285% 238U (fissionable)7Neutron-induced chain reactionNeutron interactions Fast fission neutrons (2MeV) are emitted

8、in an amount of Uranium Different probabilities of different interactions Probability called a cross-section (s) measured in “barns” (b)1. Scattering (elastic and inelastic) simply reduces energy of neutron as travels though material. s s few barns2. Radiative Capture neutron absorbed by nucleus, wh

9、ich then decays by beta and gamma decay . s s 0 to 1000s barns3. Fission neutron induced fission. s s 1 to 500 barns, increasing as energy reducesFast energies (MeV)Thermal energiesCapture resonances8Nat. UNat. Usf) bs(i) bs(r) b238U0.62.90235U1.32.30NatU0.612.90Neutron-induced chain reactionLook at

10、 cross-sectionsFast neutrons (2MeV)fission scatt. captureThermal neutrons (kT 0.02 eV)fission scatt. capturesf) bs(i) bs(r) b238U002.72235U5790101NatU4.1303.42Chain reaction feasible at thermal energies IMPLIES Neutrons slowing down to thermal energies NOT in uranium (avoid capture resonances)captur

11、e9LOSSES FROM CHAIN REACTIONFast neutrons from fissionSome fission in 235U + some capture in 235/238USome fast fission in 238Un-flux increases by factor e eSlowing down in fuel and moderatorFraction not leaking out PNLfLeakage of fast neutrons from coreSlowed to 10eV1keVFraction not captured = pRadi

12、ative capture in 238U resonancesThermal neutronsFraction not leaking out PNLthLeakage of thermal neutrons from coreThermal neutrons absorbed in coreFraction absorbed in fuel = fThermal neutrons captured in non-fuel material (e.g. moderator)Number of neutrons emitted per neutron absorbed in fuel = h

13、hFor stable chain reaction, k= PNLFPNLthepfh = 1Neutron-induced chain reaction10Thermal ReactorComponents of a reactor:Fuel: Uranium (usually enriched with more 235U, sometimes natural) Often in UO2 form, surrounded by cladding, usually rods.Moderator: Needs to be efficient in thermalising neutrons,

14、 small number of collisions so, A needs to be small (n 18 for H, 115 for C) Needs small capture cross-sectionCoolant: For carrying away energy to heat exchanger for turbine Needs small capture cross-section 211 where,1ln1/lnAAEEnfi11Magnox Reactor (UK being decommissioned)Control Rod channels - Boro

15、n steel rodsGraphite moderatorConcrete shieldCO2 coolant circulating at 360oCFuel Rods - Nat U metal, magnox claddingHeat exchangerSteam to turbines and water returnPressure Vessel12Pressurised water reactor (typical existing)Concrete shieldH2O moderator/coolant circulating at 320oC and 150 atm pres

16、sure.Fuel Rods - UO2 3% - 4.5% enrichment , steelSteam generatorSteam to turbines and water returnControl Rod channels - Boron steel rodsPressure Vessel13Reactor control and design Physics in Action Stable reactor runs at k=1 (critical) Controlled by insertion, retraction of control rods (high captu

17、re c.s.)How stable is a reactor? How quickly can a reactor respond to small transient changes in k? Sudden catastrophic incidents?Physics in Action PART I: Late (delayed) neutrons 14Reactor control and design Physics in ActionHow long do we have to respond if reactor goes super-critical?Determined b

18、y: Time between emission of prompt neutron and absorption in reactor (prompt neutron lifetime, tp), and Degree of super-criticality (k-1)tp = thermalising time + diffusion time (thermal neutron “walk”) 10-5 s 10-3 sSo, time between neutron “generations” milliseconds15Reactor control and design Physi

19、cs in ActionNeutron flux (and hence power) in a reactor varies with time approximately asFor very small excess criticality, k-1 = 0.001, and tp 1ms, power increases ase10 increase in power in 10 seconds 22,000!Would be impossible to control, but physics comes to the rescuetknnpt1exp0 tntnnexp001.000

20、1.0exp001687Br87Kr87Rb87Sr87Kr*neutron86Krb b-b b-b b-b b- Not all neutrons in a reactor are prompt fission neutrons Some fission fragments are very rich in neutrons Can beta-decay to nuclear states which emit neutronsReactor control and design Physics in ActionFor example.Half-life of 87Br is 55.7s

21、Mean time for emission (then absorption) of this neutron after fission is 55.7/ln2 80 secondsNOT 1 ms 17Reactor control and design Physics in Action0.6% of all reactor neutrons are beta-delayed, average lifetime 12.5 seconds, so for ALL neutronsSo, small excess criticality, k-1 = 0.001, and teff 80m

22、s, power increases ase1.3 increase in power in 10 seconds 3.7 (not 22,000) MAKES reactors controllable as well as.ssseff076.05.12006.0001.0994.0ttntnn132.0exp076.0001.0exp00Prompt Late18Reactor control and design Physics in ActionConsider 238U capture resonancesAtoms vibrate in lattice site, neutron

23、 energy in centre of mass oscillates “smudges” resonance energyneutron238UHigher temperature oscillations increase broader resonancesneutron238Usrneutron energyPhysics in Action PART II: “Thermal Feedback” 19Reactor control and design Physics in Action Super-critical reactorPower increasesTemperatur

24、e increasesResonances broadenmore resonant captureNeutron flux reducesPower reducesTemperature reducesResonances narrowless resonant captureNeutron flux increasesNatural thermal feedback mechanism.20Reactor control and design Physics in ActionHow much fuel - how much moderator? Too much moderator th

25、ermal neutrons more likely to be captured by moderator nuclei Too little moderator, and neutrons re-enter fuel before thermalised can be captured by the resonances. Moderator/fuel ratio crucialHomogenous Cubic U-Graphite reactor - 1.6% enrichment2030405060708090100400500600700800M/FMass of fuel (ton

26、nes)Super-criticalSub-criticalOptimum M/Fover-moderatedunder-moderated21Reactors SAFER if theyre under-moderated Imagine what happens if a “hole” (void) appears in a reactor E.g. coolant leaks out E.g. power runs away and water boils (bubbles appear) E.g. act of terrorismUsually, if VOID appears les

27、s moderation (all materials, esp. water, are moderators) some neutrons dont slow down capture in resonances fewer neutrons cause fission, reaction dies out called “NEGATIVE VOID COEFFICIENT” ESSENTIAL design featureReactor control and design Physics in Action22Homogenous Cubic U-Graphite reactor - 1

28、.6% enrichment2030405060708090100400500600700800M/FMass of fuel (tonnes)Super-criticalSub-criticalover-moderatedunder-moderatedABReactor control and design Physics in ActionMake sure of NEGATIVE void coeff under-moderated reactor23ChernobylChernobyl accident, 26/04/1985 at 0123 48s 1GW power reactor

29、, graphite moderated, 1.8% enriched fuel, water-cooled, direct water cycleExperiment performed to improve safety. Many operator errors, over-rides, etc caused the following conditions Reactor was running at 7-10% of full power Control rods fully withdrawn Emergency core cooling system had been disco

30、nnected At 0123 10s, operator error caused sudden rise in temperature steam bubbles formed. “voids”24Super-criticalSub-criticalChernobylChernobyl reactor was over-moderated.Temp rise steam bubbles voids “l(fā)oss of moderator”BUT at low power.25ChernobylLessons basic design flaw must be avoided automati

31、c “drop” control rods containment vessel on all reactorsReactors for the future Probably no more graphite-moderated reactors Almost all being built are water-moderated and water-cooledPressurized water reactorsBoiling water reactorsHeavy-water (D2O) reactors 26Web site for further reading.http:/.au

32、Australian Site wealth of papers on world status of nuclear power International Atomic Energy Authority links to many technical documents Nuclear Industry Association (UK)Many resources on the web for nuclear energy: the following are general sites and good place

33、s to start.27Energy from fissionE.g. one 238U nucleus (Z=92) splits into two 119Pd nuclei (Z=46): apply conservation of mass-energyWhere Q = energy released. 21192382119223822cQPdMUMQcPdMcUMuPdMuUM922705.118 ,050785.238119238so Q/c2 = 0.20538u, 1u= 931.5 MeV/c2, so Q = 191 MeVNote: Q is positive i.e

34、. energy is released (mass is reduced) Enormous energy released mostly in KE of fission fragments28Energy from fissionQuestion: Why doesnt 238U simply fission spontaneously? It obviously wants to!In fact, Q +ve for most nuclei over A=100, so why dont they ALL fission?Consider pot energy of two “sepa

35、rating” 119Pd fragmentsEnergyQ MeVSeparationCoulomb potentialNuclear PotentialFission barrier, D29Neutron-induced chain reactionNow a chain reaction is feasiblefQnCsRbnU2 14193235Energy released = 178 MeVOne of these (on average) needs to go on to cause another fission eventLooks easy ! Put a large lump of 235U together, and relax to enjoy fireworks !However. other things can happen to neutrons n