neutrons perform the alchemist’s magic asthey convert “fertile” fuel incapable ofsustaining a chain reaction into “fissile” fuelat a rate faster than needed to replace theoriginal fuel. Hence, in a breeder, not only isenergy generated, but excess fuel is “bred.”

But can the transformation process beadequately controlled? Physicists andengineers have long recognized that during

certain hypothetical, low-probabilityaccidents a burst of neutron productioncould generate a damaging surge of energyand pressure resulting in a potentially largeradiation release to the environment.

Thus, a s t r o n g a t t a c k o n t h e s ehypothetical accidents has been mounted,both to prevent them and to understand theirconsequences. An important analytical toolnecessary for this understanding wasdeveloped over the last six years by theEnergy and the Theoretical divisions at LosAlamos National Laboratory. The tool,SIMMER,* is a complex computer code thatexamines the dynamics of a typical breedercore when disrupted during hypotheticalaccidents. The core being studied is that of aliquid-metal fast breeder reactor, the breederof primary focus in the United States sincethe 1960s. The code couples an accountingof neutron population and power generationwith a fluid-dynamic calculation of thebehavior of all core materials. Initiallyconsidered an almost impossible problem,the development of this code is leading to amore realistic assessment of the safety ofliquid-metal fast breeders based on detailedknowledge concerning the temperatures,pressures, energies, and mass flows in adisrupted core.

The conclusions so far? The pressure andtemperature surges expected in hypotheticalaccidents appear to be much less thanp r e v i o u s l y e s t i m a t e d . A s a r e s u l t ,management of this sophisticated alchemy

*SIMMER is an acronym for Sn, implicit,multifield, multicomponent, Eulerian,recriticality.

100

Fig. 1. When neutrons are absorbed by fissile atoms, a fraction of these cause fissionsreleasing other neutrons, but the remainder are captured. The neutron -yield parame-

permission event.

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BREEDER REACTOR SAFETY—MODELING THE IMPOSSIBLE

4.0

3.0

2.0

1.0

0

— P l u t o n i u m 2 3 9

1 10

Neutron Energy (eV)

over most of the neutron energy range. (Figure adapted fromthan the “break-even” value of 2. Plutonium-239 has the ERDA-1541, Vol. 1, p. 11-77, June 1976.)

may be safer than imagined.

The Liquid-Metal Fast Breeder

NEUTRONICS. The key to a breeder is theneutron. The generation of energy, thecontrol of the reactor, the breeding of newfuel, and particular safety problems uniqueto breeders are all related to the reactor’sneutronics. For example, the pioneers innuclear physics early recognized thepotential for breeding from the fact that eachnuclear fission releases two or threeneutrons. Since one of these neutrons isnecessary to continue the chain reaction,then one or two “byproduct” neutronsremain. Some of these byproduct neutronscan be utilized through transmutationprocesses to produce fissile isotopes fromfertile isotopes. [The two main processes

LOS ALAMOS SCIENCE

contemplated f o r b r e e d e r s a r e t h e

first isotope is fertile, the last is fissile.] If, onthe average, one byproduct neutron perfission is used to provide replacement fuel,the remaining neutrons are free to breedexcess fuel.

Of course, there are a variety of fatespossible for a neutron wandering free in areactor core. Some neutrons are lost to otherprocesses: for example, absorption bynonfuel constituents or leakage from thecore. Other neutrons are captured by thefissile-fuel atoms, but are only absorbed:there is no fissioning and no further releaseof neutrons. As a result, efficient breederdesign, like efficient financing, attempts to

maxim the the return yield for eachinvestment, that is, attempts to maximize thenumber of neutrons liberated for eachabsorbed neutron. This concept and the

per absorbed neutron are illustrated in Fig. 1.

larger than 1 to account for neutron losses, achain reaction can be maintained. However,

than 2.

energy for three fissile isotopes and showsthe most promising region for breeding to bethat of “fast” or high-energy neutrons. The

fissions to captures for absorbed neutrons isrising with neutron energy; the more energythe neutron brings to the interaction, themore likely the fission event. The figure also

101

shows that, with respect to neutron yield,plutonium-239 is the preferred choice forbreeder fuel.

Neutrons released in the fission processare already fast. Commercial light-waterreactors reduce these energies, with the wateracting as moderator, to the thermal regionwhere there is high total absorption of neu-trons by the fuel. But to take advantage of a

breeders are purposefully designed with littlemoderation.

How is this population of neutrons and theensuing chain reaction controlled? The neu-trons resulting directly from the fission proc-ess are called “prompt” neutrons (Fig. 3). Inliquid-metal fast breeders, the prompt neu-trons have an average “lifetime” of about

1 0-7 second between their birth and theirdeath due to absorption or escape from thecore. Since neutron population growth isexponential, a slight overpopulation ofprompt neutrons will grow very rapidly to anew, larger population. For example, a neu-tron population only 0.1 per cent in excess ofthe stable, “critical” population will takeslightly longer than 10-4 second to triple.This is much too fast for realistic control ofthe reactor.*

Fortunately, “delayed” neutrons are also

part of the total neutron population. Theseneutrons are released in the decay of some ofthe unstable nuclei produced by the originalfission event and are thus born on the orderof seconds after that event. If the neutronpopulation is always kept underpopulated, orsubcritical, with respect to prompt neutrons,delayed neutrons can be used either tocomplete a stable, balanced population or toprovide the slight imbalance needed to alterthe population. The growth to a new stablepopulation will then be slowed considerablyand mechanical control of the process be-comes feasible.

The Clementine reactor, designed andbuilt in 1945 at Los Alamos, successfullydemonstrated the feasibility of delayed neu-tron control of a fast-neutron system. This

102

Fission

Nuclei Unstableto Neutron Decay

Fig. 3. Prompt neutrons are released during fission almost

PromptNeutrons

FissionProducts

FissionProductDaughters

DelayedNeutrons

immediately afterabsorption of the neutron triggering the event. Delayed neutrons are releasedconsiderably later whan a fission product or a fission-product daughter is producedthat is unstable to neutron decay. Other radiations have been eliminated for clarity.

very small reactor had a cylindrical core Second, the fuel is highly enriched. While0.15 meter in diameter and 0.14 meter in it is true that fast neutrons absorbed by

length, 35 plutonium metal fuel rods, and fissile atoms result in high neutron yieldsused mercury as a coolant. It produced 25kilowatts at full power. is, the probability for those absorption to

occur in the first place, is several orders ofCORE. The special need of the breeder to magnitude lower than for thermal neutrons.generate and harbor neutrons efficiently dic- The solution to this problem is to increasetates a core design that differs in several key the number of targets by increasing therespects from the thermal-neutron reactor density of fissile atoms. Thus, a typicalcore. First, breeder cores are made compact breeder fuel is enriched to between 20 and 30to minimize the masses of nonfuel materials per cent in the fissile isotope compared to 3such as stainless steel and coolant. These per cent in light-water reactor fuel. A furthermaterials decrease the average yield by mod- advantage to high fissile-fuel density is thatcrating neutron energies and the neutron neutron mean free paths are kept smallavailability by absorption. compared to the size of the core, thus

*The same is true of commerical reactors using thermal neutrons (see Fig. 2), except average lifetime isabout 10 4 second and the approximate tripling time is 0.1 second.

LOS ALAMOS SCIENCE

reducing neutron leakage.The combined result of a compact core

and high fuel density is high power density,typically about 300 megawatts per cubicmeter. This necessitates a coolant systemwith good heat-transfer properties: for exam-ple, liquid-metal coolant flowing over largesurface areas of the fuel.

Finally, a breeder core contains both anactive core that supports the chain reactionand a blanket of fertile fuel that completelysurrounds this core and captures escapingneutrons,

The manner in which these features arebrought together for the proposed ClinchRiver Breeder Reactor, chosen for construc-tion near Oak Ridge, Tennessee, is shown inFig. 4. To create the necessary heat-transferarea, the fuel is encapsulated in thousands ofsmall-diameter (6-millimeter) pins clad withstainless steel. Each of these pins is long (2.8meters) and consists of several sections. Thecenter section contains the active-core fuel,typically an oxide of the fissile isotopeplutonium-239 mixed with the oxide of thefertile isotope uranium-238. Above andbelow the core section are blanket sections offertile fuel, usually “depleted” uranium (99.8per cent uranium-238 and 0.2 per centuranium-235). A hollow section at the top ofthe fuel pin serves as a fission-gas plenumthat collects the gaseous fission productsdiffusing out of the fuel below.

Between 200 and 300 of these fuel pins arebundled into a hexagonal array within a fuelassembly. Liquid sodium coolant enters theassembly at the bottom, flows upwardamong the fuel pins, then out the top,

Fuel assemblies are themselves positionedin arrays to form the active core. Blanketassemblies of fertile fuel are arranged aboutthe active core to complete the blankethorizontally. Control rods are includedamong the fuel assemblies, and shield as-semblies encircle the entire array to blockescaping radiation. In some core designs,blanket assemblies are placed within theactive core to enhance breeding.

104

The main features of the reactor vessel forthe Clinch River Breeder are shown in Fig. 5.The vessel is approximately 6 meters indiameter and 17 meters in length, The activecore, 1.8 meters in diameter and 1 meter inlength, requires a fissile inventory of approx-imately 2 metric tons.* Two types of controlrods with completely independent actuationsystems assure reactor shutdown when de-manded either by the automatic response ofthe control system or by the operators. Sincethe coolant is liquid sodium, which readilyburns in air, the vessel must be carefullysealed and given an inert atmosphere. Theclosure head is, therefore, a complex struc-ture of thermal shields and rotating, eccen-tric plugs that allow remote-control refuelingoperations. The sodium enters at the bottom(arrows), moves up through the fuel as-semblies, mixes in the upper sodium pool,and finally flows out of the vessel to heatexchangers,

Despite high chemical reactivity with airand water, liquid sodium has several proper-ties that make it an excellent coolant for fastbreeders. First, it is a relatively poor mod-erator.** Second, its thermal conductivity

allows for rapid transfer of heat within thehigh-power-density core and so eliminatesconcerns about local boiling, surface dryout,and fuel overheating. Third, the metal is aliquid over a large temperature range. Thus,the operating temperature can be highenough to achieve high thermal efficienciesof about 40 per cent, yet is still 300 kelvinbelow the boiling point. Finally, the systemoperates at atmospheric pressure.

The characteristics of low operating pres-sure and the capability of large heat removalprior to coolant boiling have led manyengineers to argue that the liquid-metal fastbreeder is generically safer than thelight-water reactor. If control and safety

systems function as intended, the possibilityof a core meltdown should be no higher, andperhaps even less likely, than for thelight-water reactor.

The Severe Accident

REACTIVITY CHANGES. Despite those ge-neric safety features, certain aspects of thefast breeder raise a special safety threat inmany people’s minds. These aspects center,once again, on the neutron.

Unlike the light-water reactor, the core ofa liquid-metal fast breeder is not in its mostreactive configuration. Typically, there areseveral critical masses of fuel present in thebreeder core. This fact, in conjunction withthe core’s high power density, led people toconjecture accidents in which the fuel meltedand slumped into a supercritical configura-tion. Any similar slumping and compactionof fuel in a light-water reactor wouldeliminate coolant, which is important as amoderator. With the elimination of coolant,the population of thermal neutrons drivingthe chain reaction in the light-water reactorwould decrease. In contrast, elimination ofcoolant in a breeder would actually increasethe neutron population.

This concern about meltdown led to anemphasis on hypothetical core-disruptive ac-cidents for liquid-metal fast breeders. Whyhypothetical? Accidents become severewhen there is a sustained inability to removeheat from the fuel at a rate commensuratewith its generation. For this to happen, twomajor systems must fail. For example, if thereactor control system fails to control thepower level, the safety system will scram orshut down the reactor. But if both systemsfail, then a major thermal or heatup ex-cursion can occur. Likewise, a severe acci-

.*A commercial light-water reactor of the same power capacity (1000 megawatts thermal) requires only 1metric ton of fissile material.**The hydrogen atoms of water have a mass equal to that of the neutron and so can absorb a largeportion of the neutron’s energy in a single collision; the heavier sodium atoms (atomic mass = 23) cannot.

LOS ALAMOS SCIENCE

I

dent will happen when heat transport fromthe core deteriorates due to pump failures orextreme pipe breakage, but again, only whencoupled with failure of the safety system toscram. Other possibilities are associated withmalfunctions of the redundant heat removalsystems.

The system failures described can, in somecases, result in disruptive feedback: the fail-ure causes heatup, which can melt fuel; if thefuel collapses, it creates excess neutrons anda power increase which accelerates the heat-up. Central to this feedback are changes inthe neutron balance called “reactivity.”Positive reactivity involves the creation ofexcess neutrons, which, of course, increasesthe disruptive feedback; negative reactivitywould moderate or decrease the feedback.

If the generation of excess neutrons islarge enough, the controlled balance main-tained by the delayed neutrons will be de-stroyed and there will be a sudden and veryrapid rise in power. The reactor has gone“super-prompt-critical,” a potentially dan-gerous condition that, in severe cases, willterminate only after the high pressures ofhot, vaporizing core materials have dispersedthe fuel.

Unfortunately, the liquid-metal fastbreeder core designs that are most desirablein terms of performance and economics alsohave an undesirable domination of positivereactivity during severe heatup transients.For instance, core structural materials andcoolant both absorb neutrons and moderateneutron energies. Loss of these materialscontributes to positive reactivity both byincreasing available neutrons and by causinga shift to higher neutron energies and, thus,higher neutron yields (Fig. 2). This happensif the liquid sodium boils or otherwise voidsaround the fuel pins, or if the stainless-steelcladding melts and flows from the core.

Fortunately, the positive reactivity is mod-erated by several inherent negative reac-tivities. The release of fission-product gasesand the thermal expansion of core materialstend to disperse the fuel. Specific core design

106

features can be incorporated that aid dis-persal during a core-disruptive accident.Also, more neutrons are absorbed in thefertile fuel as temperature increases (theDoppler effect*).

AN ACCIDENT SCENARIO. The analysis ofa postulated accident is designed to de-termine, with reasonable confidence, thedegree of any positive reactivity, its transientbehavior, and its potential for damage. De-tails of one accident scenario—failure of allprimary sodium coolant pumps and com-plete failure of the reactor shutdown sys-tem—will provide perspective on the com-plexity involved in this chore.

First, there is gradual loss of heat trans-port from the core as coolant circulationslows to a stop. Different fuel assemblieshave different power levels and flow rates, sothey heat up at different rates. The Dopplereffect and thermal expansions of sodium,fuel, and steel help keep reactivity feedbacksand power changes small. Soon, though,sodium boiling and voiding in fuel assemblieswith the highest ratio of power to coolantflow lead to a net positive reactivity effectand accelerated heatup; then voiding beginsin other fuel assemblies.

During this phase (the first 10 to 30seconds) the dominant phenomena are thetransfer of heat between materials, boilingand voiding of the coolant, and condensationof sodium vapor on cold structures at theends of the various assemblies. Neutronicsremains relatively smooth throughout thecore. The analysis of this phase is simplifiedby the constant geometry of the core and thequasistatic character of the phenomena.

In the second phase, heat removal ishighly degraded because the coolant hasvoided. Melting of fuel and cladding occurson the order of a second after sodium voids

are formed in a particular fuel assembly. Theresulting complex situation is shownschematically in the opening figure of thearticle. The melted fuel pins in the centralportion of the active core form a two-phasecolumn of liquid fuel, liquid steel, fuel frag-ments, fission gas, fuel vapor, and steelvapor. The liquid components are im-miscible, with greatly different meltingpoints, viscosities, and thermal conduc-tivities. The gaseous phase has been gener-ated primarily near the midplane where thefission power was initially highest. The pres-sure from the gas and vapors expels liquidsand fragments to the ends of the active coreand into the colder axial blankets.

Analysis of this phase of the accident thusrequires multiphase, multicomponent fluiddynamics and variable core geometry.Moreover, characteristics of the fluids varygreatly depending on initial conditions, timeinto the accident, and status of individualfuel assemblies.

The fission process causes the fuel to havea higher temperature than the other materialswithin the fluid mixture. Thus, a bewilderingvariety of heat-transfer processes and as-sociated phase changes are possible. Some ofthe possible phase changes are illustrated inFig. 6. All these processes are transient andhave feedback effects on fluid displacementthat, in turn, produce feedback effects onneutronics, reactor power, and fuel tem-peratures. The feedbacks are not only strong,

but also highly nonlinear due to exponentialrelationships between liquid temperaturesand vapor pressures and between materialdisplacements and power. In fact, neutronicresponse changes from a relatively smoothcore-wide distribution to one with local dis-tortions and sudden peaks.

Although this complex, chaotic behavioroccurs within individual fuel assemblies, the

*Intermediate-energy neutrons are strongly absorbed at specific energies in the resonance region betweenthermal and fast neutrons (Fig. 2). As the temperature increases, these absorption broaden, allowingabsorption of a larger range of energies and, therefore, a larger fraction of the limited numbers of theseneutrons.

LOS ALAMOS SCIENCE

BREEDER REACTOR SAFETY—MODELING THE IMPOSSIBLE

MASS EXCHANGE

Fig. 6. Typical phase changes possible during a severe accident.

overall disruption process must be viewed on fluid-dynamic coupling.

a core-wide basis. Reactor neutronics and The third phase, designated the “transition

power are dependent on the behavior in all phase,” occurs when the fuel-assembly duct

the assemblies, and the common boundary walls begin to melt. Now the flow field

conditions prevailing at the inlet and outlet becomes multidimensional on a core-widesodium plena produce a core-wide scale. Local fluid dynamics are no more

complex than in the previous phase, but theextent of material relocation within the coremay be much greater. This results in adifficult neutronics problem because of largevoided and compacted regions where neu-tron mean free paths are no longer smallcompared to the dimensions of the medium.The large voids introduce strong directionaleffects, known as neutron streaming, whichare important to this phase of the accident.

Neutronic coupling in the transition phaseis potentially stronger because disrupted fuelis no longer in discrete assemblies; thuslarger masses of fuel are capable of concur-rent motion. Changes in reactivity can beboth large and rapid. At this point twodifferent outcomes are possible depending onsuch things as the reactor design or thereactor state at the beginning of the accident.First, if a large fraction of the original fuelhas managed to remain within the activecore region, a super-prompt-critical ex-cursion can occur that heats the fuel inmilliseconds to high temperatures and pres-sures. The fuel in the core, in essence, blowsapart. While the dispersal of the fuel termi-nates the neutronic excursion, the pressuresurge poses a direct mechanical threat andthe possibility of breached containment.

On the other hand, if the fuel inventoryhas been reduced to about half the originalamount by gradual leakage, or if largequantities of blanket materials have dilutedthe fuel, a severe power excursion will proba-bly not occur. Thus, fluid-neutronic couplingbecomes weak and of little further im-portance. The threat along this path is a

potential meltthrough at the bottom of thereactor vessel from decay heat sometimewithin a few days.

SAFETY DESIGN. From this brief descrip-tion of a severe accident, it is possible tounderstand why many knowledgeable scien-tists and engineers have considered detailedmechanistic analyses of these accidents to bean impossible problem. An appropriate de-script ion o f t h e t h e r m o d y n a m i c ,

LOS ALAMOS SCIENCE 107

I

fluid-dynamic, thermal, and neutronic behav-ior has been judged beyond the state of theart. As a result, the hypotheticalcore-disruptive accident has, until recently,been dealt with in two ways.

First, engineers have attempted to designreliable systems with very low probabilitiesof even entering the severe accident regime,Second, the complexity of the problem hasbeen side-stepped by basing designs on high-ly conservative bounding estimates of the“damage potential.” This is the potential forneutronically heated core materials to pro-duce high pressures damaging to contain-ment structures and is typically based on theassumption of isentropic (reversible andadiabatic) expansion of the fuel. This ap-proach worked well for small breeders suchas the second experimental breeder de-veloped by Argonne, EBR-II, which had athermal power rating of 62 megawatts.

However, for the large breeders beingconsidered today, the bounding approachplaces difficult if not impossible demands ondesign. For a hypothetical core-disruptiveaccident of a given energy-density level,damage potential increases approximately inproportion to reactor size, whereas the abili-ty of reasonable designs to absorb damagescales weakly, or even inversely, with reactorsize. As a result, if proof of containment forthese accidents is necessary and it is tied tothe demands of simple bounding analyses, animpasse may be reached in the licensingprocess.

SIMMER. Seven years ago, a team of engi-neers and scientists at Los Alamos decidedto tackle this demanding problem. With thesupport of the Nuclear Regulatory Com-mission and the Department of Energy andwith the use of the computer resources atLos Alamos, work was begun on the SIM-MER code in 1974.

The approach adopted was to develop ageneralized numerical framework based onthe conservation laws of mass, energy, andmomentum constrained by the initial and

108

boundary conditions. Models representingthe “physics” and consistent with physicallaws or state-of-the-art understanding wereto be inserted into this framework. Thisapproach permits maximum flexibility fordescription of the physical interactionsamong materials, many of which were notwell known at the time the work was begun.It also allows modeling sensitivities anduncertainties to he assessed in the interactivecontext of overall accident simulation. Thus,the impact of imperfections in knowledgecan be established in a realistic manner.

EULERIAN FRAMEWORK. The “book-keeping” needed to follow specific particlesof material moving about and mixing togeth-er during a core-disruptive accident would beunbelievably complex. As a result, anEulerian numerical approach was chosen forthe fluid dynamics. This approach followsthe evolution of material parameters at fixedpoints in space. The reactor core is dividedby a mesh into a collection of cells, and thedensities and energies of the material compo-nents are calculated at each cell as a functionof time. This technique introduces someundesirable smearing of the transported en-tities within and between’ cells, but the ap-proximation is considered acceptable.

While the fluid dynamics of core disrup-tion are three-dimensional, considerablesymmetry usually exists in the circum-ferential direction. Accordingly, a two-dimensional, cylindrical approximation isnormally used in SIMMER, and each cell isspecified by a radial and an axial coordinate.

MULTIPLE FIELDS. Because of the varietyof material phases and components, certainsimplifications must be incorporated into thefluid dynamics, The first simplification is totreat all materials having the same approx-imate velocity as a “field,” Thus, onemomentum equation at most needs to beassigned to each field. SIMMER uses threefields: structure, liquid, and vapor (Table I).The structure field includes all materials that

are stationary in space. Besides the expectedstructural materials, fission gas trapped in-side fuel pins and resolidified materials arecomponents of this field. The liquid fieldincludes all materials that flow: normalcoolant, melted solids, and solid particlesmoving with these liquids. The vapor field,the gases, generates the pressure distributionthat drives the motion of the liquid field aswell as itself.

MULTIPLE COMPONENTS. Each field has alarge number of material components, thedensities and energies of which must bespecified in each Eulerian cell. However,some of these densities and energies can becombined. For example, all gases in thevapor field have short thermal equilibriumtimes and so all gases in a given cell aregiven the temperature and energy of themixture. On the other hand, since the loca-tion of fertile and fissile fuel must be con-sidered individually for neutronic purposes,the density is specified separately for both inall three fields.

CONSERVATION LAWS. The Eulerian nu-merical framework with its three fields andmultiple components must be formulatedwith conservation laws for momentum,mass, and energy as the foundation. Thereare only two momentum equations, one eachfor the liquid and vapor fields, but none forthe structure field since it is assumed sta-tionary. There are 23 mass equations and 12energy equations, one for each density orenergy component in each field.

The equations are in terms of densities,velocities, pressures, and internal energies,but they also include many source and sinkterms to account for transfer of heat, mass,and momentum between fields. The massequations account for vaporization, con-densation, freezing, and melting; the momen-tum equations account for gravity and dragforces; the energy equations account for heatexchange and the various heats generated byphase changes, neutronics, viscous dissipa-

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BREEDER REACTOR SAFETY—MODELING THE IMPOSSIBLE

TABLE I.FIELDS AND COMPONENTS OF SIMMER FLUID DYNAMICS

Field Energy Components Density Components Geometry and ModelsStructure (stationary) Fuel pins Fertile fuel Fuel assembly geometry

Cladding steel Fissile fuel Order and thickness ofAssembly wall steel Cladding steel layers on fuel pinsFuel crust Assembly wall steel Exterior surfaces exposed toControl pins Fertile fuel crust liquid field

Fissile fuel crust Flow-channel diametersContol pinsIntergranular fission gasIntragranular fission gas

Liquid (mobile] Liquid sodium Liquid sodium Dispersed dropletsMelted fuel Melted fertile fuel in continuous vapor fieldMelted steel Melted fissile fuel Solid particle sizeMelted control pins Melted steel Liquid droplet size from:Fuel particles Melted control pins surface tensionSteel particles Fertile fuel particles internal pressure

Fissile fuel particles fluid dynamic forces (drag)Steel particles coalescence model (collisional)

Vapor (mobile) Vapor mixture Fertile fuel vapor Homogeneous mixFissile fuel vapor Local vapor volume fractionSteel vaporSodium vaporControl pin vaporReleased fission gas

I

I tion, and pressure-volume work.

I EXCHANGE FUNCTIONS. The essentialphysics is introduced through the source andsink terms in the form of exchange functions.These functions give SIMMER its flexibilitybecause each represents the modeling of aspecific, independent physical process. Im-provements in the understanding of specificphenomena are reflected as improvements inmodeling and, hence, in the exchange func-tions that are inserted into the conservationequations. Currently, the modeling area re-ceives considerable emphasis through bothanalysis and experiments.

One modeling area of particular concernis the manner in which materials break up.For instance, what distribution of particlesizes will result when a fuel pin begins to meltand crumble? What fraction will be liquid

droplets and what fraction solid particles?Another area of concern is the physicalproperties of materials at high temperatures.

A typical modeling study starts with anattempt to describe the phenomenon byusing standard engineering functions. Inthese equations appear various coefficientsor exponents that correlate forces or materialproperties; for example, a Reynold’s numbermay be used that relates dynamic pressureand viscous stress for vapor flow over aspherical particle. Many of these coefficientshave parameters that depend on the specificgeometry of the phenomenon being modeled:particle sizes, flow-channel diameters,heat-transfer contact areas, Thus, an impor-tant step in the analysis is a realistic descrip-tion of the physical configuration.

Next, attempts are made to “benchmark”the model by comparing its predictions with

experiments dealing directly with thephenomenon. Some of these experiments aredone at Los Alamos, but most are carriedout at other laboratories. SIMMER is runusing only the exchange functions, thegeometry, and those parts of the code neces-sary to the particular experiment being sim-ulated. At this point, the model can be “tinetuned” by adjusting coefficients until thedesired agreement between calculated andexperimental results is achieved.

As implied by this discussion, the Eulerianmesh imposes a certain geometrical scale onthe problem, but the exchange functionsallow for effects due to a finer scale. Eachfunction depends on local cell conditions,including the predicted characteristics of themicroscale geometry.

The properties of the microscale geometryin the structure field are based on a typical

LOS ALAMOS SCIENCE 109

TABLE IITRANSFER PROCESSES INCLUDED IN SIMMER

Sourcea Process Sink or Final Statea

MOMENTUM TRANSFER

Cladding

Assembly wall Breakup Liquid or vapor fieldFuel or control material

Vapor field Pressure change Liquid field

CladdingAssembly wall Melting (or freezing) Liquid fieldFuel or control material

Liquid field Vaporization Vapor field

Steel vaporFuel or control material Condensation Liquid fieldvapor

Viscous coupling transverse ——

to flow

—— Liquid-vapor, drag-driven ——

slip flow

MASS TRANSFER

Liquids (fuel, steel, Vaporization Vapor fieldsodium, control material)

‘–Fission gas trapped in Release Vapor fieldfuel

‘Vapors (fuel, steel, Condensing out Liquid fieldsodium, control material) onto structures

Fuel vapor Condensation Liquid fuel

Steel vapor Condensation Liquid steel

Sodium vapor Condensation Liquid sodium

‘-Control material Condensation Liquid controlvapor material

Solids (fuel, cladding Liquid fuelassembly walls, control

MeltingSteel

material, fuel particles, Control materialsteel particles, fuel crust)

Liquids (fuel, steel) Freezing out Assembly walls

Liquid steel Freezing out Cladding

Liquid control material Freezing out Control material

Liquid fuel Freezing Fuel particles—

Liquid steel Freezing Steel particles

Solids (fuel, fuel crust) Breakup Fuel particles-—-

Solids (cladding, Breakup Steel particlesassembly walls)

110 LOS ALAMOS SCIENCE

BREEDER REACTOR SAFETY—MODELING THE IMPOSSIBLE

I

ENERGY TRANSFER

Cladding

Fuel pins Heat transfer

Liquid fuel

Heat transfer

Fuel crust Heat transfer Assembly walls

Fuel particles Heat transfer Liquids (steel, sodium,control material)

Control material

Cladding Heat transfer Liquids (sodium, controlmaterial)

Vapor field

Liquids (sodium, control

Assembly walls Heat transfer material)Vapor field

Steel particles Heat transfer Liquids (sodium, controlmaterial)

Solids (cladding, assemblywalls, steel particles,control material)

Liquid steel Liquids (sodium, controlmaterial)

Vapor field

Solids (cladding, assemblywalls, fuel particles,steel particles)

Liquids (sodium, controlmaterial, steel)

Vapor field

Control material

Liquid sodium Heat transfer Liquid control material

Vapor field

Liquids (fuel, steel, Vaporization (or condensation) V a p o r f i e l d

sodium, controlmaterial

Fuel Melting Liquid fuel

Steel particles Melting (or freezing) Liquid steel

Liquid fuel Freezing Fuel particles

Liquids (fuel, steel) Freezing out—

Assembly walls

Liquid steel Freezing out Cladding

Heat transfer

Liquids (fuel, sodium,

steel, control material)Vapor field

Cladding Viscous dissipation— — .

Liquid field —

Assembly wall during momentum Vapor field

Fuel or control transfermaterial

Viscous dissipation-—-.

Liquid field during momentum Vapor fieldtransfer

Viscous dissipationduring momentum. .transfer bytransverse viscouscoupling

aSource and sink may reverse roles depending on local temperatures.

LOS ALAMOS SCIENCE 111

fuel assembly. Included are flow-channeldiameters, the properties of surfaces interact-ing with the flow of the liquid and vaporfields, and the thicknesses and order oflayered materials of the fuel pins, assemblywalls, and solidified material.

The liquid field is generally viewed asdispersed immiscible droplets in a con-tinuous vapor field. This concept is ex-trapolated to simulate situations where theliquid is continuous. Solid particle sizes are

specified directly, but liquid-dropletdiameters are computed by balancing localfluid-dynamic and surface-tension forces andby tabulating all local coalescenses.

All transfer processes expected to haveany significant strength are included in SIM-MER as exchange functions, These are listedin Table II. The sheer number of theseprocesses illustrates the high degree of in-teractivity among physical processes at-tempted in SIMMER and required of anyreliable mechanistic approach.

Also important is the ability of the code todeal with a wide range of transientphenomena in many environments. Duringan accident, stationary materials becomemobile, flow obstructions such as duct wallsare removed, and normal flow channelsbecome blocked. This alteration of normalcore geometry is included through exchangefunctions related to structure melting, struc-ture disintegration by local thermal andpressure loads, and freezing of liquids onstructures. Also, functions representing mi-croscale geometry provide areas and dis-tributions of particles and droplets for heattransfer, phase change, and coalescencephenomena calculations.

A DROPLET HEAT-TRANSFER MODEL. AS

an example of the level of detail incorporatedin the models used in SIMMER, the liq-uid-liquid heat-transfer model will be out-lined here. This model assumes that eachdroplet sweeps out a volume determined byits radius and velocity and then collides withother droplets in that volume. The average

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Fig. 7. Droplet-droplet collision and associated heat-transfer parameters.

fluctuating velocity used may differ from theliquid-field velocity or from component tocomponent because of acceleration dif-ferences due to droplet sizes and densities. Acollision rate between various liquid compo-nents is calculated for each mesh cell.

Figure 7 illustrates three other parametersused in the heat-transfer calculation. Thecollisional contact area is based on thecross-sectional area of the smaller droplet,but a correction factor is included to approx-imately account for relative velocity andangle of impact. The heat-transfer rate perunit area is assumed to be quasistatic and isbased on conduction between the two slabsof material next to the contact surface. Eachslab thickness is taken as 20 per cent of thedroplet’s radius; this short conduction lengthis due to the fact that most of the heatcapacity in a sphere is effectively near the

outer surface. Contact time is estimated fromthe time the respective droplet volumes in-tersect.

The heat-transfer rate per unit volume isthe product of contact area, time of contact,heat-transfer rate per unit area, collisionalrate, and the temperature difference betweendroplets. The final equation is in terms of cellparameters: the radius and temperature ofeach droplet, the liquid volume fraction, andthe heat conductivities of both components.

EQUATION OF STATE. The multi-component equation of state that completesthe coupling between the fields can take oneof two forms in SIMMER. An analytic equa-tion-of-state approach requires direct inputof material properties such as specific heats,heats of fusion and vaporization, and vapor

pressures. The equations then relate the

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BREEDER REACTOR SAFETY—MODELING THE IMPOSSIBLE

Fig. 8. Schematic of the coupling between the neutronics and the fluid-dynamics calculational loops in SIMMER.

microscopic density and internal energy ofthe components in each field to the pressureand temperatures. The reference energystates of all materials are synchronized to atemperature of O kelvin. Also, the vapormaterials are assumed to obey the simpleconcepts of ideal gas mixtures.

The other approach is a tabular equationof state that enables data from the LosAlamos equation-of-state library, Sesame, tobe used. This library provides a wider andmore realistic data base than can be obtainedwith an analytic approach, but the interfac-ing of the conservation equations and ex-change functions with the tables has not yetbeen fully completed.

NEUTRONICS. Coupled with the fluiddynamics analysis is a calculation of theneutronic and power response of the disrupt-ing core. Thus, as shown in Fig. 8, SIMMERconsists of two interacting calculational

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loops: one for fluid dynamics and one forneutronics.

The mesh structure used for the fluiddynamics calculations is also the basis forthe neutronics calculations. However, re-gions where neutronic effects are known tobe negligible can be eliminated. Also, specifi-ed regions can be further subdivided whenneeded to obtain realistic representations ofneutronic spatial effects.

The neutronics and fluid dynamics equa-tions are not solved for the same time step,but are required to agree at certain times.This approach is what permits the separationof the two loops. The interaction betweenloops occurs with the transfer of such keyquantities as material temperatures, densi-ties, and heat generation rates.

Three levels of sophistication are providedin SIMMER for the neutronics loop. Thesimplest approach assumes a uniform neu-tron distribution in space and an invariant

energy spectrum during the transient. Reac-tivity feedbacks are derived from overallreactivity coefficients and, for each material,a reactivity effect per unit mass. This ap-proach is known as “point kinetics” since ittreats the reactor as a single point in space.Because of its simplicity, it appears in SIM-MER merely as a step in the fluid dynamicsloop.

As the core becomes more disorganized,neutronic characteristics change markedly,requiring an approach that incorporatesspace, time, and spectral effects. In somecases, a diffusion treatment of neutron trans-port in space can be used that represents anintermediate level of sophistication and hasthe advantage of numerical economy. Ingeneral, however, an approach using the fullneutron transport or neutron conservationequation is necessary. This approach in-cludes the dependence of the neutron dis-tribution on space, time, neutron energy, and

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neutron direction. The solution of this equa-

tion is formidable and has received muchattention from reactor physicists for anumber of years. The techniques used inSIMMER are state of the art.

Severe Accident Analysis

The combination of the features discussedabove resulted in a flexible code capable ofsimulating experiments, performing con-trolled examinations of isolated phenomena,and analyzing severe accident behavior in avariety of reactor configurations. As a result,an interactive approach involving applica-tions and testing was implemented early inthe development of the code with very fruit-ful results.

The first major application came in 1977when SIMMER I, the first version, was still ina developmental stage. This application in-volved an investigation of the hypotheticalaccident already described in which the coresuffers a super-prompt-critical excursionproducing a state of high thermal energy(fuel temperatures on the order of 4000 to6000 kelvin and a maximum vapor pressureof approximately 25 megapascals). As pre-viously noted, the isentropic expansionanalysis of this event indicates that the poolof liquid sodium should surge up against thereactor head, generating large pressures andstructural deformations, and could thus posea threat to primary containment.

In 1977 the SIMMER I capabilities wereadequate for a more realistic analysis of thisexpansion process. These capabilities in-cluded the modeling of a multitude ofheat-transfer processes, structural con-straints on fluid flows, and mass-transfereffects, all in a transient context. To every-one’s surprise, the calculated mechanicalenergy was only about 5 per cent of thatfrom the isentropic expansion for identicalinitial conditions.

The impacts of this finding, if substan-tiated, are fourfold. First, the damage poten-tial of severe accidents was previously being

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100 EXPANSION

Modeling

4000 I 5000

Average Fuel Temperature (K)

Fig. 9. Reactor damage potential (fluid kinetic energy) versus accident severity (initialfuel temperature) calculated by SIMMER and by assuming an isentropic expansion ofthe fuel. The band represents the effect of SIMMER modeling uncertainties.

estimated in an overly conservative fashion.Second, the ability of reactor containmentsystems to withstand severe accidents andthereby protect the public may be substan-tially greater than thought. Third, the extentto which the highly complex parts of thesevere accidents are resolved could be relax-ed by allowing some difficult phenomena toretain large uncertainties. Finally, aphenomenological signature of the expansionwas established against which concepts and

estimates could be tested.Follow-up investigations with an im-

proved and expanded version of the code,SIMMER II, revealed the reduction in me-chanical energy to be due to interactionsamong the various aspects of the expansionprocess. For example, the pin structure in theupper core produces a strong throttling effectthat prevents rapid discharge of core materi-al into the sodium pool as well as redirectingheat flow so that not all the available energy

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BREEDER REACTOR SAFETY—MODELING THE IMPOSSIBLE

l og

1 08

6* 10 7

0 1 2 3

Time (s)

(a)

o 1 2 3 4

Time (s)

(b)

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5

0

– 5

- l o

0

- 5

- 1 0

Fig. 10. Two examples of the power andreactivity response calculated by SIM-MER for a liquid-metal fast breederduring a hypothetical accident. Initialconditions are identical except in a)large amounts of fuel are able to escapethrough the axial blanket sections whilein b) the channels within the axialblanket sections of the fuel pins areclogged and only slight amounts of fuelescape. (The unit of reactivity is thedollar; one dollar is the reactivity changeb e t w e e n d e l a y e d - c r i t i c a l a n dprompt-critical conditions.)

is delivered to the sodium. Nonuniform ex-pansion, resulting from interaction with corestructure and from preferential expansion ofthe hottest fuel, also leads to a considerabledrop in the effective expansion pressures.

The investigations also showed that thereduction was highly insensitive to modelinguncertainties. This result is summarized inFig. 9, where the calculated fluid kineticenergy due to the expansion is plottedagainst accident severity in terms of theinitial fuel temperature at the start of theexpansion. The band on the figure representsthe combined interactive influence of mod-cling uncertainties; it was determined byassigning estimated uncertainties to 25 ex-change processes important to the accident,randomly selecting values within these un-certainty ranges, and then repeatedly redoingthe SIMMER calculations, The result showsthat known modeling inadequacies can betolerated without compromising the grat-ifying reduction in damage potential.

As a result of this early work, there ispresently an international interest in SIM-MER and its capabilities. Major laboratoriesand government agencies in the United King-dom, West Germany, Italy, and Japan, aswell as industrial contractors in the UnitedStates, are actively utilizing SIMMER.

The second major application of SIMMERwas initiated in 1979. This was the first

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attempt to simulate an actual core meltdowntransient on a whole-core scale with coupledspace-time neutronics and comprehensivethermal-fluid dynamics, The results of twocalculations are shown in Fig. 10. The initialconditions and modeling assumptions areidentical for both calculations except that theresult shown in Fig. 10a assumed easy fueltransport through the axial blankets andthereby considerable fuel escape from theactive core regions while the result shown inFig. 10b assumed rapid freezing of the fuel inthe escape paths and thereby slight fuelescape. This approach illustrates the methodof dealing with modeling uncertainties byvarying one key aspect and so bracketing thephenomenon of interest between two ex-tremes.

Comparison of the transient power forthese two extremes indicates the crucialeffect of fuel removal. When fuel can escapeeasily, power dwindles to low levels within 3seconds and at no time does it get muchhigher than 109 watts. However, when fuelescape is clogged, the result is continuedpower excursions with peaks of 1012 watts aslate as 5 seconds into the accident.

This second application of SIMMER pro-vided major insights into the characteristicsof core disruption from a transient point ofview and called into question qualitativeviews derived from steady-state perceptions.This latter point of view suggested that a fewgeneric physical processes control the acci-dent behavior, such as a material boilup inthe core that permanently disperses the fueland prevents recriticality. The transient con-text indicated that these processes may notbe continuously operative; for example, evenafter boilup the fuel could flow back togetherinto another critical mass.

Since full-scale, severe accident experi-ments are not considered desirable orfeasible, there is a need to test the predictivecapability of SIMMER through application toa wide spectrum of specialized experiments.One example of the various experimentssimulated by SIMMER II has to do with the

previously mentioned freezing and pluggingphenomenon that may occur during a severeaccident. Experiments conducted at ArgonneNat ional Labora tory examined th isphenomenon, using a hot, molten thermiteinjected into the channel between steel-cladblanket fuel pins. The molten thermite con-tains molybdenum, which represents meltedstainless steel, and uranium oxides, whichrepresent melted fuel. The full experimentsimulates the pressurized flow of melted fuelup into the blanket region of the core. Thecode successfully simulated the degree oftransport of thermite into the channels, theplugging phenomenon, and the amount ofdestruction of the pins for a variety of initialconditions.

Conclusions.

Because of these SIMMER analyses, thenecessary conditions for avoiding severe ac-cidents are becoming discernible. As a result,research directions are being reassessed andthe discussion of these accidents is turningfrom broad opinions to factual support ofspecific models.

The analytical results obtained so far haveencouraged us to feel it is possible to unfoldthe accident path in a way that adequatelyrepresents reality. The fact that developmentof mechanistic computer codes has beensupported by various parties in the breedercommunity for a number of years indicates astrong desire by the industry to also face thatreality.

Moreover, since it is not reality, but ratherthe uncertainty surrounding a vague possi-bility, that leads to greater fear in the mindsof people, it is necessary to continue refiningthe analytic tools and extending the ex-perimental base for the study of severeaccidents in the fast breeder. Only then caninformed decisions be made concerning thesafety of this potentially very beneficial mod-ern alchemy. ■

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AUTHOR

Charles R. Bell has been a staff member at Los Alamos since 1975. Hereceived his Bachelor of Science degree in mechanical engineering from theUniversity of Cincinnati in 1965 and his Ph.D. in nuclear engineering fromthe Massachusetts Institute of Technology in 1970. From 1970 to 1975 heworked for Atomics International, assessing severe core-disruptive accidentson breeder reactors. Also, he led the effort to design, develop, test, and applya system analysis capability to investigate tube breaks in large sodium-watersteam generators. At Los Alamos he has been working to develop and applyadvanced techniques for detailed assessment of severe breeder reactoraccidents. He has played a major role in establishing new perspectives onaccident characteristics and in integrating these new perspectives intonational and international research and development programs. He is amember of the American Nuclear Society.

Further Reading

LaRon L. Smith, “SIMMER-II: A Computer Program for LMFBR DisruptedAlamos Scientific Laboratory report LA-7515-M, Revised (June 1980).

Proceedings of the International Meeting on Fast Reactor Safety Technology,August 19-23, 1979 (American Nuclear Society, Incorporated, LaGrange, Illinois,

Core Analysis,” Los

Seattle, Washington,1979).

Proceedings of the International Meeting on Fast Reactor Safety and Related Physics. Chicago, Illinois,October 5-8, 1976. Available from National Technical Information Service as CONF-761001.

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