Research ArticleBenchmarkAnalysis on Loss-of-Flow-without-ScramTest of FFTFUsing Refined SAC-3D Models

Siyu Lyu 12 Daogang Lu12 and Danting Sui12

1North China Electric Power University Beijing 102206 China2Beijing Key Laboratory of Passive Safety Technology of Nuclear Energy Beijing 102206 China

Correspondence should be addressed to Siyu Lyu lyu-siyuncepueducn

Received 24 August 2021 Accepted 26 October 2021 Published 10 November 2021

Academic Editor Stephen M Bajorek

Copyright copy 2021 Siyu Lyu et alis is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

e Fast Flux Test Facility (FFTF) is a liquid sodium-cooled nuclear reactor designed by the Westinghouse Electric Corporationfor the US Department of Energy In July 1986 a series of unprotected transients were performed to demonstrate the passivesafety of FFTF Among these a total of 13 loss-of-flow-without scram (LOFWOS) tests were conducted to confirm the liquidmetalreactor safety margins provide data for computer code validation and demonstrate the inherent and passive safety benefits ofspecific design features In our preliminary work we have performed relatively coarse modeling of the FFTF To better predict thetransient behavior of FFTF LOFWOS test 13 we modeled it using a more refined thermal-hydraulics model In this paper wesimulate FFTF LOFWOS test 13 with the system safety analysis code SAC-3D according to the benchmark specificationsprovided by Argonne National Laboratory (ANL) e simulation range includes the primary and secondary circuits e reactorcore was modeled by the built-in 3D neutronics calculation module and the parallel-channel thermal-hydraulics calculationmodule To better predict the reactivity feedback introduced by coolant level variations within the GEMs a real-time macro cross-section homogenization processing module was developed e steady-state power distribution was calculated as the transientsimulation initial boundary conditions In general both the steady-state calculation results and the whole-plant transient behaviorpredictions are in good agreement with the measured data e relatively large deviations in transient simulation occur in theoutlet temperature predictions of the PIOTA in row 6 It can be preliminarily explained by the reason for neglecting the heattransfer between channels in this model

1 Introduction

In 2017 the International Atomic Energy Agency (IAEA)initialed a Coordinated Research Project (CRP) on bench-mark analysis of FFTF loss-of-flow-without scram (LOF-WOS) test A total of 25 organizations from 13 countriesparticipated in this CRP e overall objective of the CRP isto improve the Member Statesrsquo analytical capabilities in thefield of fast reactor simulation and designe test defined inthis benchmark is LOFWOS test 13 which was initiated at50 power and 100 flow with the pump pony motorsturned off e conditions of the LOFWOS test along withthe feedback from FFTFrsquos limited free bow core restraintsystem and the novel passive safety gas expansion modules

(GEMs) pose a very challenging and uniquely valuablebenchmark exercise

North China Electric Power University (NCEPU) par-ticipated in both neutronics and thermal-hydraulicsbenchmark analysis tasks of the CRPe fast reactor systemanalysis code SAC-3D was selected to simulate the steady-state and transient-state for this benchmark SAC-3D wasdeveloped by NCEPU it was used in fast breeder reactorplant state design and safety analysis [1] e code wasverified using various data experimental measured atmockups with water or sodium coolant and validated usingmeasured data of the CEFR and EBR-II reactors [2] ecode can calculate the process parameters (power tem-perature and flow) of plant transients including normal

HindawiScience and Technology of Nuclear InstallationsVolume 2021 Article ID 5843910 15 pageshttpsdoiorg10115520215843910

operating anticipated operational occurrence (AOO) anddesign basis accident (DBA) In our preliminary work wehave performed relatively coarse modeling of the FFTF andcalculated neutronics and thermal-hydraulics transients [3]e neutron calculation results are in good agreement butthe thermal-hydraulic transient results deviate significantlyTo better predict the transient behavior of FFTF LOFWOStest 13 we modeled it using a more refined thermal-hy-draulics model In this work we used ERANOS to generatethe homogenized macro cross-section library first en theprimary and secondary loops were modeled by using SAC-3D e primary pumps IHX and pipes are simulatedreferring to the technical specifications provided by IAEASince the specifications provide the dump heat exchangers(DHXs) sodium outlet temperature and secondary loopmass flow rate as boundary conditions the pumps andDHXs in the secondary loops were not modeled Further-more to simulate the GEMs properly we developed a newfunction module to conduct the macro cross-section ho-mogenization during the transient simulation e blindcalculation phase is now over most of the measured data hasbeen made available to the benchmark participants Somedata such as power distribution in a steady state are stillldquoblindrdquo For the actual measurement data we compare thesimulation results with the experimental data For theldquoblindrdquo part we compared the simulation results with theresults of other participants who applied similar systemanalysis software for modeling calculations e neutronicscalculation results in both steady-state and transient-stateobtained good agreement in general e trends of thethermal-hydraulics transient calculations are in goodagreement but the values somewhat deviate

2 FFTF LOFWOS Test 13

e Fast Flux Test Facility was a 400 MW-thermal loop typeSFR prototype with mixed oxide fuel e heat was removedfrom the reactor core by liquid sodium circulating under lowpressure Sodium exited the reactor vessel into one of threeprimary sodium loops Intermediate heat exchangers (IHX)separated activated sodium coolant in the primary loopsfrom nonradioactive sodium in the secondary loops FFTFdid not generate electricity instead of rejecting all heat to theenvironment via twelve air dump heat exchangers (DHX)Figure 1 illustrates the major components in each of thethree coolant systems

LOFWOS test 13 was performed on July 18 1986Table 1 illustrates the initial conditions of FFTF LOFWOStest 13 It started from 50 power and 100 flow when thethree primary pumps were simultaneously tripped esecondary loop sodium pumps remained operationalthroughout the test e plant protection system (PPS) wasmodified to allow the test to run without the control rodsbeing inserted prematurely

e FFTF core has 199 hexagonal assemblies Figure 2shows the assembliesrsquo arrangement at steady-state prior thetest 13 which included eight different types of assembliesdriver fuel assemblies (DFA) in core shim assemblies(ICSAs) reflector assemblies (REFL) control rods (CRs)

safety rods (SRs) materials open test assembly (MOTA)fracture mechanics assembly (FMA) and gas expansionmodules (GEMs) Among these assemblies ICSA MOTAand FMA are additional types of experimental assemblieswhich serve different irradiation and testing purposesGEMs are nine specially designed assemblies for FFTF eywere introduced to the LOFWOS to create negative reac-tivity feedback Each GEM was inserted into an assemblyposition within the inner row of the radial reflector regionFigure 3 depicts the configuration of GEM It was sealed atthe top and open at the bottomeGEMutilized its internal00283m3 volume to trap an argon cover gas bubble when itwas first inserted into the sodium [4] is gas bubble wastrapped as long as the assembly remained immersed insodiume gas and sodium interface will keep a stable levelabove the active regionrsquos top according to the static sodiumhead and the pumpsrsquo pressure head in normal operatingconditions When the primary pumps are tripped thepressure head will reduce en the gas bubble in the GEMsexpands As a result the sodium level drops back downbelow the active core level introducing automatic negativereactivity feedback caused by the increasing radial neutronleakage from the core

To monitor the outlet temperatures of core assembliesduring transient conditions special fast-response thermo-couple packages were utilized for a selection of assembliesese assemblies were referred to as Proximity InstrumentedOpen Test Assemblies (PIOTAs) Above each PIOTA aseparate duct assembly with multiple thermocouples wasinstalled e instrument duct was in direct contact with theassembly duct such that sodium discharged from PIOTAassemblies flowed along with thermocouples just above theassembly outlets Two fast-response PIOTAs were installedfor Test 13 and their position is provided in Figure 2

3 Calculation Methodology

31 Neutronics Calculation Model For neutronics calcula-tion modeling the core is simulated following the assembly-by-assembly approach We modeled the FFTF reactor corewith the built-in neutronics calculation module of SAC-3D[1 5] is module uses the high-order hexagonal nodalexpansion method to solve the diffusion equationrsquos for-mulation in an unlimited number of energy groups [6]us the self-shielded macroscopic cross-sections areneeded as input terms to initiate the calculation In thisbenchmark work the celllattice calculation module (namedECCO) integrated with ERANOS [7] was used to generatethe macroscopic cross-section library of all materials As wementioned before there are a total of eight types of as-semblies within the core e ICSA FMA and MOTA haveall different geometries and material specifications as theICSA andMOTA are very similar to DFAwhile for instancethe FMA is mostly comparable to REFL Since the outputrequired by the current benchmark analysis does not includethe parameters related to the aforementioned assemblies itwas decided to group these three assemblies as DF and REFL

e benchmark specifications provided detailed materialcompositions of all assemblies ie each assembly had its

2 Science and Technology of Nuclear Installations

FROM IHX PRIMARY OUTLET

REACTOR VESSEL

PRIMARYPUMP

INTERMEDIATE HEAT EXCHANGER

(IHX)

TO REACTOR

SECONDARY PUMP EXPANSION

TANK

REACTOR CONTAINMENT FLOOR LEVEL

DUMP HEAT EXCHANGER

Figure 1 Overview of FFTF coolant system

Table 1 Initial conditions of FFTF LOFWOS test 13 [4]

Parameter Units ValuePower MWt 1992Core inlet temperature K 5904Flow through all assemblies kgs 198842Shield flow rate kgs 5632Leakage and bypass flow rate kgs 15749GEM sodium level1 cm 2216

Loop 1 Loop 2 Loop 3Primary pump speed rpm 9531 9515 9444Primary loop flow rate kgs 73691 73568 72965Secondary pump speed rpm 8582 861 8515Secondary loop flow rate kgs 73518 73759 72947Average DHX Na outlet temperature K 5758 5726 5754Secondary cold leg temperature2 K 5707 5698 57091Elevation relative to the top of inlet nozzle holes2Initial DHX outlet temperatures were higher than secondary cold leg temperatures likely due touncertainties and the location of the thermocouples within the DHX

PIOTA IN ROW 2

PIOTA IN ROW 6

Figure 2 Core loading for LOFWOS test 13

Science and Technology of Nuclear Installations 3

material composition with 13 axial variations ere are atotal of 199 assemblies which results in a large amount ofmaterial requiring cell calculation To reduce the calculationburden we grouped all materials into 13 representativemixtures for cell calculations based on the atomic density ofthe materialrsquos significant elements and the assembly typeTable 2 shows the cell calculation treatments of all 13 ma-terials As shown in Table 2 DF31 to DF42 represent theactive zone materials in each of the four types of fuel as-semblies e lower insulator and upper insulator representthe insulator zone materials of driver fuel assemblies sep-aratelye material SRCR Ab represents the absorber zone

of the safety rods and control rods Sodium CH (SRCR) andSodium CH (GEM) represent the materials in the areas ofthe control rods safety rods and GEM assemblies that arefilled with sodium coolant respectively Similarly the ma-terial GAS represents the material in the gas-filled region ofthe GEM assemblies Since the geometry and elementalcomposition of the reflector assemblies are almost constantwithin the neutronics modeled range we consider the re-flector assembly as one material

Cell calculations have been performed adopting a 33-energy-group structure and the P1 approximation forscattering treatment and evaluating the thermal expansion

A

SECTION AndashA

SECTION B-BShield Plug

Oslash 1012 cm

Oslash 889 cm

Top of Assembly (3658 m)

Handling SocketTop Load Pad

Shield OrificeRegion

NozzleRegion

Top of Shield Plug (3416 m)

Middle of Top Load Pad (3505 m)

Top of Expansion Volume (2852 m)

Bottom of Upper Volume (2713 m)Bottom of Top Section (2675 m)

Core Mid Plane (1664 m)

Top of Orifice (0546 m)

Bottom of Orifice (0394 m)

Top of Inlet Flow Holes (0202 m)

Bottom of Assembly (000 m)

XA

BB

SECTION CndashC

ExpansionVolume

CC

SECTION DndashD

SECTION XndashX

DD

X

Figure 3 Gas expansion module assembly [4]

4 Science and Technology of Nuclear Installations

and Doppler effect based on the ENDFB-VII11968-groupnuclear data library For the fissile cells the heterogeneoushexagonal geometry has been adopted in a 6-step calculationprocedure e heterogeneous hexagonal geometry de-scription has also been used for control and safety rodsspatial self-shielded cross section (4-step calculation) erest nonburnable regions (insulator reflectors etc) foresee ahomogeneous geometry description of the cell and use the 2-step calculation procedure Since the subcritical cells do nothave the inner neutron source we calculate a relative re-gionrsquos spectrum for each of them as the external neutronsource e leakage effects of these subcritical cells are alsobeing considered Users can define the geometrical bucklingof the subcritical cells in the input card of ECCO to take theleakage effects into account e leakage effects are calcu-lated by the following equations according to the codingmanual

B2

58

πLtyp

1113888 1113889

2

(1)

where B is the buckling value in the correction methodΣt + DB2 and Ltyp is the typical dimension of the subcriticalregion

To update the cross section more accurately according tothe material temperature in transient calculations we per-formed cell calculations at 500K 750K and 1000K re-spectively and obtained two sets of homogeneous macrocross-section libraries e other material cross-section li-braries under temperatures between 500K and 1000K willbe derived by linear interpolation

e neutron calculation modelrsquos computational regioncovers each assembly in the radial direction e axialcomputational region is the area from the bottom to the topof the active region Each assembly was set as one calculationnode in the radial direction Figure 4 is the radial nodedivision schematic diagram of the FFTF reactor core In theaxial direction the neutronics calculation module of SAC-3D allows users to define the calculation nodes according totheir actual needs As Figure 5 shows we divided each as-sembly model into 38 calculation blocks in the present workEach calculation block is 25 cm tall while 38 blocks have atotal of 95 cm height which respects the active regionrsquos

actual height e relative axial positions of the control rodmaterials with respect to the fuel and GEM assemblies arealso shown in Figure 5 By dividing the reactor core cal-culation model into several calculation nodes in the radialand axial directions we have 7562 calculation nodes in theneutronics calculation model Zero flux boundary condi-tions are used to close the neutronic problem at the coreedges

As mentioned earlier the sodium level in GEMs is higherthan the top of the core active region When the test beganthe sodium level in GEMs will drop rapidly to the inletnozzle region which is lower than the bottom of the activeregion To predict the sodium level the following correlationwas suggested by the technical specifications

L 265 minus539504

244013 + F2 (2)

where F is the core flow rate in percent and L is the level ofsodium above the top of the inlet flow holes

In the transient calculation sodium and gas withinGEMs might be present simultaneously in the same cal-culation blocks where the gas-liquid interface is locatederefore the original cross-sections employed in the staticcalculations of these blocks need to be specially processedWe solve this problem by conducting the cross-sectionhomogenization during the online feedback reactivity cal-culation e homogenization method was shown in Fig-ure 6 At first we assumed that each assemblyrsquos boundarycondition in the radial direction is a total reflection and keptthe axial direction boundary conditions the same as in thecore neutronics calculation en we get the neutron fluxdistribution in the axial direction by conducting the one-dimensional SN (Discrete ordinates method) calculation anddo the needed cross-section homogenization as follows [8]

1113944i

1113938

hprime

0 1113936 i1φdh + 1113938h

hprime 1113936 i2φdh

1113938h

0 φdh (3)

where Σi are the cross sections consisting of removal fissionscattering absorption and total cross sections Σi1 and Σi2are the cross sections from the two neighbor nodes re-spectively h is the height of each node hprime is the height of

Table 2 Cell calculation treatment of FFTF LOFWOS test 13

Material NO XS name Assembly type Geometry treatment XS treatment1 DF31 Driver fuel Heterogeneous Critical2 DF41 Driver fuel Heterogeneous Critical3 DF32 Driver fuel Heterogeneous Critical4 DF42 Driver fuel Heterogeneous Critical5 Lower insulator Driver fuel Homogeneous Subcritical6 Upper insulator Driver fuel Homogeneous Subcritical7 SRCR Ab SafetyControl rod Heterogeneous Subcritical8 Sodium CH (SRCR) SafetyControl rod Homogeneous Subcritical9 Below Ab SafetyControl rod Homogeneous Subcritical10 Ref 772 Reflector Homogeneous Subcritical11 Ref 9 Reflector Homogeneous Subcritical12 Sodium CH (GEM) GEM Homogeneous Subcritical13 GAS GEM Homogeneous Subcritical

Science and Technology of Nuclear Installations 5

some point of the calculation block and φ is the neutronflux

32 +ermal-Hydraulics Calculation Model e design ofthe reactor was a three-loop primary systemwhere under lowpressure the three primary loops transport the heat generatedwithin the reactor core to the intermediate heat exchangersand back to the reactor vessel Each of the three primary loopscontains the same components Given the intrinsic symmetrycharacteristics of the thermal-hydraulic conditions of theprimary loops within the framework of the present bench-mark activities it was decided for the sake of simplicity toimplement a single equivalent primary and secondary loopmodel For the IHX primary pump and pipe models in thiswork we took into account their heat transfer area mass flowrate and other factors to ensure that they could be equivalentto the IHXs primary pumps and pipes in the overall threeprimary loopserefore the SAC-3Dmodel of the IHXs andprimary pumps only consists of a single IHX and a singlepump and a single average pipe layout is defined for theprimary loops As for the primary loop a single equivalentsecondary loop is modeled in SAC-3D

Figure 7 shows the layout of the FFTF reactor systemsimulation model e primary loop simulation model was

divided into two parts the reactor vessel and the primaryloop which include the hot leg piping the primary pumpthe primary side of IHXs and the cold leg piping Hot legpiping runs from the outlet plenum of the reactor vessel tothe primary pump and into the IHX primary side Cold legpiping returns sodium from the IHX to the inlet plenum ofthe reactor vessel discharging into the inlet plenum of thereactor vessel With regard to the secondary loops only thesecondary side of the IHX was modeled imposing properboundary conditions (coolant flow rate and temperature) atthe secondary hot leg and the secondary cold leg

SAC-3D uses the parallel-channel approach to conductthe reactor vessel thermal-hydraulics calculation which doesnot consider the coolant crossflow between the internalcomponents Simultaneously the model does not considerthe fuel componentrsquos axial heat conduction [9] In thepreliminary work we used only 9 channels to simulate thecore flow path and did not consider the bypass flow [3] isapproximate treatment brings large deviations in the ther-mal-hydraulic transient results To better correct the bias dueto the roughness of the thermal-hydraulic model a morerefined modeling approach was used In this paper thereactor vessel model consists of 13 parallel flow channels (11within the core model) connecting the inlet and outletplenums e inlet and outlet plenums are modeled with azero-dimensional volume module with respect to their ef-fective height and volume Within the outlet plenum modelthe sodium level is set at its nominal value and the argon gaspressure boundary condition is set at the top of the volumeAs shown in Figure 8 the reactor core model consists of 11

Driver Fuel 32

Driver Fuel 42

Driver Fuel 31

Safety Rod

Driver Fuel 41

Control Rod

GEM

Reflector

FMAICSA

Figure 4 Loading pattern of the calculation model of FFTF in theradial direction

SafetyRod

DriverFuel

Insulator (DF)Fuel (DF)Sodium CH (SRCR)Absorber (CR)

Below Ab (CR)Sodium CH (GEM)FMA ICSAReflector (Ref7729)

ControlRod

GEM FMAICSA

Reflector

Figure 5 Schematic of calculation nodes division of FFTF in theaxial direction

6 Science and Technology of Nuclear Installations

parallel flow channels all assemblies are grouped by theircoolant flow rate power distribution and assembly typeChannels 1 to 6 with channels 10 and 11 represent driver fuelassemblies flow channels where channels 10 and 11 rep-resent the individual PIOTA channels located in rows 2 and6 respectively Figure 9 shows the nodalization scheme ofthe driver fuel channels Each of these channels connects tothe outlet model and the inlet model from their top andbottom ese models are set to take the loss of pressurecaused by the orifice region and wire-wrapped fuel pinbundle into account As shown in Figure 9 each fuel channelis divided into five calculation points in radial directions Inthe axial direction the number of control volumes is set asthe same as the neutronics model to implement neutronics

thermal-hydraulics coupling during the transient simula-tion Table 3 shows the initial condition comparison betweenthe measurements and SAC-3D model results Channels 7represent controlsafety rod flow channels Channels 8 and 9represent two types of reflector assemblies (REF 7728A arelocated in the core basket and fed by sodium from the corebasket REF 8 B9 are located in the support skirt and fed bysodium from the annular plenum) respectively In additionseveral other flow paths draw sodium from the inlet plenumand discharge sodium into the outlet plenum Leakage andbypass flow paths provide sodium flow to the in-vesselstorage region the gap between the reactor vessel and vesselthermal liner We simplify these flow paths into two flowchannels In-Vessel Storage Channel and Bypass Channel

φ

TOTA

L RE

FLEC

TIO

N

Cross-secitonsHomogenization

Figure 6 Cross-section homogenization process

PIOTA6

PIOTA2

DF

CH1

DF

CH2

DF

CH3

DF

CH4

DF

CH5

DF

CH6

CRSR

CH

REF7728A

REF8B9

IN-VESSEL

STORAGE

BYPASS

HOT LEG

OUTLET PLENUMPrimary Loop

PUMP

DHX (BC)

SecondaryLoop

IHXSEC-SIDE

IHXPRI-SIDE

IHX SEC-SIDE INLET(BC)

COLD LEG

INLET PLENUM

CORE INLET MODEL

CORE OUTLET MODEL

Figure 7 Simplified layout of FFTF Simulation Model

Science and Technology of Nuclear Installations 7

In this work the primary pump is modeled with a pumpmodule based on the pumprsquos characteristics and theirnominal operating state Initial pump speed is adjusted tothe benchmark data e pump speed history is given asinput data during the transient e benchmark

specifications provide the pump performance curves for theprimary pumps However the data for these curves were notavailable To predict the pressure head during the transientthe following set of equations of the modified homologouspump theory of Wylie and Streeter were coded into thepump model ese modified correlations provide a goodapproximation of the dimensionless pump head (H)

H N2

+ Q2

1113874 1113875Wh(x) (4)

where N is the dimensionless pump speed Q is the relativevolumetric flow rate x π + arctan(QN)

Wh(x) 11139446

i0ahix

i (5)

whose coefficients are provided in Table 4e IHXs were vertically mounted counterflow shell and

tube designs Primary sodium entered the IHX from theoutlet of the primary loop hot leg piping and flowed downthrough the active heat transfer region along the outside ofthe IHX tubes Secondary sodium entered the IHX at the topand flowed down through a central downcomer into thelower hemispherical plenum From this plenum secondarysodium entered the IHX tubes at the bottom and flowedupward along the inner side of the IHX tubes out of the IHXIn the IHX model all heat transfer tubes have been sim-plified as one representative tube In an attempt to con-sistently simplify the model there are several assumptions(1) there is an ideal mixing of coolant at the inlet and outlet(2) fully developed convective heat transfer is assumed (3)no metallic structure of the IHX other than IHX tubes andshell wall is considered hence perfect insulation is postu-lated between primary and secondary sodium in the centraldowncomer pipe (4) no heat losses are accounted forthrough the external IHX vessel to the surrounding envi-ronment As shown in Figure 10 there are four radialcalculation nodes secondary coolant tube metal primarycoolant and shell wall e temperature calculation nodes ofthe heat tube metal and shell wall are defined in the center ofthe control volume e temperature calculation nodes ofthe coolant are defined at the boundary of the control body[9]

e energy equation of the primary side coolant controlvolume can be written as

ρVP

depi+1

dt Wp epi minus epi+11113872 1113873 minus HptApt Tpii+1 minus Tti1113872 1113873

minus HpshApsh Tpii+1 minus Tshi1113872 1113873

(6)

e energy equation of the secondary side coolantcontrol volume can be written as

ρVP

desi

dt Ws esi+1 minus esi1113872 1113873 + HstAst Tti minus Tsii+11113872 1113873 (7)

e energy equation of the IHX tube metal controlvolume can be written as

Channel 1

Channel 2

Channel 6

Channel 3

Channel 5

Channel 4

Channel 7

Channel 9

Channel 11

Channel 8

Channel 10

Figure 8 SAC-3D channel layout for FFTF core

UPPER AXIAL REFLECTOR

LOWER AXIAL REFLECTOR

INSULATOR PELLETS REGION

FUEL REGION

INSULATOR PELLETS REGION

GAP

CLADDING

COOLANT

STRUCTURE

FUEL

Figure 9 ermal-hydraulics model of driver fuel channels

8 Science and Technology of Nuclear Installations

Mtcti

dTti

dt HptApt Tpii+1 minus Tti1113872 1113873 minus HpstApst Tti minus Tsii+11113872 1113873

(8)

e energy equation of the IHX shell wall control volumecan be written as

Mshcshi

dTshi

dt HpshApsh Tpii+1 minus Tshi1113872 1113873 (9)

where p represents the coolant of the primary side s rep-resents the coolant of the secondary side t represents theheat exchanger tube of IHX sh represents the shell wall ofIHX e is enthalpy Wis mass flow rate T is temperature M

is mass c is specific heat capacity V is the volume of thecontrol volume H is the heat transfer coefficient betweenfluid and structural A is the heat transfer area betweenthe fluid and the structure and Tii+1 is the average fluidtemperature within two neighbor control volumes it isdefined as

Tii+1 Ti + Tii+1

2 (10)

As shown in Figure 7 the secondary loop wasmodeled astwo boundary conditions e DHX outlet coolant tem-perature values and the secondary loop coolant mass flowrates are imposed as the boundary conditions for the inletand outlet of the IHX secondary side

4 Results and Analysis

Table 5 summarizes the comparison of measurements andcalculation results of the initial plant conditions Reactorpower was slightly less than 50 and the core inlet tem-perature was reduced by nearly 80from the nominal coreinlet temperature is was done to ensure that the peak fueltemperatures did not rise too high to limit the impact of thetest on the durability of the fuel assemblies

Note that to date the IAEArsquos FFTF CRP project has justcompleted the blind phase and ANL has released experi-mental measurements of the part of the calculated FFTFreactor parameters erefore the following results partlycompare the simulated calculations with the real measure-ments and partly compare with other participantsrsquo calcu-lations Because different participants use differentcalculation methods and models we only make data devi-ation comparisons without deviation analysis for the resultswithout measurement data

Table 6 lists the main neutron results of FFTF LOFWOStest 13 of 10 participants Most of the results like theneutron multiplication factor delayed neutron fractionDoppler coefficient fuel density coefficient etc have arelatively good agreement among participants After re-moving results that deviated from the mean by more thantwo times the standard deviation the variation coefficient(δAvg) was distributed between 1 and 27 Significantdeviations appear in the structure density and sodiumdensity coefficientsrsquo results which have a 542 and 98variation coefficient respectively

e power distribution of steady-state estimated bySAC-3D is shown in Figure 11 e axially integrated powerof each assembly ranges from 155MW to 375MW Fig-ure 12 illustrates the variation coefficient map obtained bycomparing the integrated power simulation results withJAEA and ANLrsquos results e largest variation coefficient is

Table 3 Initial core flow distribution comparison

Channel Assembly type Measured mass flow rate (kgs) FFTF model Mass flow rate (kgs) Discrepancy ()1 DF 32 63305 63282 minus 0042 DF 42 15233 1523 minus 0023 DF 31 49907 49854 minus 0114 DF 31 28973 28956 minus 0065 DF 41 9984 9996 0126 DF 41 15233 15323 0597 SRCR 4091 4076 minus 0378 REF 7728A 5238 5243 0109 REF 8 B9 2348 2353 02110 PIOTA 2 2482 2494 04811 PIOTA 6 205 2037 minus 063

Table 4 Coefficients for the pump curve

i ah0 43196691 minus 576614382 301000293 minus 75465864 8675505 minus 0260626 minus 001596

BYPASSVOLUME

Wp

Ws

SHELL SIDE

TUBE SIDE

Figure 10 IHX calculation model

Science and Technology of Nuclear Installations 9

Table 5 Comparison of benchmark and SAC-3D steady-state parameters

Parameter Unit Measured value Calculated value Discrepancy ()Core power MW 1992 1992 000Core inlet temperature K 5904 59087 008Total core flow rate kgs 220224 219798 minus 019Mass flow rate through all assemblies kgs 198844 198934 005GEM sodium level1 cm 2216 2216 000Primary hot leg temperature K mdash 67818 mdashPrimary cold leg temperature K mdash 60589 mdashSecondary hot leg temperature K mdash 65656 mdashSecondary cold leg temperature K 58306 58378 0121Elevation relative to the top of inlet nozzle holes

Table 6 Main results of FFTF LOFWOS test 13 neutronics benchmark analysis

Argonne IGCAR INEST IPPE JAEA KIT KTH PSI ROME NCEPUNeutron multiplication factor 1000 0998 0999 0992 1017 0998 1022 1006 1000 0998Delayed neutron fraction 0003 0003 0007 0003 0003 0004 0003 0003 0003 0003Axial expansion coefficient (pcmdegC) minus 032 minus 023 mdash mdash minus 032 minus minus 03 minus 022 minus 048 minus03Radial expansion coefficient (pcmdegC) minus 1 minus 122 mdash mdash minus 1 minus minus 093 minus 152 minus 587 minus094Fuel Doppler constant (pcm) minus 629 minus 508 mdash mdash minus 634 minus 509 minus 564 minus 658 minus 688 minus524Fuel density coefficient (pcm) minus 136 minus 145 mdash mdash minus 045 mdash minus 136 minus 136 minus 14 minus132Structure density coefficient (pcm) minus 012 02 mdash mdash 003 mdash 01 004 minus 01 minus001Sodium density coefficient (pcmdegC) minus 035 minus 091 mdash mdash minus 041 009 minus 094 minus 027 minus 191 minus037Control and safety rods (pcm) minus 11849 mdash mdash minus 9396 10800 mdash minus 11540 minus 11823 minus 12773 minus8343Gas expansion modules (pcm) minus 442 minus 498 mdash minus 516 minus 489 minus 448 420 minus 475 minus 1201 minus782

324

195

263

252

315

344

197

CR

GEM

GEM

GEM

GEM GEM GEM

GEM

GEM

GEM

225

274

288

325

292

245

208

268

293

247

CR

179

177 155

201

190

213

220

192

206

223

295

SR

364

342

276

306

225

174

248

ICSA

312

306

375

SR

213

216

197205

CR

304

308

364

353

326

MOTA

290

205

231

280

273

329

298

SR

217

275

229

234

253

270

298

262

244

CR

232

191

257

253

289

CR

262

168

185

215

269

188

159

166 369

312

257

CR

207

Axially integratedpower (MW)

375

155

Figure 11 Power distribution map of FFTF core

10 Science and Technology of Nuclear Installations

327 which occurred in a fuel assembly type 42D Besideswe note that other assemblies with large coefficients ofvariation are located around this fuel assembly Since we donot have the power distributionrsquos measured data we cannotobjectively assess whether these biases are significant Bycomparing the codes applied by JAEA ANL and our sidewe believe that these biases are due to at least part of themodeling methods differences and different cross-sectionlibraries

Figures 13ndash15 depict the primary looprsquos mass flow ratersquostransient profile It can be seen that the SAC-3D very wellpredicts the pump coast down Minor differences existduring the natural circulation where the mass flow rates areslightly lower than the experimental data As shown inFigure 16 this is due to the underestimation of total power

Figures 16ndash18 show the transient reactor power profilesFigures 19 and 20 are the transient reactivity profile At 0 sthe primary pump is tripped and the core flow rate decreasesrapidly Due to the rapid decrease of the core cycling ca-pacity the assembliesrsquo temperature starts to rise and in-troduce negative net reactivity to bring down the reactorpower Starting from 5 s the coolant level in the GEMs dropsrapidly and the neutron leakage rate increases significantlyintroducing a remarkable negative reactivity e fissionpower decreases rapidly and the total power drops to 42 ofthe initial power at 10 s At 20 s the introduced negativereactivity increases at a slower rate as the core flow rate andthe coolant level within the GEMs begin to decrease at a

slower rate As shown in Figure 14 at approximately 90 s thenatural cycle is established e coolant level within GEMsbegins to stabilize and the negative reactivity it introducesalso stabilizes Figure 16 shows that the fission power isoverestimated due to the underestimation of the negativenet reactivity In the long term the fission power is close to

031

031

188

136

150

010

064

CR

GEM

GEM

GEM

GEM GEM GEM

GEM

GEM

GEM

172

195

102

295

286

108

147

287

263

238

CR

098

081 173

212

087

079

230

327

150

007

112

SR

181

137

015

207

128

055

097

ICSA

202

001

182

SR

026

140

179197

CR

030

021

003

116

016

MOTA

055

017

237

143

068

142

154

SR

055

105

089

013

090

063

084

087

088

CR

046

015

079

028

015

CR

043

057

037

056

108

040

009

089

104

118

CR

254

(Standard DevAverage)

327

001

032

Figure 12 Power distribution calculation variation coefficient map of FFTF corePu

mp

Disc

harg

e Pre

ssur

e (Ca

l) (M

Pa)

0 200 400

Time (s)

600 800

Loop 1 Mass Flow Rate (Exp)Loop 1 Mass Flow Rate (Cal)

Pump Discharge Pressure (Exp)Pump Discharge Pressure (Cal)

10

08

06

04

02

00

0

100

200

300

400

500

600

700

800

LOO

P 1

Mas

s Flo

w R

ate (

Cal)

200 400 600 8000Time (s)

Figure 13 Mass flow rate in loop 1

Science and Technology of Nuclear Installations 11

zero and the total power is contributed mainly by the decaypower e underestimation of the decay power leads to anunderestimation of the total power after 200 seconds Asshown in Figure 19 although the fuel temperature decreasesintroduced by the positive Dopplerrsquos reactivity feedback andpositive axial expansion reactivity feedback the net reac-tivity still maintains a significant negative value due to thesignificant negative reactivity introduced by GEMs

Figures 21 and 22 display the transient outlet temper-ature profiles of PIOTAs e SAC-3D results show a verysimilar trend compared to the experimental data with twopeaks occurring during the entire duration of the transientIn the beginning the outlet temperature rises rapidly as the

core flow rate drops rapidly as shown in Figure 13 epower decreases slowly because of the negative reactivityfeedback introduced by the control rod driveline expansionand radial expansion e power-to-flow ratio reaches thefirst peak value as shown in Figure 23 us the PIOTAsrsquooutlet temperatures increase rapidly and reach the first peakvalue After that the rapid drop of the coolant level withinthe GEMs introduced a large amount of negative reactivitycausing the total power to drop rapidly Meanwhile thedecreasing rate of mass flow rate starts to slow down ePIOTAsrsquo outlet temperatures start to decrease because thepower-to-flow ratio rapidly decreases Starting from about20 s the decrease in total power starts to slow down due to

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

200 400 600 8000Time (s)

0

5

10

15

20

Tota

l Cor

e Pow

er (C

al) (

MW

)

Figure 16 Reactor power of FFTF LOFWOS test 13 (low range)

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

0

20

40

60

80

100

120

140

160

180

200

Tota

l Cor

e Pow

er (C

al) (

MW

)

200 400 600 8000Time (s)

Figure 17 Reactor power of FFTF LOFWOS test 13

LOOP 1 NATURAL CIRCULATION

Loop 1 Mass Flow Rate (Cal)Loop 1 Mass Flow Rate (Exp)

0

10

20

30

40

50

Mas

s Flo

w R

ate (

kgs

)

100 200 300 400 500 600 700 800 9000Time (s)

Figure 14 Mass flow rate in loop 1 (Low range)

LOOP 1 TRANSITION TO NATURAL CIRCULATION

Loop 1 Mass Flow Rate (Cal)Loop 1 Mass Flow Rate (Exp)

-100

0

100

200

300

400

500

600

700

800

Mas

s Flo

w R

ate (

kgs

)

20 40 60 80 1000Time (s)

Figure 15 Mass flow rate in loop 1 (0 sndash100 s)

12 Science and Technology of Nuclear Installations

the rebound of the negative net reactivity as shown inFigure 20 erefore the power-to-flow ratio increaseswhich make the PIOTAsrsquo temperatures rise again At about110 s the PIOTAsrsquo temperatures reach the second peak valueafter the power-to-flow ratio reaches the second peak valueSince then the natural circulation starts to be establishedand maintained at about 4 of the rated flow as shown inFigure 14 e total power continues to decrease due to thenegative net reactivity e reactor enters a long-termcooling phase

In general the predicted results of SAC-3D are in goodagreement with the trend of the experimental data but thereare still deviations in the temperature values e outlettemperature of the PIOTA in row 2 is consistently lowerthan the measured value which is caused by the bias of thesimulated value of the total power transient variationSimilarly the simulated outlet temperature of the PIOTA inrow 6 is lower than the measured data until about 20 s butstarts to be higher than themeasured data after thenere isa maximum deviation of about 40 degrees Celsius at the

Net Reactivity (Cal)Doopler (Cal)Coolant Density (Cal)Axial Expansion (Cal)

Radial Expansion (Cal)Control Rod DrivelineExpansion (Cal)GEM (Cal)Net Reactivity (Exp)

ndash15

ndash10

ndash05

00

05

10

Net

Rea

ctiv

ity (C

al) (

$)

10 20 30 40 500Time (s)

Figure 20 Reactivity Transient Profile of FFTF LOFWOS test 13(0 sndash50 s)

Row 6 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Cal)Row 6 PIOTA Outlet Temp (Cal)

360

380

400

420

440

460

480

500

520

Row

6 P

IOTA

Out

let T

emp

(degC)

200 400 600 8000Time (s)

Figure 21 Row 2 and row 6 PIOTAs outlet temperature

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

0

20

40

60

80

100

120

140

160

180

200

Tota

l Cor

e Pow

er (C

al) (

MW

)

5 10 15 20 25 30 35 400Time (s)

Figure 18 Reactor power of FFTF LOFWOS test 13 (0 sndash40 s)

Net Reactivity (Cal)Doopler (Cal)Coolant Density (Cal)Axial Expansion (Cal)

Radial Expansion (Cal)Control Rod DrivelineExpansion (Cal)GEM (Cal)Net Reactivity (Exp)

ndash15

ndash10

ndash05

00

05

10

Net

Rea

ctiv

ity (C

al) (

$)

200 400 600 8000Time (s)

Figure 19 Reactivity transient profile of FFTF LOFWOS test 13

Science and Technology of Nuclear Installations 13

peak Unlike the PIOTA in row 2 the PIOTA in row 6 islocated at the outermost ring of the fuel assembly and is nextto a GEM assembly and a reflector assembly We believe thatthere are at least two possible reasons for this anomaly Oneis that even though the transientrsquos overall mass flow rate is ingood agreement with the measurement data it is stillpossible that the simulated mass flow rate variation withineach channel may not match the actual situation all that welle other important factor is the fact that the channel-to-channel heat transfer is not considered in the present worke neglect of heat transfer between the PIOTA in row 6 andGEM and reflector assembly introduced positive tempera-ture errors

5 Conclusions and Perspective

In the blind calculation phase of the IAEA FFTF LOFWOStest 13 CRP we modeled the FFTF reactor system by usingthe SAC-3D system analysis code e SAC-3D calculationresults have reasonably good agreement with the measureddata After benchmark analyzing the EBR-II [2] and FFTFreactors SAC-3D shows its good capability to predict thefast reactor behaviors under ATWS transient conditionsHowever the SAC-3D and FFTF models still have room forimprovement e deviations in total power transient cal-culations suggest further improvement in the reactivityfeedback models as well as the decay heat prediction modelAnomalies in the transient temperature prediction of thePIOTA in row 6 indicate that the thermal-hydraulics cal-culation module needs to consider the heat transfer betweenchannels In the next phase of the work we will examine thedeviations between simulation results further and refine theFFTF model based on the blind phase benchmark analysisresults e specific calculation modules of SAC-3D will alsobe improved to predict the fast reactorrsquos behavior better

Data Availability

e data that support the findings of this study are availablefrom IAEA Restrictions apply to the availability of thesedata which were used under license for this study Data areavailable from the corresponding author with the permis-sion of IAEA

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e authors would like to express their thanks to IAEAParticipation in the CRP on the FFTF LOFWOS test 13 isunder a research agreement between the North ChinaElectric Power University and the IAEA CRP numberI32011 is work was partially financially supported by theNational Natural Science Foundation of China (GrantNo11705057)

References

[1] D Sui D Lu L Ren and Y Liu ldquoDevelopment of three-di-mensional hot pool model in a system analysis code for pool-type FBRrdquo Nuclear Engineering and Design vol 256pp 264ndash273 2012

[2] D Lu S Lyu and D Sui ldquoVerification of SAC-3D based onEBR-II SHRT-45R benchmark datardquo in Proceedings of the 18thInternational Topical Meeting on Nuclear Reactor +ermalHydraulics Portland OR USA August 2019

[3] D Lu S Lyu and D Sui ldquoSimulation of FFTF loss of flowwithout scram test based on system code SAC-3Drdquo AtomicEnergy Science and Technology vol 55 no 8 pp 1345ndash13522021

[4] T Sumner A Moisseytsev F Heidet D W WootanA M Casella and J V Nelson Benchmark Specification forFFTF LOFWOS Test 13 IAEA Vienna Austria 2017

Row 6 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Cal)Row 6 PIOTA Outlet Temp (Cal)

360

380

400

420

440

460

480

500

520

Row

6 P

IOTA

Out

let T

emp

(degC)

2000Time (s)

Figure 22 Row 2 and row 6 PIOTAs outlet temperature(0 sndash200 s)

22

20

18

16

14

12

08

06

Dim

ensio

nles

s Pow

er-F

low

Rat

io

0 20 40 60 80 100 120Time (s)

140 160 180 200

Dimensionless Power-Flow Ratio

Dimensionless Power-Flow Ratio

200 400 600 8000Time (s)

06

08

12

10

14

16

18

20

22

Dim

ensio

nles

s Pow

er-F

low

Rat

io

Figure 23 Dimensionless power-flow ratio

14 Science and Technology of Nuclear Installations

[5] C Guo D Lu X Zhang and D Sui ldquoDevelopment and ap-plication of a safety analysis code for small Lead cooled FastReactor SVBR 75100rdquo Annals of Nuclear Energy vol 81pp 62ndash72 2015

[6] D Lu C Guo and D Sui ldquoA three-dimensional nodal neutronkinetics code with a higher-accuracy algorithm for reactor corein hexagonal-z geometryrdquo Annals of Nuclear Energy vol 101pp 250ndash261 2017

[7] J M Ruggieri J Tommasi J F Lebrat et al ldquoEranos 21International code system for GEN IV fast reactor analysisrdquo inProceedings of the 2006 International Congress on Advances inNuclear Power Plants ICAPPrsquo06 pp 2432ndash2439 Seoul KoreaJuly 2006

[8] S Lyu D Lu and D Sui ldquoNeutronics benchmark analysis ofthe EBR-II SHRT-45R with SAC-3Drdquo Nuclear Engineering andDesign vol 364 p 110679 2020

[9] C Guo D Lu D Sui and X Zhang ldquoSAC-CFR computer codeverification with Experimental Breeder Reactor II loss-of-primary-flow-without-scram tests datardquo Annals of NuclearEnergy vol 71 pp 166ndash173 2014

Science and Technology of Nuclear Installations 15

FROM IHX PRIMARY OUTLET

REACTOR VESSEL

PRIMARYPUMP

INTERMEDIATE HEAT EXCHANGER

(IHX)

TO REACTOR

SECONDARY PUMP EXPANSION

TANK

REACTOR CONTAINMENT FLOOR LEVEL

DUMP HEAT EXCHANGER

Figure 1 Overview of FFTF coolant system

Table 1 Initial conditions of FFTF LOFWOS test 13 [4]

Parameter Units ValuePower MWt 1992Core inlet temperature K 5904Flow through all assemblies kgs 198842Shield flow rate kgs 5632Leakage and bypass flow rate kgs 15749GEM sodium level1 cm 2216

Loop 1 Loop 2 Loop 3Primary pump speed rpm 9531 9515 9444Primary loop flow rate kgs 73691 73568 72965Secondary pump speed rpm 8582 861 8515Secondary loop flow rate kgs 73518 73759 72947Average DHX Na outlet temperature K 5758 5726 5754Secondary cold leg temperature2 K 5707 5698 57091Elevation relative to the top of inlet nozzle holes2Initial DHX outlet temperatures were higher than secondary cold leg temperatures likely due touncertainties and the location of the thermocouples within the DHX

PIOTA IN ROW 2

PIOTA IN ROW 6

Figure 2 Core loading for LOFWOS test 13

Science and Technology of Nuclear Installations 3

material composition with 13 axial variations ere are atotal of 199 assemblies which results in a large amount ofmaterial requiring cell calculation To reduce the calculationburden we grouped all materials into 13 representativemixtures for cell calculations based on the atomic density ofthe materialrsquos significant elements and the assembly typeTable 2 shows the cell calculation treatments of all 13 ma-terials As shown in Table 2 DF31 to DF42 represent theactive zone materials in each of the four types of fuel as-semblies e lower insulator and upper insulator representthe insulator zone materials of driver fuel assemblies sep-aratelye material SRCR Ab represents the absorber zone

of the safety rods and control rods Sodium CH (SRCR) andSodium CH (GEM) represent the materials in the areas ofthe control rods safety rods and GEM assemblies that arefilled with sodium coolant respectively Similarly the ma-terial GAS represents the material in the gas-filled region ofthe GEM assemblies Since the geometry and elementalcomposition of the reflector assemblies are almost constantwithin the neutronics modeled range we consider the re-flector assembly as one material

Cell calculations have been performed adopting a 33-energy-group structure and the P1 approximation forscattering treatment and evaluating the thermal expansion

A

SECTION AndashA

SECTION B-BShield Plug

Oslash 1012 cm

Oslash 889 cm

Top of Assembly (3658 m)

Handling SocketTop Load Pad

Shield OrificeRegion

NozzleRegion

Top of Shield Plug (3416 m)

Middle of Top Load Pad (3505 m)

Top of Expansion Volume (2852 m)

Bottom of Upper Volume (2713 m)Bottom of Top Section (2675 m)

Core Mid Plane (1664 m)

Top of Orifice (0546 m)

Bottom of Orifice (0394 m)

Top of Inlet Flow Holes (0202 m)

Bottom of Assembly (000 m)

XA

BB

SECTION CndashC

ExpansionVolume

CC

SECTION DndashD

SECTION XndashX

DD

X

Figure 3 Gas expansion module assembly [4]

4 Science and Technology of Nuclear Installations

and Doppler effect based on the ENDFB-VII11968-groupnuclear data library For the fissile cells the heterogeneoushexagonal geometry has been adopted in a 6-step calculationprocedure e heterogeneous hexagonal geometry de-scription has also been used for control and safety rodsspatial self-shielded cross section (4-step calculation) erest nonburnable regions (insulator reflectors etc) foresee ahomogeneous geometry description of the cell and use the 2-step calculation procedure Since the subcritical cells do nothave the inner neutron source we calculate a relative re-gionrsquos spectrum for each of them as the external neutronsource e leakage effects of these subcritical cells are alsobeing considered Users can define the geometrical bucklingof the subcritical cells in the input card of ECCO to take theleakage effects into account e leakage effects are calcu-lated by the following equations according to the codingmanual

B2

58

πLtyp

1113888 1113889

2

(1)

where B is the buckling value in the correction methodΣt + DB2 and Ltyp is the typical dimension of the subcriticalregion

To update the cross section more accurately according tothe material temperature in transient calculations we per-formed cell calculations at 500K 750K and 1000K re-spectively and obtained two sets of homogeneous macrocross-section libraries e other material cross-section li-braries under temperatures between 500K and 1000K willbe derived by linear interpolation

e neutron calculation modelrsquos computational regioncovers each assembly in the radial direction e axialcomputational region is the area from the bottom to the topof the active region Each assembly was set as one calculationnode in the radial direction Figure 4 is the radial nodedivision schematic diagram of the FFTF reactor core In theaxial direction the neutronics calculation module of SAC-3D allows users to define the calculation nodes according totheir actual needs As Figure 5 shows we divided each as-sembly model into 38 calculation blocks in the present workEach calculation block is 25 cm tall while 38 blocks have atotal of 95 cm height which respects the active regionrsquos

actual height e relative axial positions of the control rodmaterials with respect to the fuel and GEM assemblies arealso shown in Figure 5 By dividing the reactor core cal-culation model into several calculation nodes in the radialand axial directions we have 7562 calculation nodes in theneutronics calculation model Zero flux boundary condi-tions are used to close the neutronic problem at the coreedges

As mentioned earlier the sodium level in GEMs is higherthan the top of the core active region When the test beganthe sodium level in GEMs will drop rapidly to the inletnozzle region which is lower than the bottom of the activeregion To predict the sodium level the following correlationwas suggested by the technical specifications

L 265 minus539504

244013 + F2 (2)

where F is the core flow rate in percent and L is the level ofsodium above the top of the inlet flow holes

In the transient calculation sodium and gas withinGEMs might be present simultaneously in the same cal-culation blocks where the gas-liquid interface is locatederefore the original cross-sections employed in the staticcalculations of these blocks need to be specially processedWe solve this problem by conducting the cross-sectionhomogenization during the online feedback reactivity cal-culation e homogenization method was shown in Fig-ure 6 At first we assumed that each assemblyrsquos boundarycondition in the radial direction is a total reflection and keptthe axial direction boundary conditions the same as in thecore neutronics calculation en we get the neutron fluxdistribution in the axial direction by conducting the one-dimensional SN (Discrete ordinates method) calculation anddo the needed cross-section homogenization as follows [8]

1113944i

1113938

hprime

0 1113936 i1φdh + 1113938h

hprime 1113936 i2φdh

1113938h

0 φdh (3)

where Σi are the cross sections consisting of removal fissionscattering absorption and total cross sections Σi1 and Σi2are the cross sections from the two neighbor nodes re-spectively h is the height of each node hprime is the height of

Table 2 Cell calculation treatment of FFTF LOFWOS test 13

Material NO XS name Assembly type Geometry treatment XS treatment1 DF31 Driver fuel Heterogeneous Critical2 DF41 Driver fuel Heterogeneous Critical3 DF32 Driver fuel Heterogeneous Critical4 DF42 Driver fuel Heterogeneous Critical5 Lower insulator Driver fuel Homogeneous Subcritical6 Upper insulator Driver fuel Homogeneous Subcritical7 SRCR Ab SafetyControl rod Heterogeneous Subcritical8 Sodium CH (SRCR) SafetyControl rod Homogeneous Subcritical9 Below Ab SafetyControl rod Homogeneous Subcritical10 Ref 772 Reflector Homogeneous Subcritical11 Ref 9 Reflector Homogeneous Subcritical12 Sodium CH (GEM) GEM Homogeneous Subcritical13 GAS GEM Homogeneous Subcritical

Science and Technology of Nuclear Installations 5

some point of the calculation block and φ is the neutronflux

32 +ermal-Hydraulics Calculation Model e design ofthe reactor was a three-loop primary systemwhere under lowpressure the three primary loops transport the heat generatedwithin the reactor core to the intermediate heat exchangersand back to the reactor vessel Each of the three primary loopscontains the same components Given the intrinsic symmetrycharacteristics of the thermal-hydraulic conditions of theprimary loops within the framework of the present bench-mark activities it was decided for the sake of simplicity toimplement a single equivalent primary and secondary loopmodel For the IHX primary pump and pipe models in thiswork we took into account their heat transfer area mass flowrate and other factors to ensure that they could be equivalentto the IHXs primary pumps and pipes in the overall threeprimary loopserefore the SAC-3Dmodel of the IHXs andprimary pumps only consists of a single IHX and a singlepump and a single average pipe layout is defined for theprimary loops As for the primary loop a single equivalentsecondary loop is modeled in SAC-3D

Figure 7 shows the layout of the FFTF reactor systemsimulation model e primary loop simulation model was

divided into two parts the reactor vessel and the primaryloop which include the hot leg piping the primary pumpthe primary side of IHXs and the cold leg piping Hot legpiping runs from the outlet plenum of the reactor vessel tothe primary pump and into the IHX primary side Cold legpiping returns sodium from the IHX to the inlet plenum ofthe reactor vessel discharging into the inlet plenum of thereactor vessel With regard to the secondary loops only thesecondary side of the IHX was modeled imposing properboundary conditions (coolant flow rate and temperature) atthe secondary hot leg and the secondary cold leg

SAC-3D uses the parallel-channel approach to conductthe reactor vessel thermal-hydraulics calculation which doesnot consider the coolant crossflow between the internalcomponents Simultaneously the model does not considerthe fuel componentrsquos axial heat conduction [9] In thepreliminary work we used only 9 channels to simulate thecore flow path and did not consider the bypass flow [3] isapproximate treatment brings large deviations in the ther-mal-hydraulic transient results To better correct the bias dueto the roughness of the thermal-hydraulic model a morerefined modeling approach was used In this paper thereactor vessel model consists of 13 parallel flow channels (11within the core model) connecting the inlet and outletplenums e inlet and outlet plenums are modeled with azero-dimensional volume module with respect to their ef-fective height and volume Within the outlet plenum modelthe sodium level is set at its nominal value and the argon gaspressure boundary condition is set at the top of the volumeAs shown in Figure 8 the reactor core model consists of 11

Driver Fuel 32

Driver Fuel 42

Driver Fuel 31

Safety Rod

Driver Fuel 41

Control Rod

GEM

Reflector

FMAICSA

Figure 4 Loading pattern of the calculation model of FFTF in theradial direction

SafetyRod

DriverFuel

Insulator (DF)Fuel (DF)Sodium CH (SRCR)Absorber (CR)

Below Ab (CR)Sodium CH (GEM)FMA ICSAReflector (Ref7729)

ControlRod

GEM FMAICSA

Reflector

Figure 5 Schematic of calculation nodes division of FFTF in theaxial direction

6 Science and Technology of Nuclear Installations

parallel flow channels all assemblies are grouped by theircoolant flow rate power distribution and assembly typeChannels 1 to 6 with channels 10 and 11 represent driver fuelassemblies flow channels where channels 10 and 11 rep-resent the individual PIOTA channels located in rows 2 and6 respectively Figure 9 shows the nodalization scheme ofthe driver fuel channels Each of these channels connects tothe outlet model and the inlet model from their top andbottom ese models are set to take the loss of pressurecaused by the orifice region and wire-wrapped fuel pinbundle into account As shown in Figure 9 each fuel channelis divided into five calculation points in radial directions Inthe axial direction the number of control volumes is set asthe same as the neutronics model to implement neutronics

thermal-hydraulics coupling during the transient simula-tion Table 3 shows the initial condition comparison betweenthe measurements and SAC-3D model results Channels 7represent controlsafety rod flow channels Channels 8 and 9represent two types of reflector assemblies (REF 7728A arelocated in the core basket and fed by sodium from the corebasket REF 8 B9 are located in the support skirt and fed bysodium from the annular plenum) respectively In additionseveral other flow paths draw sodium from the inlet plenumand discharge sodium into the outlet plenum Leakage andbypass flow paths provide sodium flow to the in-vesselstorage region the gap between the reactor vessel and vesselthermal liner We simplify these flow paths into two flowchannels In-Vessel Storage Channel and Bypass Channel

φ

TOTA

L RE

FLEC

TIO

N

Cross-secitonsHomogenization

Figure 6 Cross-section homogenization process

PIOTA6

PIOTA2

DF

CH1

DF

CH2

DF

CH3

DF

CH4

DF

CH5

DF

CH6

CRSR

CH

REF7728A

REF8B9

IN-VESSEL

STORAGE

BYPASS

HOT LEG

OUTLET PLENUMPrimary Loop

PUMP

DHX (BC)

SecondaryLoop

IHXSEC-SIDE

IHXPRI-SIDE

IHX SEC-SIDE INLET(BC)

COLD LEG

INLET PLENUM

CORE INLET MODEL

CORE OUTLET MODEL

Figure 7 Simplified layout of FFTF Simulation Model

Science and Technology of Nuclear Installations 7

In this work the primary pump is modeled with a pumpmodule based on the pumprsquos characteristics and theirnominal operating state Initial pump speed is adjusted tothe benchmark data e pump speed history is given asinput data during the transient e benchmark

specifications provide the pump performance curves for theprimary pumps However the data for these curves were notavailable To predict the pressure head during the transientthe following set of equations of the modified homologouspump theory of Wylie and Streeter were coded into thepump model ese modified correlations provide a goodapproximation of the dimensionless pump head (H)

H N2

+ Q2

1113874 1113875Wh(x) (4)

where N is the dimensionless pump speed Q is the relativevolumetric flow rate x π + arctan(QN)

Wh(x) 11139446

i0ahix

i (5)

whose coefficients are provided in Table 4e IHXs were vertically mounted counterflow shell and

tube designs Primary sodium entered the IHX from theoutlet of the primary loop hot leg piping and flowed downthrough the active heat transfer region along the outside ofthe IHX tubes Secondary sodium entered the IHX at the topand flowed down through a central downcomer into thelower hemispherical plenum From this plenum secondarysodium entered the IHX tubes at the bottom and flowedupward along the inner side of the IHX tubes out of the IHXIn the IHX model all heat transfer tubes have been sim-plified as one representative tube In an attempt to con-sistently simplify the model there are several assumptions(1) there is an ideal mixing of coolant at the inlet and outlet(2) fully developed convective heat transfer is assumed (3)no metallic structure of the IHX other than IHX tubes andshell wall is considered hence perfect insulation is postu-lated between primary and secondary sodium in the centraldowncomer pipe (4) no heat losses are accounted forthrough the external IHX vessel to the surrounding envi-ronment As shown in Figure 10 there are four radialcalculation nodes secondary coolant tube metal primarycoolant and shell wall e temperature calculation nodes ofthe heat tube metal and shell wall are defined in the center ofthe control volume e temperature calculation nodes ofthe coolant are defined at the boundary of the control body[9]

e energy equation of the primary side coolant controlvolume can be written as

ρVP

depi+1

dt Wp epi minus epi+11113872 1113873 minus HptApt Tpii+1 minus Tti1113872 1113873

minus HpshApsh Tpii+1 minus Tshi1113872 1113873

(6)

e energy equation of the secondary side coolantcontrol volume can be written as

ρVP

desi

dt Ws esi+1 minus esi1113872 1113873 + HstAst Tti minus Tsii+11113872 1113873 (7)

e energy equation of the IHX tube metal controlvolume can be written as

Channel 1

Channel 2

Channel 6

Channel 3

Channel 5

Channel 4

Channel 7

Channel 9

Channel 11

Channel 8

Channel 10

Figure 8 SAC-3D channel layout for FFTF core

UPPER AXIAL REFLECTOR

LOWER AXIAL REFLECTOR

INSULATOR PELLETS REGION

FUEL REGION

INSULATOR PELLETS REGION

GAP

CLADDING

COOLANT

STRUCTURE

FUEL

Figure 9 ermal-hydraulics model of driver fuel channels

8 Science and Technology of Nuclear Installations

Mtcti

dTti

dt HptApt Tpii+1 minus Tti1113872 1113873 minus HpstApst Tti minus Tsii+11113872 1113873

(8)

e energy equation of the IHX shell wall control volumecan be written as

Mshcshi

dTshi

dt HpshApsh Tpii+1 minus Tshi1113872 1113873 (9)

where p represents the coolant of the primary side s rep-resents the coolant of the secondary side t represents theheat exchanger tube of IHX sh represents the shell wall ofIHX e is enthalpy Wis mass flow rate T is temperature M

is mass c is specific heat capacity V is the volume of thecontrol volume H is the heat transfer coefficient betweenfluid and structural A is the heat transfer area betweenthe fluid and the structure and Tii+1 is the average fluidtemperature within two neighbor control volumes it isdefined as

Tii+1 Ti + Tii+1

2 (10)

As shown in Figure 7 the secondary loop wasmodeled astwo boundary conditions e DHX outlet coolant tem-perature values and the secondary loop coolant mass flowrates are imposed as the boundary conditions for the inletand outlet of the IHX secondary side

4 Results and Analysis

Table 5 summarizes the comparison of measurements andcalculation results of the initial plant conditions Reactorpower was slightly less than 50 and the core inlet tem-perature was reduced by nearly 80from the nominal coreinlet temperature is was done to ensure that the peak fueltemperatures did not rise too high to limit the impact of thetest on the durability of the fuel assemblies

Note that to date the IAEArsquos FFTF CRP project has justcompleted the blind phase and ANL has released experi-mental measurements of the part of the calculated FFTFreactor parameters erefore the following results partlycompare the simulated calculations with the real measure-ments and partly compare with other participantsrsquo calcu-lations Because different participants use differentcalculation methods and models we only make data devi-ation comparisons without deviation analysis for the resultswithout measurement data

Table 6 lists the main neutron results of FFTF LOFWOStest 13 of 10 participants Most of the results like theneutron multiplication factor delayed neutron fractionDoppler coefficient fuel density coefficient etc have arelatively good agreement among participants After re-moving results that deviated from the mean by more thantwo times the standard deviation the variation coefficient(δAvg) was distributed between 1 and 27 Significantdeviations appear in the structure density and sodiumdensity coefficientsrsquo results which have a 542 and 98variation coefficient respectively

e power distribution of steady-state estimated bySAC-3D is shown in Figure 11 e axially integrated powerof each assembly ranges from 155MW to 375MW Fig-ure 12 illustrates the variation coefficient map obtained bycomparing the integrated power simulation results withJAEA and ANLrsquos results e largest variation coefficient is

Table 3 Initial core flow distribution comparison

Channel Assembly type Measured mass flow rate (kgs) FFTF model Mass flow rate (kgs) Discrepancy ()1 DF 32 63305 63282 minus 0042 DF 42 15233 1523 minus 0023 DF 31 49907 49854 minus 0114 DF 31 28973 28956 minus 0065 DF 41 9984 9996 0126 DF 41 15233 15323 0597 SRCR 4091 4076 minus 0378 REF 7728A 5238 5243 0109 REF 8 B9 2348 2353 02110 PIOTA 2 2482 2494 04811 PIOTA 6 205 2037 minus 063

Table 4 Coefficients for the pump curve

i ah0 43196691 minus 576614382 301000293 minus 75465864 8675505 minus 0260626 minus 001596

BYPASSVOLUME

Wp

Ws

SHELL SIDE

TUBE SIDE

Figure 10 IHX calculation model

Science and Technology of Nuclear Installations 9

Table 5 Comparison of benchmark and SAC-3D steady-state parameters

Parameter Unit Measured value Calculated value Discrepancy ()Core power MW 1992 1992 000Core inlet temperature K 5904 59087 008Total core flow rate kgs 220224 219798 minus 019Mass flow rate through all assemblies kgs 198844 198934 005GEM sodium level1 cm 2216 2216 000Primary hot leg temperature K mdash 67818 mdashPrimary cold leg temperature K mdash 60589 mdashSecondary hot leg temperature K mdash 65656 mdashSecondary cold leg temperature K 58306 58378 0121Elevation relative to the top of inlet nozzle holes

Table 6 Main results of FFTF LOFWOS test 13 neutronics benchmark analysis

Argonne IGCAR INEST IPPE JAEA KIT KTH PSI ROME NCEPUNeutron multiplication factor 1000 0998 0999 0992 1017 0998 1022 1006 1000 0998Delayed neutron fraction 0003 0003 0007 0003 0003 0004 0003 0003 0003 0003Axial expansion coefficient (pcmdegC) minus 032 minus 023 mdash mdash minus 032 minus minus 03 minus 022 minus 048 minus03Radial expansion coefficient (pcmdegC) minus 1 minus 122 mdash mdash minus 1 minus minus 093 minus 152 minus 587 minus094Fuel Doppler constant (pcm) minus 629 minus 508 mdash mdash minus 634 minus 509 minus 564 minus 658 minus 688 minus524Fuel density coefficient (pcm) minus 136 minus 145 mdash mdash minus 045 mdash minus 136 minus 136 minus 14 minus132Structure density coefficient (pcm) minus 012 02 mdash mdash 003 mdash 01 004 minus 01 minus001Sodium density coefficient (pcmdegC) minus 035 minus 091 mdash mdash minus 041 009 minus 094 minus 027 minus 191 minus037Control and safety rods (pcm) minus 11849 mdash mdash minus 9396 10800 mdash minus 11540 minus 11823 minus 12773 minus8343Gas expansion modules (pcm) minus 442 minus 498 mdash minus 516 minus 489 minus 448 420 minus 475 minus 1201 minus782

324

195

263

252

315

344

197

CR

GEM

GEM

GEM

GEM GEM GEM

GEM

GEM

GEM

225

274

288

325

292

245

208

268

293

247

CR

179

177 155

201

190

213

220

192

206

223

295

SR

364

342

276

306

225

174

248

ICSA

312

306

375

SR

213

216

197205

CR

304

308

364

353

326

MOTA

290

205

231

280

273

329

298

SR

217

275

229

234

253

270

298

262

244

CR

232

191

257

253

289

CR

262

168

185

215

269

188

159

166 369

312

257

CR

207

Axially integratedpower (MW)

375

155

Figure 11 Power distribution map of FFTF core

10 Science and Technology of Nuclear Installations

327 which occurred in a fuel assembly type 42D Besideswe note that other assemblies with large coefficients ofvariation are located around this fuel assembly Since we donot have the power distributionrsquos measured data we cannotobjectively assess whether these biases are significant Bycomparing the codes applied by JAEA ANL and our sidewe believe that these biases are due to at least part of themodeling methods differences and different cross-sectionlibraries

Figures 13ndash15 depict the primary looprsquos mass flow ratersquostransient profile It can be seen that the SAC-3D very wellpredicts the pump coast down Minor differences existduring the natural circulation where the mass flow rates areslightly lower than the experimental data As shown inFigure 16 this is due to the underestimation of total power

Figures 16ndash18 show the transient reactor power profilesFigures 19 and 20 are the transient reactivity profile At 0 sthe primary pump is tripped and the core flow rate decreasesrapidly Due to the rapid decrease of the core cycling ca-pacity the assembliesrsquo temperature starts to rise and in-troduce negative net reactivity to bring down the reactorpower Starting from 5 s the coolant level in the GEMs dropsrapidly and the neutron leakage rate increases significantlyintroducing a remarkable negative reactivity e fissionpower decreases rapidly and the total power drops to 42 ofthe initial power at 10 s At 20 s the introduced negativereactivity increases at a slower rate as the core flow rate andthe coolant level within the GEMs begin to decrease at a

slower rate As shown in Figure 14 at approximately 90 s thenatural cycle is established e coolant level within GEMsbegins to stabilize and the negative reactivity it introducesalso stabilizes Figure 16 shows that the fission power isoverestimated due to the underestimation of the negativenet reactivity In the long term the fission power is close to

031

031

188

136

150

010

064

CR

GEM

GEM

GEM

GEM GEM GEM

GEM

GEM

GEM

172

195

102

295

286

108

147

287

263

238

CR

098

081 173

212

087

079

230

327

150

007

112

SR

181

137

015

207

128

055

097

ICSA

202

001

182

SR

026

140

179197

CR

030

021

003

116

016

MOTA

055

017

237

143

068

142

154

SR

055

105

089

013

090

063

084

087

088

CR

046

015

079

028

015

CR

043

057

037

056

108

040

009

089

104

118

CR

254

(Standard DevAverage)

327

001

032

Figure 12 Power distribution calculation variation coefficient map of FFTF corePu

mp

Disc

harg

e Pre

ssur

e (Ca

l) (M

Pa)

0 200 400

Time (s)

600 800

Loop 1 Mass Flow Rate (Exp)Loop 1 Mass Flow Rate (Cal)

Pump Discharge Pressure (Exp)Pump Discharge Pressure (Cal)

10

08

06

04

02

00

0

100

200

300

400

500

600

700

800

LOO

P 1

Mas

s Flo

w R

ate (

Cal)

200 400 600 8000Time (s)

Figure 13 Mass flow rate in loop 1

Science and Technology of Nuclear Installations 11

zero and the total power is contributed mainly by the decaypower e underestimation of the decay power leads to anunderestimation of the total power after 200 seconds Asshown in Figure 19 although the fuel temperature decreasesintroduced by the positive Dopplerrsquos reactivity feedback andpositive axial expansion reactivity feedback the net reac-tivity still maintains a significant negative value due to thesignificant negative reactivity introduced by GEMs

Figures 21 and 22 display the transient outlet temper-ature profiles of PIOTAs e SAC-3D results show a verysimilar trend compared to the experimental data with twopeaks occurring during the entire duration of the transientIn the beginning the outlet temperature rises rapidly as the

core flow rate drops rapidly as shown in Figure 13 epower decreases slowly because of the negative reactivityfeedback introduced by the control rod driveline expansionand radial expansion e power-to-flow ratio reaches thefirst peak value as shown in Figure 23 us the PIOTAsrsquooutlet temperatures increase rapidly and reach the first peakvalue After that the rapid drop of the coolant level withinthe GEMs introduced a large amount of negative reactivitycausing the total power to drop rapidly Meanwhile thedecreasing rate of mass flow rate starts to slow down ePIOTAsrsquo outlet temperatures start to decrease because thepower-to-flow ratio rapidly decreases Starting from about20 s the decrease in total power starts to slow down due to

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

200 400 600 8000Time (s)

0

5

10

15

20

Tota

l Cor

e Pow

er (C

al) (

MW

)

Figure 16 Reactor power of FFTF LOFWOS test 13 (low range)

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

0

20

40

60

80

100

120

140

160

180

200

Tota

l Cor

e Pow

er (C

al) (

MW

)

200 400 600 8000Time (s)

Figure 17 Reactor power of FFTF LOFWOS test 13

LOOP 1 NATURAL CIRCULATION

Loop 1 Mass Flow Rate (Cal)Loop 1 Mass Flow Rate (Exp)

0

10

20

30

40

50

Mas

s Flo

w R

ate (

kgs

)

100 200 300 400 500 600 700 800 9000Time (s)

Figure 14 Mass flow rate in loop 1 (Low range)

LOOP 1 TRANSITION TO NATURAL CIRCULATION

Loop 1 Mass Flow Rate (Cal)Loop 1 Mass Flow Rate (Exp)

-100

0

100

200

300

400

500

600

700

800

Mas

s Flo

w R

ate (

kgs

)

20 40 60 80 1000Time (s)

Figure 15 Mass flow rate in loop 1 (0 sndash100 s)

12 Science and Technology of Nuclear Installations

the rebound of the negative net reactivity as shown inFigure 20 erefore the power-to-flow ratio increaseswhich make the PIOTAsrsquo temperatures rise again At about110 s the PIOTAsrsquo temperatures reach the second peak valueafter the power-to-flow ratio reaches the second peak valueSince then the natural circulation starts to be establishedand maintained at about 4 of the rated flow as shown inFigure 14 e total power continues to decrease due to thenegative net reactivity e reactor enters a long-termcooling phase

In general the predicted results of SAC-3D are in goodagreement with the trend of the experimental data but thereare still deviations in the temperature values e outlettemperature of the PIOTA in row 2 is consistently lowerthan the measured value which is caused by the bias of thesimulated value of the total power transient variationSimilarly the simulated outlet temperature of the PIOTA inrow 6 is lower than the measured data until about 20 s butstarts to be higher than themeasured data after thenere isa maximum deviation of about 40 degrees Celsius at the

Net Reactivity (Cal)Doopler (Cal)Coolant Density (Cal)Axial Expansion (Cal)

Radial Expansion (Cal)Control Rod DrivelineExpansion (Cal)GEM (Cal)Net Reactivity (Exp)

ndash15

ndash10

ndash05

00

05

10

Net

Rea

ctiv

ity (C

al) (

$)

10 20 30 40 500Time (s)

Figure 20 Reactivity Transient Profile of FFTF LOFWOS test 13(0 sndash50 s)

Row 6 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Cal)Row 6 PIOTA Outlet Temp (Cal)

360

380

400

420

440

460

480

500

520

Row

6 P

IOTA

Out

let T

emp

(degC)

200 400 600 8000Time (s)

Figure 21 Row 2 and row 6 PIOTAs outlet temperature

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

0

20

40

60

80

100

120

140

160

180

200

Tota

l Cor

e Pow

er (C

al) (

MW

)

5 10 15 20 25 30 35 400Time (s)

Figure 18 Reactor power of FFTF LOFWOS test 13 (0 sndash40 s)

Net Reactivity (Cal)Doopler (Cal)Coolant Density (Cal)Axial Expansion (Cal)

Radial Expansion (Cal)Control Rod DrivelineExpansion (Cal)GEM (Cal)Net Reactivity (Exp)

ndash15

ndash10

ndash05

00

05

10

Net

Rea

ctiv

ity (C

al) (

$)

200 400 600 8000Time (s)

Figure 19 Reactivity transient profile of FFTF LOFWOS test 13

Science and Technology of Nuclear Installations 13

peak Unlike the PIOTA in row 2 the PIOTA in row 6 islocated at the outermost ring of the fuel assembly and is nextto a GEM assembly and a reflector assembly We believe thatthere are at least two possible reasons for this anomaly Oneis that even though the transientrsquos overall mass flow rate is ingood agreement with the measurement data it is stillpossible that the simulated mass flow rate variation withineach channel may not match the actual situation all that welle other important factor is the fact that the channel-to-channel heat transfer is not considered in the present worke neglect of heat transfer between the PIOTA in row 6 andGEM and reflector assembly introduced positive tempera-ture errors

5 Conclusions and Perspective

In the blind calculation phase of the IAEA FFTF LOFWOStest 13 CRP we modeled the FFTF reactor system by usingthe SAC-3D system analysis code e SAC-3D calculationresults have reasonably good agreement with the measureddata After benchmark analyzing the EBR-II [2] and FFTFreactors SAC-3D shows its good capability to predict thefast reactor behaviors under ATWS transient conditionsHowever the SAC-3D and FFTF models still have room forimprovement e deviations in total power transient cal-culations suggest further improvement in the reactivityfeedback models as well as the decay heat prediction modelAnomalies in the transient temperature prediction of thePIOTA in row 6 indicate that the thermal-hydraulics cal-culation module needs to consider the heat transfer betweenchannels In the next phase of the work we will examine thedeviations between simulation results further and refine theFFTF model based on the blind phase benchmark analysisresults e specific calculation modules of SAC-3D will alsobe improved to predict the fast reactorrsquos behavior better

Data Availability

e data that support the findings of this study are availablefrom IAEA Restrictions apply to the availability of thesedata which were used under license for this study Data areavailable from the corresponding author with the permis-sion of IAEA

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e authors would like to express their thanks to IAEAParticipation in the CRP on the FFTF LOFWOS test 13 isunder a research agreement between the North ChinaElectric Power University and the IAEA CRP numberI32011 is work was partially financially supported by theNational Natural Science Foundation of China (GrantNo11705057)

References

[1] D Sui D Lu L Ren and Y Liu ldquoDevelopment of three-di-mensional hot pool model in a system analysis code for pool-type FBRrdquo Nuclear Engineering and Design vol 256pp 264ndash273 2012

[2] D Lu S Lyu and D Sui ldquoVerification of SAC-3D based onEBR-II SHRT-45R benchmark datardquo in Proceedings of the 18thInternational Topical Meeting on Nuclear Reactor +ermalHydraulics Portland OR USA August 2019

[3] D Lu S Lyu and D Sui ldquoSimulation of FFTF loss of flowwithout scram test based on system code SAC-3Drdquo AtomicEnergy Science and Technology vol 55 no 8 pp 1345ndash13522021

[4] T Sumner A Moisseytsev F Heidet D W WootanA M Casella and J V Nelson Benchmark Specification forFFTF LOFWOS Test 13 IAEA Vienna Austria 2017

Row 6 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Cal)Row 6 PIOTA Outlet Temp (Cal)

360

380

400

420

440

460

480

500

520

Row

6 P

IOTA

Out

let T

emp

(degC)

2000Time (s)

Figure 22 Row 2 and row 6 PIOTAs outlet temperature(0 sndash200 s)

22

20

18

16

14

12

08

06

Dim

ensio

nles

s Pow

er-F

low

Rat

io

0 20 40 60 80 100 120Time (s)

140 160 180 200

Dimensionless Power-Flow Ratio

Dimensionless Power-Flow Ratio

200 400 600 8000Time (s)

06

08

12

10

14

16

18

20

22

Dim

ensio

nles

s Pow

er-F

low

Rat

io

Figure 23 Dimensionless power-flow ratio

14 Science and Technology of Nuclear Installations

[5] C Guo D Lu X Zhang and D Sui ldquoDevelopment and ap-plication of a safety analysis code for small Lead cooled FastReactor SVBR 75100rdquo Annals of Nuclear Energy vol 81pp 62ndash72 2015

[6] D Lu C Guo and D Sui ldquoA three-dimensional nodal neutronkinetics code with a higher-accuracy algorithm for reactor corein hexagonal-z geometryrdquo Annals of Nuclear Energy vol 101pp 250ndash261 2017

[7] J M Ruggieri J Tommasi J F Lebrat et al ldquoEranos 21International code system for GEN IV fast reactor analysisrdquo inProceedings of the 2006 International Congress on Advances inNuclear Power Plants ICAPPrsquo06 pp 2432ndash2439 Seoul KoreaJuly 2006

[8] S Lyu D Lu and D Sui ldquoNeutronics benchmark analysis ofthe EBR-II SHRT-45R with SAC-3Drdquo Nuclear Engineering andDesign vol 364 p 110679 2020

[9] C Guo D Lu D Sui and X Zhang ldquoSAC-CFR computer codeverification with Experimental Breeder Reactor II loss-of-primary-flow-without-scram tests datardquo Annals of NuclearEnergy vol 71 pp 166ndash173 2014

Science and Technology of Nuclear Installations 15

material composition with 13 axial variations ere are atotal of 199 assemblies which results in a large amount ofmaterial requiring cell calculation To reduce the calculationburden we grouped all materials into 13 representativemixtures for cell calculations based on the atomic density ofthe materialrsquos significant elements and the assembly typeTable 2 shows the cell calculation treatments of all 13 ma-terials As shown in Table 2 DF31 to DF42 represent theactive zone materials in each of the four types of fuel as-semblies e lower insulator and upper insulator representthe insulator zone materials of driver fuel assemblies sep-aratelye material SRCR Ab represents the absorber zone

of the safety rods and control rods Sodium CH (SRCR) andSodium CH (GEM) represent the materials in the areas ofthe control rods safety rods and GEM assemblies that arefilled with sodium coolant respectively Similarly the ma-terial GAS represents the material in the gas-filled region ofthe GEM assemblies Since the geometry and elementalcomposition of the reflector assemblies are almost constantwithin the neutronics modeled range we consider the re-flector assembly as one material

Cell calculations have been performed adopting a 33-energy-group structure and the P1 approximation forscattering treatment and evaluating the thermal expansion

A

SECTION AndashA

SECTION B-BShield Plug

Oslash 1012 cm

Oslash 889 cm

Top of Assembly (3658 m)

Handling SocketTop Load Pad

Shield OrificeRegion

NozzleRegion

Top of Shield Plug (3416 m)

Middle of Top Load Pad (3505 m)

Top of Expansion Volume (2852 m)

Bottom of Upper Volume (2713 m)Bottom of Top Section (2675 m)

Core Mid Plane (1664 m)

Top of Orifice (0546 m)

Bottom of Orifice (0394 m)

Top of Inlet Flow Holes (0202 m)

Bottom of Assembly (000 m)

XA

BB

SECTION CndashC

ExpansionVolume

CC

SECTION DndashD

SECTION XndashX

DD

X

Figure 3 Gas expansion module assembly [4]

4 Science and Technology of Nuclear Installations

and Doppler effect based on the ENDFB-VII11968-groupnuclear data library For the fissile cells the heterogeneoushexagonal geometry has been adopted in a 6-step calculationprocedure e heterogeneous hexagonal geometry de-scription has also been used for control and safety rodsspatial self-shielded cross section (4-step calculation) erest nonburnable regions (insulator reflectors etc) foresee ahomogeneous geometry description of the cell and use the 2-step calculation procedure Since the subcritical cells do nothave the inner neutron source we calculate a relative re-gionrsquos spectrum for each of them as the external neutronsource e leakage effects of these subcritical cells are alsobeing considered Users can define the geometrical bucklingof the subcritical cells in the input card of ECCO to take theleakage effects into account e leakage effects are calcu-lated by the following equations according to the codingmanual

B2

58

πLtyp

1113888 1113889

2

(1)

where B is the buckling value in the correction methodΣt + DB2 and Ltyp is the typical dimension of the subcriticalregion

To update the cross section more accurately according tothe material temperature in transient calculations we per-formed cell calculations at 500K 750K and 1000K re-spectively and obtained two sets of homogeneous macrocross-section libraries e other material cross-section li-braries under temperatures between 500K and 1000K willbe derived by linear interpolation

e neutron calculation modelrsquos computational regioncovers each assembly in the radial direction e axialcomputational region is the area from the bottom to the topof the active region Each assembly was set as one calculationnode in the radial direction Figure 4 is the radial nodedivision schematic diagram of the FFTF reactor core In theaxial direction the neutronics calculation module of SAC-3D allows users to define the calculation nodes according totheir actual needs As Figure 5 shows we divided each as-sembly model into 38 calculation blocks in the present workEach calculation block is 25 cm tall while 38 blocks have atotal of 95 cm height which respects the active regionrsquos

actual height e relative axial positions of the control rodmaterials with respect to the fuel and GEM assemblies arealso shown in Figure 5 By dividing the reactor core cal-culation model into several calculation nodes in the radialand axial directions we have 7562 calculation nodes in theneutronics calculation model Zero flux boundary condi-tions are used to close the neutronic problem at the coreedges

As mentioned earlier the sodium level in GEMs is higherthan the top of the core active region When the test beganthe sodium level in GEMs will drop rapidly to the inletnozzle region which is lower than the bottom of the activeregion To predict the sodium level the following correlationwas suggested by the technical specifications

L 265 minus539504

244013 + F2 (2)

where F is the core flow rate in percent and L is the level ofsodium above the top of the inlet flow holes

In the transient calculation sodium and gas withinGEMs might be present simultaneously in the same cal-culation blocks where the gas-liquid interface is locatederefore the original cross-sections employed in the staticcalculations of these blocks need to be specially processedWe solve this problem by conducting the cross-sectionhomogenization during the online feedback reactivity cal-culation e homogenization method was shown in Fig-ure 6 At first we assumed that each assemblyrsquos boundarycondition in the radial direction is a total reflection and keptthe axial direction boundary conditions the same as in thecore neutronics calculation en we get the neutron fluxdistribution in the axial direction by conducting the one-dimensional SN (Discrete ordinates method) calculation anddo the needed cross-section homogenization as follows [8]

1113944i

1113938

hprime

0 1113936 i1φdh + 1113938h

hprime 1113936 i2φdh

1113938h

0 φdh (3)

where Σi are the cross sections consisting of removal fissionscattering absorption and total cross sections Σi1 and Σi2are the cross sections from the two neighbor nodes re-spectively h is the height of each node hprime is the height of

Table 2 Cell calculation treatment of FFTF LOFWOS test 13

Material NO XS name Assembly type Geometry treatment XS treatment1 DF31 Driver fuel Heterogeneous Critical2 DF41 Driver fuel Heterogeneous Critical3 DF32 Driver fuel Heterogeneous Critical4 DF42 Driver fuel Heterogeneous Critical5 Lower insulator Driver fuel Homogeneous Subcritical6 Upper insulator Driver fuel Homogeneous Subcritical7 SRCR Ab SafetyControl rod Heterogeneous Subcritical8 Sodium CH (SRCR) SafetyControl rod Homogeneous Subcritical9 Below Ab SafetyControl rod Homogeneous Subcritical10 Ref 772 Reflector Homogeneous Subcritical11 Ref 9 Reflector Homogeneous Subcritical12 Sodium CH (GEM) GEM Homogeneous Subcritical13 GAS GEM Homogeneous Subcritical

Science and Technology of Nuclear Installations 5

some point of the calculation block and φ is the neutronflux

32 +ermal-Hydraulics Calculation Model e design ofthe reactor was a three-loop primary systemwhere under lowpressure the three primary loops transport the heat generatedwithin the reactor core to the intermediate heat exchangersand back to the reactor vessel Each of the three primary loopscontains the same components Given the intrinsic symmetrycharacteristics of the thermal-hydraulic conditions of theprimary loops within the framework of the present bench-mark activities it was decided for the sake of simplicity toimplement a single equivalent primary and secondary loopmodel For the IHX primary pump and pipe models in thiswork we took into account their heat transfer area mass flowrate and other factors to ensure that they could be equivalentto the IHXs primary pumps and pipes in the overall threeprimary loopserefore the SAC-3Dmodel of the IHXs andprimary pumps only consists of a single IHX and a singlepump and a single average pipe layout is defined for theprimary loops As for the primary loop a single equivalentsecondary loop is modeled in SAC-3D

Figure 7 shows the layout of the FFTF reactor systemsimulation model e primary loop simulation model was

divided into two parts the reactor vessel and the primaryloop which include the hot leg piping the primary pumpthe primary side of IHXs and the cold leg piping Hot legpiping runs from the outlet plenum of the reactor vessel tothe primary pump and into the IHX primary side Cold legpiping returns sodium from the IHX to the inlet plenum ofthe reactor vessel discharging into the inlet plenum of thereactor vessel With regard to the secondary loops only thesecondary side of the IHX was modeled imposing properboundary conditions (coolant flow rate and temperature) atthe secondary hot leg and the secondary cold leg

SAC-3D uses the parallel-channel approach to conductthe reactor vessel thermal-hydraulics calculation which doesnot consider the coolant crossflow between the internalcomponents Simultaneously the model does not considerthe fuel componentrsquos axial heat conduction [9] In thepreliminary work we used only 9 channels to simulate thecore flow path and did not consider the bypass flow [3] isapproximate treatment brings large deviations in the ther-mal-hydraulic transient results To better correct the bias dueto the roughness of the thermal-hydraulic model a morerefined modeling approach was used In this paper thereactor vessel model consists of 13 parallel flow channels (11within the core model) connecting the inlet and outletplenums e inlet and outlet plenums are modeled with azero-dimensional volume module with respect to their ef-fective height and volume Within the outlet plenum modelthe sodium level is set at its nominal value and the argon gaspressure boundary condition is set at the top of the volumeAs shown in Figure 8 the reactor core model consists of 11

Driver Fuel 32

Driver Fuel 42

Driver Fuel 31

Safety Rod

Driver Fuel 41

Control Rod

GEM

Reflector

FMAICSA

Figure 4 Loading pattern of the calculation model of FFTF in theradial direction

SafetyRod

DriverFuel

Insulator (DF)Fuel (DF)Sodium CH (SRCR)Absorber (CR)

Below Ab (CR)Sodium CH (GEM)FMA ICSAReflector (Ref7729)

ControlRod

GEM FMAICSA

Reflector

Figure 5 Schematic of calculation nodes division of FFTF in theaxial direction

6 Science and Technology of Nuclear Installations

parallel flow channels all assemblies are grouped by theircoolant flow rate power distribution and assembly typeChannels 1 to 6 with channels 10 and 11 represent driver fuelassemblies flow channels where channels 10 and 11 rep-resent the individual PIOTA channels located in rows 2 and6 respectively Figure 9 shows the nodalization scheme ofthe driver fuel channels Each of these channels connects tothe outlet model and the inlet model from their top andbottom ese models are set to take the loss of pressurecaused by the orifice region and wire-wrapped fuel pinbundle into account As shown in Figure 9 each fuel channelis divided into five calculation points in radial directions Inthe axial direction the number of control volumes is set asthe same as the neutronics model to implement neutronics

thermal-hydraulics coupling during the transient simula-tion Table 3 shows the initial condition comparison betweenthe measurements and SAC-3D model results Channels 7represent controlsafety rod flow channels Channels 8 and 9represent two types of reflector assemblies (REF 7728A arelocated in the core basket and fed by sodium from the corebasket REF 8 B9 are located in the support skirt and fed bysodium from the annular plenum) respectively In additionseveral other flow paths draw sodium from the inlet plenumand discharge sodium into the outlet plenum Leakage andbypass flow paths provide sodium flow to the in-vesselstorage region the gap between the reactor vessel and vesselthermal liner We simplify these flow paths into two flowchannels In-Vessel Storage Channel and Bypass Channel

φ

TOTA

L RE

FLEC

TIO

N

Cross-secitonsHomogenization

Figure 6 Cross-section homogenization process

PIOTA6

PIOTA2

DF

CH1

DF

CH2

DF

CH3

DF

CH4

DF

CH5

DF

CH6

CRSR

CH

REF7728A

REF8B9

IN-VESSEL

STORAGE

BYPASS

HOT LEG

OUTLET PLENUMPrimary Loop

PUMP

DHX (BC)

SecondaryLoop

IHXSEC-SIDE

IHXPRI-SIDE

IHX SEC-SIDE INLET(BC)

COLD LEG

INLET PLENUM

CORE INLET MODEL

CORE OUTLET MODEL

Figure 7 Simplified layout of FFTF Simulation Model

Science and Technology of Nuclear Installations 7

In this work the primary pump is modeled with a pumpmodule based on the pumprsquos characteristics and theirnominal operating state Initial pump speed is adjusted tothe benchmark data e pump speed history is given asinput data during the transient e benchmark

specifications provide the pump performance curves for theprimary pumps However the data for these curves were notavailable To predict the pressure head during the transientthe following set of equations of the modified homologouspump theory of Wylie and Streeter were coded into thepump model ese modified correlations provide a goodapproximation of the dimensionless pump head (H)

H N2

+ Q2

1113874 1113875Wh(x) (4)

where N is the dimensionless pump speed Q is the relativevolumetric flow rate x π + arctan(QN)

Wh(x) 11139446

i0ahix

i (5)

whose coefficients are provided in Table 4e IHXs were vertically mounted counterflow shell and

tube designs Primary sodium entered the IHX from theoutlet of the primary loop hot leg piping and flowed downthrough the active heat transfer region along the outside ofthe IHX tubes Secondary sodium entered the IHX at the topand flowed down through a central downcomer into thelower hemispherical plenum From this plenum secondarysodium entered the IHX tubes at the bottom and flowedupward along the inner side of the IHX tubes out of the IHXIn the IHX model all heat transfer tubes have been sim-plified as one representative tube In an attempt to con-sistently simplify the model there are several assumptions(1) there is an ideal mixing of coolant at the inlet and outlet(2) fully developed convective heat transfer is assumed (3)no metallic structure of the IHX other than IHX tubes andshell wall is considered hence perfect insulation is postu-lated between primary and secondary sodium in the centraldowncomer pipe (4) no heat losses are accounted forthrough the external IHX vessel to the surrounding envi-ronment As shown in Figure 10 there are four radialcalculation nodes secondary coolant tube metal primarycoolant and shell wall e temperature calculation nodes ofthe heat tube metal and shell wall are defined in the center ofthe control volume e temperature calculation nodes ofthe coolant are defined at the boundary of the control body[9]

e energy equation of the primary side coolant controlvolume can be written as

ρVP

depi+1

dt Wp epi minus epi+11113872 1113873 minus HptApt Tpii+1 minus Tti1113872 1113873

minus HpshApsh Tpii+1 minus Tshi1113872 1113873

(6)

e energy equation of the secondary side coolantcontrol volume can be written as

ρVP

desi

dt Ws esi+1 minus esi1113872 1113873 + HstAst Tti minus Tsii+11113872 1113873 (7)

e energy equation of the IHX tube metal controlvolume can be written as

Channel 1

Channel 2

Channel 6

Channel 3

Channel 5

Channel 4

Channel 7

Channel 9

Channel 11

Channel 8

Channel 10

Figure 8 SAC-3D channel layout for FFTF core

UPPER AXIAL REFLECTOR

LOWER AXIAL REFLECTOR

INSULATOR PELLETS REGION

FUEL REGION

INSULATOR PELLETS REGION

GAP

CLADDING

COOLANT

STRUCTURE

FUEL

Figure 9 ermal-hydraulics model of driver fuel channels

8 Science and Technology of Nuclear Installations

Mtcti

dTti

dt HptApt Tpii+1 minus Tti1113872 1113873 minus HpstApst Tti minus Tsii+11113872 1113873

(8)

e energy equation of the IHX shell wall control volumecan be written as

Mshcshi

dTshi

dt HpshApsh Tpii+1 minus Tshi1113872 1113873 (9)

where p represents the coolant of the primary side s rep-resents the coolant of the secondary side t represents theheat exchanger tube of IHX sh represents the shell wall ofIHX e is enthalpy Wis mass flow rate T is temperature M

is mass c is specific heat capacity V is the volume of thecontrol volume H is the heat transfer coefficient betweenfluid and structural A is the heat transfer area betweenthe fluid and the structure and Tii+1 is the average fluidtemperature within two neighbor control volumes it isdefined as

Tii+1 Ti + Tii+1

2 (10)

As shown in Figure 7 the secondary loop wasmodeled astwo boundary conditions e DHX outlet coolant tem-perature values and the secondary loop coolant mass flowrates are imposed as the boundary conditions for the inletand outlet of the IHX secondary side

4 Results and Analysis

Table 5 summarizes the comparison of measurements andcalculation results of the initial plant conditions Reactorpower was slightly less than 50 and the core inlet tem-perature was reduced by nearly 80from the nominal coreinlet temperature is was done to ensure that the peak fueltemperatures did not rise too high to limit the impact of thetest on the durability of the fuel assemblies

Note that to date the IAEArsquos FFTF CRP project has justcompleted the blind phase and ANL has released experi-mental measurements of the part of the calculated FFTFreactor parameters erefore the following results partlycompare the simulated calculations with the real measure-ments and partly compare with other participantsrsquo calcu-lations Because different participants use differentcalculation methods and models we only make data devi-ation comparisons without deviation analysis for the resultswithout measurement data

Table 6 lists the main neutron results of FFTF LOFWOStest 13 of 10 participants Most of the results like theneutron multiplication factor delayed neutron fractionDoppler coefficient fuel density coefficient etc have arelatively good agreement among participants After re-moving results that deviated from the mean by more thantwo times the standard deviation the variation coefficient(δAvg) was distributed between 1 and 27 Significantdeviations appear in the structure density and sodiumdensity coefficientsrsquo results which have a 542 and 98variation coefficient respectively

e power distribution of steady-state estimated bySAC-3D is shown in Figure 11 e axially integrated powerof each assembly ranges from 155MW to 375MW Fig-ure 12 illustrates the variation coefficient map obtained bycomparing the integrated power simulation results withJAEA and ANLrsquos results e largest variation coefficient is

Table 3 Initial core flow distribution comparison

Channel Assembly type Measured mass flow rate (kgs) FFTF model Mass flow rate (kgs) Discrepancy ()1 DF 32 63305 63282 minus 0042 DF 42 15233 1523 minus 0023 DF 31 49907 49854 minus 0114 DF 31 28973 28956 minus 0065 DF 41 9984 9996 0126 DF 41 15233 15323 0597 SRCR 4091 4076 minus 0378 REF 7728A 5238 5243 0109 REF 8 B9 2348 2353 02110 PIOTA 2 2482 2494 04811 PIOTA 6 205 2037 minus 063

Table 4 Coefficients for the pump curve

i ah0 43196691 minus 576614382 301000293 minus 75465864 8675505 minus 0260626 minus 001596

BYPASSVOLUME

Wp

Ws

SHELL SIDE

TUBE SIDE

Figure 10 IHX calculation model

Science and Technology of Nuclear Installations 9

Table 5 Comparison of benchmark and SAC-3D steady-state parameters

Parameter Unit Measured value Calculated value Discrepancy ()Core power MW 1992 1992 000Core inlet temperature K 5904 59087 008Total core flow rate kgs 220224 219798 minus 019Mass flow rate through all assemblies kgs 198844 198934 005GEM sodium level1 cm 2216 2216 000Primary hot leg temperature K mdash 67818 mdashPrimary cold leg temperature K mdash 60589 mdashSecondary hot leg temperature K mdash 65656 mdashSecondary cold leg temperature K 58306 58378 0121Elevation relative to the top of inlet nozzle holes

Table 6 Main results of FFTF LOFWOS test 13 neutronics benchmark analysis

Argonne IGCAR INEST IPPE JAEA KIT KTH PSI ROME NCEPUNeutron multiplication factor 1000 0998 0999 0992 1017 0998 1022 1006 1000 0998Delayed neutron fraction 0003 0003 0007 0003 0003 0004 0003 0003 0003 0003Axial expansion coefficient (pcmdegC) minus 032 minus 023 mdash mdash minus 032 minus minus 03 minus 022 minus 048 minus03Radial expansion coefficient (pcmdegC) minus 1 minus 122 mdash mdash minus 1 minus minus 093 minus 152 minus 587 minus094Fuel Doppler constant (pcm) minus 629 minus 508 mdash mdash minus 634 minus 509 minus 564 minus 658 minus 688 minus524Fuel density coefficient (pcm) minus 136 minus 145 mdash mdash minus 045 mdash minus 136 minus 136 minus 14 minus132Structure density coefficient (pcm) minus 012 02 mdash mdash 003 mdash 01 004 minus 01 minus001Sodium density coefficient (pcmdegC) minus 035 minus 091 mdash mdash minus 041 009 minus 094 minus 027 minus 191 minus037Control and safety rods (pcm) minus 11849 mdash mdash minus 9396 10800 mdash minus 11540 minus 11823 minus 12773 minus8343Gas expansion modules (pcm) minus 442 minus 498 mdash minus 516 minus 489 minus 448 420 minus 475 minus 1201 minus782

324

195

263

252

315

344

197

CR

GEM

GEM

GEM

GEM GEM GEM

GEM

GEM

GEM

225

274

288

325

292

245

208

268

293

247

CR

179

177 155

201

190

213

220

192

206

223

295

SR

364

342

276

306

225

174

248

ICSA

312

306

375

SR

213

216

197205

CR

304

308

364

353

326

MOTA

290

205

231

280

273

329

298

SR

217

275

229

234

253

270

298

262

244

CR

232

191

257

253

289

CR

262

168

185

215

269

188

159

166 369

312

257

CR

207

Axially integratedpower (MW)

375

155

Figure 11 Power distribution map of FFTF core

10 Science and Technology of Nuclear Installations

327 which occurred in a fuel assembly type 42D Besideswe note that other assemblies with large coefficients ofvariation are located around this fuel assembly Since we donot have the power distributionrsquos measured data we cannotobjectively assess whether these biases are significant Bycomparing the codes applied by JAEA ANL and our sidewe believe that these biases are due to at least part of themodeling methods differences and different cross-sectionlibraries

Figures 13ndash15 depict the primary looprsquos mass flow ratersquostransient profile It can be seen that the SAC-3D very wellpredicts the pump coast down Minor differences existduring the natural circulation where the mass flow rates areslightly lower than the experimental data As shown inFigure 16 this is due to the underestimation of total power

Figures 16ndash18 show the transient reactor power profilesFigures 19 and 20 are the transient reactivity profile At 0 sthe primary pump is tripped and the core flow rate decreasesrapidly Due to the rapid decrease of the core cycling ca-pacity the assembliesrsquo temperature starts to rise and in-troduce negative net reactivity to bring down the reactorpower Starting from 5 s the coolant level in the GEMs dropsrapidly and the neutron leakage rate increases significantlyintroducing a remarkable negative reactivity e fissionpower decreases rapidly and the total power drops to 42 ofthe initial power at 10 s At 20 s the introduced negativereactivity increases at a slower rate as the core flow rate andthe coolant level within the GEMs begin to decrease at a

slower rate As shown in Figure 14 at approximately 90 s thenatural cycle is established e coolant level within GEMsbegins to stabilize and the negative reactivity it introducesalso stabilizes Figure 16 shows that the fission power isoverestimated due to the underestimation of the negativenet reactivity In the long term the fission power is close to

031

031

188

136

150

010

064

CR

GEM

GEM

GEM

GEM GEM GEM

GEM

GEM

GEM

172

195

102

295

286

108

147

287

263

238

CR

098

081 173

212

087

079

230

327

150

007

112

SR

181

137

015

207

128

055

097

ICSA

202

001

182

SR

026

140

179197

CR

030

021

003

116

016

MOTA

055

017

237

143

068

142

154

SR

055

105

089

013

090

063

084

087

088

CR

046

015

079

028

015

CR

043

057

037

056

108

040

009

089

104

118

CR

254

(Standard DevAverage)

327

001

032

Figure 12 Power distribution calculation variation coefficient map of FFTF corePu

mp

Disc

harg

e Pre

ssur

e (Ca

l) (M

Pa)

0 200 400

Time (s)

600 800

Loop 1 Mass Flow Rate (Exp)Loop 1 Mass Flow Rate (Cal)

Pump Discharge Pressure (Exp)Pump Discharge Pressure (Cal)

10

08

06

04

02

00

0

100

200

300

400

500

600

700

800

LOO

P 1

Mas

s Flo

w R

ate (

Cal)

200 400 600 8000Time (s)

Figure 13 Mass flow rate in loop 1

Science and Technology of Nuclear Installations 11

zero and the total power is contributed mainly by the decaypower e underestimation of the decay power leads to anunderestimation of the total power after 200 seconds Asshown in Figure 19 although the fuel temperature decreasesintroduced by the positive Dopplerrsquos reactivity feedback andpositive axial expansion reactivity feedback the net reac-tivity still maintains a significant negative value due to thesignificant negative reactivity introduced by GEMs

Figures 21 and 22 display the transient outlet temper-ature profiles of PIOTAs e SAC-3D results show a verysimilar trend compared to the experimental data with twopeaks occurring during the entire duration of the transientIn the beginning the outlet temperature rises rapidly as the

core flow rate drops rapidly as shown in Figure 13 epower decreases slowly because of the negative reactivityfeedback introduced by the control rod driveline expansionand radial expansion e power-to-flow ratio reaches thefirst peak value as shown in Figure 23 us the PIOTAsrsquooutlet temperatures increase rapidly and reach the first peakvalue After that the rapid drop of the coolant level withinthe GEMs introduced a large amount of negative reactivitycausing the total power to drop rapidly Meanwhile thedecreasing rate of mass flow rate starts to slow down ePIOTAsrsquo outlet temperatures start to decrease because thepower-to-flow ratio rapidly decreases Starting from about20 s the decrease in total power starts to slow down due to

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

200 400 600 8000Time (s)

0

5

10

15

20

Tota

l Cor

e Pow

er (C

al) (

MW

)

Figure 16 Reactor power of FFTF LOFWOS test 13 (low range)

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

0

20

40

60

80

100

120

140

160

180

200

Tota

l Cor

e Pow

er (C

al) (

MW

)

200 400 600 8000Time (s)

Figure 17 Reactor power of FFTF LOFWOS test 13

LOOP 1 NATURAL CIRCULATION

Loop 1 Mass Flow Rate (Cal)Loop 1 Mass Flow Rate (Exp)

0

10

20

30

40

50

Mas

s Flo

w R

ate (

kgs

)

100 200 300 400 500 600 700 800 9000Time (s)

Figure 14 Mass flow rate in loop 1 (Low range)

LOOP 1 TRANSITION TO NATURAL CIRCULATION

Loop 1 Mass Flow Rate (Cal)Loop 1 Mass Flow Rate (Exp)

-100

0

100

200

300

400

500

600

700

800

Mas

s Flo

w R

ate (

kgs

)

20 40 60 80 1000Time (s)

Figure 15 Mass flow rate in loop 1 (0 sndash100 s)

12 Science and Technology of Nuclear Installations

the rebound of the negative net reactivity as shown inFigure 20 erefore the power-to-flow ratio increaseswhich make the PIOTAsrsquo temperatures rise again At about110 s the PIOTAsrsquo temperatures reach the second peak valueafter the power-to-flow ratio reaches the second peak valueSince then the natural circulation starts to be establishedand maintained at about 4 of the rated flow as shown inFigure 14 e total power continues to decrease due to thenegative net reactivity e reactor enters a long-termcooling phase

In general the predicted results of SAC-3D are in goodagreement with the trend of the experimental data but thereare still deviations in the temperature values e outlettemperature of the PIOTA in row 2 is consistently lowerthan the measured value which is caused by the bias of thesimulated value of the total power transient variationSimilarly the simulated outlet temperature of the PIOTA inrow 6 is lower than the measured data until about 20 s butstarts to be higher than themeasured data after thenere isa maximum deviation of about 40 degrees Celsius at the

Net Reactivity (Cal)Doopler (Cal)Coolant Density (Cal)Axial Expansion (Cal)

Radial Expansion (Cal)Control Rod DrivelineExpansion (Cal)GEM (Cal)Net Reactivity (Exp)

ndash15

ndash10

ndash05

00

05

10

Net

Rea

ctiv

ity (C

al) (

$)

10 20 30 40 500Time (s)

Figure 20 Reactivity Transient Profile of FFTF LOFWOS test 13(0 sndash50 s)

Row 6 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Cal)Row 6 PIOTA Outlet Temp (Cal)

360

380

400

420

440

460

480

500

520

Row

6 P

IOTA

Out

let T

emp

(degC)

200 400 600 8000Time (s)

Figure 21 Row 2 and row 6 PIOTAs outlet temperature

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

0

20

40

60

80

100

120

140

160

180

200

Tota

l Cor

e Pow

er (C

al) (

MW

)

5 10 15 20 25 30 35 400Time (s)

Figure 18 Reactor power of FFTF LOFWOS test 13 (0 sndash40 s)

Net Reactivity (Cal)Doopler (Cal)Coolant Density (Cal)Axial Expansion (Cal)

Radial Expansion (Cal)Control Rod DrivelineExpansion (Cal)GEM (Cal)Net Reactivity (Exp)

ndash15

ndash10

ndash05

00

05

10

Net

Rea

ctiv

ity (C

al) (

$)

200 400 600 8000Time (s)

Figure 19 Reactivity transient profile of FFTF LOFWOS test 13

Science and Technology of Nuclear Installations 13

peak Unlike the PIOTA in row 2 the PIOTA in row 6 islocated at the outermost ring of the fuel assembly and is nextto a GEM assembly and a reflector assembly We believe thatthere are at least two possible reasons for this anomaly Oneis that even though the transientrsquos overall mass flow rate is ingood agreement with the measurement data it is stillpossible that the simulated mass flow rate variation withineach channel may not match the actual situation all that welle other important factor is the fact that the channel-to-channel heat transfer is not considered in the present worke neglect of heat transfer between the PIOTA in row 6 andGEM and reflector assembly introduced positive tempera-ture errors

5 Conclusions and Perspective

In the blind calculation phase of the IAEA FFTF LOFWOStest 13 CRP we modeled the FFTF reactor system by usingthe SAC-3D system analysis code e SAC-3D calculationresults have reasonably good agreement with the measureddata After benchmark analyzing the EBR-II [2] and FFTFreactors SAC-3D shows its good capability to predict thefast reactor behaviors under ATWS transient conditionsHowever the SAC-3D and FFTF models still have room forimprovement e deviations in total power transient cal-culations suggest further improvement in the reactivityfeedback models as well as the decay heat prediction modelAnomalies in the transient temperature prediction of thePIOTA in row 6 indicate that the thermal-hydraulics cal-culation module needs to consider the heat transfer betweenchannels In the next phase of the work we will examine thedeviations between simulation results further and refine theFFTF model based on the blind phase benchmark analysisresults e specific calculation modules of SAC-3D will alsobe improved to predict the fast reactorrsquos behavior better

Data Availability

e data that support the findings of this study are availablefrom IAEA Restrictions apply to the availability of thesedata which were used under license for this study Data areavailable from the corresponding author with the permis-sion of IAEA

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e authors would like to express their thanks to IAEAParticipation in the CRP on the FFTF LOFWOS test 13 isunder a research agreement between the North ChinaElectric Power University and the IAEA CRP numberI32011 is work was partially financially supported by theNational Natural Science Foundation of China (GrantNo11705057)

References

[1] D Sui D Lu L Ren and Y Liu ldquoDevelopment of three-di-mensional hot pool model in a system analysis code for pool-type FBRrdquo Nuclear Engineering and Design vol 256pp 264ndash273 2012

[2] D Lu S Lyu and D Sui ldquoVerification of SAC-3D based onEBR-II SHRT-45R benchmark datardquo in Proceedings of the 18thInternational Topical Meeting on Nuclear Reactor +ermalHydraulics Portland OR USA August 2019

[3] D Lu S Lyu and D Sui ldquoSimulation of FFTF loss of flowwithout scram test based on system code SAC-3Drdquo AtomicEnergy Science and Technology vol 55 no 8 pp 1345ndash13522021

[4] T Sumner A Moisseytsev F Heidet D W WootanA M Casella and J V Nelson Benchmark Specification forFFTF LOFWOS Test 13 IAEA Vienna Austria 2017

Row 6 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Cal)Row 6 PIOTA Outlet Temp (Cal)

360

380

400

420

440

460

480

500

520

Row

6 P

IOTA

Out

let T

emp

(degC)

2000Time (s)

Figure 22 Row 2 and row 6 PIOTAs outlet temperature(0 sndash200 s)

22

20

18

16

14

12

08

06

Dim

ensio

nles

s Pow

er-F

low

Rat

io

0 20 40 60 80 100 120Time (s)

140 160 180 200

Dimensionless Power-Flow Ratio

Dimensionless Power-Flow Ratio

200 400 600 8000Time (s)

06

08

12

10

14

16

18

20

22

Dim

ensio

nles

s Pow

er-F

low

Rat

io

Figure 23 Dimensionless power-flow ratio

14 Science and Technology of Nuclear Installations

[5] C Guo D Lu X Zhang and D Sui ldquoDevelopment and ap-plication of a safety analysis code for small Lead cooled FastReactor SVBR 75100rdquo Annals of Nuclear Energy vol 81pp 62ndash72 2015

[6] D Lu C Guo and D Sui ldquoA three-dimensional nodal neutronkinetics code with a higher-accuracy algorithm for reactor corein hexagonal-z geometryrdquo Annals of Nuclear Energy vol 101pp 250ndash261 2017

[7] J M Ruggieri J Tommasi J F Lebrat et al ldquoEranos 21International code system for GEN IV fast reactor analysisrdquo inProceedings of the 2006 International Congress on Advances inNuclear Power Plants ICAPPrsquo06 pp 2432ndash2439 Seoul KoreaJuly 2006

[8] S Lyu D Lu and D Sui ldquoNeutronics benchmark analysis ofthe EBR-II SHRT-45R with SAC-3Drdquo Nuclear Engineering andDesign vol 364 p 110679 2020

[9] C Guo D Lu D Sui and X Zhang ldquoSAC-CFR computer codeverification with Experimental Breeder Reactor II loss-of-primary-flow-without-scram tests datardquo Annals of NuclearEnergy vol 71 pp 166ndash173 2014

Science and Technology of Nuclear Installations 15

and Doppler effect based on the ENDFB-VII11968-groupnuclear data library For the fissile cells the heterogeneoushexagonal geometry has been adopted in a 6-step calculationprocedure e heterogeneous hexagonal geometry de-scription has also been used for control and safety rodsspatial self-shielded cross section (4-step calculation) erest nonburnable regions (insulator reflectors etc) foresee ahomogeneous geometry description of the cell and use the 2-step calculation procedure Since the subcritical cells do nothave the inner neutron source we calculate a relative re-gionrsquos spectrum for each of them as the external neutronsource e leakage effects of these subcritical cells are alsobeing considered Users can define the geometrical bucklingof the subcritical cells in the input card of ECCO to take theleakage effects into account e leakage effects are calcu-lated by the following equations according to the codingmanual

B2

58

πLtyp

1113888 1113889

2

(1)

where B is the buckling value in the correction methodΣt + DB2 and Ltyp is the typical dimension of the subcriticalregion

To update the cross section more accurately according tothe material temperature in transient calculations we per-formed cell calculations at 500K 750K and 1000K re-spectively and obtained two sets of homogeneous macrocross-section libraries e other material cross-section li-braries under temperatures between 500K and 1000K willbe derived by linear interpolation

e neutron calculation modelrsquos computational regioncovers each assembly in the radial direction e axialcomputational region is the area from the bottom to the topof the active region Each assembly was set as one calculationnode in the radial direction Figure 4 is the radial nodedivision schematic diagram of the FFTF reactor core In theaxial direction the neutronics calculation module of SAC-3D allows users to define the calculation nodes according totheir actual needs As Figure 5 shows we divided each as-sembly model into 38 calculation blocks in the present workEach calculation block is 25 cm tall while 38 blocks have atotal of 95 cm height which respects the active regionrsquos

actual height e relative axial positions of the control rodmaterials with respect to the fuel and GEM assemblies arealso shown in Figure 5 By dividing the reactor core cal-culation model into several calculation nodes in the radialand axial directions we have 7562 calculation nodes in theneutronics calculation model Zero flux boundary condi-tions are used to close the neutronic problem at the coreedges

As mentioned earlier the sodium level in GEMs is higherthan the top of the core active region When the test beganthe sodium level in GEMs will drop rapidly to the inletnozzle region which is lower than the bottom of the activeregion To predict the sodium level the following correlationwas suggested by the technical specifications

L 265 minus539504

244013 + F2 (2)

where F is the core flow rate in percent and L is the level ofsodium above the top of the inlet flow holes

In the transient calculation sodium and gas withinGEMs might be present simultaneously in the same cal-culation blocks where the gas-liquid interface is locatederefore the original cross-sections employed in the staticcalculations of these blocks need to be specially processedWe solve this problem by conducting the cross-sectionhomogenization during the online feedback reactivity cal-culation e homogenization method was shown in Fig-ure 6 At first we assumed that each assemblyrsquos boundarycondition in the radial direction is a total reflection and keptthe axial direction boundary conditions the same as in thecore neutronics calculation en we get the neutron fluxdistribution in the axial direction by conducting the one-dimensional SN (Discrete ordinates method) calculation anddo the needed cross-section homogenization as follows [8]

1113944i

1113938

hprime

0 1113936 i1φdh + 1113938h

hprime 1113936 i2φdh

1113938h

0 φdh (3)

where Σi are the cross sections consisting of removal fissionscattering absorption and total cross sections Σi1 and Σi2are the cross sections from the two neighbor nodes re-spectively h is the height of each node hprime is the height of

Table 2 Cell calculation treatment of FFTF LOFWOS test 13

Material NO XS name Assembly type Geometry treatment XS treatment1 DF31 Driver fuel Heterogeneous Critical2 DF41 Driver fuel Heterogeneous Critical3 DF32 Driver fuel Heterogeneous Critical4 DF42 Driver fuel Heterogeneous Critical5 Lower insulator Driver fuel Homogeneous Subcritical6 Upper insulator Driver fuel Homogeneous Subcritical7 SRCR Ab SafetyControl rod Heterogeneous Subcritical8 Sodium CH (SRCR) SafetyControl rod Homogeneous Subcritical9 Below Ab SafetyControl rod Homogeneous Subcritical10 Ref 772 Reflector Homogeneous Subcritical11 Ref 9 Reflector Homogeneous Subcritical12 Sodium CH (GEM) GEM Homogeneous Subcritical13 GAS GEM Homogeneous Subcritical

Science and Technology of Nuclear Installations 5

some point of the calculation block and φ is the neutronflux

32 +ermal-Hydraulics Calculation Model e design ofthe reactor was a three-loop primary systemwhere under lowpressure the three primary loops transport the heat generatedwithin the reactor core to the intermediate heat exchangersand back to the reactor vessel Each of the three primary loopscontains the same components Given the intrinsic symmetrycharacteristics of the thermal-hydraulic conditions of theprimary loops within the framework of the present bench-mark activities it was decided for the sake of simplicity toimplement a single equivalent primary and secondary loopmodel For the IHX primary pump and pipe models in thiswork we took into account their heat transfer area mass flowrate and other factors to ensure that they could be equivalentto the IHXs primary pumps and pipes in the overall threeprimary loopserefore the SAC-3Dmodel of the IHXs andprimary pumps only consists of a single IHX and a singlepump and a single average pipe layout is defined for theprimary loops As for the primary loop a single equivalentsecondary loop is modeled in SAC-3D

Figure 7 shows the layout of the FFTF reactor systemsimulation model e primary loop simulation model was

divided into two parts the reactor vessel and the primaryloop which include the hot leg piping the primary pumpthe primary side of IHXs and the cold leg piping Hot legpiping runs from the outlet plenum of the reactor vessel tothe primary pump and into the IHX primary side Cold legpiping returns sodium from the IHX to the inlet plenum ofthe reactor vessel discharging into the inlet plenum of thereactor vessel With regard to the secondary loops only thesecondary side of the IHX was modeled imposing properboundary conditions (coolant flow rate and temperature) atthe secondary hot leg and the secondary cold leg

SAC-3D uses the parallel-channel approach to conductthe reactor vessel thermal-hydraulics calculation which doesnot consider the coolant crossflow between the internalcomponents Simultaneously the model does not considerthe fuel componentrsquos axial heat conduction [9] In thepreliminary work we used only 9 channels to simulate thecore flow path and did not consider the bypass flow [3] isapproximate treatment brings large deviations in the ther-mal-hydraulic transient results To better correct the bias dueto the roughness of the thermal-hydraulic model a morerefined modeling approach was used In this paper thereactor vessel model consists of 13 parallel flow channels (11within the core model) connecting the inlet and outletplenums e inlet and outlet plenums are modeled with azero-dimensional volume module with respect to their ef-fective height and volume Within the outlet plenum modelthe sodium level is set at its nominal value and the argon gaspressure boundary condition is set at the top of the volumeAs shown in Figure 8 the reactor core model consists of 11

Driver Fuel 32

Driver Fuel 42

Driver Fuel 31

Safety Rod

Driver Fuel 41

Control Rod

GEM

Reflector

FMAICSA

Figure 4 Loading pattern of the calculation model of FFTF in theradial direction

SafetyRod

DriverFuel

Insulator (DF)Fuel (DF)Sodium CH (SRCR)Absorber (CR)

Below Ab (CR)Sodium CH (GEM)FMA ICSAReflector (Ref7729)

ControlRod

GEM FMAICSA

Reflector

Figure 5 Schematic of calculation nodes division of FFTF in theaxial direction

6 Science and Technology of Nuclear Installations

parallel flow channels all assemblies are grouped by theircoolant flow rate power distribution and assembly typeChannels 1 to 6 with channels 10 and 11 represent driver fuelassemblies flow channels where channels 10 and 11 rep-resent the individual PIOTA channels located in rows 2 and6 respectively Figure 9 shows the nodalization scheme ofthe driver fuel channels Each of these channels connects tothe outlet model and the inlet model from their top andbottom ese models are set to take the loss of pressurecaused by the orifice region and wire-wrapped fuel pinbundle into account As shown in Figure 9 each fuel channelis divided into five calculation points in radial directions Inthe axial direction the number of control volumes is set asthe same as the neutronics model to implement neutronics

thermal-hydraulics coupling during the transient simula-tion Table 3 shows the initial condition comparison betweenthe measurements and SAC-3D model results Channels 7represent controlsafety rod flow channels Channels 8 and 9represent two types of reflector assemblies (REF 7728A arelocated in the core basket and fed by sodium from the corebasket REF 8 B9 are located in the support skirt and fed bysodium from the annular plenum) respectively In additionseveral other flow paths draw sodium from the inlet plenumand discharge sodium into the outlet plenum Leakage andbypass flow paths provide sodium flow to the in-vesselstorage region the gap between the reactor vessel and vesselthermal liner We simplify these flow paths into two flowchannels In-Vessel Storage Channel and Bypass Channel

φ

TOTA

L RE

FLEC

TIO

N

Cross-secitonsHomogenization

Figure 6 Cross-section homogenization process

PIOTA6

PIOTA2

DF

CH1

DF

CH2

DF

CH3

DF

CH4

DF

CH5

DF

CH6

CRSR

CH

REF7728A

REF8B9

IN-VESSEL

STORAGE

BYPASS

HOT LEG

OUTLET PLENUMPrimary Loop

PUMP

DHX (BC)

SecondaryLoop

IHXSEC-SIDE

IHXPRI-SIDE

IHX SEC-SIDE INLET(BC)

COLD LEG

INLET PLENUM

CORE INLET MODEL

CORE OUTLET MODEL

Figure 7 Simplified layout of FFTF Simulation Model

Science and Technology of Nuclear Installations 7

In this work the primary pump is modeled with a pumpmodule based on the pumprsquos characteristics and theirnominal operating state Initial pump speed is adjusted tothe benchmark data e pump speed history is given asinput data during the transient e benchmark

specifications provide the pump performance curves for theprimary pumps However the data for these curves were notavailable To predict the pressure head during the transientthe following set of equations of the modified homologouspump theory of Wylie and Streeter were coded into thepump model ese modified correlations provide a goodapproximation of the dimensionless pump head (H)

H N2

+ Q2

1113874 1113875Wh(x) (4)

where N is the dimensionless pump speed Q is the relativevolumetric flow rate x π + arctan(QN)

Wh(x) 11139446

i0ahix

i (5)

whose coefficients are provided in Table 4e IHXs were vertically mounted counterflow shell and

tube designs Primary sodium entered the IHX from theoutlet of the primary loop hot leg piping and flowed downthrough the active heat transfer region along the outside ofthe IHX tubes Secondary sodium entered the IHX at the topand flowed down through a central downcomer into thelower hemispherical plenum From this plenum secondarysodium entered the IHX tubes at the bottom and flowedupward along the inner side of the IHX tubes out of the IHXIn the IHX model all heat transfer tubes have been sim-plified as one representative tube In an attempt to con-sistently simplify the model there are several assumptions(1) there is an ideal mixing of coolant at the inlet and outlet(2) fully developed convective heat transfer is assumed (3)no metallic structure of the IHX other than IHX tubes andshell wall is considered hence perfect insulation is postu-lated between primary and secondary sodium in the centraldowncomer pipe (4) no heat losses are accounted forthrough the external IHX vessel to the surrounding envi-ronment As shown in Figure 10 there are four radialcalculation nodes secondary coolant tube metal primarycoolant and shell wall e temperature calculation nodes ofthe heat tube metal and shell wall are defined in the center ofthe control volume e temperature calculation nodes ofthe coolant are defined at the boundary of the control body[9]

e energy equation of the primary side coolant controlvolume can be written as

ρVP

depi+1

dt Wp epi minus epi+11113872 1113873 minus HptApt Tpii+1 minus Tti1113872 1113873

minus HpshApsh Tpii+1 minus Tshi1113872 1113873

(6)

e energy equation of the secondary side coolantcontrol volume can be written as

ρVP

desi

dt Ws esi+1 minus esi1113872 1113873 + HstAst Tti minus Tsii+11113872 1113873 (7)

e energy equation of the IHX tube metal controlvolume can be written as

Channel 1

Channel 2

Channel 6

Channel 3

Channel 5

Channel 4

Channel 7

Channel 9

Channel 11

Channel 8

Channel 10

Figure 8 SAC-3D channel layout for FFTF core

UPPER AXIAL REFLECTOR

LOWER AXIAL REFLECTOR

INSULATOR PELLETS REGION

FUEL REGION

INSULATOR PELLETS REGION

GAP

CLADDING

COOLANT

STRUCTURE

FUEL

Figure 9 ermal-hydraulics model of driver fuel channels

8 Science and Technology of Nuclear Installations

Mtcti

dTti

dt HptApt Tpii+1 minus Tti1113872 1113873 minus HpstApst Tti minus Tsii+11113872 1113873

(8)

e energy equation of the IHX shell wall control volumecan be written as

Mshcshi

dTshi

dt HpshApsh Tpii+1 minus Tshi1113872 1113873 (9)

where p represents the coolant of the primary side s rep-resents the coolant of the secondary side t represents theheat exchanger tube of IHX sh represents the shell wall ofIHX e is enthalpy Wis mass flow rate T is temperature M

is mass c is specific heat capacity V is the volume of thecontrol volume H is the heat transfer coefficient betweenfluid and structural A is the heat transfer area betweenthe fluid and the structure and Tii+1 is the average fluidtemperature within two neighbor control volumes it isdefined as

Tii+1 Ti + Tii+1

2 (10)

As shown in Figure 7 the secondary loop wasmodeled astwo boundary conditions e DHX outlet coolant tem-perature values and the secondary loop coolant mass flowrates are imposed as the boundary conditions for the inletand outlet of the IHX secondary side

4 Results and Analysis

Table 5 summarizes the comparison of measurements andcalculation results of the initial plant conditions Reactorpower was slightly less than 50 and the core inlet tem-perature was reduced by nearly 80from the nominal coreinlet temperature is was done to ensure that the peak fueltemperatures did not rise too high to limit the impact of thetest on the durability of the fuel assemblies

Note that to date the IAEArsquos FFTF CRP project has justcompleted the blind phase and ANL has released experi-mental measurements of the part of the calculated FFTFreactor parameters erefore the following results partlycompare the simulated calculations with the real measure-ments and partly compare with other participantsrsquo calcu-lations Because different participants use differentcalculation methods and models we only make data devi-ation comparisons without deviation analysis for the resultswithout measurement data

Table 6 lists the main neutron results of FFTF LOFWOStest 13 of 10 participants Most of the results like theneutron multiplication factor delayed neutron fractionDoppler coefficient fuel density coefficient etc have arelatively good agreement among participants After re-moving results that deviated from the mean by more thantwo times the standard deviation the variation coefficient(δAvg) was distributed between 1 and 27 Significantdeviations appear in the structure density and sodiumdensity coefficientsrsquo results which have a 542 and 98variation coefficient respectively

e power distribution of steady-state estimated bySAC-3D is shown in Figure 11 e axially integrated powerof each assembly ranges from 155MW to 375MW Fig-ure 12 illustrates the variation coefficient map obtained bycomparing the integrated power simulation results withJAEA and ANLrsquos results e largest variation coefficient is

Table 3 Initial core flow distribution comparison

Channel Assembly type Measured mass flow rate (kgs) FFTF model Mass flow rate (kgs) Discrepancy ()1 DF 32 63305 63282 minus 0042 DF 42 15233 1523 minus 0023 DF 31 49907 49854 minus 0114 DF 31 28973 28956 minus 0065 DF 41 9984 9996 0126 DF 41 15233 15323 0597 SRCR 4091 4076 minus 0378 REF 7728A 5238 5243 0109 REF 8 B9 2348 2353 02110 PIOTA 2 2482 2494 04811 PIOTA 6 205 2037 minus 063

Table 4 Coefficients for the pump curve

i ah0 43196691 minus 576614382 301000293 minus 75465864 8675505 minus 0260626 minus 001596

BYPASSVOLUME

Wp

Ws

SHELL SIDE

TUBE SIDE

Figure 10 IHX calculation model

Science and Technology of Nuclear Installations 9

Table 5 Comparison of benchmark and SAC-3D steady-state parameters

Parameter Unit Measured value Calculated value Discrepancy ()Core power MW 1992 1992 000Core inlet temperature K 5904 59087 008Total core flow rate kgs 220224 219798 minus 019Mass flow rate through all assemblies kgs 198844 198934 005GEM sodium level1 cm 2216 2216 000Primary hot leg temperature K mdash 67818 mdashPrimary cold leg temperature K mdash 60589 mdashSecondary hot leg temperature K mdash 65656 mdashSecondary cold leg temperature K 58306 58378 0121Elevation relative to the top of inlet nozzle holes

Table 6 Main results of FFTF LOFWOS test 13 neutronics benchmark analysis

Argonne IGCAR INEST IPPE JAEA KIT KTH PSI ROME NCEPUNeutron multiplication factor 1000 0998 0999 0992 1017 0998 1022 1006 1000 0998Delayed neutron fraction 0003 0003 0007 0003 0003 0004 0003 0003 0003 0003Axial expansion coefficient (pcmdegC) minus 032 minus 023 mdash mdash minus 032 minus minus 03 minus 022 minus 048 minus03Radial expansion coefficient (pcmdegC) minus 1 minus 122 mdash mdash minus 1 minus minus 093 minus 152 minus 587 minus094Fuel Doppler constant (pcm) minus 629 minus 508 mdash mdash minus 634 minus 509 minus 564 minus 658 minus 688 minus524Fuel density coefficient (pcm) minus 136 minus 145 mdash mdash minus 045 mdash minus 136 minus 136 minus 14 minus132Structure density coefficient (pcm) minus 012 02 mdash mdash 003 mdash 01 004 minus 01 minus001Sodium density coefficient (pcmdegC) minus 035 minus 091 mdash mdash minus 041 009 minus 094 minus 027 minus 191 minus037Control and safety rods (pcm) minus 11849 mdash mdash minus 9396 10800 mdash minus 11540 minus 11823 minus 12773 minus8343Gas expansion modules (pcm) minus 442 minus 498 mdash minus 516 minus 489 minus 448 420 minus 475 minus 1201 minus782

324

195

263

252

315

344

197

CR

GEM

GEM

GEM

GEM GEM GEM

GEM

GEM

GEM

225

274

288

325

292

245

208

268

293

247

CR

179

177 155

201

190

213

220

192

206

223

295

SR

364

342

276

306

225

174

248

ICSA

312

306

375

SR

213

216

197205

CR

304

308

364

353

326

MOTA

290

205

231

280

273

329

298

SR

217

275

229

234

253

270

298

262

244

CR

232

191

257

253

289

CR

262

168

185

215

269

188

159

166 369

312

257

CR

207

Axially integratedpower (MW)

375

155

Figure 11 Power distribution map of FFTF core

10 Science and Technology of Nuclear Installations

327 which occurred in a fuel assembly type 42D Besideswe note that other assemblies with large coefficients ofvariation are located around this fuel assembly Since we donot have the power distributionrsquos measured data we cannotobjectively assess whether these biases are significant Bycomparing the codes applied by JAEA ANL and our sidewe believe that these biases are due to at least part of themodeling methods differences and different cross-sectionlibraries

Figures 13ndash15 depict the primary looprsquos mass flow ratersquostransient profile It can be seen that the SAC-3D very wellpredicts the pump coast down Minor differences existduring the natural circulation where the mass flow rates areslightly lower than the experimental data As shown inFigure 16 this is due to the underestimation of total power

Figures 16ndash18 show the transient reactor power profilesFigures 19 and 20 are the transient reactivity profile At 0 sthe primary pump is tripped and the core flow rate decreasesrapidly Due to the rapid decrease of the core cycling ca-pacity the assembliesrsquo temperature starts to rise and in-troduce negative net reactivity to bring down the reactorpower Starting from 5 s the coolant level in the GEMs dropsrapidly and the neutron leakage rate increases significantlyintroducing a remarkable negative reactivity e fissionpower decreases rapidly and the total power drops to 42 ofthe initial power at 10 s At 20 s the introduced negativereactivity increases at a slower rate as the core flow rate andthe coolant level within the GEMs begin to decrease at a

slower rate As shown in Figure 14 at approximately 90 s thenatural cycle is established e coolant level within GEMsbegins to stabilize and the negative reactivity it introducesalso stabilizes Figure 16 shows that the fission power isoverestimated due to the underestimation of the negativenet reactivity In the long term the fission power is close to

031

031

188

136

150

010

064

CR

GEM

GEM

GEM

GEM GEM GEM

GEM

GEM

GEM

172

195

102

295

286

108

147

287

263

238

CR

098

081 173

212

087

079

230

327

150

007

112

SR

181

137

015

207

128

055

097

ICSA

202

001

182

SR

026

140

179197

CR

030

021

003

116

016

MOTA

055

017

237

143

068

142

154

SR

055

105

089

013

090

063

084

087

088

CR

046

015

079

028

015

CR

043

057

037

056

108

040

009

089

104

118

CR

254

(Standard DevAverage)

327

001

032

Figure 12 Power distribution calculation variation coefficient map of FFTF corePu

mp

Disc

harg

e Pre

ssur

e (Ca

l) (M

Pa)

0 200 400

Time (s)

600 800

Loop 1 Mass Flow Rate (Exp)Loop 1 Mass Flow Rate (Cal)

Pump Discharge Pressure (Exp)Pump Discharge Pressure (Cal)

10

08

06

04

02

00

0

100

200

300

400

500

600

700

800

LOO

P 1

Mas

s Flo

w R

ate (

Cal)

200 400 600 8000Time (s)

Figure 13 Mass flow rate in loop 1

Science and Technology of Nuclear Installations 11

zero and the total power is contributed mainly by the decaypower e underestimation of the decay power leads to anunderestimation of the total power after 200 seconds Asshown in Figure 19 although the fuel temperature decreasesintroduced by the positive Dopplerrsquos reactivity feedback andpositive axial expansion reactivity feedback the net reac-tivity still maintains a significant negative value due to thesignificant negative reactivity introduced by GEMs

Figures 21 and 22 display the transient outlet temper-ature profiles of PIOTAs e SAC-3D results show a verysimilar trend compared to the experimental data with twopeaks occurring during the entire duration of the transientIn the beginning the outlet temperature rises rapidly as the

core flow rate drops rapidly as shown in Figure 13 epower decreases slowly because of the negative reactivityfeedback introduced by the control rod driveline expansionand radial expansion e power-to-flow ratio reaches thefirst peak value as shown in Figure 23 us the PIOTAsrsquooutlet temperatures increase rapidly and reach the first peakvalue After that the rapid drop of the coolant level withinthe GEMs introduced a large amount of negative reactivitycausing the total power to drop rapidly Meanwhile thedecreasing rate of mass flow rate starts to slow down ePIOTAsrsquo outlet temperatures start to decrease because thepower-to-flow ratio rapidly decreases Starting from about20 s the decrease in total power starts to slow down due to

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

200 400 600 8000Time (s)

0

5

10

15

20

Tota

l Cor

e Pow

er (C

al) (

MW

)

Figure 16 Reactor power of FFTF LOFWOS test 13 (low range)

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

0

20

40

60

80

100

120

140

160

180

200

Tota

l Cor

e Pow

er (C

al) (

MW

)

200 400 600 8000Time (s)

Figure 17 Reactor power of FFTF LOFWOS test 13

LOOP 1 NATURAL CIRCULATION

Loop 1 Mass Flow Rate (Cal)Loop 1 Mass Flow Rate (Exp)

0

10

20

30

40

50

Mas

s Flo

w R

ate (

kgs

)

100 200 300 400 500 600 700 800 9000Time (s)

Figure 14 Mass flow rate in loop 1 (Low range)

LOOP 1 TRANSITION TO NATURAL CIRCULATION

Loop 1 Mass Flow Rate (Cal)Loop 1 Mass Flow Rate (Exp)

-100

0

100

200

300

400

500

600

700

800

Mas

s Flo

w R

ate (

kgs

)

20 40 60 80 1000Time (s)

Figure 15 Mass flow rate in loop 1 (0 sndash100 s)

12 Science and Technology of Nuclear Installations

the rebound of the negative net reactivity as shown inFigure 20 erefore the power-to-flow ratio increaseswhich make the PIOTAsrsquo temperatures rise again At about110 s the PIOTAsrsquo temperatures reach the second peak valueafter the power-to-flow ratio reaches the second peak valueSince then the natural circulation starts to be establishedand maintained at about 4 of the rated flow as shown inFigure 14 e total power continues to decrease due to thenegative net reactivity e reactor enters a long-termcooling phase

In general the predicted results of SAC-3D are in goodagreement with the trend of the experimental data but thereare still deviations in the temperature values e outlettemperature of the PIOTA in row 2 is consistently lowerthan the measured value which is caused by the bias of thesimulated value of the total power transient variationSimilarly the simulated outlet temperature of the PIOTA inrow 6 is lower than the measured data until about 20 s butstarts to be higher than themeasured data after thenere isa maximum deviation of about 40 degrees Celsius at the

Net Reactivity (Cal)Doopler (Cal)Coolant Density (Cal)Axial Expansion (Cal)

Radial Expansion (Cal)Control Rod DrivelineExpansion (Cal)GEM (Cal)Net Reactivity (Exp)

ndash15

ndash10

ndash05

00

05

10

Net

Rea

ctiv

ity (C

al) (

$)

10 20 30 40 500Time (s)

Figure 20 Reactivity Transient Profile of FFTF LOFWOS test 13(0 sndash50 s)

Row 6 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Cal)Row 6 PIOTA Outlet Temp (Cal)

360

380

400

420

440

460

480

500

520

Row

6 P

IOTA

Out

let T

emp

(degC)

200 400 600 8000Time (s)

Figure 21 Row 2 and row 6 PIOTAs outlet temperature

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

0

20

40

60

80

100

120

140

160

180

200

Tota

l Cor

e Pow

er (C

al) (

MW

)

5 10 15 20 25 30 35 400Time (s)

Figure 18 Reactor power of FFTF LOFWOS test 13 (0 sndash40 s)

Net Reactivity (Cal)Doopler (Cal)Coolant Density (Cal)Axial Expansion (Cal)

Radial Expansion (Cal)Control Rod DrivelineExpansion (Cal)GEM (Cal)Net Reactivity (Exp)

ndash15

ndash10

ndash05

00

05

10

Net

Rea

ctiv

ity (C

al) (

$)

200 400 600 8000Time (s)

Figure 19 Reactivity transient profile of FFTF LOFWOS test 13

Science and Technology of Nuclear Installations 13

peak Unlike the PIOTA in row 2 the PIOTA in row 6 islocated at the outermost ring of the fuel assembly and is nextto a GEM assembly and a reflector assembly We believe thatthere are at least two possible reasons for this anomaly Oneis that even though the transientrsquos overall mass flow rate is ingood agreement with the measurement data it is stillpossible that the simulated mass flow rate variation withineach channel may not match the actual situation all that welle other important factor is the fact that the channel-to-channel heat transfer is not considered in the present worke neglect of heat transfer between the PIOTA in row 6 andGEM and reflector assembly introduced positive tempera-ture errors

5 Conclusions and Perspective

In the blind calculation phase of the IAEA FFTF LOFWOStest 13 CRP we modeled the FFTF reactor system by usingthe SAC-3D system analysis code e SAC-3D calculationresults have reasonably good agreement with the measureddata After benchmark analyzing the EBR-II [2] and FFTFreactors SAC-3D shows its good capability to predict thefast reactor behaviors under ATWS transient conditionsHowever the SAC-3D and FFTF models still have room forimprovement e deviations in total power transient cal-culations suggest further improvement in the reactivityfeedback models as well as the decay heat prediction modelAnomalies in the transient temperature prediction of thePIOTA in row 6 indicate that the thermal-hydraulics cal-culation module needs to consider the heat transfer betweenchannels In the next phase of the work we will examine thedeviations between simulation results further and refine theFFTF model based on the blind phase benchmark analysisresults e specific calculation modules of SAC-3D will alsobe improved to predict the fast reactorrsquos behavior better

Data Availability

e data that support the findings of this study are availablefrom IAEA Restrictions apply to the availability of thesedata which were used under license for this study Data areavailable from the corresponding author with the permis-sion of IAEA

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e authors would like to express their thanks to IAEAParticipation in the CRP on the FFTF LOFWOS test 13 isunder a research agreement between the North ChinaElectric Power University and the IAEA CRP numberI32011 is work was partially financially supported by theNational Natural Science Foundation of China (GrantNo11705057)

References

[1] D Sui D Lu L Ren and Y Liu ldquoDevelopment of three-di-mensional hot pool model in a system analysis code for pool-type FBRrdquo Nuclear Engineering and Design vol 256pp 264ndash273 2012

[2] D Lu S Lyu and D Sui ldquoVerification of SAC-3D based onEBR-II SHRT-45R benchmark datardquo in Proceedings of the 18thInternational Topical Meeting on Nuclear Reactor +ermalHydraulics Portland OR USA August 2019

[3] D Lu S Lyu and D Sui ldquoSimulation of FFTF loss of flowwithout scram test based on system code SAC-3Drdquo AtomicEnergy Science and Technology vol 55 no 8 pp 1345ndash13522021

[4] T Sumner A Moisseytsev F Heidet D W WootanA M Casella and J V Nelson Benchmark Specification forFFTF LOFWOS Test 13 IAEA Vienna Austria 2017

Row 6 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Cal)Row 6 PIOTA Outlet Temp (Cal)

360

380

400

420

440

460

480

500

520

Row

6 P

IOTA

Out

let T

emp

(degC)

2000Time (s)

Figure 22 Row 2 and row 6 PIOTAs outlet temperature(0 sndash200 s)

22

20

18

16

14

12

08

06

Dim

ensio

nles

s Pow

er-F

low

Rat

io

0 20 40 60 80 100 120Time (s)

140 160 180 200

Dimensionless Power-Flow Ratio

Dimensionless Power-Flow Ratio

200 400 600 8000Time (s)

06

08

12

10

14

16

18

20

22

Dim

ensio

nles

s Pow

er-F

low

Rat

io

Figure 23 Dimensionless power-flow ratio

14 Science and Technology of Nuclear Installations

[5] C Guo D Lu X Zhang and D Sui ldquoDevelopment and ap-plication of a safety analysis code for small Lead cooled FastReactor SVBR 75100rdquo Annals of Nuclear Energy vol 81pp 62ndash72 2015

[6] D Lu C Guo and D Sui ldquoA three-dimensional nodal neutronkinetics code with a higher-accuracy algorithm for reactor corein hexagonal-z geometryrdquo Annals of Nuclear Energy vol 101pp 250ndash261 2017

[7] J M Ruggieri J Tommasi J F Lebrat et al ldquoEranos 21International code system for GEN IV fast reactor analysisrdquo inProceedings of the 2006 International Congress on Advances inNuclear Power Plants ICAPPrsquo06 pp 2432ndash2439 Seoul KoreaJuly 2006

[8] S Lyu D Lu and D Sui ldquoNeutronics benchmark analysis ofthe EBR-II SHRT-45R with SAC-3Drdquo Nuclear Engineering andDesign vol 364 p 110679 2020

[9] C Guo D Lu D Sui and X Zhang ldquoSAC-CFR computer codeverification with Experimental Breeder Reactor II loss-of-primary-flow-without-scram tests datardquo Annals of NuclearEnergy vol 71 pp 166ndash173 2014

Science and Technology of Nuclear Installations 15

some point of the calculation block and φ is the neutronflux

32 +ermal-Hydraulics Calculation Model e design ofthe reactor was a three-loop primary systemwhere under lowpressure the three primary loops transport the heat generatedwithin the reactor core to the intermediate heat exchangersand back to the reactor vessel Each of the three primary loopscontains the same components Given the intrinsic symmetrycharacteristics of the thermal-hydraulic conditions of theprimary loops within the framework of the present bench-mark activities it was decided for the sake of simplicity toimplement a single equivalent primary and secondary loopmodel For the IHX primary pump and pipe models in thiswork we took into account their heat transfer area mass flowrate and other factors to ensure that they could be equivalentto the IHXs primary pumps and pipes in the overall threeprimary loopserefore the SAC-3Dmodel of the IHXs andprimary pumps only consists of a single IHX and a singlepump and a single average pipe layout is defined for theprimary loops As for the primary loop a single equivalentsecondary loop is modeled in SAC-3D

Figure 7 shows the layout of the FFTF reactor systemsimulation model e primary loop simulation model was

divided into two parts the reactor vessel and the primaryloop which include the hot leg piping the primary pumpthe primary side of IHXs and the cold leg piping Hot legpiping runs from the outlet plenum of the reactor vessel tothe primary pump and into the IHX primary side Cold legpiping returns sodium from the IHX to the inlet plenum ofthe reactor vessel discharging into the inlet plenum of thereactor vessel With regard to the secondary loops only thesecondary side of the IHX was modeled imposing properboundary conditions (coolant flow rate and temperature) atthe secondary hot leg and the secondary cold leg

SAC-3D uses the parallel-channel approach to conductthe reactor vessel thermal-hydraulics calculation which doesnot consider the coolant crossflow between the internalcomponents Simultaneously the model does not considerthe fuel componentrsquos axial heat conduction [9] In thepreliminary work we used only 9 channels to simulate thecore flow path and did not consider the bypass flow [3] isapproximate treatment brings large deviations in the ther-mal-hydraulic transient results To better correct the bias dueto the roughness of the thermal-hydraulic model a morerefined modeling approach was used In this paper thereactor vessel model consists of 13 parallel flow channels (11within the core model) connecting the inlet and outletplenums e inlet and outlet plenums are modeled with azero-dimensional volume module with respect to their ef-fective height and volume Within the outlet plenum modelthe sodium level is set at its nominal value and the argon gaspressure boundary condition is set at the top of the volumeAs shown in Figure 8 the reactor core model consists of 11

Driver Fuel 32

Driver Fuel 42

Driver Fuel 31

Safety Rod

Driver Fuel 41

Control Rod

GEM

Reflector

FMAICSA

Figure 4 Loading pattern of the calculation model of FFTF in theradial direction

SafetyRod

DriverFuel

Insulator (DF)Fuel (DF)Sodium CH (SRCR)Absorber (CR)

Below Ab (CR)Sodium CH (GEM)FMA ICSAReflector (Ref7729)

ControlRod

GEM FMAICSA

Reflector

Figure 5 Schematic of calculation nodes division of FFTF in theaxial direction

6 Science and Technology of Nuclear Installations

parallel flow channels all assemblies are grouped by theircoolant flow rate power distribution and assembly typeChannels 1 to 6 with channels 10 and 11 represent driver fuelassemblies flow channels where channels 10 and 11 rep-resent the individual PIOTA channels located in rows 2 and6 respectively Figure 9 shows the nodalization scheme ofthe driver fuel channels Each of these channels connects tothe outlet model and the inlet model from their top andbottom ese models are set to take the loss of pressurecaused by the orifice region and wire-wrapped fuel pinbundle into account As shown in Figure 9 each fuel channelis divided into five calculation points in radial directions Inthe axial direction the number of control volumes is set asthe same as the neutronics model to implement neutronics

thermal-hydraulics coupling during the transient simula-tion Table 3 shows the initial condition comparison betweenthe measurements and SAC-3D model results Channels 7represent controlsafety rod flow channels Channels 8 and 9represent two types of reflector assemblies (REF 7728A arelocated in the core basket and fed by sodium from the corebasket REF 8 B9 are located in the support skirt and fed bysodium from the annular plenum) respectively In additionseveral other flow paths draw sodium from the inlet plenumand discharge sodium into the outlet plenum Leakage andbypass flow paths provide sodium flow to the in-vesselstorage region the gap between the reactor vessel and vesselthermal liner We simplify these flow paths into two flowchannels In-Vessel Storage Channel and Bypass Channel

φ

TOTA

L RE

FLEC

TIO

N

Cross-secitonsHomogenization

Figure 6 Cross-section homogenization process

PIOTA6

PIOTA2

DF

CH1

DF

CH2

DF

CH3

DF

CH4

DF

CH5

DF

CH6

CRSR

CH

REF7728A

REF8B9

IN-VESSEL

STORAGE

BYPASS

HOT LEG

OUTLET PLENUMPrimary Loop

PUMP

DHX (BC)

SecondaryLoop

IHXSEC-SIDE

IHXPRI-SIDE

IHX SEC-SIDE INLET(BC)

COLD LEG

INLET PLENUM

CORE INLET MODEL

CORE OUTLET MODEL

Figure 7 Simplified layout of FFTF Simulation Model

Science and Technology of Nuclear Installations 7

In this work the primary pump is modeled with a pumpmodule based on the pumprsquos characteristics and theirnominal operating state Initial pump speed is adjusted tothe benchmark data e pump speed history is given asinput data during the transient e benchmark

specifications provide the pump performance curves for theprimary pumps However the data for these curves were notavailable To predict the pressure head during the transientthe following set of equations of the modified homologouspump theory of Wylie and Streeter were coded into thepump model ese modified correlations provide a goodapproximation of the dimensionless pump head (H)

H N2

+ Q2

1113874 1113875Wh(x) (4)

where N is the dimensionless pump speed Q is the relativevolumetric flow rate x π + arctan(QN)

Wh(x) 11139446

i0ahix

i (5)

whose coefficients are provided in Table 4e IHXs were vertically mounted counterflow shell and

tube designs Primary sodium entered the IHX from theoutlet of the primary loop hot leg piping and flowed downthrough the active heat transfer region along the outside ofthe IHX tubes Secondary sodium entered the IHX at the topand flowed down through a central downcomer into thelower hemispherical plenum From this plenum secondarysodium entered the IHX tubes at the bottom and flowedupward along the inner side of the IHX tubes out of the IHXIn the IHX model all heat transfer tubes have been sim-plified as one representative tube In an attempt to con-sistently simplify the model there are several assumptions(1) there is an ideal mixing of coolant at the inlet and outlet(2) fully developed convective heat transfer is assumed (3)no metallic structure of the IHX other than IHX tubes andshell wall is considered hence perfect insulation is postu-lated between primary and secondary sodium in the centraldowncomer pipe (4) no heat losses are accounted forthrough the external IHX vessel to the surrounding envi-ronment As shown in Figure 10 there are four radialcalculation nodes secondary coolant tube metal primarycoolant and shell wall e temperature calculation nodes ofthe heat tube metal and shell wall are defined in the center ofthe control volume e temperature calculation nodes ofthe coolant are defined at the boundary of the control body[9]

e energy equation of the primary side coolant controlvolume can be written as

ρVP

depi+1

dt Wp epi minus epi+11113872 1113873 minus HptApt Tpii+1 minus Tti1113872 1113873

minus HpshApsh Tpii+1 minus Tshi1113872 1113873

(6)

e energy equation of the secondary side coolantcontrol volume can be written as

ρVP

desi

dt Ws esi+1 minus esi1113872 1113873 + HstAst Tti minus Tsii+11113872 1113873 (7)

e energy equation of the IHX tube metal controlvolume can be written as

Channel 1

Channel 2

Channel 6

Channel 3

Channel 5

Channel 4

Channel 7

Channel 9

Channel 11

Channel 8

Channel 10

Figure 8 SAC-3D channel layout for FFTF core

UPPER AXIAL REFLECTOR

LOWER AXIAL REFLECTOR

INSULATOR PELLETS REGION

FUEL REGION

INSULATOR PELLETS REGION

GAP

CLADDING

COOLANT

STRUCTURE

FUEL

Figure 9 ermal-hydraulics model of driver fuel channels

8 Science and Technology of Nuclear Installations

Mtcti

dTti

dt HptApt Tpii+1 minus Tti1113872 1113873 minus HpstApst Tti minus Tsii+11113872 1113873

(8)

e energy equation of the IHX shell wall control volumecan be written as

Mshcshi

dTshi

dt HpshApsh Tpii+1 minus Tshi1113872 1113873 (9)

where p represents the coolant of the primary side s rep-resents the coolant of the secondary side t represents theheat exchanger tube of IHX sh represents the shell wall ofIHX e is enthalpy Wis mass flow rate T is temperature M

is mass c is specific heat capacity V is the volume of thecontrol volume H is the heat transfer coefficient betweenfluid and structural A is the heat transfer area betweenthe fluid and the structure and Tii+1 is the average fluidtemperature within two neighbor control volumes it isdefined as

Tii+1 Ti + Tii+1

2 (10)

As shown in Figure 7 the secondary loop wasmodeled astwo boundary conditions e DHX outlet coolant tem-perature values and the secondary loop coolant mass flowrates are imposed as the boundary conditions for the inletand outlet of the IHX secondary side

4 Results and Analysis

Table 5 summarizes the comparison of measurements andcalculation results of the initial plant conditions Reactorpower was slightly less than 50 and the core inlet tem-perature was reduced by nearly 80from the nominal coreinlet temperature is was done to ensure that the peak fueltemperatures did not rise too high to limit the impact of thetest on the durability of the fuel assemblies

Note that to date the IAEArsquos FFTF CRP project has justcompleted the blind phase and ANL has released experi-mental measurements of the part of the calculated FFTFreactor parameters erefore the following results partlycompare the simulated calculations with the real measure-ments and partly compare with other participantsrsquo calcu-lations Because different participants use differentcalculation methods and models we only make data devi-ation comparisons without deviation analysis for the resultswithout measurement data

Table 6 lists the main neutron results of FFTF LOFWOStest 13 of 10 participants Most of the results like theneutron multiplication factor delayed neutron fractionDoppler coefficient fuel density coefficient etc have arelatively good agreement among participants After re-moving results that deviated from the mean by more thantwo times the standard deviation the variation coefficient(δAvg) was distributed between 1 and 27 Significantdeviations appear in the structure density and sodiumdensity coefficientsrsquo results which have a 542 and 98variation coefficient respectively

e power distribution of steady-state estimated bySAC-3D is shown in Figure 11 e axially integrated powerof each assembly ranges from 155MW to 375MW Fig-ure 12 illustrates the variation coefficient map obtained bycomparing the integrated power simulation results withJAEA and ANLrsquos results e largest variation coefficient is

Table 3 Initial core flow distribution comparison

Channel Assembly type Measured mass flow rate (kgs) FFTF model Mass flow rate (kgs) Discrepancy ()1 DF 32 63305 63282 minus 0042 DF 42 15233 1523 minus 0023 DF 31 49907 49854 minus 0114 DF 31 28973 28956 minus 0065 DF 41 9984 9996 0126 DF 41 15233 15323 0597 SRCR 4091 4076 minus 0378 REF 7728A 5238 5243 0109 REF 8 B9 2348 2353 02110 PIOTA 2 2482 2494 04811 PIOTA 6 205 2037 minus 063

Table 4 Coefficients for the pump curve

i ah0 43196691 minus 576614382 301000293 minus 75465864 8675505 minus 0260626 minus 001596

BYPASSVOLUME

Wp

Ws

SHELL SIDE

TUBE SIDE

Figure 10 IHX calculation model

Science and Technology of Nuclear Installations 9

Table 5 Comparison of benchmark and SAC-3D steady-state parameters

Parameter Unit Measured value Calculated value Discrepancy ()Core power MW 1992 1992 000Core inlet temperature K 5904 59087 008Total core flow rate kgs 220224 219798 minus 019Mass flow rate through all assemblies kgs 198844 198934 005GEM sodium level1 cm 2216 2216 000Primary hot leg temperature K mdash 67818 mdashPrimary cold leg temperature K mdash 60589 mdashSecondary hot leg temperature K mdash 65656 mdashSecondary cold leg temperature K 58306 58378 0121Elevation relative to the top of inlet nozzle holes

Table 6 Main results of FFTF LOFWOS test 13 neutronics benchmark analysis

Argonne IGCAR INEST IPPE JAEA KIT KTH PSI ROME NCEPUNeutron multiplication factor 1000 0998 0999 0992 1017 0998 1022 1006 1000 0998Delayed neutron fraction 0003 0003 0007 0003 0003 0004 0003 0003 0003 0003Axial expansion coefficient (pcmdegC) minus 032 minus 023 mdash mdash minus 032 minus minus 03 minus 022 minus 048 minus03Radial expansion coefficient (pcmdegC) minus 1 minus 122 mdash mdash minus 1 minus minus 093 minus 152 minus 587 minus094Fuel Doppler constant (pcm) minus 629 minus 508 mdash mdash minus 634 minus 509 minus 564 minus 658 minus 688 minus524Fuel density coefficient (pcm) minus 136 minus 145 mdash mdash minus 045 mdash minus 136 minus 136 minus 14 minus132Structure density coefficient (pcm) minus 012 02 mdash mdash 003 mdash 01 004 minus 01 minus001Sodium density coefficient (pcmdegC) minus 035 minus 091 mdash mdash minus 041 009 minus 094 minus 027 minus 191 minus037Control and safety rods (pcm) minus 11849 mdash mdash minus 9396 10800 mdash minus 11540 minus 11823 minus 12773 minus8343Gas expansion modules (pcm) minus 442 minus 498 mdash minus 516 minus 489 minus 448 420 minus 475 minus 1201 minus782

324

195

263

252

315

344

197

CR

GEM

GEM

GEM

GEM GEM GEM

GEM

GEM

GEM

225

274

288

325

292

245

208

268

293

247

CR

179

177 155

201

190

213

220

192

206

223

295

SR

364

342

276

306

225

174

248

ICSA

312

306

375

SR

213

216

197205

CR

304

308

364

353

326

MOTA

290

205

231

280

273

329

298

SR

217

275

229

234

253

270

298

262

244

CR

232

191

257

253

289

CR

262

168

185

215

269

188

159

166 369

312

257

CR

207

Axially integratedpower (MW)

375

155

Figure 11 Power distribution map of FFTF core

10 Science and Technology of Nuclear Installations

327 which occurred in a fuel assembly type 42D Besideswe note that other assemblies with large coefficients ofvariation are located around this fuel assembly Since we donot have the power distributionrsquos measured data we cannotobjectively assess whether these biases are significant Bycomparing the codes applied by JAEA ANL and our sidewe believe that these biases are due to at least part of themodeling methods differences and different cross-sectionlibraries

Figures 13ndash15 depict the primary looprsquos mass flow ratersquostransient profile It can be seen that the SAC-3D very wellpredicts the pump coast down Minor differences existduring the natural circulation where the mass flow rates areslightly lower than the experimental data As shown inFigure 16 this is due to the underestimation of total power

Figures 16ndash18 show the transient reactor power profilesFigures 19 and 20 are the transient reactivity profile At 0 sthe primary pump is tripped and the core flow rate decreasesrapidly Due to the rapid decrease of the core cycling ca-pacity the assembliesrsquo temperature starts to rise and in-troduce negative net reactivity to bring down the reactorpower Starting from 5 s the coolant level in the GEMs dropsrapidly and the neutron leakage rate increases significantlyintroducing a remarkable negative reactivity e fissionpower decreases rapidly and the total power drops to 42 ofthe initial power at 10 s At 20 s the introduced negativereactivity increases at a slower rate as the core flow rate andthe coolant level within the GEMs begin to decrease at a

slower rate As shown in Figure 14 at approximately 90 s thenatural cycle is established e coolant level within GEMsbegins to stabilize and the negative reactivity it introducesalso stabilizes Figure 16 shows that the fission power isoverestimated due to the underestimation of the negativenet reactivity In the long term the fission power is close to

031

031

188

136

150

010

064

CR

GEM

GEM

GEM

GEM GEM GEM

GEM

GEM

GEM

172

195

102

295

286

108

147

287

263

238

CR

098

081 173

212

087

079

230

327

150

007

112

SR

181

137

015

207

128

055

097

ICSA

202

001

182

SR

026

140

179197

CR

030

021

003

116

016

MOTA

055

017

237

143

068

142

154

SR

055

105

089

013

090

063

084

087

088

CR

046

015

079

028

015

CR

043

057

037

056

108

040

009

089

104

118

CR

254

(Standard DevAverage)

327

001

032

Figure 12 Power distribution calculation variation coefficient map of FFTF corePu

mp

Disc

harg

e Pre

ssur

e (Ca

l) (M

Pa)

0 200 400

Time (s)

600 800

Loop 1 Mass Flow Rate (Exp)Loop 1 Mass Flow Rate (Cal)

Pump Discharge Pressure (Exp)Pump Discharge Pressure (Cal)

10

08

06

04

02

00

0

100

200

300

400

500

600

700

800

LOO

P 1

Mas

s Flo

w R

ate (

Cal)

200 400 600 8000Time (s)

Figure 13 Mass flow rate in loop 1

Science and Technology of Nuclear Installations 11

zero and the total power is contributed mainly by the decaypower e underestimation of the decay power leads to anunderestimation of the total power after 200 seconds Asshown in Figure 19 although the fuel temperature decreasesintroduced by the positive Dopplerrsquos reactivity feedback andpositive axial expansion reactivity feedback the net reac-tivity still maintains a significant negative value due to thesignificant negative reactivity introduced by GEMs

Figures 21 and 22 display the transient outlet temper-ature profiles of PIOTAs e SAC-3D results show a verysimilar trend compared to the experimental data with twopeaks occurring during the entire duration of the transientIn the beginning the outlet temperature rises rapidly as the

core flow rate drops rapidly as shown in Figure 13 epower decreases slowly because of the negative reactivityfeedback introduced by the control rod driveline expansionand radial expansion e power-to-flow ratio reaches thefirst peak value as shown in Figure 23 us the PIOTAsrsquooutlet temperatures increase rapidly and reach the first peakvalue After that the rapid drop of the coolant level withinthe GEMs introduced a large amount of negative reactivitycausing the total power to drop rapidly Meanwhile thedecreasing rate of mass flow rate starts to slow down ePIOTAsrsquo outlet temperatures start to decrease because thepower-to-flow ratio rapidly decreases Starting from about20 s the decrease in total power starts to slow down due to

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

200 400 600 8000Time (s)

0

5

10

15

20

Tota

l Cor

e Pow

er (C

al) (

MW

)

Figure 16 Reactor power of FFTF LOFWOS test 13 (low range)

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

0

20

40

60

80

100

120

140

160

180

200

Tota

l Cor

e Pow

er (C

al) (

MW

)

200 400 600 8000Time (s)

Figure 17 Reactor power of FFTF LOFWOS test 13

LOOP 1 NATURAL CIRCULATION

Loop 1 Mass Flow Rate (Cal)Loop 1 Mass Flow Rate (Exp)

0

10

20

30

40

50

Mas

s Flo

w R

ate (

kgs

)

100 200 300 400 500 600 700 800 9000Time (s)

Figure 14 Mass flow rate in loop 1 (Low range)

LOOP 1 TRANSITION TO NATURAL CIRCULATION

Loop 1 Mass Flow Rate (Cal)Loop 1 Mass Flow Rate (Exp)

-100

0

100

200

300

400

500

600

700

800

Mas

s Flo

w R

ate (

kgs

)

20 40 60 80 1000Time (s)

Figure 15 Mass flow rate in loop 1 (0 sndash100 s)

12 Science and Technology of Nuclear Installations

the rebound of the negative net reactivity as shown inFigure 20 erefore the power-to-flow ratio increaseswhich make the PIOTAsrsquo temperatures rise again At about110 s the PIOTAsrsquo temperatures reach the second peak valueafter the power-to-flow ratio reaches the second peak valueSince then the natural circulation starts to be establishedand maintained at about 4 of the rated flow as shown inFigure 14 e total power continues to decrease due to thenegative net reactivity e reactor enters a long-termcooling phase

In general the predicted results of SAC-3D are in goodagreement with the trend of the experimental data but thereare still deviations in the temperature values e outlettemperature of the PIOTA in row 2 is consistently lowerthan the measured value which is caused by the bias of thesimulated value of the total power transient variationSimilarly the simulated outlet temperature of the PIOTA inrow 6 is lower than the measured data until about 20 s butstarts to be higher than themeasured data after thenere isa maximum deviation of about 40 degrees Celsius at the

Net Reactivity (Cal)Doopler (Cal)Coolant Density (Cal)Axial Expansion (Cal)

Radial Expansion (Cal)Control Rod DrivelineExpansion (Cal)GEM (Cal)Net Reactivity (Exp)

ndash15

ndash10

ndash05

00

05

10

Net

Rea

ctiv

ity (C

al) (

$)

10 20 30 40 500Time (s)

Figure 20 Reactivity Transient Profile of FFTF LOFWOS test 13(0 sndash50 s)

Row 6 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Cal)Row 6 PIOTA Outlet Temp (Cal)

360

380

400

420

440

460

480

500

520

Row

6 P

IOTA

Out

let T

emp

(degC)

200 400 600 8000Time (s)

Figure 21 Row 2 and row 6 PIOTAs outlet temperature

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

0

20

40

60

80

100

120

140

160

180

200

Tota

l Cor

e Pow

er (C

al) (

MW

)

5 10 15 20 25 30 35 400Time (s)

Figure 18 Reactor power of FFTF LOFWOS test 13 (0 sndash40 s)

Net Reactivity (Cal)Doopler (Cal)Coolant Density (Cal)Axial Expansion (Cal)

Radial Expansion (Cal)Control Rod DrivelineExpansion (Cal)GEM (Cal)Net Reactivity (Exp)

ndash15

ndash10

ndash05

00

05

10

Net

Rea

ctiv

ity (C

al) (

$)

200 400 600 8000Time (s)

Figure 19 Reactivity transient profile of FFTF LOFWOS test 13

Science and Technology of Nuclear Installations 13

peak Unlike the PIOTA in row 2 the PIOTA in row 6 islocated at the outermost ring of the fuel assembly and is nextto a GEM assembly and a reflector assembly We believe thatthere are at least two possible reasons for this anomaly Oneis that even though the transientrsquos overall mass flow rate is ingood agreement with the measurement data it is stillpossible that the simulated mass flow rate variation withineach channel may not match the actual situation all that welle other important factor is the fact that the channel-to-channel heat transfer is not considered in the present worke neglect of heat transfer between the PIOTA in row 6 andGEM and reflector assembly introduced positive tempera-ture errors

5 Conclusions and Perspective

In the blind calculation phase of the IAEA FFTF LOFWOStest 13 CRP we modeled the FFTF reactor system by usingthe SAC-3D system analysis code e SAC-3D calculationresults have reasonably good agreement with the measureddata After benchmark analyzing the EBR-II [2] and FFTFreactors SAC-3D shows its good capability to predict thefast reactor behaviors under ATWS transient conditionsHowever the SAC-3D and FFTF models still have room forimprovement e deviations in total power transient cal-culations suggest further improvement in the reactivityfeedback models as well as the decay heat prediction modelAnomalies in the transient temperature prediction of thePIOTA in row 6 indicate that the thermal-hydraulics cal-culation module needs to consider the heat transfer betweenchannels In the next phase of the work we will examine thedeviations between simulation results further and refine theFFTF model based on the blind phase benchmark analysisresults e specific calculation modules of SAC-3D will alsobe improved to predict the fast reactorrsquos behavior better

Data Availability

e data that support the findings of this study are availablefrom IAEA Restrictions apply to the availability of thesedata which were used under license for this study Data areavailable from the corresponding author with the permis-sion of IAEA

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e authors would like to express their thanks to IAEAParticipation in the CRP on the FFTF LOFWOS test 13 isunder a research agreement between the North ChinaElectric Power University and the IAEA CRP numberI32011 is work was partially financially supported by theNational Natural Science Foundation of China (GrantNo11705057)

References

[1] D Sui D Lu L Ren and Y Liu ldquoDevelopment of three-di-mensional hot pool model in a system analysis code for pool-type FBRrdquo Nuclear Engineering and Design vol 256pp 264ndash273 2012

[2] D Lu S Lyu and D Sui ldquoVerification of SAC-3D based onEBR-II SHRT-45R benchmark datardquo in Proceedings of the 18thInternational Topical Meeting on Nuclear Reactor +ermalHydraulics Portland OR USA August 2019

[3] D Lu S Lyu and D Sui ldquoSimulation of FFTF loss of flowwithout scram test based on system code SAC-3Drdquo AtomicEnergy Science and Technology vol 55 no 8 pp 1345ndash13522021

[4] T Sumner A Moisseytsev F Heidet D W WootanA M Casella and J V Nelson Benchmark Specification forFFTF LOFWOS Test 13 IAEA Vienna Austria 2017

Row 6 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Cal)Row 6 PIOTA Outlet Temp (Cal)

360

380

400

420

440

460

480

500

520

Row

6 P

IOTA

Out

let T

emp

(degC)

2000Time (s)

Figure 22 Row 2 and row 6 PIOTAs outlet temperature(0 sndash200 s)

22

20

18

16

14

12

08

06

Dim

ensio

nles

s Pow

er-F

low

Rat

io

0 20 40 60 80 100 120Time (s)

140 160 180 200

Dimensionless Power-Flow Ratio

Dimensionless Power-Flow Ratio

200 400 600 8000Time (s)

06

08

12

10

14

16

18

20

22

Dim

ensio

nles

s Pow

er-F

low

Rat

io

Figure 23 Dimensionless power-flow ratio

14 Science and Technology of Nuclear Installations

[5] C Guo D Lu X Zhang and D Sui ldquoDevelopment and ap-plication of a safety analysis code for small Lead cooled FastReactor SVBR 75100rdquo Annals of Nuclear Energy vol 81pp 62ndash72 2015

[6] D Lu C Guo and D Sui ldquoA three-dimensional nodal neutronkinetics code with a higher-accuracy algorithm for reactor corein hexagonal-z geometryrdquo Annals of Nuclear Energy vol 101pp 250ndash261 2017

[7] J M Ruggieri J Tommasi J F Lebrat et al ldquoEranos 21International code system for GEN IV fast reactor analysisrdquo inProceedings of the 2006 International Congress on Advances inNuclear Power Plants ICAPPrsquo06 pp 2432ndash2439 Seoul KoreaJuly 2006

[8] S Lyu D Lu and D Sui ldquoNeutronics benchmark analysis ofthe EBR-II SHRT-45R with SAC-3Drdquo Nuclear Engineering andDesign vol 364 p 110679 2020

[9] C Guo D Lu D Sui and X Zhang ldquoSAC-CFR computer codeverification with Experimental Breeder Reactor II loss-of-primary-flow-without-scram tests datardquo Annals of NuclearEnergy vol 71 pp 166ndash173 2014

Science and Technology of Nuclear Installations 15

parallel flow channels all assemblies are grouped by theircoolant flow rate power distribution and assembly typeChannels 1 to 6 with channels 10 and 11 represent driver fuelassemblies flow channels where channels 10 and 11 rep-resent the individual PIOTA channels located in rows 2 and6 respectively Figure 9 shows the nodalization scheme ofthe driver fuel channels Each of these channels connects tothe outlet model and the inlet model from their top andbottom ese models are set to take the loss of pressurecaused by the orifice region and wire-wrapped fuel pinbundle into account As shown in Figure 9 each fuel channelis divided into five calculation points in radial directions Inthe axial direction the number of control volumes is set asthe same as the neutronics model to implement neutronics

thermal-hydraulics coupling during the transient simula-tion Table 3 shows the initial condition comparison betweenthe measurements and SAC-3D model results Channels 7represent controlsafety rod flow channels Channels 8 and 9represent two types of reflector assemblies (REF 7728A arelocated in the core basket and fed by sodium from the corebasket REF 8 B9 are located in the support skirt and fed bysodium from the annular plenum) respectively In additionseveral other flow paths draw sodium from the inlet plenumand discharge sodium into the outlet plenum Leakage andbypass flow paths provide sodium flow to the in-vesselstorage region the gap between the reactor vessel and vesselthermal liner We simplify these flow paths into two flowchannels In-Vessel Storage Channel and Bypass Channel

φ

TOTA

L RE

FLEC

TIO

N

Cross-secitonsHomogenization

Figure 6 Cross-section homogenization process

PIOTA6

PIOTA2

DF

CH1

DF

CH2

DF

CH3

DF

CH4

DF

CH5

DF

CH6

CRSR

CH

REF7728A

REF8B9

IN-VESSEL

STORAGE

BYPASS

HOT LEG

OUTLET PLENUMPrimary Loop

PUMP

DHX (BC)

SecondaryLoop

IHXSEC-SIDE

IHXPRI-SIDE

IHX SEC-SIDE INLET(BC)

COLD LEG

INLET PLENUM

CORE INLET MODEL

CORE OUTLET MODEL

Figure 7 Simplified layout of FFTF Simulation Model

Science and Technology of Nuclear Installations 7

In this work the primary pump is modeled with a pumpmodule based on the pumprsquos characteristics and theirnominal operating state Initial pump speed is adjusted tothe benchmark data e pump speed history is given asinput data during the transient e benchmark

specifications provide the pump performance curves for theprimary pumps However the data for these curves were notavailable To predict the pressure head during the transientthe following set of equations of the modified homologouspump theory of Wylie and Streeter were coded into thepump model ese modified correlations provide a goodapproximation of the dimensionless pump head (H)

H N2

+ Q2

1113874 1113875Wh(x) (4)

where N is the dimensionless pump speed Q is the relativevolumetric flow rate x π + arctan(QN)

Wh(x) 11139446

i0ahix

i (5)

whose coefficients are provided in Table 4e IHXs were vertically mounted counterflow shell and

tube designs Primary sodium entered the IHX from theoutlet of the primary loop hot leg piping and flowed downthrough the active heat transfer region along the outside ofthe IHX tubes Secondary sodium entered the IHX at the topand flowed down through a central downcomer into thelower hemispherical plenum From this plenum secondarysodium entered the IHX tubes at the bottom and flowedupward along the inner side of the IHX tubes out of the IHXIn the IHX model all heat transfer tubes have been sim-plified as one representative tube In an attempt to con-sistently simplify the model there are several assumptions(1) there is an ideal mixing of coolant at the inlet and outlet(2) fully developed convective heat transfer is assumed (3)no metallic structure of the IHX other than IHX tubes andshell wall is considered hence perfect insulation is postu-lated between primary and secondary sodium in the centraldowncomer pipe (4) no heat losses are accounted forthrough the external IHX vessel to the surrounding envi-ronment As shown in Figure 10 there are four radialcalculation nodes secondary coolant tube metal primarycoolant and shell wall e temperature calculation nodes ofthe heat tube metal and shell wall are defined in the center ofthe control volume e temperature calculation nodes ofthe coolant are defined at the boundary of the control body[9]

e energy equation of the primary side coolant controlvolume can be written as

ρVP

depi+1

dt Wp epi minus epi+11113872 1113873 minus HptApt Tpii+1 minus Tti1113872 1113873

minus HpshApsh Tpii+1 minus Tshi1113872 1113873

(6)

e energy equation of the secondary side coolantcontrol volume can be written as

ρVP

desi

dt Ws esi+1 minus esi1113872 1113873 + HstAst Tti minus Tsii+11113872 1113873 (7)

e energy equation of the IHX tube metal controlvolume can be written as

Channel 1

Channel 2

Channel 6

Channel 3

Channel 5

Channel 4

Channel 7

Channel 9

Channel 11

Channel 8

Channel 10

Figure 8 SAC-3D channel layout for FFTF core

UPPER AXIAL REFLECTOR

LOWER AXIAL REFLECTOR

INSULATOR PELLETS REGION

FUEL REGION

INSULATOR PELLETS REGION

GAP

CLADDING

COOLANT

STRUCTURE

FUEL

Figure 9 ermal-hydraulics model of driver fuel channels

8 Science and Technology of Nuclear Installations

Mtcti

dTti

dt HptApt Tpii+1 minus Tti1113872 1113873 minus HpstApst Tti minus Tsii+11113872 1113873

(8)

e energy equation of the IHX shell wall control volumecan be written as

Mshcshi

dTshi

dt HpshApsh Tpii+1 minus Tshi1113872 1113873 (9)

where p represents the coolant of the primary side s rep-resents the coolant of the secondary side t represents theheat exchanger tube of IHX sh represents the shell wall ofIHX e is enthalpy Wis mass flow rate T is temperature M

is mass c is specific heat capacity V is the volume of thecontrol volume H is the heat transfer coefficient betweenfluid and structural A is the heat transfer area betweenthe fluid and the structure and Tii+1 is the average fluidtemperature within two neighbor control volumes it isdefined as

Tii+1 Ti + Tii+1

2 (10)

As shown in Figure 7 the secondary loop wasmodeled astwo boundary conditions e DHX outlet coolant tem-perature values and the secondary loop coolant mass flowrates are imposed as the boundary conditions for the inletand outlet of the IHX secondary side

4 Results and Analysis

Table 5 summarizes the comparison of measurements andcalculation results of the initial plant conditions Reactorpower was slightly less than 50 and the core inlet tem-perature was reduced by nearly 80from the nominal coreinlet temperature is was done to ensure that the peak fueltemperatures did not rise too high to limit the impact of thetest on the durability of the fuel assemblies

Note that to date the IAEArsquos FFTF CRP project has justcompleted the blind phase and ANL has released experi-mental measurements of the part of the calculated FFTFreactor parameters erefore the following results partlycompare the simulated calculations with the real measure-ments and partly compare with other participantsrsquo calcu-lations Because different participants use differentcalculation methods and models we only make data devi-ation comparisons without deviation analysis for the resultswithout measurement data

Table 6 lists the main neutron results of FFTF LOFWOStest 13 of 10 participants Most of the results like theneutron multiplication factor delayed neutron fractionDoppler coefficient fuel density coefficient etc have arelatively good agreement among participants After re-moving results that deviated from the mean by more thantwo times the standard deviation the variation coefficient(δAvg) was distributed between 1 and 27 Significantdeviations appear in the structure density and sodiumdensity coefficientsrsquo results which have a 542 and 98variation coefficient respectively

e power distribution of steady-state estimated bySAC-3D is shown in Figure 11 e axially integrated powerof each assembly ranges from 155MW to 375MW Fig-ure 12 illustrates the variation coefficient map obtained bycomparing the integrated power simulation results withJAEA and ANLrsquos results e largest variation coefficient is

Table 3 Initial core flow distribution comparison

Channel Assembly type Measured mass flow rate (kgs) FFTF model Mass flow rate (kgs) Discrepancy ()1 DF 32 63305 63282 minus 0042 DF 42 15233 1523 minus 0023 DF 31 49907 49854 minus 0114 DF 31 28973 28956 minus 0065 DF 41 9984 9996 0126 DF 41 15233 15323 0597 SRCR 4091 4076 minus 0378 REF 7728A 5238 5243 0109 REF 8 B9 2348 2353 02110 PIOTA 2 2482 2494 04811 PIOTA 6 205 2037 minus 063

Table 4 Coefficients for the pump curve

i ah0 43196691 minus 576614382 301000293 minus 75465864 8675505 minus 0260626 minus 001596

BYPASSVOLUME

Wp

Ws

SHELL SIDE

TUBE SIDE

Figure 10 IHX calculation model

Science and Technology of Nuclear Installations 9

Table 5 Comparison of benchmark and SAC-3D steady-state parameters

Parameter Unit Measured value Calculated value Discrepancy ()Core power MW 1992 1992 000Core inlet temperature K 5904 59087 008Total core flow rate kgs 220224 219798 minus 019Mass flow rate through all assemblies kgs 198844 198934 005GEM sodium level1 cm 2216 2216 000Primary hot leg temperature K mdash 67818 mdashPrimary cold leg temperature K mdash 60589 mdashSecondary hot leg temperature K mdash 65656 mdashSecondary cold leg temperature K 58306 58378 0121Elevation relative to the top of inlet nozzle holes

Table 6 Main results of FFTF LOFWOS test 13 neutronics benchmark analysis

Argonne IGCAR INEST IPPE JAEA KIT KTH PSI ROME NCEPUNeutron multiplication factor 1000 0998 0999 0992 1017 0998 1022 1006 1000 0998Delayed neutron fraction 0003 0003 0007 0003 0003 0004 0003 0003 0003 0003Axial expansion coefficient (pcmdegC) minus 032 minus 023 mdash mdash minus 032 minus minus 03 minus 022 minus 048 minus03Radial expansion coefficient (pcmdegC) minus 1 minus 122 mdash mdash minus 1 minus minus 093 minus 152 minus 587 minus094Fuel Doppler constant (pcm) minus 629 minus 508 mdash mdash minus 634 minus 509 minus 564 minus 658 minus 688 minus524Fuel density coefficient (pcm) minus 136 minus 145 mdash mdash minus 045 mdash minus 136 minus 136 minus 14 minus132Structure density coefficient (pcm) minus 012 02 mdash mdash 003 mdash 01 004 minus 01 minus001Sodium density coefficient (pcmdegC) minus 035 minus 091 mdash mdash minus 041 009 minus 094 minus 027 minus 191 minus037Control and safety rods (pcm) minus 11849 mdash mdash minus 9396 10800 mdash minus 11540 minus 11823 minus 12773 minus8343Gas expansion modules (pcm) minus 442 minus 498 mdash minus 516 minus 489 minus 448 420 minus 475 minus 1201 minus782

324

195

263

252

315

344

197

CR

GEM

GEM

GEM

GEM GEM GEM

GEM

GEM

GEM

225

274

288

325

292

245

208

268

293

247

CR

179

177 155

201

190

213

220

192

206

223

295

SR

364

342

276

306

225

174

248

ICSA

312

306

375

SR

213

216

197205

CR

304

308

364

353

326

MOTA

290

205

231

280

273

329

298

SR

217

275

229

234

253

270

298

262

244

CR

232

191

257

253

289

CR

262

168

185

215

269

188

159

166 369

312

257

CR

207

Axially integratedpower (MW)

375

155

Figure 11 Power distribution map of FFTF core

10 Science and Technology of Nuclear Installations

327 which occurred in a fuel assembly type 42D Besideswe note that other assemblies with large coefficients ofvariation are located around this fuel assembly Since we donot have the power distributionrsquos measured data we cannotobjectively assess whether these biases are significant Bycomparing the codes applied by JAEA ANL and our sidewe believe that these biases are due to at least part of themodeling methods differences and different cross-sectionlibraries

Figures 13ndash15 depict the primary looprsquos mass flow ratersquostransient profile It can be seen that the SAC-3D very wellpredicts the pump coast down Minor differences existduring the natural circulation where the mass flow rates areslightly lower than the experimental data As shown inFigure 16 this is due to the underestimation of total power

Figures 16ndash18 show the transient reactor power profilesFigures 19 and 20 are the transient reactivity profile At 0 sthe primary pump is tripped and the core flow rate decreasesrapidly Due to the rapid decrease of the core cycling ca-pacity the assembliesrsquo temperature starts to rise and in-troduce negative net reactivity to bring down the reactorpower Starting from 5 s the coolant level in the GEMs dropsrapidly and the neutron leakage rate increases significantlyintroducing a remarkable negative reactivity e fissionpower decreases rapidly and the total power drops to 42 ofthe initial power at 10 s At 20 s the introduced negativereactivity increases at a slower rate as the core flow rate andthe coolant level within the GEMs begin to decrease at a

slower rate As shown in Figure 14 at approximately 90 s thenatural cycle is established e coolant level within GEMsbegins to stabilize and the negative reactivity it introducesalso stabilizes Figure 16 shows that the fission power isoverestimated due to the underestimation of the negativenet reactivity In the long term the fission power is close to

031

031

188

136

150

010

064

CR

GEM

GEM

GEM

GEM GEM GEM

GEM

GEM

GEM

172

195

102

295

286

108

147

287

263

238

CR

098

081 173

212

087

079

230

327

150

007

112

SR

181

137

015

207

128

055

097

ICSA

202

001

182

SR

026

140

179197

CR

030

021

003

116

016

MOTA

055

017

237

143

068

142

154

SR

055

105

089

013

090

063

084

087

088

CR

046

015

079

028

015

CR

043

057

037

056

108

040

009

089

104

118

CR

254

(Standard DevAverage)

327

001

032

Figure 12 Power distribution calculation variation coefficient map of FFTF corePu

mp

Disc

harg

e Pre

ssur

e (Ca

l) (M

Pa)

0 200 400

Time (s)

600 800

Loop 1 Mass Flow Rate (Exp)Loop 1 Mass Flow Rate (Cal)

Pump Discharge Pressure (Exp)Pump Discharge Pressure (Cal)

10

08

06

04

02

00

0

100

200

300

400

500

600

700

800

LOO

P 1

Mas

s Flo

w R

ate (

Cal)

200 400 600 8000Time (s)

Figure 13 Mass flow rate in loop 1

Science and Technology of Nuclear Installations 11

zero and the total power is contributed mainly by the decaypower e underestimation of the decay power leads to anunderestimation of the total power after 200 seconds Asshown in Figure 19 although the fuel temperature decreasesintroduced by the positive Dopplerrsquos reactivity feedback andpositive axial expansion reactivity feedback the net reac-tivity still maintains a significant negative value due to thesignificant negative reactivity introduced by GEMs

Figures 21 and 22 display the transient outlet temper-ature profiles of PIOTAs e SAC-3D results show a verysimilar trend compared to the experimental data with twopeaks occurring during the entire duration of the transientIn the beginning the outlet temperature rises rapidly as the

core flow rate drops rapidly as shown in Figure 13 epower decreases slowly because of the negative reactivityfeedback introduced by the control rod driveline expansionand radial expansion e power-to-flow ratio reaches thefirst peak value as shown in Figure 23 us the PIOTAsrsquooutlet temperatures increase rapidly and reach the first peakvalue After that the rapid drop of the coolant level withinthe GEMs introduced a large amount of negative reactivitycausing the total power to drop rapidly Meanwhile thedecreasing rate of mass flow rate starts to slow down ePIOTAsrsquo outlet temperatures start to decrease because thepower-to-flow ratio rapidly decreases Starting from about20 s the decrease in total power starts to slow down due to

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

200 400 600 8000Time (s)

0

5

10

15

20

Tota

l Cor

e Pow

er (C

al) (

MW

)

Figure 16 Reactor power of FFTF LOFWOS test 13 (low range)

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

0

20

40

60

80

100

120

140

160

180

200

Tota

l Cor

e Pow

er (C

al) (

MW

)

200 400 600 8000Time (s)

Figure 17 Reactor power of FFTF LOFWOS test 13

LOOP 1 NATURAL CIRCULATION

Loop 1 Mass Flow Rate (Cal)Loop 1 Mass Flow Rate (Exp)

0

10

20

30

40

50

Mas

s Flo

w R

ate (

kgs

)

100 200 300 400 500 600 700 800 9000Time (s)

Figure 14 Mass flow rate in loop 1 (Low range)

LOOP 1 TRANSITION TO NATURAL CIRCULATION

Loop 1 Mass Flow Rate (Cal)Loop 1 Mass Flow Rate (Exp)

-100

0

100

200

300

400

500

600

700

800

Mas

s Flo

w R

ate (

kgs

)

20 40 60 80 1000Time (s)

Figure 15 Mass flow rate in loop 1 (0 sndash100 s)

12 Science and Technology of Nuclear Installations

the rebound of the negative net reactivity as shown inFigure 20 erefore the power-to-flow ratio increaseswhich make the PIOTAsrsquo temperatures rise again At about110 s the PIOTAsrsquo temperatures reach the second peak valueafter the power-to-flow ratio reaches the second peak valueSince then the natural circulation starts to be establishedand maintained at about 4 of the rated flow as shown inFigure 14 e total power continues to decrease due to thenegative net reactivity e reactor enters a long-termcooling phase

In general the predicted results of SAC-3D are in goodagreement with the trend of the experimental data but thereare still deviations in the temperature values e outlettemperature of the PIOTA in row 2 is consistently lowerthan the measured value which is caused by the bias of thesimulated value of the total power transient variationSimilarly the simulated outlet temperature of the PIOTA inrow 6 is lower than the measured data until about 20 s butstarts to be higher than themeasured data after thenere isa maximum deviation of about 40 degrees Celsius at the

Net Reactivity (Cal)Doopler (Cal)Coolant Density (Cal)Axial Expansion (Cal)

Radial Expansion (Cal)Control Rod DrivelineExpansion (Cal)GEM (Cal)Net Reactivity (Exp)

ndash15

ndash10

ndash05

00

05

10

Net

Rea

ctiv

ity (C

al) (

$)

10 20 30 40 500Time (s)

Figure 20 Reactivity Transient Profile of FFTF LOFWOS test 13(0 sndash50 s)

Row 6 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Cal)Row 6 PIOTA Outlet Temp (Cal)

360

380

400

420

440

460

480

500

520

Row

6 P

IOTA

Out

let T

emp

(degC)

200 400 600 8000Time (s)

Figure 21 Row 2 and row 6 PIOTAs outlet temperature

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

0

20

40

60

80

100

120

140

160

180

200

Tota

l Cor

e Pow

er (C

al) (

MW

)

5 10 15 20 25 30 35 400Time (s)

Figure 18 Reactor power of FFTF LOFWOS test 13 (0 sndash40 s)

Net Reactivity (Cal)Doopler (Cal)Coolant Density (Cal)Axial Expansion (Cal)

Radial Expansion (Cal)Control Rod DrivelineExpansion (Cal)GEM (Cal)Net Reactivity (Exp)

ndash15

ndash10

ndash05

00

05

10

Net

Rea

ctiv

ity (C

al) (

$)

200 400 600 8000Time (s)

Figure 19 Reactivity transient profile of FFTF LOFWOS test 13

Science and Technology of Nuclear Installations 13

peak Unlike the PIOTA in row 2 the PIOTA in row 6 islocated at the outermost ring of the fuel assembly and is nextto a GEM assembly and a reflector assembly We believe thatthere are at least two possible reasons for this anomaly Oneis that even though the transientrsquos overall mass flow rate is ingood agreement with the measurement data it is stillpossible that the simulated mass flow rate variation withineach channel may not match the actual situation all that welle other important factor is the fact that the channel-to-channel heat transfer is not considered in the present worke neglect of heat transfer between the PIOTA in row 6 andGEM and reflector assembly introduced positive tempera-ture errors

5 Conclusions and Perspective

In the blind calculation phase of the IAEA FFTF LOFWOStest 13 CRP we modeled the FFTF reactor system by usingthe SAC-3D system analysis code e SAC-3D calculationresults have reasonably good agreement with the measureddata After benchmark analyzing the EBR-II [2] and FFTFreactors SAC-3D shows its good capability to predict thefast reactor behaviors under ATWS transient conditionsHowever the SAC-3D and FFTF models still have room forimprovement e deviations in total power transient cal-culations suggest further improvement in the reactivityfeedback models as well as the decay heat prediction modelAnomalies in the transient temperature prediction of thePIOTA in row 6 indicate that the thermal-hydraulics cal-culation module needs to consider the heat transfer betweenchannels In the next phase of the work we will examine thedeviations between simulation results further and refine theFFTF model based on the blind phase benchmark analysisresults e specific calculation modules of SAC-3D will alsobe improved to predict the fast reactorrsquos behavior better

Data Availability

e data that support the findings of this study are availablefrom IAEA Restrictions apply to the availability of thesedata which were used under license for this study Data areavailable from the corresponding author with the permis-sion of IAEA

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e authors would like to express their thanks to IAEAParticipation in the CRP on the FFTF LOFWOS test 13 isunder a research agreement between the North ChinaElectric Power University and the IAEA CRP numberI32011 is work was partially financially supported by theNational Natural Science Foundation of China (GrantNo11705057)

References

[1] D Sui D Lu L Ren and Y Liu ldquoDevelopment of three-di-mensional hot pool model in a system analysis code for pool-type FBRrdquo Nuclear Engineering and Design vol 256pp 264ndash273 2012

[2] D Lu S Lyu and D Sui ldquoVerification of SAC-3D based onEBR-II SHRT-45R benchmark datardquo in Proceedings of the 18thInternational Topical Meeting on Nuclear Reactor +ermalHydraulics Portland OR USA August 2019

[3] D Lu S Lyu and D Sui ldquoSimulation of FFTF loss of flowwithout scram test based on system code SAC-3Drdquo AtomicEnergy Science and Technology vol 55 no 8 pp 1345ndash13522021

[4] T Sumner A Moisseytsev F Heidet D W WootanA M Casella and J V Nelson Benchmark Specification forFFTF LOFWOS Test 13 IAEA Vienna Austria 2017

Row 6 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Cal)Row 6 PIOTA Outlet Temp (Cal)

360

380

400

420

440

460

480

500

520

Row

6 P

IOTA

Out

let T

emp

(degC)

2000Time (s)

Figure 22 Row 2 and row 6 PIOTAs outlet temperature(0 sndash200 s)

22

20

18

16

14

12

08

06

Dim

ensio

nles

s Pow

er-F

low

Rat

io

0 20 40 60 80 100 120Time (s)

140 160 180 200

Dimensionless Power-Flow Ratio

Dimensionless Power-Flow Ratio

200 400 600 8000Time (s)

06

08

12

10

14

16

18

20

22

Dim

ensio

nles

s Pow

er-F

low

Rat

io

Figure 23 Dimensionless power-flow ratio

14 Science and Technology of Nuclear Installations

[5] C Guo D Lu X Zhang and D Sui ldquoDevelopment and ap-plication of a safety analysis code for small Lead cooled FastReactor SVBR 75100rdquo Annals of Nuclear Energy vol 81pp 62ndash72 2015

[6] D Lu C Guo and D Sui ldquoA three-dimensional nodal neutronkinetics code with a higher-accuracy algorithm for reactor corein hexagonal-z geometryrdquo Annals of Nuclear Energy vol 101pp 250ndash261 2017

[7] J M Ruggieri J Tommasi J F Lebrat et al ldquoEranos 21International code system for GEN IV fast reactor analysisrdquo inProceedings of the 2006 International Congress on Advances inNuclear Power Plants ICAPPrsquo06 pp 2432ndash2439 Seoul KoreaJuly 2006

[8] S Lyu D Lu and D Sui ldquoNeutronics benchmark analysis ofthe EBR-II SHRT-45R with SAC-3Drdquo Nuclear Engineering andDesign vol 364 p 110679 2020

[9] C Guo D Lu D Sui and X Zhang ldquoSAC-CFR computer codeverification with Experimental Breeder Reactor II loss-of-primary-flow-without-scram tests datardquo Annals of NuclearEnergy vol 71 pp 166ndash173 2014

Science and Technology of Nuclear Installations 15

In this work the primary pump is modeled with a pumpmodule based on the pumprsquos characteristics and theirnominal operating state Initial pump speed is adjusted tothe benchmark data e pump speed history is given asinput data during the transient e benchmark

specifications provide the pump performance curves for theprimary pumps However the data for these curves were notavailable To predict the pressure head during the transientthe following set of equations of the modified homologouspump theory of Wylie and Streeter were coded into thepump model ese modified correlations provide a goodapproximation of the dimensionless pump head (H)

H N2

+ Q2

1113874 1113875Wh(x) (4)

where N is the dimensionless pump speed Q is the relativevolumetric flow rate x π + arctan(QN)

Wh(x) 11139446

i0ahix

i (5)

whose coefficients are provided in Table 4e IHXs were vertically mounted counterflow shell and

tube designs Primary sodium entered the IHX from theoutlet of the primary loop hot leg piping and flowed downthrough the active heat transfer region along the outside ofthe IHX tubes Secondary sodium entered the IHX at the topand flowed down through a central downcomer into thelower hemispherical plenum From this plenum secondarysodium entered the IHX tubes at the bottom and flowedupward along the inner side of the IHX tubes out of the IHXIn the IHX model all heat transfer tubes have been sim-plified as one representative tube In an attempt to con-sistently simplify the model there are several assumptions(1) there is an ideal mixing of coolant at the inlet and outlet(2) fully developed convective heat transfer is assumed (3)no metallic structure of the IHX other than IHX tubes andshell wall is considered hence perfect insulation is postu-lated between primary and secondary sodium in the centraldowncomer pipe (4) no heat losses are accounted forthrough the external IHX vessel to the surrounding envi-ronment As shown in Figure 10 there are four radialcalculation nodes secondary coolant tube metal primarycoolant and shell wall e temperature calculation nodes ofthe heat tube metal and shell wall are defined in the center ofthe control volume e temperature calculation nodes ofthe coolant are defined at the boundary of the control body[9]

e energy equation of the primary side coolant controlvolume can be written as

ρVP

depi+1

dt Wp epi minus epi+11113872 1113873 minus HptApt Tpii+1 minus Tti1113872 1113873

minus HpshApsh Tpii+1 minus Tshi1113872 1113873

(6)

e energy equation of the secondary side coolantcontrol volume can be written as

ρVP

desi

dt Ws esi+1 minus esi1113872 1113873 + HstAst Tti minus Tsii+11113872 1113873 (7)

e energy equation of the IHX tube metal controlvolume can be written as

Channel 1

Channel 2

Channel 6

Channel 3

Channel 5

Channel 4

Channel 7

Channel 9

Channel 11

Channel 8

Channel 10

Figure 8 SAC-3D channel layout for FFTF core

UPPER AXIAL REFLECTOR

LOWER AXIAL REFLECTOR

INSULATOR PELLETS REGION

FUEL REGION

INSULATOR PELLETS REGION

GAP

CLADDING

COOLANT

STRUCTURE

FUEL

Figure 9 ermal-hydraulics model of driver fuel channels

8 Science and Technology of Nuclear Installations

Mtcti

dTti

dt HptApt Tpii+1 minus Tti1113872 1113873 minus HpstApst Tti minus Tsii+11113872 1113873

(8)

e energy equation of the IHX shell wall control volumecan be written as

Mshcshi

dTshi

dt HpshApsh Tpii+1 minus Tshi1113872 1113873 (9)

where p represents the coolant of the primary side s rep-resents the coolant of the secondary side t represents theheat exchanger tube of IHX sh represents the shell wall ofIHX e is enthalpy Wis mass flow rate T is temperature M

is mass c is specific heat capacity V is the volume of thecontrol volume H is the heat transfer coefficient betweenfluid and structural A is the heat transfer area betweenthe fluid and the structure and Tii+1 is the average fluidtemperature within two neighbor control volumes it isdefined as

Tii+1 Ti + Tii+1

2 (10)

As shown in Figure 7 the secondary loop wasmodeled astwo boundary conditions e DHX outlet coolant tem-perature values and the secondary loop coolant mass flowrates are imposed as the boundary conditions for the inletand outlet of the IHX secondary side

4 Results and Analysis

Table 5 summarizes the comparison of measurements andcalculation results of the initial plant conditions Reactorpower was slightly less than 50 and the core inlet tem-perature was reduced by nearly 80from the nominal coreinlet temperature is was done to ensure that the peak fueltemperatures did not rise too high to limit the impact of thetest on the durability of the fuel assemblies

Note that to date the IAEArsquos FFTF CRP project has justcompleted the blind phase and ANL has released experi-mental measurements of the part of the calculated FFTFreactor parameters erefore the following results partlycompare the simulated calculations with the real measure-ments and partly compare with other participantsrsquo calcu-lations Because different participants use differentcalculation methods and models we only make data devi-ation comparisons without deviation analysis for the resultswithout measurement data

Table 6 lists the main neutron results of FFTF LOFWOStest 13 of 10 participants Most of the results like theneutron multiplication factor delayed neutron fractionDoppler coefficient fuel density coefficient etc have arelatively good agreement among participants After re-moving results that deviated from the mean by more thantwo times the standard deviation the variation coefficient(δAvg) was distributed between 1 and 27 Significantdeviations appear in the structure density and sodiumdensity coefficientsrsquo results which have a 542 and 98variation coefficient respectively

e power distribution of steady-state estimated bySAC-3D is shown in Figure 11 e axially integrated powerof each assembly ranges from 155MW to 375MW Fig-ure 12 illustrates the variation coefficient map obtained bycomparing the integrated power simulation results withJAEA and ANLrsquos results e largest variation coefficient is

Table 3 Initial core flow distribution comparison

Channel Assembly type Measured mass flow rate (kgs) FFTF model Mass flow rate (kgs) Discrepancy ()1 DF 32 63305 63282 minus 0042 DF 42 15233 1523 minus 0023 DF 31 49907 49854 minus 0114 DF 31 28973 28956 minus 0065 DF 41 9984 9996 0126 DF 41 15233 15323 0597 SRCR 4091 4076 minus 0378 REF 7728A 5238 5243 0109 REF 8 B9 2348 2353 02110 PIOTA 2 2482 2494 04811 PIOTA 6 205 2037 minus 063

Table 4 Coefficients for the pump curve

i ah0 43196691 minus 576614382 301000293 minus 75465864 8675505 minus 0260626 minus 001596

BYPASSVOLUME

Wp

Ws

SHELL SIDE

TUBE SIDE

Figure 10 IHX calculation model

Science and Technology of Nuclear Installations 9

Table 5 Comparison of benchmark and SAC-3D steady-state parameters

Parameter Unit Measured value Calculated value Discrepancy ()Core power MW 1992 1992 000Core inlet temperature K 5904 59087 008Total core flow rate kgs 220224 219798 minus 019Mass flow rate through all assemblies kgs 198844 198934 005GEM sodium level1 cm 2216 2216 000Primary hot leg temperature K mdash 67818 mdashPrimary cold leg temperature K mdash 60589 mdashSecondary hot leg temperature K mdash 65656 mdashSecondary cold leg temperature K 58306 58378 0121Elevation relative to the top of inlet nozzle holes

Table 6 Main results of FFTF LOFWOS test 13 neutronics benchmark analysis

Argonne IGCAR INEST IPPE JAEA KIT KTH PSI ROME NCEPUNeutron multiplication factor 1000 0998 0999 0992 1017 0998 1022 1006 1000 0998Delayed neutron fraction 0003 0003 0007 0003 0003 0004 0003 0003 0003 0003Axial expansion coefficient (pcmdegC) minus 032 minus 023 mdash mdash minus 032 minus minus 03 minus 022 minus 048 minus03Radial expansion coefficient (pcmdegC) minus 1 minus 122 mdash mdash minus 1 minus minus 093 minus 152 minus 587 minus094Fuel Doppler constant (pcm) minus 629 minus 508 mdash mdash minus 634 minus 509 minus 564 minus 658 minus 688 minus524Fuel density coefficient (pcm) minus 136 minus 145 mdash mdash minus 045 mdash minus 136 minus 136 minus 14 minus132Structure density coefficient (pcm) minus 012 02 mdash mdash 003 mdash 01 004 minus 01 minus001Sodium density coefficient (pcmdegC) minus 035 minus 091 mdash mdash minus 041 009 minus 094 minus 027 minus 191 minus037Control and safety rods (pcm) minus 11849 mdash mdash minus 9396 10800 mdash minus 11540 minus 11823 minus 12773 minus8343Gas expansion modules (pcm) minus 442 minus 498 mdash minus 516 minus 489 minus 448 420 minus 475 minus 1201 minus782

324

195

263

252

315

344

197

CR

GEM

GEM

GEM

GEM GEM GEM

GEM

GEM

GEM

225

274

288

325

292

245

208

268

293

247

CR

179

177 155

201

190

213

220

192

206

223

295

SR

364

342

276

306

225

174

248

ICSA

312

306

375

SR

213

216

197205

CR

304

308

364

353

326

MOTA

290

205

231

280

273

329

298

SR

217

275

229

234

253

270

298

262

244

CR

232

191

257

253

289

CR

262

168

185

215

269

188

159

166 369

312

257

CR

207

Axially integratedpower (MW)

375

155

Figure 11 Power distribution map of FFTF core

10 Science and Technology of Nuclear Installations

327 which occurred in a fuel assembly type 42D Besideswe note that other assemblies with large coefficients ofvariation are located around this fuel assembly Since we donot have the power distributionrsquos measured data we cannotobjectively assess whether these biases are significant Bycomparing the codes applied by JAEA ANL and our sidewe believe that these biases are due to at least part of themodeling methods differences and different cross-sectionlibraries

Figures 13ndash15 depict the primary looprsquos mass flow ratersquostransient profile It can be seen that the SAC-3D very wellpredicts the pump coast down Minor differences existduring the natural circulation where the mass flow rates areslightly lower than the experimental data As shown inFigure 16 this is due to the underestimation of total power

Figures 16ndash18 show the transient reactor power profilesFigures 19 and 20 are the transient reactivity profile At 0 sthe primary pump is tripped and the core flow rate decreasesrapidly Due to the rapid decrease of the core cycling ca-pacity the assembliesrsquo temperature starts to rise and in-troduce negative net reactivity to bring down the reactorpower Starting from 5 s the coolant level in the GEMs dropsrapidly and the neutron leakage rate increases significantlyintroducing a remarkable negative reactivity e fissionpower decreases rapidly and the total power drops to 42 ofthe initial power at 10 s At 20 s the introduced negativereactivity increases at a slower rate as the core flow rate andthe coolant level within the GEMs begin to decrease at a

slower rate As shown in Figure 14 at approximately 90 s thenatural cycle is established e coolant level within GEMsbegins to stabilize and the negative reactivity it introducesalso stabilizes Figure 16 shows that the fission power isoverestimated due to the underestimation of the negativenet reactivity In the long term the fission power is close to

031

031

188

136

150

010

064

CR

GEM

GEM

GEM

GEM GEM GEM

GEM

GEM

GEM

172

195

102

295

286

108

147

287

263

238

CR

098

081 173

212

087

079

230

327

150

007

112

SR

181

137

015

207

128

055

097

ICSA

202

001

182

SR

026

140

179197

CR

030

021

003

116

016

MOTA

055

017

237

143

068

142

154

SR

055

105

089

013

090

063

084

087

088

CR

046

015

079

028

015

CR

043

057

037

056

108

040

009

089

104

118

CR

254

(Standard DevAverage)

327

001

032

Figure 12 Power distribution calculation variation coefficient map of FFTF corePu

mp

Disc

harg

e Pre

ssur

e (Ca

l) (M

Pa)

0 200 400

Time (s)

600 800

Loop 1 Mass Flow Rate (Exp)Loop 1 Mass Flow Rate (Cal)

Pump Discharge Pressure (Exp)Pump Discharge Pressure (Cal)

10

08

06

04

02

00

0

100

200

300

400

500

600

700

800

LOO

P 1

Mas

s Flo

w R

ate (

Cal)

200 400 600 8000Time (s)

Figure 13 Mass flow rate in loop 1

Science and Technology of Nuclear Installations 11

zero and the total power is contributed mainly by the decaypower e underestimation of the decay power leads to anunderestimation of the total power after 200 seconds Asshown in Figure 19 although the fuel temperature decreasesintroduced by the positive Dopplerrsquos reactivity feedback andpositive axial expansion reactivity feedback the net reac-tivity still maintains a significant negative value due to thesignificant negative reactivity introduced by GEMs

Figures 21 and 22 display the transient outlet temper-ature profiles of PIOTAs e SAC-3D results show a verysimilar trend compared to the experimental data with twopeaks occurring during the entire duration of the transientIn the beginning the outlet temperature rises rapidly as the

core flow rate drops rapidly as shown in Figure 13 epower decreases slowly because of the negative reactivityfeedback introduced by the control rod driveline expansionand radial expansion e power-to-flow ratio reaches thefirst peak value as shown in Figure 23 us the PIOTAsrsquooutlet temperatures increase rapidly and reach the first peakvalue After that the rapid drop of the coolant level withinthe GEMs introduced a large amount of negative reactivitycausing the total power to drop rapidly Meanwhile thedecreasing rate of mass flow rate starts to slow down ePIOTAsrsquo outlet temperatures start to decrease because thepower-to-flow ratio rapidly decreases Starting from about20 s the decrease in total power starts to slow down due to

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

200 400 600 8000Time (s)

0

5

10

15

20

Tota

l Cor

e Pow

er (C

al) (

MW

)

Figure 16 Reactor power of FFTF LOFWOS test 13 (low range)

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

0

20

40

60

80

100

120

140

160

180

200

Tota

l Cor

e Pow

er (C

al) (

MW

)

200 400 600 8000Time (s)

Figure 17 Reactor power of FFTF LOFWOS test 13

LOOP 1 NATURAL CIRCULATION

Loop 1 Mass Flow Rate (Cal)Loop 1 Mass Flow Rate (Exp)

0

10

20

30

40

50

Mas

s Flo

w R

ate (

kgs

)

100 200 300 400 500 600 700 800 9000Time (s)

Figure 14 Mass flow rate in loop 1 (Low range)

LOOP 1 TRANSITION TO NATURAL CIRCULATION

Loop 1 Mass Flow Rate (Cal)Loop 1 Mass Flow Rate (Exp)

-100

0

100

200

300

400

500

600

700

800

Mas

s Flo

w R

ate (

kgs

)

20 40 60 80 1000Time (s)

Figure 15 Mass flow rate in loop 1 (0 sndash100 s)

12 Science and Technology of Nuclear Installations

the rebound of the negative net reactivity as shown inFigure 20 erefore the power-to-flow ratio increaseswhich make the PIOTAsrsquo temperatures rise again At about110 s the PIOTAsrsquo temperatures reach the second peak valueafter the power-to-flow ratio reaches the second peak valueSince then the natural circulation starts to be establishedand maintained at about 4 of the rated flow as shown inFigure 14 e total power continues to decrease due to thenegative net reactivity e reactor enters a long-termcooling phase

In general the predicted results of SAC-3D are in goodagreement with the trend of the experimental data but thereare still deviations in the temperature values e outlettemperature of the PIOTA in row 2 is consistently lowerthan the measured value which is caused by the bias of thesimulated value of the total power transient variationSimilarly the simulated outlet temperature of the PIOTA inrow 6 is lower than the measured data until about 20 s butstarts to be higher than themeasured data after thenere isa maximum deviation of about 40 degrees Celsius at the

Net Reactivity (Cal)Doopler (Cal)Coolant Density (Cal)Axial Expansion (Cal)

Radial Expansion (Cal)Control Rod DrivelineExpansion (Cal)GEM (Cal)Net Reactivity (Exp)

ndash15

ndash10

ndash05

00

05

10

Net

Rea

ctiv

ity (C

al) (

$)

10 20 30 40 500Time (s)

Figure 20 Reactivity Transient Profile of FFTF LOFWOS test 13(0 sndash50 s)

Row 6 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Cal)Row 6 PIOTA Outlet Temp (Cal)

360

380

400

420

440

460

480

500

520

Row

6 P

IOTA

Out

let T

emp

(degC)

200 400 600 8000Time (s)

Figure 21 Row 2 and row 6 PIOTAs outlet temperature

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

0

20

40

60

80

100

120

140

160

180

200

Tota

l Cor

e Pow

er (C

al) (

MW

)

5 10 15 20 25 30 35 400Time (s)

Figure 18 Reactor power of FFTF LOFWOS test 13 (0 sndash40 s)

Net Reactivity (Cal)Doopler (Cal)Coolant Density (Cal)Axial Expansion (Cal)

Radial Expansion (Cal)Control Rod DrivelineExpansion (Cal)GEM (Cal)Net Reactivity (Exp)

ndash15

ndash10

ndash05

00

05

10

Net

Rea

ctiv

ity (C

al) (

$)

200 400 600 8000Time (s)

Figure 19 Reactivity transient profile of FFTF LOFWOS test 13

Science and Technology of Nuclear Installations 13

peak Unlike the PIOTA in row 2 the PIOTA in row 6 islocated at the outermost ring of the fuel assembly and is nextto a GEM assembly and a reflector assembly We believe thatthere are at least two possible reasons for this anomaly Oneis that even though the transientrsquos overall mass flow rate is ingood agreement with the measurement data it is stillpossible that the simulated mass flow rate variation withineach channel may not match the actual situation all that welle other important factor is the fact that the channel-to-channel heat transfer is not considered in the present worke neglect of heat transfer between the PIOTA in row 6 andGEM and reflector assembly introduced positive tempera-ture errors

5 Conclusions and Perspective

In the blind calculation phase of the IAEA FFTF LOFWOStest 13 CRP we modeled the FFTF reactor system by usingthe SAC-3D system analysis code e SAC-3D calculationresults have reasonably good agreement with the measureddata After benchmark analyzing the EBR-II [2] and FFTFreactors SAC-3D shows its good capability to predict thefast reactor behaviors under ATWS transient conditionsHowever the SAC-3D and FFTF models still have room forimprovement e deviations in total power transient cal-culations suggest further improvement in the reactivityfeedback models as well as the decay heat prediction modelAnomalies in the transient temperature prediction of thePIOTA in row 6 indicate that the thermal-hydraulics cal-culation module needs to consider the heat transfer betweenchannels In the next phase of the work we will examine thedeviations between simulation results further and refine theFFTF model based on the blind phase benchmark analysisresults e specific calculation modules of SAC-3D will alsobe improved to predict the fast reactorrsquos behavior better

Data Availability

e data that support the findings of this study are availablefrom IAEA Restrictions apply to the availability of thesedata which were used under license for this study Data areavailable from the corresponding author with the permis-sion of IAEA

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e authors would like to express their thanks to IAEAParticipation in the CRP on the FFTF LOFWOS test 13 isunder a research agreement between the North ChinaElectric Power University and the IAEA CRP numberI32011 is work was partially financially supported by theNational Natural Science Foundation of China (GrantNo11705057)

References

[1] D Sui D Lu L Ren and Y Liu ldquoDevelopment of three-di-mensional hot pool model in a system analysis code for pool-type FBRrdquo Nuclear Engineering and Design vol 256pp 264ndash273 2012

[2] D Lu S Lyu and D Sui ldquoVerification of SAC-3D based onEBR-II SHRT-45R benchmark datardquo in Proceedings of the 18thInternational Topical Meeting on Nuclear Reactor +ermalHydraulics Portland OR USA August 2019

[3] D Lu S Lyu and D Sui ldquoSimulation of FFTF loss of flowwithout scram test based on system code SAC-3Drdquo AtomicEnergy Science and Technology vol 55 no 8 pp 1345ndash13522021

[4] T Sumner A Moisseytsev F Heidet D W WootanA M Casella and J V Nelson Benchmark Specification forFFTF LOFWOS Test 13 IAEA Vienna Austria 2017

Row 6 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Cal)Row 6 PIOTA Outlet Temp (Cal)

360

380

400

420

440

460

480

500

520

Row

6 P

IOTA

Out

let T

emp

(degC)

2000Time (s)

Figure 22 Row 2 and row 6 PIOTAs outlet temperature(0 sndash200 s)

22

20

18

16

14

12

08

06

Dim

ensio

nles

s Pow

er-F

low

Rat

io

0 20 40 60 80 100 120Time (s)

140 160 180 200

Dimensionless Power-Flow Ratio

Dimensionless Power-Flow Ratio

200 400 600 8000Time (s)

06

08

12

10

14

16

18

20

22

Dim

ensio

nles

s Pow

er-F

low

Rat

io

Figure 23 Dimensionless power-flow ratio

14 Science and Technology of Nuclear Installations

[5] C Guo D Lu X Zhang and D Sui ldquoDevelopment and ap-plication of a safety analysis code for small Lead cooled FastReactor SVBR 75100rdquo Annals of Nuclear Energy vol 81pp 62ndash72 2015

[6] D Lu C Guo and D Sui ldquoA three-dimensional nodal neutronkinetics code with a higher-accuracy algorithm for reactor corein hexagonal-z geometryrdquo Annals of Nuclear Energy vol 101pp 250ndash261 2017

[7] J M Ruggieri J Tommasi J F Lebrat et al ldquoEranos 21International code system for GEN IV fast reactor analysisrdquo inProceedings of the 2006 International Congress on Advances inNuclear Power Plants ICAPPrsquo06 pp 2432ndash2439 Seoul KoreaJuly 2006

[8] S Lyu D Lu and D Sui ldquoNeutronics benchmark analysis ofthe EBR-II SHRT-45R with SAC-3Drdquo Nuclear Engineering andDesign vol 364 p 110679 2020

[9] C Guo D Lu D Sui and X Zhang ldquoSAC-CFR computer codeverification with Experimental Breeder Reactor II loss-of-primary-flow-without-scram tests datardquo Annals of NuclearEnergy vol 71 pp 166ndash173 2014

Science and Technology of Nuclear Installations 15

Mtcti

dTti

dt HptApt Tpii+1 minus Tti1113872 1113873 minus HpstApst Tti minus Tsii+11113872 1113873

(8)

e energy equation of the IHX shell wall control volumecan be written as

Mshcshi

dTshi

dt HpshApsh Tpii+1 minus Tshi1113872 1113873 (9)

where p represents the coolant of the primary side s rep-resents the coolant of the secondary side t represents theheat exchanger tube of IHX sh represents the shell wall ofIHX e is enthalpy Wis mass flow rate T is temperature M

is mass c is specific heat capacity V is the volume of thecontrol volume H is the heat transfer coefficient betweenfluid and structural A is the heat transfer area betweenthe fluid and the structure and Tii+1 is the average fluidtemperature within two neighbor control volumes it isdefined as

Tii+1 Ti + Tii+1

2 (10)

As shown in Figure 7 the secondary loop wasmodeled astwo boundary conditions e DHX outlet coolant tem-perature values and the secondary loop coolant mass flowrates are imposed as the boundary conditions for the inletand outlet of the IHX secondary side

4 Results and Analysis

Table 5 summarizes the comparison of measurements andcalculation results of the initial plant conditions Reactorpower was slightly less than 50 and the core inlet tem-perature was reduced by nearly 80from the nominal coreinlet temperature is was done to ensure that the peak fueltemperatures did not rise too high to limit the impact of thetest on the durability of the fuel assemblies

Note that to date the IAEArsquos FFTF CRP project has justcompleted the blind phase and ANL has released experi-mental measurements of the part of the calculated FFTFreactor parameters erefore the following results partlycompare the simulated calculations with the real measure-ments and partly compare with other participantsrsquo calcu-lations Because different participants use differentcalculation methods and models we only make data devi-ation comparisons without deviation analysis for the resultswithout measurement data

Table 6 lists the main neutron results of FFTF LOFWOStest 13 of 10 participants Most of the results like theneutron multiplication factor delayed neutron fractionDoppler coefficient fuel density coefficient etc have arelatively good agreement among participants After re-moving results that deviated from the mean by more thantwo times the standard deviation the variation coefficient(δAvg) was distributed between 1 and 27 Significantdeviations appear in the structure density and sodiumdensity coefficientsrsquo results which have a 542 and 98variation coefficient respectively

e power distribution of steady-state estimated bySAC-3D is shown in Figure 11 e axially integrated powerof each assembly ranges from 155MW to 375MW Fig-ure 12 illustrates the variation coefficient map obtained bycomparing the integrated power simulation results withJAEA and ANLrsquos results e largest variation coefficient is

Table 3 Initial core flow distribution comparison

Channel Assembly type Measured mass flow rate (kgs) FFTF model Mass flow rate (kgs) Discrepancy ()1 DF 32 63305 63282 minus 0042 DF 42 15233 1523 minus 0023 DF 31 49907 49854 minus 0114 DF 31 28973 28956 minus 0065 DF 41 9984 9996 0126 DF 41 15233 15323 0597 SRCR 4091 4076 minus 0378 REF 7728A 5238 5243 0109 REF 8 B9 2348 2353 02110 PIOTA 2 2482 2494 04811 PIOTA 6 205 2037 minus 063

Table 4 Coefficients for the pump curve

i ah0 43196691 minus 576614382 301000293 minus 75465864 8675505 minus 0260626 minus 001596

BYPASSVOLUME

Wp

Ws

SHELL SIDE

TUBE SIDE

Figure 10 IHX calculation model

Science and Technology of Nuclear Installations 9

Table 5 Comparison of benchmark and SAC-3D steady-state parameters

Parameter Unit Measured value Calculated value Discrepancy ()Core power MW 1992 1992 000Core inlet temperature K 5904 59087 008Total core flow rate kgs 220224 219798 minus 019Mass flow rate through all assemblies kgs 198844 198934 005GEM sodium level1 cm 2216 2216 000Primary hot leg temperature K mdash 67818 mdashPrimary cold leg temperature K mdash 60589 mdashSecondary hot leg temperature K mdash 65656 mdashSecondary cold leg temperature K 58306 58378 0121Elevation relative to the top of inlet nozzle holes

Table 6 Main results of FFTF LOFWOS test 13 neutronics benchmark analysis

Argonne IGCAR INEST IPPE JAEA KIT KTH PSI ROME NCEPUNeutron multiplication factor 1000 0998 0999 0992 1017 0998 1022 1006 1000 0998Delayed neutron fraction 0003 0003 0007 0003 0003 0004 0003 0003 0003 0003Axial expansion coefficient (pcmdegC) minus 032 minus 023 mdash mdash minus 032 minus minus 03 minus 022 minus 048 minus03Radial expansion coefficient (pcmdegC) minus 1 minus 122 mdash mdash minus 1 minus minus 093 minus 152 minus 587 minus094Fuel Doppler constant (pcm) minus 629 minus 508 mdash mdash minus 634 minus 509 minus 564 minus 658 minus 688 minus524Fuel density coefficient (pcm) minus 136 minus 145 mdash mdash minus 045 mdash minus 136 minus 136 minus 14 minus132Structure density coefficient (pcm) minus 012 02 mdash mdash 003 mdash 01 004 minus 01 minus001Sodium density coefficient (pcmdegC) minus 035 minus 091 mdash mdash minus 041 009 minus 094 minus 027 minus 191 minus037Control and safety rods (pcm) minus 11849 mdash mdash minus 9396 10800 mdash minus 11540 minus 11823 minus 12773 minus8343Gas expansion modules (pcm) minus 442 minus 498 mdash minus 516 minus 489 minus 448 420 minus 475 minus 1201 minus782

324

195

263

252

315

344

197

CR

GEM

GEM

GEM

GEM GEM GEM

GEM

GEM

GEM

225

274

288

325

292

245

208

268

293

247

CR

179

177 155

201

190

213

220

192

206

223

295

SR

364

342

276

306

225

174

248

ICSA

312

306

375

SR

213

216

197205

CR

304

308

364

353

326

MOTA

290

205

231

280

273

329

298

SR

217

275

229

234

253

270

298

262

244

CR

232

191

257

253

289

CR

262

168

185

215

269

188

159

166 369

312

257

CR

207

Axially integratedpower (MW)

375

155

Figure 11 Power distribution map of FFTF core

10 Science and Technology of Nuclear Installations

327 which occurred in a fuel assembly type 42D Besideswe note that other assemblies with large coefficients ofvariation are located around this fuel assembly Since we donot have the power distributionrsquos measured data we cannotobjectively assess whether these biases are significant Bycomparing the codes applied by JAEA ANL and our sidewe believe that these biases are due to at least part of themodeling methods differences and different cross-sectionlibraries

Figures 13ndash15 depict the primary looprsquos mass flow ratersquostransient profile It can be seen that the SAC-3D very wellpredicts the pump coast down Minor differences existduring the natural circulation where the mass flow rates areslightly lower than the experimental data As shown inFigure 16 this is due to the underestimation of total power

Figures 16ndash18 show the transient reactor power profilesFigures 19 and 20 are the transient reactivity profile At 0 sthe primary pump is tripped and the core flow rate decreasesrapidly Due to the rapid decrease of the core cycling ca-pacity the assembliesrsquo temperature starts to rise and in-troduce negative net reactivity to bring down the reactorpower Starting from 5 s the coolant level in the GEMs dropsrapidly and the neutron leakage rate increases significantlyintroducing a remarkable negative reactivity e fissionpower decreases rapidly and the total power drops to 42 ofthe initial power at 10 s At 20 s the introduced negativereactivity increases at a slower rate as the core flow rate andthe coolant level within the GEMs begin to decrease at a

slower rate As shown in Figure 14 at approximately 90 s thenatural cycle is established e coolant level within GEMsbegins to stabilize and the negative reactivity it introducesalso stabilizes Figure 16 shows that the fission power isoverestimated due to the underestimation of the negativenet reactivity In the long term the fission power is close to

031

031

188

136

150

010

064

CR

GEM

GEM

GEM

GEM GEM GEM

GEM

GEM

GEM

172

195

102

295

286

108

147

287

263

238

CR

098

081 173

212

087

079

230

327

150

007

112

SR

181

137

015

207

128

055

097

ICSA

202

001

182

SR

026

140

179197

CR

030

021

003

116

016

MOTA

055

017

237

143

068

142

154

SR

055

105

089

013

090

063

084

087

088

CR

046

015

079

028

015

CR

043

057

037

056

108

040

009

089

104

118

CR

254

(Standard DevAverage)

327

001

032

Figure 12 Power distribution calculation variation coefficient map of FFTF corePu

mp

Disc

harg

e Pre

ssur

e (Ca

l) (M

Pa)

0 200 400

Time (s)

600 800

Loop 1 Mass Flow Rate (Exp)Loop 1 Mass Flow Rate (Cal)

Pump Discharge Pressure (Exp)Pump Discharge Pressure (Cal)

10

08

06

04

02

00

0

100

200

300

400

500

600

700

800

LOO

P 1

Mas

s Flo

w R

ate (

Cal)

200 400 600 8000Time (s)

Figure 13 Mass flow rate in loop 1

Science and Technology of Nuclear Installations 11

zero and the total power is contributed mainly by the decaypower e underestimation of the decay power leads to anunderestimation of the total power after 200 seconds Asshown in Figure 19 although the fuel temperature decreasesintroduced by the positive Dopplerrsquos reactivity feedback andpositive axial expansion reactivity feedback the net reac-tivity still maintains a significant negative value due to thesignificant negative reactivity introduced by GEMs

Figures 21 and 22 display the transient outlet temper-ature profiles of PIOTAs e SAC-3D results show a verysimilar trend compared to the experimental data with twopeaks occurring during the entire duration of the transientIn the beginning the outlet temperature rises rapidly as the

core flow rate drops rapidly as shown in Figure 13 epower decreases slowly because of the negative reactivityfeedback introduced by the control rod driveline expansionand radial expansion e power-to-flow ratio reaches thefirst peak value as shown in Figure 23 us the PIOTAsrsquooutlet temperatures increase rapidly and reach the first peakvalue After that the rapid drop of the coolant level withinthe GEMs introduced a large amount of negative reactivitycausing the total power to drop rapidly Meanwhile thedecreasing rate of mass flow rate starts to slow down ePIOTAsrsquo outlet temperatures start to decrease because thepower-to-flow ratio rapidly decreases Starting from about20 s the decrease in total power starts to slow down due to

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

200 400 600 8000Time (s)

0

5

10

15

20

Tota

l Cor

e Pow

er (C

al) (

MW

)

Figure 16 Reactor power of FFTF LOFWOS test 13 (low range)

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

0

20

40

60

80

100

120

140

160

180

200

Tota

l Cor

e Pow

er (C

al) (

MW

)

200 400 600 8000Time (s)

Figure 17 Reactor power of FFTF LOFWOS test 13

LOOP 1 NATURAL CIRCULATION

Loop 1 Mass Flow Rate (Cal)Loop 1 Mass Flow Rate (Exp)

0

10

20

30

40

50

Mas

s Flo

w R

ate (

kgs

)

100 200 300 400 500 600 700 800 9000Time (s)

Figure 14 Mass flow rate in loop 1 (Low range)

LOOP 1 TRANSITION TO NATURAL CIRCULATION

Loop 1 Mass Flow Rate (Cal)Loop 1 Mass Flow Rate (Exp)

-100

0

100

200

300

400

500

600

700

800

Mas

s Flo

w R

ate (

kgs

)

20 40 60 80 1000Time (s)

Figure 15 Mass flow rate in loop 1 (0 sndash100 s)

12 Science and Technology of Nuclear Installations

the rebound of the negative net reactivity as shown inFigure 20 erefore the power-to-flow ratio increaseswhich make the PIOTAsrsquo temperatures rise again At about110 s the PIOTAsrsquo temperatures reach the second peak valueafter the power-to-flow ratio reaches the second peak valueSince then the natural circulation starts to be establishedand maintained at about 4 of the rated flow as shown inFigure 14 e total power continues to decrease due to thenegative net reactivity e reactor enters a long-termcooling phase

In general the predicted results of SAC-3D are in goodagreement with the trend of the experimental data but thereare still deviations in the temperature values e outlettemperature of the PIOTA in row 2 is consistently lowerthan the measured value which is caused by the bias of thesimulated value of the total power transient variationSimilarly the simulated outlet temperature of the PIOTA inrow 6 is lower than the measured data until about 20 s butstarts to be higher than themeasured data after thenere isa maximum deviation of about 40 degrees Celsius at the

Net Reactivity (Cal)Doopler (Cal)Coolant Density (Cal)Axial Expansion (Cal)

Radial Expansion (Cal)Control Rod DrivelineExpansion (Cal)GEM (Cal)Net Reactivity (Exp)

ndash15

ndash10

ndash05

00

05

10

Net

Rea

ctiv

ity (C

al) (

$)

10 20 30 40 500Time (s)

Figure 20 Reactivity Transient Profile of FFTF LOFWOS test 13(0 sndash50 s)

Row 6 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Cal)Row 6 PIOTA Outlet Temp (Cal)

360

380

400

420

440

460

480

500

520

Row

6 P

IOTA

Out

let T

emp

(degC)

200 400 600 8000Time (s)

Figure 21 Row 2 and row 6 PIOTAs outlet temperature

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

0

20

40

60

80

100

120

140

160

180

200

Tota

l Cor

e Pow

er (C

al) (

MW

)

5 10 15 20 25 30 35 400Time (s)

Figure 18 Reactor power of FFTF LOFWOS test 13 (0 sndash40 s)

Net Reactivity (Cal)Doopler (Cal)Coolant Density (Cal)Axial Expansion (Cal)

Radial Expansion (Cal)Control Rod DrivelineExpansion (Cal)GEM (Cal)Net Reactivity (Exp)

ndash15

ndash10

ndash05

00

05

10

Net

Rea

ctiv

ity (C

al) (

$)

200 400 600 8000Time (s)

Figure 19 Reactivity transient profile of FFTF LOFWOS test 13

Science and Technology of Nuclear Installations 13

peak Unlike the PIOTA in row 2 the PIOTA in row 6 islocated at the outermost ring of the fuel assembly and is nextto a GEM assembly and a reflector assembly We believe thatthere are at least two possible reasons for this anomaly Oneis that even though the transientrsquos overall mass flow rate is ingood agreement with the measurement data it is stillpossible that the simulated mass flow rate variation withineach channel may not match the actual situation all that welle other important factor is the fact that the channel-to-channel heat transfer is not considered in the present worke neglect of heat transfer between the PIOTA in row 6 andGEM and reflector assembly introduced positive tempera-ture errors

5 Conclusions and Perspective

In the blind calculation phase of the IAEA FFTF LOFWOStest 13 CRP we modeled the FFTF reactor system by usingthe SAC-3D system analysis code e SAC-3D calculationresults have reasonably good agreement with the measureddata After benchmark analyzing the EBR-II [2] and FFTFreactors SAC-3D shows its good capability to predict thefast reactor behaviors under ATWS transient conditionsHowever the SAC-3D and FFTF models still have room forimprovement e deviations in total power transient cal-culations suggest further improvement in the reactivityfeedback models as well as the decay heat prediction modelAnomalies in the transient temperature prediction of thePIOTA in row 6 indicate that the thermal-hydraulics cal-culation module needs to consider the heat transfer betweenchannels In the next phase of the work we will examine thedeviations between simulation results further and refine theFFTF model based on the blind phase benchmark analysisresults e specific calculation modules of SAC-3D will alsobe improved to predict the fast reactorrsquos behavior better

Data Availability

e data that support the findings of this study are availablefrom IAEA Restrictions apply to the availability of thesedata which were used under license for this study Data areavailable from the corresponding author with the permis-sion of IAEA

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e authors would like to express their thanks to IAEAParticipation in the CRP on the FFTF LOFWOS test 13 isunder a research agreement between the North ChinaElectric Power University and the IAEA CRP numberI32011 is work was partially financially supported by theNational Natural Science Foundation of China (GrantNo11705057)

References

[1] D Sui D Lu L Ren and Y Liu ldquoDevelopment of three-di-mensional hot pool model in a system analysis code for pool-type FBRrdquo Nuclear Engineering and Design vol 256pp 264ndash273 2012

[2] D Lu S Lyu and D Sui ldquoVerification of SAC-3D based onEBR-II SHRT-45R benchmark datardquo in Proceedings of the 18thInternational Topical Meeting on Nuclear Reactor +ermalHydraulics Portland OR USA August 2019

[3] D Lu S Lyu and D Sui ldquoSimulation of FFTF loss of flowwithout scram test based on system code SAC-3Drdquo AtomicEnergy Science and Technology vol 55 no 8 pp 1345ndash13522021

[4] T Sumner A Moisseytsev F Heidet D W WootanA M Casella and J V Nelson Benchmark Specification forFFTF LOFWOS Test 13 IAEA Vienna Austria 2017

Row 6 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Cal)Row 6 PIOTA Outlet Temp (Cal)

360

380

400

420

440

460

480

500

520

Row

6 P

IOTA

Out

let T

emp

(degC)

2000Time (s)

Figure 22 Row 2 and row 6 PIOTAs outlet temperature(0 sndash200 s)

22

20

18

16

14

12

08

06

Dim

ensio

nles

s Pow

er-F

low

Rat

io

0 20 40 60 80 100 120Time (s)

140 160 180 200

Dimensionless Power-Flow Ratio

Dimensionless Power-Flow Ratio

200 400 600 8000Time (s)

06

08

12

10

14

16

18

20

22

Dim

ensio

nles

s Pow

er-F

low

Rat

io

Figure 23 Dimensionless power-flow ratio

14 Science and Technology of Nuclear Installations

[5] C Guo D Lu X Zhang and D Sui ldquoDevelopment and ap-plication of a safety analysis code for small Lead cooled FastReactor SVBR 75100rdquo Annals of Nuclear Energy vol 81pp 62ndash72 2015

[6] D Lu C Guo and D Sui ldquoA three-dimensional nodal neutronkinetics code with a higher-accuracy algorithm for reactor corein hexagonal-z geometryrdquo Annals of Nuclear Energy vol 101pp 250ndash261 2017

[7] J M Ruggieri J Tommasi J F Lebrat et al ldquoEranos 21International code system for GEN IV fast reactor analysisrdquo inProceedings of the 2006 International Congress on Advances inNuclear Power Plants ICAPPrsquo06 pp 2432ndash2439 Seoul KoreaJuly 2006

[8] S Lyu D Lu and D Sui ldquoNeutronics benchmark analysis ofthe EBR-II SHRT-45R with SAC-3Drdquo Nuclear Engineering andDesign vol 364 p 110679 2020

[9] C Guo D Lu D Sui and X Zhang ldquoSAC-CFR computer codeverification with Experimental Breeder Reactor II loss-of-primary-flow-without-scram tests datardquo Annals of NuclearEnergy vol 71 pp 166ndash173 2014

Science and Technology of Nuclear Installations 15

Table 5 Comparison of benchmark and SAC-3D steady-state parameters

Parameter Unit Measured value Calculated value Discrepancy ()Core power MW 1992 1992 000Core inlet temperature K 5904 59087 008Total core flow rate kgs 220224 219798 minus 019Mass flow rate through all assemblies kgs 198844 198934 005GEM sodium level1 cm 2216 2216 000Primary hot leg temperature K mdash 67818 mdashPrimary cold leg temperature K mdash 60589 mdashSecondary hot leg temperature K mdash 65656 mdashSecondary cold leg temperature K 58306 58378 0121Elevation relative to the top of inlet nozzle holes

Table 6 Main results of FFTF LOFWOS test 13 neutronics benchmark analysis

Argonne IGCAR INEST IPPE JAEA KIT KTH PSI ROME NCEPUNeutron multiplication factor 1000 0998 0999 0992 1017 0998 1022 1006 1000 0998Delayed neutron fraction 0003 0003 0007 0003 0003 0004 0003 0003 0003 0003Axial expansion coefficient (pcmdegC) minus 032 minus 023 mdash mdash minus 032 minus minus 03 minus 022 minus 048 minus03Radial expansion coefficient (pcmdegC) minus 1 minus 122 mdash mdash minus 1 minus minus 093 minus 152 minus 587 minus094Fuel Doppler constant (pcm) minus 629 minus 508 mdash mdash minus 634 minus 509 minus 564 minus 658 minus 688 minus524Fuel density coefficient (pcm) minus 136 minus 145 mdash mdash minus 045 mdash minus 136 minus 136 minus 14 minus132Structure density coefficient (pcm) minus 012 02 mdash mdash 003 mdash 01 004 minus 01 minus001Sodium density coefficient (pcmdegC) minus 035 minus 091 mdash mdash minus 041 009 minus 094 minus 027 minus 191 minus037Control and safety rods (pcm) minus 11849 mdash mdash minus 9396 10800 mdash minus 11540 minus 11823 minus 12773 minus8343Gas expansion modules (pcm) minus 442 minus 498 mdash minus 516 minus 489 minus 448 420 minus 475 minus 1201 minus782

324

195

263

252

315

344

197

CR

GEM

GEM

GEM

GEM GEM GEM

GEM

GEM

GEM

225

274

288

325

292

245

208

268

293

247

CR

179

177 155

201

190

213

220

192

206

223

295

SR

364

342

276

306

225

174

248

ICSA

312

306

375

SR

213

216

197205

CR

304

308

364

353

326

MOTA

290

205

231

280

273

329

298

SR

217

275

229

234

253

270

298

262

244

CR

232

191

257

253

289

CR

262

168

185

215

269

188

159

166 369

312

257

CR

207

Axially integratedpower (MW)

375

155

Figure 11 Power distribution map of FFTF core

10 Science and Technology of Nuclear Installations

327 which occurred in a fuel assembly type 42D Besideswe note that other assemblies with large coefficients ofvariation are located around this fuel assembly Since we donot have the power distributionrsquos measured data we cannotobjectively assess whether these biases are significant Bycomparing the codes applied by JAEA ANL and our sidewe believe that these biases are due to at least part of themodeling methods differences and different cross-sectionlibraries

Figures 13ndash15 depict the primary looprsquos mass flow ratersquostransient profile It can be seen that the SAC-3D very wellpredicts the pump coast down Minor differences existduring the natural circulation where the mass flow rates areslightly lower than the experimental data As shown inFigure 16 this is due to the underestimation of total power

Figures 16ndash18 show the transient reactor power profilesFigures 19 and 20 are the transient reactivity profile At 0 sthe primary pump is tripped and the core flow rate decreasesrapidly Due to the rapid decrease of the core cycling ca-pacity the assembliesrsquo temperature starts to rise and in-troduce negative net reactivity to bring down the reactorpower Starting from 5 s the coolant level in the GEMs dropsrapidly and the neutron leakage rate increases significantlyintroducing a remarkable negative reactivity e fissionpower decreases rapidly and the total power drops to 42 ofthe initial power at 10 s At 20 s the introduced negativereactivity increases at a slower rate as the core flow rate andthe coolant level within the GEMs begin to decrease at a

slower rate As shown in Figure 14 at approximately 90 s thenatural cycle is established e coolant level within GEMsbegins to stabilize and the negative reactivity it introducesalso stabilizes Figure 16 shows that the fission power isoverestimated due to the underestimation of the negativenet reactivity In the long term the fission power is close to

031

031

188

136

150

010

064

CR

GEM

GEM

GEM

GEM GEM GEM

GEM

GEM

GEM

172

195

102

295

286

108

147

287

263

238

CR

098

081 173

212

087

079

230

327

150

007

112

SR

181

137

015

207

128

055

097

ICSA

202

001

182

SR

026

140

179197

CR

030

021

003

116

016

MOTA

055

017

237

143

068

142

154

SR

055

105

089

013

090

063

084

087

088

CR

046

015

079

028

015

CR

043

057

037

056

108

040

009

089

104

118

CR

254

(Standard DevAverage)

327

001

032

Figure 12 Power distribution calculation variation coefficient map of FFTF corePu

mp

Disc

harg

e Pre

ssur

e (Ca

l) (M

Pa)

0 200 400

Time (s)

600 800

Loop 1 Mass Flow Rate (Exp)Loop 1 Mass Flow Rate (Cal)

Pump Discharge Pressure (Exp)Pump Discharge Pressure (Cal)

10

08

06

04

02

00

0

100

200

300

400

500

600

700

800

LOO

P 1

Mas

s Flo

w R

ate (

Cal)

200 400 600 8000Time (s)

Figure 13 Mass flow rate in loop 1

Science and Technology of Nuclear Installations 11

zero and the total power is contributed mainly by the decaypower e underestimation of the decay power leads to anunderestimation of the total power after 200 seconds Asshown in Figure 19 although the fuel temperature decreasesintroduced by the positive Dopplerrsquos reactivity feedback andpositive axial expansion reactivity feedback the net reac-tivity still maintains a significant negative value due to thesignificant negative reactivity introduced by GEMs

Figures 21 and 22 display the transient outlet temper-ature profiles of PIOTAs e SAC-3D results show a verysimilar trend compared to the experimental data with twopeaks occurring during the entire duration of the transientIn the beginning the outlet temperature rises rapidly as the

core flow rate drops rapidly as shown in Figure 13 epower decreases slowly because of the negative reactivityfeedback introduced by the control rod driveline expansionand radial expansion e power-to-flow ratio reaches thefirst peak value as shown in Figure 23 us the PIOTAsrsquooutlet temperatures increase rapidly and reach the first peakvalue After that the rapid drop of the coolant level withinthe GEMs introduced a large amount of negative reactivitycausing the total power to drop rapidly Meanwhile thedecreasing rate of mass flow rate starts to slow down ePIOTAsrsquo outlet temperatures start to decrease because thepower-to-flow ratio rapidly decreases Starting from about20 s the decrease in total power starts to slow down due to

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

200 400 600 8000Time (s)

0

5

10

15

20

Tota

l Cor

e Pow

er (C

al) (

MW

)

Figure 16 Reactor power of FFTF LOFWOS test 13 (low range)

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

0

20

40

60

80

100

120

140

160

180

200

Tota

l Cor

e Pow

er (C

al) (

MW

)

200 400 600 8000Time (s)

Figure 17 Reactor power of FFTF LOFWOS test 13

LOOP 1 NATURAL CIRCULATION

Loop 1 Mass Flow Rate (Cal)Loop 1 Mass Flow Rate (Exp)

0

10

20

30

40

50

Mas

s Flo

w R

ate (

kgs

)

100 200 300 400 500 600 700 800 9000Time (s)

Figure 14 Mass flow rate in loop 1 (Low range)

LOOP 1 TRANSITION TO NATURAL CIRCULATION

Loop 1 Mass Flow Rate (Cal)Loop 1 Mass Flow Rate (Exp)

-100

0

100

200

300

400

500

600

700

800

Mas

s Flo

w R

ate (

kgs

)

20 40 60 80 1000Time (s)

Figure 15 Mass flow rate in loop 1 (0 sndash100 s)

12 Science and Technology of Nuclear Installations

the rebound of the negative net reactivity as shown inFigure 20 erefore the power-to-flow ratio increaseswhich make the PIOTAsrsquo temperatures rise again At about110 s the PIOTAsrsquo temperatures reach the second peak valueafter the power-to-flow ratio reaches the second peak valueSince then the natural circulation starts to be establishedand maintained at about 4 of the rated flow as shown inFigure 14 e total power continues to decrease due to thenegative net reactivity e reactor enters a long-termcooling phase

In general the predicted results of SAC-3D are in goodagreement with the trend of the experimental data but thereare still deviations in the temperature values e outlettemperature of the PIOTA in row 2 is consistently lowerthan the measured value which is caused by the bias of thesimulated value of the total power transient variationSimilarly the simulated outlet temperature of the PIOTA inrow 6 is lower than the measured data until about 20 s butstarts to be higher than themeasured data after thenere isa maximum deviation of about 40 degrees Celsius at the

Net Reactivity (Cal)Doopler (Cal)Coolant Density (Cal)Axial Expansion (Cal)

Radial Expansion (Cal)Control Rod DrivelineExpansion (Cal)GEM (Cal)Net Reactivity (Exp)

ndash15

ndash10

ndash05

00

05

10

Net

Rea

ctiv

ity (C

al) (

$)

10 20 30 40 500Time (s)

Figure 20 Reactivity Transient Profile of FFTF LOFWOS test 13(0 sndash50 s)

Row 6 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Cal)Row 6 PIOTA Outlet Temp (Cal)

360

380

400

420

440

460

480

500

520

Row

6 P

IOTA

Out

let T

emp

(degC)

200 400 600 8000Time (s)

Figure 21 Row 2 and row 6 PIOTAs outlet temperature

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

0

20

40

60

80

100

120

140

160

180

200

Tota

l Cor

e Pow

er (C

al) (

MW

)

5 10 15 20 25 30 35 400Time (s)

Figure 18 Reactor power of FFTF LOFWOS test 13 (0 sndash40 s)

Net Reactivity (Cal)Doopler (Cal)Coolant Density (Cal)Axial Expansion (Cal)

Radial Expansion (Cal)Control Rod DrivelineExpansion (Cal)GEM (Cal)Net Reactivity (Exp)

ndash15

ndash10

ndash05

00

05

10

Net

Rea

ctiv

ity (C

al) (

$)

200 400 600 8000Time (s)

Figure 19 Reactivity transient profile of FFTF LOFWOS test 13

Science and Technology of Nuclear Installations 13

peak Unlike the PIOTA in row 2 the PIOTA in row 6 islocated at the outermost ring of the fuel assembly and is nextto a GEM assembly and a reflector assembly We believe thatthere are at least two possible reasons for this anomaly Oneis that even though the transientrsquos overall mass flow rate is ingood agreement with the measurement data it is stillpossible that the simulated mass flow rate variation withineach channel may not match the actual situation all that welle other important factor is the fact that the channel-to-channel heat transfer is not considered in the present worke neglect of heat transfer between the PIOTA in row 6 andGEM and reflector assembly introduced positive tempera-ture errors

5 Conclusions and Perspective

In the blind calculation phase of the IAEA FFTF LOFWOStest 13 CRP we modeled the FFTF reactor system by usingthe SAC-3D system analysis code e SAC-3D calculationresults have reasonably good agreement with the measureddata After benchmark analyzing the EBR-II [2] and FFTFreactors SAC-3D shows its good capability to predict thefast reactor behaviors under ATWS transient conditionsHowever the SAC-3D and FFTF models still have room forimprovement e deviations in total power transient cal-culations suggest further improvement in the reactivityfeedback models as well as the decay heat prediction modelAnomalies in the transient temperature prediction of thePIOTA in row 6 indicate that the thermal-hydraulics cal-culation module needs to consider the heat transfer betweenchannels In the next phase of the work we will examine thedeviations between simulation results further and refine theFFTF model based on the blind phase benchmark analysisresults e specific calculation modules of SAC-3D will alsobe improved to predict the fast reactorrsquos behavior better

Data Availability

e data that support the findings of this study are availablefrom IAEA Restrictions apply to the availability of thesedata which were used under license for this study Data areavailable from the corresponding author with the permis-sion of IAEA

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e authors would like to express their thanks to IAEAParticipation in the CRP on the FFTF LOFWOS test 13 isunder a research agreement between the North ChinaElectric Power University and the IAEA CRP numberI32011 is work was partially financially supported by theNational Natural Science Foundation of China (GrantNo11705057)

References

[1] D Sui D Lu L Ren and Y Liu ldquoDevelopment of three-di-mensional hot pool model in a system analysis code for pool-type FBRrdquo Nuclear Engineering and Design vol 256pp 264ndash273 2012

[2] D Lu S Lyu and D Sui ldquoVerification of SAC-3D based onEBR-II SHRT-45R benchmark datardquo in Proceedings of the 18thInternational Topical Meeting on Nuclear Reactor +ermalHydraulics Portland OR USA August 2019

[3] D Lu S Lyu and D Sui ldquoSimulation of FFTF loss of flowwithout scram test based on system code SAC-3Drdquo AtomicEnergy Science and Technology vol 55 no 8 pp 1345ndash13522021

[4] T Sumner A Moisseytsev F Heidet D W WootanA M Casella and J V Nelson Benchmark Specification forFFTF LOFWOS Test 13 IAEA Vienna Austria 2017

Row 6 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Cal)Row 6 PIOTA Outlet Temp (Cal)

360

380

400

420

440

460

480

500

520

Row

6 P

IOTA

Out

let T

emp

(degC)

2000Time (s)

Figure 22 Row 2 and row 6 PIOTAs outlet temperature(0 sndash200 s)

22

20

18

16

14

12

08

06

Dim

ensio

nles

s Pow

er-F

low

Rat

io

0 20 40 60 80 100 120Time (s)

140 160 180 200

Dimensionless Power-Flow Ratio

Dimensionless Power-Flow Ratio

200 400 600 8000Time (s)

06

08

12

10

14

16

18

20

22

Dim

ensio

nles

s Pow

er-F

low

Rat

io

Figure 23 Dimensionless power-flow ratio

14 Science and Technology of Nuclear Installations

[5] C Guo D Lu X Zhang and D Sui ldquoDevelopment and ap-plication of a safety analysis code for small Lead cooled FastReactor SVBR 75100rdquo Annals of Nuclear Energy vol 81pp 62ndash72 2015

[6] D Lu C Guo and D Sui ldquoA three-dimensional nodal neutronkinetics code with a higher-accuracy algorithm for reactor corein hexagonal-z geometryrdquo Annals of Nuclear Energy vol 101pp 250ndash261 2017

[7] J M Ruggieri J Tommasi J F Lebrat et al ldquoEranos 21International code system for GEN IV fast reactor analysisrdquo inProceedings of the 2006 International Congress on Advances inNuclear Power Plants ICAPPrsquo06 pp 2432ndash2439 Seoul KoreaJuly 2006

[8] S Lyu D Lu and D Sui ldquoNeutronics benchmark analysis ofthe EBR-II SHRT-45R with SAC-3Drdquo Nuclear Engineering andDesign vol 364 p 110679 2020

[9] C Guo D Lu D Sui and X Zhang ldquoSAC-CFR computer codeverification with Experimental Breeder Reactor II loss-of-primary-flow-without-scram tests datardquo Annals of NuclearEnergy vol 71 pp 166ndash173 2014

Science and Technology of Nuclear Installations 15

327 which occurred in a fuel assembly type 42D Besideswe note that other assemblies with large coefficients ofvariation are located around this fuel assembly Since we donot have the power distributionrsquos measured data we cannotobjectively assess whether these biases are significant Bycomparing the codes applied by JAEA ANL and our sidewe believe that these biases are due to at least part of themodeling methods differences and different cross-sectionlibraries

Figures 13ndash15 depict the primary looprsquos mass flow ratersquostransient profile It can be seen that the SAC-3D very wellpredicts the pump coast down Minor differences existduring the natural circulation where the mass flow rates areslightly lower than the experimental data As shown inFigure 16 this is due to the underestimation of total power

Figures 16ndash18 show the transient reactor power profilesFigures 19 and 20 are the transient reactivity profile At 0 sthe primary pump is tripped and the core flow rate decreasesrapidly Due to the rapid decrease of the core cycling ca-pacity the assembliesrsquo temperature starts to rise and in-troduce negative net reactivity to bring down the reactorpower Starting from 5 s the coolant level in the GEMs dropsrapidly and the neutron leakage rate increases significantlyintroducing a remarkable negative reactivity e fissionpower decreases rapidly and the total power drops to 42 ofthe initial power at 10 s At 20 s the introduced negativereactivity increases at a slower rate as the core flow rate andthe coolant level within the GEMs begin to decrease at a

slower rate As shown in Figure 14 at approximately 90 s thenatural cycle is established e coolant level within GEMsbegins to stabilize and the negative reactivity it introducesalso stabilizes Figure 16 shows that the fission power isoverestimated due to the underestimation of the negativenet reactivity In the long term the fission power is close to

031

031

188

136

150

010

064

CR

GEM

GEM

GEM

GEM GEM GEM

GEM

GEM

GEM

172

195

102

295

286

108

147

287

263

238

CR

098

081 173

212

087

079

230

327

150

007

112

SR

181

137

015

207

128

055

097

ICSA

202

001

182

SR

026

140

179197

CR

030

021

003

116

016

MOTA

055

017

237

143

068

142

154

SR

055

105

089

013

090

063

084

087

088

CR

046

015

079

028

015

CR

043

057

037

056

108

040

009

089

104

118

CR

254

(Standard DevAverage)

327

001

032

Figure 12 Power distribution calculation variation coefficient map of FFTF corePu

mp

Disc

harg

e Pre

ssur

e (Ca

l) (M

Pa)

0 200 400

Time (s)

600 800

Loop 1 Mass Flow Rate (Exp)Loop 1 Mass Flow Rate (Cal)

Pump Discharge Pressure (Exp)Pump Discharge Pressure (Cal)

10

08

06

04

02

00

0

100

200

300

400

500

600

700

800

LOO

P 1

Mas

s Flo

w R

ate (

Cal)

200 400 600 8000Time (s)

Figure 13 Mass flow rate in loop 1

Science and Technology of Nuclear Installations 11

zero and the total power is contributed mainly by the decaypower e underestimation of the decay power leads to anunderestimation of the total power after 200 seconds Asshown in Figure 19 although the fuel temperature decreasesintroduced by the positive Dopplerrsquos reactivity feedback andpositive axial expansion reactivity feedback the net reac-tivity still maintains a significant negative value due to thesignificant negative reactivity introduced by GEMs

Figures 21 and 22 display the transient outlet temper-ature profiles of PIOTAs e SAC-3D results show a verysimilar trend compared to the experimental data with twopeaks occurring during the entire duration of the transientIn the beginning the outlet temperature rises rapidly as the

core flow rate drops rapidly as shown in Figure 13 epower decreases slowly because of the negative reactivityfeedback introduced by the control rod driveline expansionand radial expansion e power-to-flow ratio reaches thefirst peak value as shown in Figure 23 us the PIOTAsrsquooutlet temperatures increase rapidly and reach the first peakvalue After that the rapid drop of the coolant level withinthe GEMs introduced a large amount of negative reactivitycausing the total power to drop rapidly Meanwhile thedecreasing rate of mass flow rate starts to slow down ePIOTAsrsquo outlet temperatures start to decrease because thepower-to-flow ratio rapidly decreases Starting from about20 s the decrease in total power starts to slow down due to

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

200 400 600 8000Time (s)

0

5

10

15

20

Tota

l Cor

e Pow

er (C

al) (

MW

)

Figure 16 Reactor power of FFTF LOFWOS test 13 (low range)

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

0

20

40

60

80

100

120

140

160

180

200

Tota

l Cor

e Pow

er (C

al) (

MW

)

200 400 600 8000Time (s)

Figure 17 Reactor power of FFTF LOFWOS test 13

LOOP 1 NATURAL CIRCULATION

Loop 1 Mass Flow Rate (Cal)Loop 1 Mass Flow Rate (Exp)

0

10

20

30

40

50

Mas

s Flo

w R

ate (

kgs

)

100 200 300 400 500 600 700 800 9000Time (s)

Figure 14 Mass flow rate in loop 1 (Low range)

LOOP 1 TRANSITION TO NATURAL CIRCULATION

Loop 1 Mass Flow Rate (Cal)Loop 1 Mass Flow Rate (Exp)

-100

0

100

200

300

400

500

600

700

800

Mas

s Flo

w R

ate (

kgs

)

20 40 60 80 1000Time (s)

Figure 15 Mass flow rate in loop 1 (0 sndash100 s)

12 Science and Technology of Nuclear Installations

the rebound of the negative net reactivity as shown inFigure 20 erefore the power-to-flow ratio increaseswhich make the PIOTAsrsquo temperatures rise again At about110 s the PIOTAsrsquo temperatures reach the second peak valueafter the power-to-flow ratio reaches the second peak valueSince then the natural circulation starts to be establishedand maintained at about 4 of the rated flow as shown inFigure 14 e total power continues to decrease due to thenegative net reactivity e reactor enters a long-termcooling phase

In general the predicted results of SAC-3D are in goodagreement with the trend of the experimental data but thereare still deviations in the temperature values e outlettemperature of the PIOTA in row 2 is consistently lowerthan the measured value which is caused by the bias of thesimulated value of the total power transient variationSimilarly the simulated outlet temperature of the PIOTA inrow 6 is lower than the measured data until about 20 s butstarts to be higher than themeasured data after thenere isa maximum deviation of about 40 degrees Celsius at the

Net Reactivity (Cal)Doopler (Cal)Coolant Density (Cal)Axial Expansion (Cal)

Radial Expansion (Cal)Control Rod DrivelineExpansion (Cal)GEM (Cal)Net Reactivity (Exp)

ndash15

ndash10

ndash05

00

05

10

Net

Rea

ctiv

ity (C

al) (

$)

10 20 30 40 500Time (s)

Figure 20 Reactivity Transient Profile of FFTF LOFWOS test 13(0 sndash50 s)

Row 6 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Cal)Row 6 PIOTA Outlet Temp (Cal)

360

380

400

420

440

460

480

500

520

Row

6 P

IOTA

Out

let T

emp

(degC)

200 400 600 8000Time (s)

Figure 21 Row 2 and row 6 PIOTAs outlet temperature

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

0

20

40

60

80

100

120

140

160

180

200

Tota

l Cor

e Pow

er (C

al) (

MW

)

5 10 15 20 25 30 35 400Time (s)

Figure 18 Reactor power of FFTF LOFWOS test 13 (0 sndash40 s)

Net Reactivity (Cal)Doopler (Cal)Coolant Density (Cal)Axial Expansion (Cal)

Radial Expansion (Cal)Control Rod DrivelineExpansion (Cal)GEM (Cal)Net Reactivity (Exp)

ndash15

ndash10

ndash05

00

05

10

Net

Rea

ctiv

ity (C

al) (

$)

200 400 600 8000Time (s)

Figure 19 Reactivity transient profile of FFTF LOFWOS test 13

Science and Technology of Nuclear Installations 13

peak Unlike the PIOTA in row 2 the PIOTA in row 6 islocated at the outermost ring of the fuel assembly and is nextto a GEM assembly and a reflector assembly We believe thatthere are at least two possible reasons for this anomaly Oneis that even though the transientrsquos overall mass flow rate is ingood agreement with the measurement data it is stillpossible that the simulated mass flow rate variation withineach channel may not match the actual situation all that welle other important factor is the fact that the channel-to-channel heat transfer is not considered in the present worke neglect of heat transfer between the PIOTA in row 6 andGEM and reflector assembly introduced positive tempera-ture errors

5 Conclusions and Perspective

In the blind calculation phase of the IAEA FFTF LOFWOStest 13 CRP we modeled the FFTF reactor system by usingthe SAC-3D system analysis code e SAC-3D calculationresults have reasonably good agreement with the measureddata After benchmark analyzing the EBR-II [2] and FFTFreactors SAC-3D shows its good capability to predict thefast reactor behaviors under ATWS transient conditionsHowever the SAC-3D and FFTF models still have room forimprovement e deviations in total power transient cal-culations suggest further improvement in the reactivityfeedback models as well as the decay heat prediction modelAnomalies in the transient temperature prediction of thePIOTA in row 6 indicate that the thermal-hydraulics cal-culation module needs to consider the heat transfer betweenchannels In the next phase of the work we will examine thedeviations between simulation results further and refine theFFTF model based on the blind phase benchmark analysisresults e specific calculation modules of SAC-3D will alsobe improved to predict the fast reactorrsquos behavior better

Data Availability

e data that support the findings of this study are availablefrom IAEA Restrictions apply to the availability of thesedata which were used under license for this study Data areavailable from the corresponding author with the permis-sion of IAEA

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e authors would like to express their thanks to IAEAParticipation in the CRP on the FFTF LOFWOS test 13 isunder a research agreement between the North ChinaElectric Power University and the IAEA CRP numberI32011 is work was partially financially supported by theNational Natural Science Foundation of China (GrantNo11705057)

References

[1] D Sui D Lu L Ren and Y Liu ldquoDevelopment of three-di-mensional hot pool model in a system analysis code for pool-type FBRrdquo Nuclear Engineering and Design vol 256pp 264ndash273 2012

[2] D Lu S Lyu and D Sui ldquoVerification of SAC-3D based onEBR-II SHRT-45R benchmark datardquo in Proceedings of the 18thInternational Topical Meeting on Nuclear Reactor +ermalHydraulics Portland OR USA August 2019

[3] D Lu S Lyu and D Sui ldquoSimulation of FFTF loss of flowwithout scram test based on system code SAC-3Drdquo AtomicEnergy Science and Technology vol 55 no 8 pp 1345ndash13522021

[4] T Sumner A Moisseytsev F Heidet D W WootanA M Casella and J V Nelson Benchmark Specification forFFTF LOFWOS Test 13 IAEA Vienna Austria 2017

Row 6 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Cal)Row 6 PIOTA Outlet Temp (Cal)

360

380

400

420

440

460

480

500

520

Row

6 P

IOTA

Out

let T

emp

(degC)

2000Time (s)

Figure 22 Row 2 and row 6 PIOTAs outlet temperature(0 sndash200 s)

22

20

18

16

14

12

08

06

Dim

ensio

nles

s Pow

er-F

low

Rat

io

0 20 40 60 80 100 120Time (s)

140 160 180 200

Dimensionless Power-Flow Ratio

Dimensionless Power-Flow Ratio

200 400 600 8000Time (s)

06

08

12

10

14

16

18

20

22

Dim

ensio

nles

s Pow

er-F

low

Rat

io

Figure 23 Dimensionless power-flow ratio

14 Science and Technology of Nuclear Installations

[5] C Guo D Lu X Zhang and D Sui ldquoDevelopment and ap-plication of a safety analysis code for small Lead cooled FastReactor SVBR 75100rdquo Annals of Nuclear Energy vol 81pp 62ndash72 2015

[6] D Lu C Guo and D Sui ldquoA three-dimensional nodal neutronkinetics code with a higher-accuracy algorithm for reactor corein hexagonal-z geometryrdquo Annals of Nuclear Energy vol 101pp 250ndash261 2017

[7] J M Ruggieri J Tommasi J F Lebrat et al ldquoEranos 21International code system for GEN IV fast reactor analysisrdquo inProceedings of the 2006 International Congress on Advances inNuclear Power Plants ICAPPrsquo06 pp 2432ndash2439 Seoul KoreaJuly 2006

[8] S Lyu D Lu and D Sui ldquoNeutronics benchmark analysis ofthe EBR-II SHRT-45R with SAC-3Drdquo Nuclear Engineering andDesign vol 364 p 110679 2020

[9] C Guo D Lu D Sui and X Zhang ldquoSAC-CFR computer codeverification with Experimental Breeder Reactor II loss-of-primary-flow-without-scram tests datardquo Annals of NuclearEnergy vol 71 pp 166ndash173 2014

Science and Technology of Nuclear Installations 15

zero and the total power is contributed mainly by the decaypower e underestimation of the decay power leads to anunderestimation of the total power after 200 seconds Asshown in Figure 19 although the fuel temperature decreasesintroduced by the positive Dopplerrsquos reactivity feedback andpositive axial expansion reactivity feedback the net reac-tivity still maintains a significant negative value due to thesignificant negative reactivity introduced by GEMs

Figures 21 and 22 display the transient outlet temper-ature profiles of PIOTAs e SAC-3D results show a verysimilar trend compared to the experimental data with twopeaks occurring during the entire duration of the transientIn the beginning the outlet temperature rises rapidly as the

core flow rate drops rapidly as shown in Figure 13 epower decreases slowly because of the negative reactivityfeedback introduced by the control rod driveline expansionand radial expansion e power-to-flow ratio reaches thefirst peak value as shown in Figure 23 us the PIOTAsrsquooutlet temperatures increase rapidly and reach the first peakvalue After that the rapid drop of the coolant level withinthe GEMs introduced a large amount of negative reactivitycausing the total power to drop rapidly Meanwhile thedecreasing rate of mass flow rate starts to slow down ePIOTAsrsquo outlet temperatures start to decrease because thepower-to-flow ratio rapidly decreases Starting from about20 s the decrease in total power starts to slow down due to

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

200 400 600 8000Time (s)

0

5

10

15

20

Tota

l Cor

e Pow

er (C

al) (

MW

)

Figure 16 Reactor power of FFTF LOFWOS test 13 (low range)

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

0

20

40

60

80

100

120

140

160

180

200

Tota

l Cor

e Pow

er (C

al) (

MW

)

200 400 600 8000Time (s)

Figure 17 Reactor power of FFTF LOFWOS test 13

LOOP 1 NATURAL CIRCULATION

Loop 1 Mass Flow Rate (Cal)Loop 1 Mass Flow Rate (Exp)

0

10

20

30

40

50

Mas

s Flo

w R

ate (

kgs

)

100 200 300 400 500 600 700 800 9000Time (s)

Figure 14 Mass flow rate in loop 1 (Low range)

LOOP 1 TRANSITION TO NATURAL CIRCULATION

Loop 1 Mass Flow Rate (Cal)Loop 1 Mass Flow Rate (Exp)

-100

0

100

200

300

400

500

600

700

800

Mas

s Flo

w R

ate (

kgs

)

20 40 60 80 1000Time (s)

Figure 15 Mass flow rate in loop 1 (0 sndash100 s)

12 Science and Technology of Nuclear Installations

the rebound of the negative net reactivity as shown inFigure 20 erefore the power-to-flow ratio increaseswhich make the PIOTAsrsquo temperatures rise again At about110 s the PIOTAsrsquo temperatures reach the second peak valueafter the power-to-flow ratio reaches the second peak valueSince then the natural circulation starts to be establishedand maintained at about 4 of the rated flow as shown inFigure 14 e total power continues to decrease due to thenegative net reactivity e reactor enters a long-termcooling phase

In general the predicted results of SAC-3D are in goodagreement with the trend of the experimental data but thereare still deviations in the temperature values e outlettemperature of the PIOTA in row 2 is consistently lowerthan the measured value which is caused by the bias of thesimulated value of the total power transient variationSimilarly the simulated outlet temperature of the PIOTA inrow 6 is lower than the measured data until about 20 s butstarts to be higher than themeasured data after thenere isa maximum deviation of about 40 degrees Celsius at the

Net Reactivity (Cal)Doopler (Cal)Coolant Density (Cal)Axial Expansion (Cal)

Radial Expansion (Cal)Control Rod DrivelineExpansion (Cal)GEM (Cal)Net Reactivity (Exp)

ndash15

ndash10

ndash05

00

05

10

Net

Rea

ctiv

ity (C

al) (

$)

10 20 30 40 500Time (s)

Figure 20 Reactivity Transient Profile of FFTF LOFWOS test 13(0 sndash50 s)

Row 6 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Cal)Row 6 PIOTA Outlet Temp (Cal)

360

380

400

420

440

460

480

500

520

Row

6 P

IOTA

Out

let T

emp

(degC)

200 400 600 8000Time (s)

Figure 21 Row 2 and row 6 PIOTAs outlet temperature

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

0

20

40

60

80

100

120

140

160

180

200

Tota

l Cor

e Pow

er (C

al) (

MW

)

5 10 15 20 25 30 35 400Time (s)

Figure 18 Reactor power of FFTF LOFWOS test 13 (0 sndash40 s)

Net Reactivity (Cal)Doopler (Cal)Coolant Density (Cal)Axial Expansion (Cal)

Radial Expansion (Cal)Control Rod DrivelineExpansion (Cal)GEM (Cal)Net Reactivity (Exp)

ndash15

ndash10

ndash05

00

05

10

Net

Rea

ctiv

ity (C

al) (

$)

200 400 600 8000Time (s)

Figure 19 Reactivity transient profile of FFTF LOFWOS test 13

Science and Technology of Nuclear Installations 13

peak Unlike the PIOTA in row 2 the PIOTA in row 6 islocated at the outermost ring of the fuel assembly and is nextto a GEM assembly and a reflector assembly We believe thatthere are at least two possible reasons for this anomaly Oneis that even though the transientrsquos overall mass flow rate is ingood agreement with the measurement data it is stillpossible that the simulated mass flow rate variation withineach channel may not match the actual situation all that welle other important factor is the fact that the channel-to-channel heat transfer is not considered in the present worke neglect of heat transfer between the PIOTA in row 6 andGEM and reflector assembly introduced positive tempera-ture errors

5 Conclusions and Perspective

In the blind calculation phase of the IAEA FFTF LOFWOStest 13 CRP we modeled the FFTF reactor system by usingthe SAC-3D system analysis code e SAC-3D calculationresults have reasonably good agreement with the measureddata After benchmark analyzing the EBR-II [2] and FFTFreactors SAC-3D shows its good capability to predict thefast reactor behaviors under ATWS transient conditionsHowever the SAC-3D and FFTF models still have room forimprovement e deviations in total power transient cal-culations suggest further improvement in the reactivityfeedback models as well as the decay heat prediction modelAnomalies in the transient temperature prediction of thePIOTA in row 6 indicate that the thermal-hydraulics cal-culation module needs to consider the heat transfer betweenchannels In the next phase of the work we will examine thedeviations between simulation results further and refine theFFTF model based on the blind phase benchmark analysisresults e specific calculation modules of SAC-3D will alsobe improved to predict the fast reactorrsquos behavior better

Data Availability

e data that support the findings of this study are availablefrom IAEA Restrictions apply to the availability of thesedata which were used under license for this study Data areavailable from the corresponding author with the permis-sion of IAEA

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e authors would like to express their thanks to IAEAParticipation in the CRP on the FFTF LOFWOS test 13 isunder a research agreement between the North ChinaElectric Power University and the IAEA CRP numberI32011 is work was partially financially supported by theNational Natural Science Foundation of China (GrantNo11705057)

References

[1] D Sui D Lu L Ren and Y Liu ldquoDevelopment of three-di-mensional hot pool model in a system analysis code for pool-type FBRrdquo Nuclear Engineering and Design vol 256pp 264ndash273 2012

[2] D Lu S Lyu and D Sui ldquoVerification of SAC-3D based onEBR-II SHRT-45R benchmark datardquo in Proceedings of the 18thInternational Topical Meeting on Nuclear Reactor +ermalHydraulics Portland OR USA August 2019

[3] D Lu S Lyu and D Sui ldquoSimulation of FFTF loss of flowwithout scram test based on system code SAC-3Drdquo AtomicEnergy Science and Technology vol 55 no 8 pp 1345ndash13522021

[4] T Sumner A Moisseytsev F Heidet D W WootanA M Casella and J V Nelson Benchmark Specification forFFTF LOFWOS Test 13 IAEA Vienna Austria 2017

Row 6 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Cal)Row 6 PIOTA Outlet Temp (Cal)

360

380

400

420

440

460

480

500

520

Row

6 P

IOTA

Out

let T

emp

(degC)

2000Time (s)

Figure 22 Row 2 and row 6 PIOTAs outlet temperature(0 sndash200 s)

22

20

18

16

14

12

08

06

Dim

ensio

nles

s Pow

er-F

low

Rat

io

0 20 40 60 80 100 120Time (s)

140 160 180 200

Dimensionless Power-Flow Ratio

Dimensionless Power-Flow Ratio

200 400 600 8000Time (s)

06

08

12

10

14

16

18

20

22

Dim

ensio

nles

s Pow

er-F

low

Rat

io

Figure 23 Dimensionless power-flow ratio

14 Science and Technology of Nuclear Installations

[5] C Guo D Lu X Zhang and D Sui ldquoDevelopment and ap-plication of a safety analysis code for small Lead cooled FastReactor SVBR 75100rdquo Annals of Nuclear Energy vol 81pp 62ndash72 2015

[6] D Lu C Guo and D Sui ldquoA three-dimensional nodal neutronkinetics code with a higher-accuracy algorithm for reactor corein hexagonal-z geometryrdquo Annals of Nuclear Energy vol 101pp 250ndash261 2017

[7] J M Ruggieri J Tommasi J F Lebrat et al ldquoEranos 21International code system for GEN IV fast reactor analysisrdquo inProceedings of the 2006 International Congress on Advances inNuclear Power Plants ICAPPrsquo06 pp 2432ndash2439 Seoul KoreaJuly 2006

[8] S Lyu D Lu and D Sui ldquoNeutronics benchmark analysis ofthe EBR-II SHRT-45R with SAC-3Drdquo Nuclear Engineering andDesign vol 364 p 110679 2020

[9] C Guo D Lu D Sui and X Zhang ldquoSAC-CFR computer codeverification with Experimental Breeder Reactor II loss-of-primary-flow-without-scram tests datardquo Annals of NuclearEnergy vol 71 pp 166ndash173 2014

Science and Technology of Nuclear Installations 15

the rebound of the negative net reactivity as shown inFigure 20 erefore the power-to-flow ratio increaseswhich make the PIOTAsrsquo temperatures rise again At about110 s the PIOTAsrsquo temperatures reach the second peak valueafter the power-to-flow ratio reaches the second peak valueSince then the natural circulation starts to be establishedand maintained at about 4 of the rated flow as shown inFigure 14 e total power continues to decrease due to thenegative net reactivity e reactor enters a long-termcooling phase

In general the predicted results of SAC-3D are in goodagreement with the trend of the experimental data but thereare still deviations in the temperature values e outlettemperature of the PIOTA in row 2 is consistently lowerthan the measured value which is caused by the bias of thesimulated value of the total power transient variationSimilarly the simulated outlet temperature of the PIOTA inrow 6 is lower than the measured data until about 20 s butstarts to be higher than themeasured data after thenere isa maximum deviation of about 40 degrees Celsius at the

Net Reactivity (Cal)Doopler (Cal)Coolant Density (Cal)Axial Expansion (Cal)

Radial Expansion (Cal)Control Rod DrivelineExpansion (Cal)GEM (Cal)Net Reactivity (Exp)

ndash15

ndash10

ndash05

00

05

10

Net

Rea

ctiv

ity (C

al) (

$)

10 20 30 40 500Time (s)

Figure 20 Reactivity Transient Profile of FFTF LOFWOS test 13(0 sndash50 s)

Row 6 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Cal)Row 6 PIOTA Outlet Temp (Cal)

360

380

400

420

440

460

480

500

520

Row

6 P

IOTA

Out

let T

emp

(degC)

200 400 600 8000Time (s)

Figure 21 Row 2 and row 6 PIOTAs outlet temperature

Total Core Power (Cal)Fission Power (Cal)Decay Heat (Cal)

Total Core Power (Exp)Fission Power (Exp)Decay Heat (Exp)

0

20

40

60

80

100

120

140

160

180

200

Tota

l Cor

e Pow

er (C

al) (

MW

)

5 10 15 20 25 30 35 400Time (s)

Figure 18 Reactor power of FFTF LOFWOS test 13 (0 sndash40 s)

Net Reactivity (Cal)Doopler (Cal)Coolant Density (Cal)Axial Expansion (Cal)

Radial Expansion (Cal)Control Rod DrivelineExpansion (Cal)GEM (Cal)Net Reactivity (Exp)

ndash15

ndash10

ndash05

00

05

10

Net

Rea

ctiv

ity (C

al) (

$)

200 400 600 8000Time (s)

Figure 19 Reactivity transient profile of FFTF LOFWOS test 13

Science and Technology of Nuclear Installations 13

peak Unlike the PIOTA in row 2 the PIOTA in row 6 islocated at the outermost ring of the fuel assembly and is nextto a GEM assembly and a reflector assembly We believe thatthere are at least two possible reasons for this anomaly Oneis that even though the transientrsquos overall mass flow rate is ingood agreement with the measurement data it is stillpossible that the simulated mass flow rate variation withineach channel may not match the actual situation all that welle other important factor is the fact that the channel-to-channel heat transfer is not considered in the present worke neglect of heat transfer between the PIOTA in row 6 andGEM and reflector assembly introduced positive tempera-ture errors

5 Conclusions and Perspective

In the blind calculation phase of the IAEA FFTF LOFWOStest 13 CRP we modeled the FFTF reactor system by usingthe SAC-3D system analysis code e SAC-3D calculationresults have reasonably good agreement with the measureddata After benchmark analyzing the EBR-II [2] and FFTFreactors SAC-3D shows its good capability to predict thefast reactor behaviors under ATWS transient conditionsHowever the SAC-3D and FFTF models still have room forimprovement e deviations in total power transient cal-culations suggest further improvement in the reactivityfeedback models as well as the decay heat prediction modelAnomalies in the transient temperature prediction of thePIOTA in row 6 indicate that the thermal-hydraulics cal-culation module needs to consider the heat transfer betweenchannels In the next phase of the work we will examine thedeviations between simulation results further and refine theFFTF model based on the blind phase benchmark analysisresults e specific calculation modules of SAC-3D will alsobe improved to predict the fast reactorrsquos behavior better

Data Availability

e data that support the findings of this study are availablefrom IAEA Restrictions apply to the availability of thesedata which were used under license for this study Data areavailable from the corresponding author with the permis-sion of IAEA

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e authors would like to express their thanks to IAEAParticipation in the CRP on the FFTF LOFWOS test 13 isunder a research agreement between the North ChinaElectric Power University and the IAEA CRP numberI32011 is work was partially financially supported by theNational Natural Science Foundation of China (GrantNo11705057)

References

[1] D Sui D Lu L Ren and Y Liu ldquoDevelopment of three-di-mensional hot pool model in a system analysis code for pool-type FBRrdquo Nuclear Engineering and Design vol 256pp 264ndash273 2012

[2] D Lu S Lyu and D Sui ldquoVerification of SAC-3D based onEBR-II SHRT-45R benchmark datardquo in Proceedings of the 18thInternational Topical Meeting on Nuclear Reactor +ermalHydraulics Portland OR USA August 2019

[3] D Lu S Lyu and D Sui ldquoSimulation of FFTF loss of flowwithout scram test based on system code SAC-3Drdquo AtomicEnergy Science and Technology vol 55 no 8 pp 1345ndash13522021

[4] T Sumner A Moisseytsev F Heidet D W WootanA M Casella and J V Nelson Benchmark Specification forFFTF LOFWOS Test 13 IAEA Vienna Austria 2017

Row 6 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Cal)Row 6 PIOTA Outlet Temp (Cal)

360

380

400

420

440

460

480

500

520

Row

6 P

IOTA

Out

let T

emp

(degC)

2000Time (s)

Figure 22 Row 2 and row 6 PIOTAs outlet temperature(0 sndash200 s)

22

20

18

16

14

12

08

06

Dim

ensio

nles

s Pow

er-F

low

Rat

io

0 20 40 60 80 100 120Time (s)

140 160 180 200

Dimensionless Power-Flow Ratio

Dimensionless Power-Flow Ratio

200 400 600 8000Time (s)

06

08

12

10

14

16

18

20

22

Dim

ensio

nles

s Pow

er-F

low

Rat

io

Figure 23 Dimensionless power-flow ratio

14 Science and Technology of Nuclear Installations

[5] C Guo D Lu X Zhang and D Sui ldquoDevelopment and ap-plication of a safety analysis code for small Lead cooled FastReactor SVBR 75100rdquo Annals of Nuclear Energy vol 81pp 62ndash72 2015

[6] D Lu C Guo and D Sui ldquoA three-dimensional nodal neutronkinetics code with a higher-accuracy algorithm for reactor corein hexagonal-z geometryrdquo Annals of Nuclear Energy vol 101pp 250ndash261 2017

[7] J M Ruggieri J Tommasi J F Lebrat et al ldquoEranos 21International code system for GEN IV fast reactor analysisrdquo inProceedings of the 2006 International Congress on Advances inNuclear Power Plants ICAPPrsquo06 pp 2432ndash2439 Seoul KoreaJuly 2006

[8] S Lyu D Lu and D Sui ldquoNeutronics benchmark analysis ofthe EBR-II SHRT-45R with SAC-3Drdquo Nuclear Engineering andDesign vol 364 p 110679 2020

[9] C Guo D Lu D Sui and X Zhang ldquoSAC-CFR computer codeverification with Experimental Breeder Reactor II loss-of-primary-flow-without-scram tests datardquo Annals of NuclearEnergy vol 71 pp 166ndash173 2014

Science and Technology of Nuclear Installations 15

peak Unlike the PIOTA in row 2 the PIOTA in row 6 islocated at the outermost ring of the fuel assembly and is nextto a GEM assembly and a reflector assembly We believe thatthere are at least two possible reasons for this anomaly Oneis that even though the transientrsquos overall mass flow rate is ingood agreement with the measurement data it is stillpossible that the simulated mass flow rate variation withineach channel may not match the actual situation all that welle other important factor is the fact that the channel-to-channel heat transfer is not considered in the present worke neglect of heat transfer between the PIOTA in row 6 andGEM and reflector assembly introduced positive tempera-ture errors

5 Conclusions and Perspective

In the blind calculation phase of the IAEA FFTF LOFWOStest 13 CRP we modeled the FFTF reactor system by usingthe SAC-3D system analysis code e SAC-3D calculationresults have reasonably good agreement with the measureddata After benchmark analyzing the EBR-II [2] and FFTFreactors SAC-3D shows its good capability to predict thefast reactor behaviors under ATWS transient conditionsHowever the SAC-3D and FFTF models still have room forimprovement e deviations in total power transient cal-culations suggest further improvement in the reactivityfeedback models as well as the decay heat prediction modelAnomalies in the transient temperature prediction of thePIOTA in row 6 indicate that the thermal-hydraulics cal-culation module needs to consider the heat transfer betweenchannels In the next phase of the work we will examine thedeviations between simulation results further and refine theFFTF model based on the blind phase benchmark analysisresults e specific calculation modules of SAC-3D will alsobe improved to predict the fast reactorrsquos behavior better

Data Availability

e data that support the findings of this study are availablefrom IAEA Restrictions apply to the availability of thesedata which were used under license for this study Data areavailable from the corresponding author with the permis-sion of IAEA

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e authors would like to express their thanks to IAEAParticipation in the CRP on the FFTF LOFWOS test 13 isunder a research agreement between the North ChinaElectric Power University and the IAEA CRP numberI32011 is work was partially financially supported by theNational Natural Science Foundation of China (GrantNo11705057)

References

[1] D Sui D Lu L Ren and Y Liu ldquoDevelopment of three-di-mensional hot pool model in a system analysis code for pool-type FBRrdquo Nuclear Engineering and Design vol 256pp 264ndash273 2012

[2] D Lu S Lyu and D Sui ldquoVerification of SAC-3D based onEBR-II SHRT-45R benchmark datardquo in Proceedings of the 18thInternational Topical Meeting on Nuclear Reactor +ermalHydraulics Portland OR USA August 2019

[3] D Lu S Lyu and D Sui ldquoSimulation of FFTF loss of flowwithout scram test based on system code SAC-3Drdquo AtomicEnergy Science and Technology vol 55 no 8 pp 1345ndash13522021

[4] T Sumner A Moisseytsev F Heidet D W WootanA M Casella and J V Nelson Benchmark Specification forFFTF LOFWOS Test 13 IAEA Vienna Austria 2017

Row 6 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Exp)Row 2 PIOTA Outlet Temp (Cal)Row 6 PIOTA Outlet Temp (Cal)

360

380

400

420

440

460

480

500

520

Row

6 P

IOTA

Out

let T

emp

(degC)

2000Time (s)

Figure 22 Row 2 and row 6 PIOTAs outlet temperature(0 sndash200 s)

22

20

18

16

14

12

08

06

Dim

ensio

nles

s Pow

er-F

low

Rat

io

0 20 40 60 80 100 120Time (s)

140 160 180 200

Dimensionless Power-Flow Ratio

Dimensionless Power-Flow Ratio

200 400 600 8000Time (s)

06

08

12

10

14

16

18

20

22

Dim

ensio

nles

s Pow

er-F

low

Rat

io

Figure 23 Dimensionless power-flow ratio

14 Science and Technology of Nuclear Installations

[5] C Guo D Lu X Zhang and D Sui ldquoDevelopment and ap-plication of a safety analysis code for small Lead cooled FastReactor SVBR 75100rdquo Annals of Nuclear Energy vol 81pp 62ndash72 2015

[6] D Lu C Guo and D Sui ldquoA three-dimensional nodal neutronkinetics code with a higher-accuracy algorithm for reactor corein hexagonal-z geometryrdquo Annals of Nuclear Energy vol 101pp 250ndash261 2017

[7] J M Ruggieri J Tommasi J F Lebrat et al ldquoEranos 21International code system for GEN IV fast reactor analysisrdquo inProceedings of the 2006 International Congress on Advances inNuclear Power Plants ICAPPrsquo06 pp 2432ndash2439 Seoul KoreaJuly 2006

[8] S Lyu D Lu and D Sui ldquoNeutronics benchmark analysis ofthe EBR-II SHRT-45R with SAC-3Drdquo Nuclear Engineering andDesign vol 364 p 110679 2020

[9] C Guo D Lu D Sui and X Zhang ldquoSAC-CFR computer codeverification with Experimental Breeder Reactor II loss-of-primary-flow-without-scram tests datardquo Annals of NuclearEnergy vol 71 pp 166ndash173 2014

Science and Technology of Nuclear Installations 15

[5] C Guo D Lu X Zhang and D Sui ldquoDevelopment and ap-plication of a safety analysis code for small Lead cooled FastReactor SVBR 75100rdquo Annals of Nuclear Energy vol 81pp 62ndash72 2015

[6] D Lu C Guo and D Sui ldquoA three-dimensional nodal neutronkinetics code with a higher-accuracy algorithm for reactor corein hexagonal-z geometryrdquo Annals of Nuclear Energy vol 101pp 250ndash261 2017

[7] J M Ruggieri J Tommasi J F Lebrat et al ldquoEranos 21International code system for GEN IV fast reactor analysisrdquo inProceedings of the 2006 International Congress on Advances inNuclear Power Plants ICAPPrsquo06 pp 2432ndash2439 Seoul KoreaJuly 2006

[8] S Lyu D Lu and D Sui ldquoNeutronics benchmark analysis ofthe EBR-II SHRT-45R with SAC-3Drdquo Nuclear Engineering andDesign vol 364 p 110679 2020

[9] C Guo D Lu D Sui and X Zhang ldquoSAC-CFR computer codeverification with Experimental Breeder Reactor II loss-of-primary-flow-without-scram tests datardquo Annals of NuclearEnergy vol 71 pp 166ndash173 2014

Science and Technology of Nuclear Installations 15