validation of the dalton-thermix thermal · pdf fileof the stresses in the fuel coating layers...

THERMAL HYDRAULICS

KEYWORDS: PBMR, DALTON-THERMIX, HTR-10

VALIDATION OF THE DALTON-THERMIXCODE SYSTEM WITH TRANSIENTANALYSES OF THE HTR-10 ANDAPPLICATION TO THE PBMRB. BOER,a D. LATHOUWERS,a J. L. KLOOSTERMAN,a*T. H. J. J. VAN DER HAGEN,a and G. STRYDOMb

aDelft University of Technology, Mekelweg 15, 2629 JB, Delft, The NetherlandsbPBMR Pty (Ltd.), 1279 Mike Crawford Avenue, Centurion 0046, South Africa

Received January 26, 2009Accepted for Publication September 1, 2009

The DALTON-THERMIX code system has been de-veloped for safety analysis and core optimization ofpebble-bed reactors. The code system consists of the newthree-dimensional diffusion code DALTON, which is cou-pled to the existing thermal-hydraulic code THERMIX.These codes are linked to a database procedure for thegeneration of neutron cross sections using SCALE-5.

The behavior of pebble-bed reactors during a loss offorced cooling (LOFC) transient is of particular interestsince the absence of forced cooling could lead to a sig-nificant increase of the temperature of the coated parti-cle fuel. Therefore, the reactor power may be constrainedduring normal operation to limit the temperature.

For validation purposes, calculation results of nor-mal operation, an LOFC transient, and a control rodwithdrawal transient without SCRAM have been com-pared with experimental data obtained in the High Tem-

perature Reactor–10 (HTR-10). The code system has beenapplied to the 400-MW(thermal) pebble bed modularreactor (PBMR) design, including the analysis of threedifferent LOFC transients. Theses results are verified bya comparison with the results of the existing TINTE codesystem.

It was found that the code system is capable of mod-eling both small (HTR-10) and large (PBMR) pebble-bedreactors and therefore provides a flexible tool for safetyanalysis and core optimization of future reactor designs.The analyses of the LOFC transients show that the peakfuel temperature is only slightly elevated (less than�1008C) as compared to its nominal value in the HTR-10but reaches a maximum value of 16488C during the de-pressurized LOFC case of the PBMR benchmark, whichis significantly higher than the peak fuel temperature(9768C) during normal operation.

I. INTRODUCTION

Compared with pebble-bed reactors, such as the AVRand THTR, that operated in the past, the very high tem-perature reactor ~VHTR! as proposed by the GenerationIV initiative1 is envisaged to operate at a helium outlettemperature of 10008C together with a high fuel burnuplevel ~.95 MWd0kg U!. This has significant conse-quences for the fuel temperature not only during normaloperation but especially during a loss of forced cooling~LOFC! incident, in which the maximum fuel tempera-ture of the core is generally above its nominal value. The

core power density largely determines the peak temper-ature during this transient and is expected to be consid-erably higher in the VHTR design than in the past reactordesigns. A higher fuel temperature results in an increaseof the stresses in the fuel coating layers and possiblecoating failure. This might constrain the power level andoperating temperature during normal operation. The ex-istence of a validated code system for the evaluation ofthe fuel temperature during normal and LOFC conditionsis therefore a key element in the development of theVHTR.

In this paper the methodology and validation of acode system for neutronic and thermal-hydraulic analy-sis of pebble-bed–type high-temperature reactors ~HTRs!*E-mail: [email protected]

306 NUCLEAR TECHNOLOGY VOL. 170 MAY 2010

are presented. The code system can be split up into twoparts. The first focuses on the generation of nuclear datafor the full-core analysis. These data are used in the sec-ond part, which is concerned with the neutronic andthermal-hydraulic analysis of the reactor. The main pur-pose of the code is to calculate the fuel temperature forboth normal and accident conditions for various reactordesigns. In addition, other parameters of the core, such asthe neutron flux and power profile, can be calculated forthe evaluation of the fuel performance.

The neutronic and thermal-hydraulic part of the codesystem consists of the new DALTON time-dependentthree-dimensional ~3-D! diffusion code,2 which has beencoupled to the existing THERMIX two-dimensional ~2-D!thermal-hydraulics code.3 The followed approach formodeling HTR dynamics is similar to other recent codesystems such as PANTHERMIX, DORT-TD, PEBBED-THERMIX~KONVEK!, and PARCS-THERMIX ~Refs. 4through 7, respectively!, in which a diffusion ~or trans-port! code for the neutronics is coupled to THERMIX~KONVEK0DIREKT!. Other HTR dynamics codes thatdo not make use of THERMIX for the thermal hydraulicsare MARS-GCR0CAPP and the TINTE code system~Refs. 8 and 9, respectively!.

DALTON-THERMIX is part of a larger code systemunder development that is able to perform fuel depletion,treat pebble recirculation,10 and generate temperature-dependent neutron cross sections for transient analysis.To this end, DALTON-THERMIX has been linked toSCALE-5 ~Ref. 11! ~see Sec. II!, thereby creating a flex-ible tool for modeling and optimization of pebble-bedreactors. A code system that has been used extensively inthe past for this purpose is Very Superior Old Programs12

~VSOP!, which combines neutron cross-section process-ing routines with a diffusion and thermal-hydraulic model.The new code system includes the following improve-ments of the numerical methods: the direct determinationof the equilibrium core composition,6,10 the use of mod-ern acceleration schemes for the neutronic solver,13,14 afast analytical method for the treatment of double het-erogeneity,15 and the capability of calculating coupledneutronic and thermal-hydraulic transients.

Past experience with HTR technology provides valu-able information for validating codes. In 2003, experi-ments were conducted on the HTR-10 in China ~see Table Iand Fig. 1a!. In this 10-MW pebble-bed research reactor,a pressurized loss of forced cooling ~PLOFC! and a con-trol rod withdrawal ~CRW! experiment were performed.This reactor has a reactor cavity cooling system ~RCCS!with a capacity of only 200 kW that is located outside thereactor pressure vessel for the removal of the decay heatduring incidents. The passive removal of the decay heatby an RCCS during an accident situation was proposedfirst for HTR-MODUL ~Ref. 16! and has also been adoptedfor modern large designs, such as the 400-MW~thermal!pebble bed modular reactor ~PBMR! ~see Table I andFig. 1b!. In the PBMR design the average power density

is considerably larger ~4.6 MW0m3! than the power den-sity of the HTR-10 ~2.0 MW0m3!. Therefore, it can beexpected that the peak fuel temperatures during LOFCtransients in this design are higher.

First, the DALTON-THERMIX code system is vali-dated against the experimental results of normal opera-tion and LOFC transients in the small HTR-10 ~Ref. 17!.Results of this comparison are presented in Sec. III. Sec-ond, the code system is applied to the PBMR to analyzenormal and LOFC transients @PLOFC and depressurized

TABLE I

Main Characteristics of the HTR-10 and the PBMR Designs*

Reactor HTR-10 PBMR

First power operation 2000 —Country China South AfricaPower @MW~thermal!# 10 400Pebble-bed diameter ~inside0outside!

~m!001.9 2.003.7

Pebble-bed height ~m! 1.8 11Power density ~MW0m3! 2.0 4.6Efficiency ~%! — 41Fuel loading UO2 UO2

Enrichment 235U ~%! 17 9.6Maximum fuel burnup ~MWd0kg! 100 95Coolant Tin ~8C! 250 500Coolant Tout ~8C! 750 900Pressure ~MPa! 2.5 9.0Thermodynamic cycle Steam Brayton ~direct!

*HTR-10 and PBMR characteristics taken from Refs. 36 and 37,respectively.

Fig. 1. Schematic overview of ~a! HTR-10 core layout36 and~b! PBMR core layout.37

Boer et al. DALTON-THERMIX CODE VALIDATION FOR HTR-10 AND PBMR

NUCLEAR TECHNOLOGY VOL. 170 MAY 2010 307

LOFC ~DLOFC!# . Since no experimental data are avail-able for this design, the results of the simulations are com-pared with calculations of the TINTE code system~Sec. IV!, which were performed in the framework of theNuclear Energy Agency ~NEA! Organisation for Eco-nomic Co-operation and Development PBMR-400benchmark.18

The peak fuel temperature during these LOFC tran-sients determines whether an increase in reactor power,with the aim of increasing the coolant outlet temperaturefrom 900 to 10008C, would be allowable for the presentPBMR design.

II. OVERVIEW OF THE CODE SYSTEM

Figure 2 gives a schematic overview of the coupledcode system. A description of each component of thesystem is given in the following sections.

II.A. Processing of Neutron Cross Sections

Before the thermal-hydraulic and neutronic calcula-tions are started, a neutron cross-section library is cre-ated as a function of the fuel and moderator temperaturesand the xenon concentration. For the simulation of thePBMR, the cross sections were taken from the bench-mark description.18 These cross sections are also depen-dent on the local fast and thermal buckling. For thesimulation of the HTR-10 transients, both a point-kinetics model19 with externally calculated reactivitycoefficients and a 2-D model in DALTON with space-and temperature-dependent neutron cross sections usinga similar procedure have been used. The procedure usesseveral modules of the SCALE-5 code system11 in orderto take into account the double heterogeneity of the fuel

~TRISO and pebble! and the geometry of the reactor.The calculation steps are as follows:

1. The TRISO particles in the graphite matrix aremodeled by using the CSASIX module of SCALE-5. Inthis module, the NITAWL-III and BONAMI modules~Refs. 20 and 21, respectively! are used for the evalua-tion of the resolved and unresolved resonances, whichare treated by the Nordheim integral method and theBondarenko method, respectively. A one-dimensional~1-D! discrete ordinates transport calculation usingXSDRNPM ~Ref. 22! is made of a fuel kernel sur-rounded by cladding ~material from the carbon buffer,and the inner pyrolytic carbon, silicon carbide, and outerpyrolytic carbon layers! and moderator ~graphite! mate-rial ~see Fig. 3!. The moderator volume having radius R0is equal to the volume of the fuel zone of the pebbledivided by the number of TRISOs. From this last calcu-lation, homogenized neutron cross sections are made for“TRISO material.” For this purpose a 172-energy-group~XMAS! library is used, based on the JEFF2.203.0 andJENDL3.3 libraries and processed with NJOY. To ac-count for the fuel-shadowing effect of the fuel kernels inthe graphite matrix of the pebbles, a Dancoff factor isused, which is analytically determined15 and is a func-tion of the number of fuel particles and the radii of thekernel, the fuel zone, and the pebble.

2. The homogenized neutron cross sections for theTRISO material are used in a 1-D transport ~XSDRNPM!calculation in which a sphere of TRISO material, withradius R1, is surrounded by a layer of graphite and he-lium with radius R2 ~see Fig. 3!. In this calculation R1 isequal to the fuel zone in the pebble, and R2 can be cal-culated from the packing fraction c ~� 0.61! and theratio of moderator to fuel pebbles f by the followingrelation:

Fig. 2. Schematic overview of the coupled code system ~XS �cross section!.

Fig. 3. TRISO and pebble model used in calculation of ho-mogenized cross sections for the pebble-bed region ofthe reactor. A white boundary condition on the outersurface was applied in both the TRISO and pebblegeometries.



R2 � 3�Rpeb3

1 � f

c. ~1!

If no moderator pebbles are present, f equals zero. In thecase of the HTR-10, f � 43057, and since the fuel zone ofthe pebble is 2.5 cm and the pebble outer radius is 3 cm,a value of 4.26 cm is found for R2.

This transport calculation results in homogenizedcross sections for “pebble bed material.”

3. As a last calculation step, several 1-D transportcalculations, corresponding to a certain axial or radialcross section of the core, are performed. In general, thegeometry consists of a pebble-bed region surrounded bygraphite reflector regions. These regions are split up intoseveral zones to generate zone-weighted few-group crosssections. In order to model the transverse neutron leak-age in these 1-D calculations, the reactor height ~or width!is supplied from which a buckling factor is derived. Thezone-weighted cross sections of these 1-D calculationsare allocated to the positions of the corresponding mate-rial in a 2-D cross section map.

It is noted that the nuclide densities in the core can becalculated by the code system10 prior to the above pro-cedure using a method that converges directly to the equi-librium core.6

The above described procedure is repeated for sev-eral fuel and moderator temperatures resulting in a 2-Dtemperature-dependent cross-section library. Directional-dependent diffusion coefficients are calculated with ananalytical solution23 to treat the void regions in the core,such as the helium plenum above the pebble bed. Re-gions containing the control rods are treated in a separateCSAS ~criticality safety analysis sequence! run repre-senting a horizontal cross section of the rod and surround-ing material ~graphite and pebble bed!. The resultingcell-weighted cross sections are transformed to a “greycurtain” region for the 2-D ~r-z! cross-section map byconservation of the neutron absorption reaction rates.

For the HTR-10 benchmark, both reactivity co-efficients as well as zone-weighted cross sections havebeen calculated with the above procedure for the point-kinetics model and the 2-D model in DALTON,respectively.

II.B. DALTON

The DALTON code can solve the 3-D multigroupdiffusion equations on structured grids ~x-y-z or r-z-ucoordinates!. The code’s capabilities include both the fun-damental and higher lambda modes and time eigenvaluesthrough the Arnoldi method by linking with the AR-PACK package.24 Transient analysis in forward and ad-joint modes is possible with or without precursors. Spatialdiscretization is performed using a second-order accu-rate finite volume method. The precursor concentration

at the new time level is eliminated from the flux equa-tion.25 Effectively, the system can then be solved in adecoupled manner by solving for the multigroup fluxfirst and subsequently for the precursor groups.

DALTON uses an adaptive time-stepping algorithmthat is based on the use of the second-order time-accurateBackward-2 scheme. This scheme is fully implicit andunconditionally stable. Whether or not a time step isaccepted in a time-dependent calculation depends on themaximum allowed absolute error ATOL and relative errorRTOL as supplied by the user:

� 1

N (i�1

N � LTEi

ATOL � RTOL � fi�2

� 1 , ~2!

where

fi � neutron flux

LTE � local truncation error of the Backward-2scheme.

To predict the time step to be used in the next step, asimilar procedure is adopted. The linear systems arisingfrom discretization are solved using the preconditionedconjugate gradient where the preconditioner is based onan incomplete factorization. In the multigroup case, ac-celeration of the Gauss-Seidel group-by-group solutionprocedure is obtained by the techniques introduced inRefs. 13 and 14.

A 2-D ~r-z! model is used in the DALTON code tocalculate a 2-D zone-averaged power profile using neu-tron cross sections that have been obtained through linearinterpolation using the local temperature and xenon con-centration. In the case that the point-kinetics equationsare used, a fixed power distribution is scaled to the cal-culated total power.

II.C. THERMIX

THERMIX~-DIREKT! ~Ref. 3! is a 2-D thermal-hydraulic code that consists of the two modules: THER-MIX ~heat conduction and thermal radiation! and DIREKT~convection!. The power profile calculated by DALTONis used in THERMIX to calculate the temperature profilein the reactor at the new time point.

The pebble-bed region is treated as a porous me-dium. In THERMIX both the conduction in the pebblesand the radiation between the pebble surfaces are treated,while the 2-D helium flow in the bed is treated by DIREKT.These two models are coupled by the heat transfer fromthe pebble surface to the helium coolant.

For the core region, 2-D temperature profiles for fueland moderator temperatures of the pebbles are calcu-lated. To this end, a 1-D calculation for the temperatureprofile inside the pebbles is used, taking into account thatthe pebbles have a fuel-free ~graphite! zone in the outer~0.5-cm! shell.



Besides the power profile, the temperature and heattransfer coefficient at the outer surface of the reactor,determined by the RCCS, are used as boundary condi-tions for the THERMIX model. The boundary conditionsfor the DIREKT model are the helium inlet pressure,temperature, and mass flow.

II.D. Additional Scripts for Time-Step Control

and Cross-Section Updating

Next to the above-described main components of thecode system, the following codes and scripts are used inthe calculations for updating the cross section and con-trolling the ~global! time step.

MASTER

Depending on the type of transient, the MASTERprogram decides how often data are exchanged ~globaltime step! between the different codes and what thecalculation mode type of the codes has to be, i.e., steady-state ~eigenvalue! or transient mode. For transientcalculations DALTON and THERMIX are used consec-utively without performing additional iterations, updat-ing the cross sections for each global time step. Thetime-step control within the codes is done indepen-dently of each other. The ~global! time step can be cho-sen manually or with a control algorithm that ensuresconvergence and stability of the coupled calculation re-sult. The algorithm that was adopted is similar to thetime-step control in DALTON. Following Eq. ~2!, thecriterion for a time step to be accepted or not dependson the maximum allowable absolute error ATOL andrelative error RTOL as supplied by the user. However,instead of the neutron flux fi that is used in Eq. ~2!, avector y containing N state variables is used to checkthe “global” time step and predict the new step size. Arestart of the coupled code system from the previoustime point is required if the criterion is not met. Thevector y contains the following variables: the averagehelium temperature, the average fuel temperature, andthe total reactor power.

The calculation mode type can be adjusted for cer-tain transient simulations, such as LOFCs ~with or with-out SCRAM!, in which the reactor is in a subcriticalcondition for a long period and therefore the fission poweris negligible. In these cases a THERMIX stand-alonecalculation is performed combined with an eigenvaluecalculation in DALTON up to the point of recriticality,when the calculation mode is switched back to fully cou-pled dynamics. At this point the flux and precursor levelare normalized to a low power level, e.g., 1 W.

MIXER

An in-house perl script ~MIXER! updates for eachglobal calculation step the neutron cross sections by lin-

ear interpolation using several routines of the SCALE-5code system.11

Xenon

The xenon concentration is determined using the well-known simplified depletion chains for xenon and iodine.26

III. SIMULATION OF HTR-10

Apart from the calculation of the initial criticalityand normal operation of the HTR-10, two transient casesare investigated for code validation purposes, namely, asimulation of a PLOFC and a CRW, which also leads tothe shutdown of the blower and consequent shutdownof active core cooling. These cases can be consideredthe most demanding transients in a nuclear reactor andwere performed in the HTR-10 to demonstrate the in-herent safety characteristics of a pebble-bed reactor usingonly the RCCS as an active heat sink.17 Results of cal-culations made of both THERMIX coupled to a point-kinetics model ~PK-THERMIX! and the coupled 2-DDALTON-THERMIX model are compared with exper-imental data from the HTR-10.

III.A. Initial Criticality and Normal Operation

The initial core was composed of a mixture of peb-bles containing 5 g of 17% enriched uranium and pebblescontaining graphite only ~dummy pebbles! in a ratio of57:43 ~Ref. 27!. The pebble discharge tube and the bot-tom cone-shaped part of the core region were filled withdummy pebbles. A mixture of the fuel and dummy peb-bles was added to the core at room temperature untilcriticality was reached. Criticality was reached after add-ing 16 890 mixed pebbles at 158C corresponding to apebble-bed height of 123 cm at 278C ~Ref. 27!.

After the initial criticality was reached in December2000, additional fuel and dummy pebbles were added tothe core in order to maintain criticality at hot conditions.In the following 820 equivalent full-power days, a mix-ture of fuel and dummy pebbles is added, while the dummypebbles that filled the entire bottom region of the core aredischarged.28 After this period, fresh fuel pebbles areadded to the core in combination with recycling of fuelpebbles. It is therefore assumed that the core, when thetransient test was performed in October 2003, consistedof a combination of fuel pebbles having a certain burnupvalue and dummy pebbles.

The point of criticality has been calculated with thecross-section procedure of Sec. II.A combined with a2-D calculation for a fixed temperature of 278C. Thecross-section generation procedure predicted a k` of1.7625 for the pebble-bed material ~see Fig. 3!, which isclose to the value of 1.76155 calculated with TRIPOLI~Ref. 29!. For pebble-bed heights of 108 and 126 cm,



DALTON predicts a keff of 0.9698 and 1.0268, respec-tively, which leads to a critical height of 117 cm ~TRIP-OLI, Hcrit � 117.4 cm!. It is expected that the treatmentof the void regions for the movement of the control rodsand the absorber balls, which were modeled by reducingthe density of the graphite in those areas, leads to anunderestimation of the neutron streaming effects and there-fore in an overestimation of the keff ~Ref. 30!.

In the coupled DALTON-THERMIX calculations, itwas assumed that the entire discharge tube was filledwith a mixture of fuel and dummy pebbles and that thefuel in the core has a homogeneous average burnup value.Furthermore, it is assumed that the control rods remain inthe upper position. These lead to keff ’s of 0.9497 and1.0132 at burnup values of 8.5 and 6.8% FIMA ~fissionsper initial heavy metal atom!, respectively, for a coupledDALTON-THERMIX calculation.

The results of the temperatures ~burnup of 8.5%FIMA! at specific locations in the core ~Fig. 8 and Ref. 31!of a coupled calculation are presented in Table II. It isnoted that the calculated temperatures are higher for thetop reflector ~2428C! and the metal support structure~1928C! as compared to the experimental values of 230and 1808C, respectively. An explanation for these differ-ences could be found in the uncertainty in the specificlocations of the thermocouples. Furthermore, the 2-Dmodel in THERMIX does not capture the 3-D effects,which are especially important in the region of the re-flectors and the metal support structure at the bottom,which both contain the holes for the helium coolant.

III.B. PLOFC Transient

The PLOFC simulation is initiated by shutting downthe primary helium blower during steady-state operationof the reactor. As a result, the helium flow in the primaryloop is stopped, and the reactor is isolated from the water-cooling systems on the secondary side of the steam gen-erator. For calculation purposes, it is assumed that thehelium flow reduces linearly within 12 s ~Ref. 17!.

For both the PLOFC and the CRW simulations, thereactor conditions and assumptions were as follows:

1. The reactor has reached steady-state operation ata partial load of 30% of full power, i.e., 3 MW at the startof the transient in both the calculation model and in reality.

2. It is assumed that the primary helium pressure atsteady-state partial load operation is 2.5 MPa and re-mains unchanged during the transient. In reality, the re-actor pressure is almost constant, reducing slowly to 2.4MPa in 2.8 h ~Ref. 32!.

3. The measured helium temperatures at the reactorinlet and outlet of 215 and 6508C, respectively, at steady-state partial load operation were adopted in the THER-MIX model. The helium flow rate is defined by thistemperature difference and the measured helium pressure.

4. The control rods are modeled to remain at a fixed~uppermost! position in the DALTON model. The reac-tivity insertion by rod movement in the CRW simulationis simulated by rescaling the fission source in DALTONand introducing external reactivity in the point-kineticsmodel. The power density distribution is assumed to befixed. In reality, the power profile is asymmetrical afterthe movement of a single control rod. The impact on thepower profile is expected to be small since the core isoptically small for neutrons.

5. The temperature at the radial side boundary, wherethe decay heat removal system is located, is set to a fixedtemperature of 508C in THERMIX, which corresponds tothe average water temperature in the decay heat removalsystem resulting in a heat loss equal to the 206 kW of thecooling power of this system in reality. The top and bot-tom concrete structures surrounding the air cavity in whichthe reactor is placed were set to 358C, resulting in anegligible heat loss over the top and bottom boundaries.

6. The dummy pebbles were not modeled explicitlyin THERMIX. Instead, in the calculation of the temper-ature profile inside the pebbles, a reduced thermal con-ductivity was adopted, which was weighted with the fuel–to–dummy pebble ratio. In this way the temperature profileinside a fuel pebble was calculated, taking into accountthat only the fuel pebbles generate power.

7. Reactivity coefficients for the point-kinetics modelwere calculated with a DALTON-THERMIX calculationby varying the fuel, moderator, and reflector tempera-tures from their steady-state values.The following coef-ficients were used, respectively, for the fuel, moderator,and reflector: aF � �8.16 � 10�5 K�1, aM � �9.15 �10�5 K�1, and aR � 6.41 � 10�6 K�1.

The calculation and experimental results for the PLOFCare presented in Figs. 4, 5, and 6. One can see that thehelium mass flow reduction causes the temperatures ofthe fuel and moderator to increase, resulting in a negativereactivity feedback caused by increased resonance ab-sorption ~Doppler effect! in the fuel and the shift in ther-mal spectrum. Feedback from the reflector temperature

TABLE II

Temperatures at Several Locations in the HTR-10Calculated with DALTON-THERMIX and

Measured During Operation*

LocationExperiment

~8C!DALTON-THERMIX

~8C!

Top reflector 230 242Side reflector ~low! 460 457Metal support structure 180 194Outlet mixing room 810 810

*See Fig. 8 for temperature locations.



is small since the average change in reflector temperaturein the beginning of the transient is small and is delayed incomparison to the fuel and moderator temperature re-sponses. The feedback results in a fast reduction of thefission reactor power, and within 500 s the reactor poweris determined by the decay heat power only ~see Fig. 4!.

During the transient, natural convection flows en-able relatively cold helium from the helium cavities lo-cated on top and below the core ~see Fig. 1a! to enter thepebble discharge tube. Furthermore, the natural convec-

tion flow transports heat from the bottom to the top of ofthe pebble bed. The above described effects cause thebottom of the core to cool down while the top is heatedup, which can be seen from the calculated temperatureprofiles of the solid structures at the beginning and theend of the transient ~Figs. 7a and 7b!. One can see fromFigs. 7a and 7b that although the location of the peaktemperature shifts, there is not a large increase in itsmagnitude. The temperature at specific positions ~seeFig. 8! in the reflector, the core outlet and bottom

Fig. 4. Reactor ~fission! power during the first 500 s during thePLOFC transient in the HTR-10 measured during theexperiment and calculated with the PK-THERMIX andthe ~2-D! DALTON-THERMIX models. It is noted thatthe DALTON-THERMIX and experimental results arealmost identical.

Fig. 5. Reactor ~fission! power during the entire calculationdomain of the PLOFC transient in the HTR-10 mea-sured during the experiment and calculated with thePK-THERMIX and the ~2-D! DALTON-THERMIXmodels.

Fig. 6. Difference in the fuel, moderator, and reflector temper-atures compared to values at normal operating condi-tions calculated with DALTON-THERMIX model.

Fig. 7. Temperature profile of solid structures at ~a! beginning~t � 0 s! and ~b! end ~t � 7200 s! of the PLOFC tran-sient in the HTR-10.



support structure were recorded during the experiment.17

A large temperature difference between the beginningand the end of the transient was found at the top reflector,namely, �2158C. Temperature differences in the side re-flector were relatively small, but a large decrease of thetemperature by 3158C was recorded for the core outlet~located next to the pebble defueling chute!. Figure 9shows that the calculated temperatures agree within 10%of the measured data.

According to the measurements, the bottom part ofthe core has cooled down sufficiently to reach criticalityagain, and after 4200 s, the core is generating a signifi-cant amount of fission power ~see Fig. 5! according to themeasurement. This results in an increase of the powerand a corresponding rise in fuel and moderator temper-atures. The increase of fuel and moderator temperaturesresults again in negative reactivity feedback, which causesthe reactor power to come down again. This oscillatorybehavior occurs several times until a quasi-stationarysituation is reached at elevated temperatures at low re-actor power. The power level equals the amount of heattransferred to the decay heat removal system, which is;200 kW ~Ref. 17!.

Both the PK-THERMIX and the DALTON-THERMIX models show trends in power and tempera-

ture similar to the measured data. Some differencesbetween the codes and the experiment can be identified:

1. The point of recriticality predicted by theDALTON-THERMIX and PK-THERMIX models oc-curs at ;700 and 500 s, respectively, before the mea-sured point. The time of recriticality depends on thetemperatures in the core and their corresponding temper-ature reactivity feedback. The heat transfer from the coreto the RCCS and the thermal capacity determine the tem-perature in the pebble bed. It was found that the heattransfer rate to the cooler, which was modeled using afixed temperature and heat transfer coefficient at the outersurface of the reactor, was overestimated by THERMIX.The calculated heat transfer rate was 220 kW at the endof the transient ~6000 s! compared to the experimentalvalue of 206 kW. This results in a faster cooldown of thecore and a higher power level at the end of the transient~Fig. 5! than in reality.

2. Furthermore, the buildup of the 135Xe concentra-tion in the fuel will result in a negative reactivity feed-back effect, which will further delay the time point ofrecriticality. This latter effect was not taken into accountin the calculation models. Using the cross-section gen-eration procedure of Sec. II.A, it is calculated that theone-group neutron cross section at the start of the tran-sient sXe � 8.0 �105 b. The reactivity effect is calculatedusing the well-known equations for xenon and iodine.26

At the time point of recriticality, it was found that DrXe ��5.2 � 10�4. From the cooling-down rate ~see Fig. 6!and the temperature reactivity coefficients, it follows thatthe time point of recriticality would be delayed further by;300 s if the xenon poisoning effect were taken intoaccount, assuming a Xe equilibrium concentration at thestart of the transient.

Fig. 8. Schematic overview of the HTR-10 reactor design show-ing measurement points for the top reflector, core out-let, and metal support structure.

Fig. 9. Temperature during the PLOFC transient of the topreflector, core outlet, and metal support structure. Themeasured data are shown by the markers, while thesolid lines show the calculated results.



3. The maximum prompt power after recriticality—24.5% if the initial prompt power according to themeasurement—is better predicted with the DALTON-THERMIX model ~25.5%! than with the PK-THERMIXmodel ~43.5%!. This can be attributed to the detailedneutronics ~2-D! model in DALTON-THERMIXcompared to the simplified point-kinetics model inPK-THERMIX.

4. The power oscillations after recriticality inDALTON-THERMIX have a shorter period than the mea-surements, indicating that the feedback in DALTON-THERMIX is stronger than in reality. The oscillationsare dependent on the fuel and moderator temperaturesand their corresponding temperature reactivity effects.These temperatures are mainly dependent on the thermalcapacity of the graphite in the pebbles. The reduced timeperiod of the oscillations can therefore be sought in anunderestimation of the thermal capacity or an overesti-mation of the temperature reactivity effect of the fuel andmoderator in the DALTON-THERMIX model.

III.C. CRW Without SCRAM

In a second experiment the loss of flow is com-bined with the withdrawal of a control rod. The tran-sient is started ~time point zero! by withdrawing onecontrol rod at operational speed introducing positivereactivity17; see Fig. 10. After 12 s, the reactor protec-tion system was initiated by the signal “power increas-ing rate exceeds 3.5%0s.” This system shuts down thehelium blower, but because of its mechanical inertia,the speed of the blower reduces only gradually17 tozero. At the same time a flapper valve is closed toisolate the reactor from the rest of the primary loop.The core mass flow was not recorded during the tran-sient. Therefore, it is assumed that after the initiation ofthe reactor protection system, the mass flow is reduced

linearly and is completely stopped at t � 80 s, whichcorresponds to the reduction in the flow rate of thehelium blower according to measurements.17

The temperatures and prompt reactor power duringthe first 500 s of the experiment are shown in Figs. 11 and12a, respectively. The insertion of positive reactivity bythe CRW results in a rapid increase of the reactor powerduring the first 30 s of the transient. The increase in fueland moderator temperatures causes a negative tempera-ture feedback, which is stronger than the reactivity addedby the control rods, and within 500 s the contribution ofthe fission power to the total reactor power is negligible.Criticality is reached again ~see Fig. 12b!, after sufficientcooling down of the core, similar to the core behaviorduring the PLOFC transient. The reactor reaches the timepoint of recriticality earlier compared to the PLOFC tran-sient since positive reactivity was added by the CRW.

Although the shape of the power history is similarfor the first 500 s of the transient ~Fig. 12a!, the maxi-mum value reached is significantly lower for the PK-THERMIX ~187% of the initial fission power P0! and theDALTON-THERMIX ~1.89P0! calculations compared tothe measured value ~2.13P0!. It was found that the max-imum power reached is sensitive to the time point atwhich the mass flow reduction is initiated and the massflow reduction rate. If a fast reduction of the mass flow inthe first 16 s of the transient is assumed, the maximumpower reaches a value of only 1.5P0. In Ref. 17, both theblower speed and the relative flow rate are given graph-ically. The coastdown of the blower takes up to 400 s,while the flow rate of the blower is close to zero after80 s. It is unclear what the exact value of the flow rate inthe core was and if a small amount of flow remains after80 s. Moreover, the flapper valve apparently allows formass flow from the core after it is initiated ~at t � 12 s!.Fig. 10. Inserted reactivity by CRW.

Fig. 11. Difference in the fuel, moderator, and reflector tem-peratures compared to values at normal operating con-ditions used in the PK-THERMIX model to determinethe temperature reactivity feedback during the CRWtransient.



For a slow reduction to zero mass flow in 300 s, thefission power reaches 2.0P0 at its maximum and remainsconsiderable up to 600 s. Therefore, the uncertainty inthe exact value of the core mass flow could explain thedifference between the calculated and experimental re-sults for the beginning of the transient.

Similar to the PLOFC transient, the calculated pointof recriticality occurs ~250 s for DALTON-THERMIX!before the measured time point, and the maximum powerreached after this time point is 22% of the initial powerfor DALTON-THERMIX and 36% for PK-THERMIXcompared to the measured 23%. Similar to what wasfound for the PLOFC transient, the point-kinetics re-sults are similar to the DALTON results at the begin-ning of the transient. However, at the point of recriticality,the temperature and power profiles have changed sig-nificantly as compared to their shapes at nominal con-ditions. Therefore, the ~2-D! DALTON results are inbetter accordance with the experiments than the point-kinetics results. Similar to what was estimated for thePLOFC transient, including the Xe poisoning effect

would delay the calculated point of recriticality by;300 s.

IV. SIMULATION OF PBMR

The PBMR is a high-temperature gas-cooled reactorthat is currently being designed by PBMR Pty ~Ltd.!~Ref. 33!. In contrast with the HTR-10, this reactor is acommercial design with a significantly higher power ~den-sity!. Therefore, the increase in peak fuel temperatureduring anticipated LOFC transients is expected to be largerwhen compared to the HTR-10.

Steady-state and transient benchmark exercises wereorganized by the NEA ~Ref. 18!. The results of theDALTON-THERMIX code system for a coupled steadystate and DLOFC0PLOFC transient cases of the PBMRbenchmark are compared with the results of the TINTEcode system9,34 in this section.

The control rods that are located in the side reflectorare modeled as a uniform grey curtain according to thebenchmark description. The plenum above the pebblebed and the helium gap between the side reflector and thecore barrel are modeled as void regions using directionaldiffusion coefficients.23

Neutron cross sections that depend on the fuel tem-perature, moderator temperature, xenon concentration,and local fast and thermal buckling were provided as partof the benchmark description.18 The buckling depen-dence was included to capture the spectral effects result-ing from changes in the environment of a given coreregion.

IV.A. Normal Operating Conditions

A coupled neutronics0thermal-hydraulic calculationis performed to determine the conditions of the reactorduring normal operation. In this case the resulting neu-tron flux profile from a DALTON eigenvalue calculationwas normalized to a fixed power level of 400 MW, whilekeff was allowed to deviate from unity. Several iterativeruns of DALTON and THERMIX are performed untilconvergence is reached on keff . The results for the neu-tron flux profiles, axial temperature, and power profilesare shown in Figs. 13a, 13b, 14, and 15.

The flux profiles in Figs. 13a and 13b show a peak atthe top of the pebble bed, which is caused by the fact thatfresh fuel is inserted at the top of the core and removed atthe bottom. The thermal flux profile shows peaks in theinner and outer reflectors, resulting in power peaks nearthe radial edges of the pebble bed.

In Table III some key results of the two code sys-tems are compared. The power profile in DALTON hasa higher peak, which also results in a higher maximumneutron flux compared to TINTE. The differences forthe average temperatures are within several degrees Cel-sius. This can also be seen from Fig. 14 in which the

Fig. 12. Reactor ~prompt! power of the HTR-10 during theCRW transient of HTR-10 during ~a! the first 500 s~t � 500 s! and ~b! the entire time domain ~t � 7000 s!.



axial profiles of the maximum and average fuel temper-atures are shown.

In general, good agreement between the two codesystems is found for the steady-state results, although

slightly higher peak values for neutron fluxes and powerwere found with DALTON in comparison with TINTE.In order to start from an exactly critical reactor at thebeginning of the transient calculations, the fission sourcewas scaled with the eigenvalue.

IV.B. DLOFC Transient

The first transient is a DLOFC without SCRAM.Starting from full-load operating conditions, the massflow is reduced to 0.2 kg0s, and the pressure is reduced to1 bar assuming a linear reduction over 13 s. In a secondcase, assuming a SCRAM after 13 s, the control rods arefully inserted within 3 s. Furthermore, the mass flow isreduced to 0 kg0s instead of the trickle flow of 0.2 kg0s,according to the benchmark specification.

The response of the reactor power for both cases~with or without SCRAM! of the DALTON-THERMIXcalculation during the first 300 s is presented in Fig. 16.The temperature feedback causes a reduction in the fis-sion power of the reactor. In the case that a reactor SCRAMis included, the fission power is reduced rapidly, and thetotal reactor power is determined by the decay heat within20 s after the SCRAM.

In the case that no SCRAM is initiated, the reactorbecomes critical again after it has sufficiently cooleddown. The point of recriticality occurs in the DALTON-THERMIX calculation after 51.8 h, compared to 50.0 hfor the TINTE calculation. After several oscillations inpower and temperature, the fission power reaches a quasisteady state ~see Fig. 17!, while the average and maxi-mum temperatures of the pebble bed increase in the fol-lowing hours ~see Fig. 18!.

The fuel temperature histories for the DLOFC withSCRAM are presented in Fig. 19. The resulting tem-peratures are higher than for the case without the

Fig. 13. ~a! The fast flux profile and ~b! the thermal flux pro-file in PBMR at normal operating conditions showingthe location of the peaks. The solid line shows theregion of the pebble bed.

Fig. 14. Comparison of the axial profile of the average andmaximum fuel temperatures for DALTON-THERMIXand TINTE results at normal operating conditions ofPBMR.

Fig. 15. Comparison of the axial power profile of DALTON-THERMIX and TINTE results at normal operatingconditions of PBMR.



Fig. 16. Power ~total and decay! history of DALTON-THERMIX for the first 300 s of the DLOFC transientshowing the effect of a SCRAM.

Fig. 17. Power ~total and decay! history of DALTON-THERMIX results ~between 50 and 60 h! of theDLOFC ~no SCRAM! transient showing the oscilla-tions in fission power after recriticality.

Fig. 18. Maximum ~max! and average ~ave! temperature his-tory of DALTON-THERMIX and TINTE results forthe DLOFC transient ~without SCRAM!.

Fig. 19. Maximum ~max! and average ~ave! temperature his-tory of DALTON-THERMIX and TINTE results forthe entire DLOFC ~with SCRAM! transient.

TABLE III

Comparison of Steady-State Results Between DALTON-THERMIX and TINTE

Item DALTON-THERMIX TINTE

keff 0.99364 0.99396Maximum power density ~MW0m3 ! 10.64 10.55Maximum fast flux ~cm�2 s�1 ! 2.27 � 1014 2.14 � 1014

Maximum thermal flux ~cm�2 s�1 ! 3.37 � 1014 3.17 � 1014

Outlet helium temperature ~8C! 898.2 898.5Pressure drop ~kPa! 297.9 294.2Average fuel temperature ~8C! 807.4 813.0Average moderator temperature ~8C! 794.0 787.2Average helium temperature ~8C! 748.2 742.3Heat loss to RCCS ~MW! 1.17 1.15



SCRAM since the trickle flow of 0.2 kg0s is absent.The results for the average and peak fuel temperaturescalculated with DALTON-THERMIX and TINTE aresimilar.

IV.C. LOFC Transients with SCRAM

The PLOFC case is similar to the DLOFC case withSCRAM with the difference that the system pressure isreduced from 90 to 60 bars during the first 13 s of thetransient and the mass flow is reduced to 0 kg0s insteadof 0.2 kg0s. After the pressure reduction it is assumedthat the helium inventory of the reactor remains constant,allowing the pressure to vary over time depending on thehelium temperature.

The power history of the PLOFC transient is almostidentical to the power history for the DLOFC withSCRAM of Fig. 16 except for minor differences duringthe first 13 s. The results for the fuel temperatures inFig. 20 of the two codes again show a similar trend. Thenatural convection in the reactor increases the ability ofthe reactor to remove the decay heat, resulting in lowertemperatures. In Figs. 21 and 22, the temperature profilesin the reactor are shown after 50 h in the PLOFC transientand after 100 h in the DLOFC transient. It can be seenthat for the PLOFC case, which includes natural convec-tion, the heat is transported to the top region of the core.The maximum fuel temperature for the PLOFC is 13828C,which is significantly lower than the 16488C that wasfound for the DLOFC case.

V. CONCLUSIONS

This paper presents a new code system for the analy-sis of static and dynamic behaviors of pebble-bed reac-tors. Comparisons of the results of this code system with

Fig. 20. Maximum ~max! and average ~ave! temperature his-tory of DALTON-THERMIX and TINTE results forthe entire PLOFC ~with SCRAM! transient.

Fig. 21. Temperature profile ~8C! at t � 100 h of the DLOFCsimulation with SCRAM

Fig. 22. Temperature ~8C! profile at t � 50 h of the PLOFCsimulation with SCRAM.



experimental data of the HTR-10 and with the TINTEcode for the PBMR were made. Special attention hasgone to simulation of the LOFC transient, which repre-sents a worst-case scenario for HTRs.

V.A. Code System Validation

It was found that the DALTON-THERMIX code sys-tem captures the gross behavior in the core as reflectedby the agreement with the HTR-10 power and tempera-ture trajectories for the LOFC transients. Furthermore,application to the PBMR verified that the predicted fueltemperatures of the transient simulations were in agree-ment with the results of the TINTE code. The code sys-tem captures the dynamic behavior of the reactor and istherefore a useful tool in determining the inherent safetycapabilities of pebble-bed HTR designs.

A point-kinetics model can be an effective tool formodeling the neutronics of small pebble-bed HTRs forLOFC transients. However, the large change in the tem-perature and power profile during a DLOFC0PLOFCtransient without SCRAM, even in small cores such asthe HTR-10, results in significant differences betweenthe point-kinetics and ~2-D! neutronic calculation re-sults at the time point of recriticality. It is noted that theapplication of the ~2-D! DALTON model for neutronicsinstead of point kinetics did not lead to a major improve-ment of the results of the HTR-10 simulations. Themaximum power level reached after recriticality was inbetter agreement with the measured data for the DAL-TON model, while the prediction of the time point ofrecriticality was slightly worse than the point-kineticsresult.

The results of the HTR-10 benchmark indicate thatthe thermal-hydraulic side of the code system is the lim-iting factor in the accuracy of the results. A variation inthe mass flow reduction at the beginning of the transientrevealed that a relatively small deviation in this flow canhave a significant effect on the reactivity feedback andheat transfer. Future development to improve especiallythis part of the code system by modeling bypass flowsand a 3-D thermal-hydraulic model is therefore consid-ered. The burnup value of the fuel of the HTR-10 was notexactly known at the time of the transient. This led tosome uncertainty in the cross sections and the conse-quent reactivity feedback. Moreover, improvement of thethermal hydraulics, improving the data on the nuclidedensities ~fuel content, fission products, and actinides!,could therefore improve the results.

V.B. Transient Analysis of HTR-10 and PBMR

During normal operation of a pebble-bed reactor,the convective heat transfer from the pebbles to thehelium coolant effectively removes the heat from thecore. Only a small portion ~,1% of the total power! ofthe generated heat is transferred to the surroundings

by conduction and thermal radiation. In the absence offorced cooling during DLOFC0PLOFC transients, thevalue of this small heat loss determines the behavior ofthe reactor. The maximum temperature reached, the rateat which the core cools down thereafter, and the result-ing time point of recriticality ~if no SCRAM is per-formed! are largely dependent on this heat loss.Furthermore, the steady-state power level reached afterrecriticality ~no SCRAM! is equal to the reactor totalheat loss.

From the viewpoint of HTR safety, it was found thatin small HTR designs, such as the HTR-10, the increaseof the maximum fuel temperature during a DLOFC0PLOFC compared to normal operation is within 1008C.However, in the DLOFC case ~without SCRAM and no“trickle flow”! of the PBMR benchmark, it was foundthat the maximum fuel temperature during the transientis 16488C. It is noted that the benchmark definition adoptsa simplified version of the PBMR design.

The high fuel temperature is caused by the high ~peak!power density in the PBMR of 10.6 MW0m3. The reactorpower could be increased, or the helium flow rate can bedecreased, aiming at an increase of the helium outlettemperature to 10008C. An increase of the reactor poweris economically the most attractive of the two but leads toan increased power density and a higher fuel temperatureas a result. Furthermore, an increase of the power densitypeak increases the maximum fuel temperature during aDLOFC transient. Optimization of the in-core fuel man-agement aiming at an increase of the helium outlet tem-perature, with the peak fuel temperature as a constraint,is the subject of another study.10

The large helium cavities containing relatively coldhelium at the top and bottom of the HTR-10 have a largeinfluence on the transient behavior. Their presence influ-ences the way that the natural-circulation flows areestablished.

For the simulation of CRW in the HTR-10, it wasfound that small core flows can be of major importanceto the transient core behavior. It can therefore be ex-pected that the impact of bypass flows is significant. Thisis caused by the resulting effect on the fuel and moder-ator temperatures, which have a large temperature reac-tivity feedback. It is therefore recommended that theseflows be recorded during experiments and be incorpo-rated into benchmark exercises.

Further validation of the code system with experi-mental data of the AVR reactor, including a DLOFC tran-sient, is to be published in a separate paper.35

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validation of the dalton-thermix thermal · pdf fileof the stresses in the fuel coating layers...

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