Models for reactor physics calculations for HTR pebble · PDF fileNuclear Engineering and Design 222 (2003) 331–347 Models for reactor physics calculations for HTR pebble bed modular

Nuclear Engineering and Design 222 (2003) 331–347

Models for reactor physics calculations for HTRpebble bed modular reactors

W. Bernnata,∗, W. Feltesba Institut fuer Kernenergetk und Energiesysteme, Universität Stuttgart, Pfaffenwaldring 31 D 70550 Stuttgart, Germany

b Framatome ANP GmbH, Department FGTS, P.O. Box 3220, D 91550 Erlangen, Germany

Received 14 March 2002; received in revised form 19 December 2002; accepted 20 December 2002

Abstract

For reactor physics calculations for modular pebble bed reactors program systems and nuclear data have to be used to getreliable results for important operational and safety related parameters. For cylindrical or annular core geometry such parameterscan be calculated with the modular program system ZIRKUS and additionally with common reactor physics programs based onSN and Monte Carlo theory. The modules of the ZIRKUS system were developed by Framatome ANP GmbH and extensively usedfor design calculations for the 200 MWel HTR-MODUL and verified by means of experiments and operational data mainly fromAVR. The models used in ZIRKUS will be described and discussed for typical design calculations for HTR pebble bed reactors.© 2003 Elsevier Science B.V. All rights reserved.

1. Introduction

For the determination of the power distribution andsafety related parameters of a HTR pebble bed reactor(Lohnert, 1992) coupled neutron physics, thermal hy-draulic and burn-up calculations must be performedto regard all important physical interactions. The mostcommon method for treating the neutron diffusion inHTR is the solution of multigroup diffusion equationfor core and reflector with some special treatment ofabsorbers in the side reflector and the cavity above thepebble bed core. For the preparation of cross-sectionsin multigroup approximation for the core the dou-ble heterogeneity of the fuel and the correspondingself shielding have to be taken into account. Thecalculation of fuel and moderator temperature whichinfluences the neutron spectra and effective resonanceabsorption must be calculated by an adequate model

∗ Corresponding author.E-mail address: [email protected] (W. Bernnat).

taking into account the coolant flow through reflectorand pebble bed core. Finally, the circulation of peb-bles through the core and the burn-up during theirresidence in high neutron flux density has to be calcu-lated. The variety of different tasks requires a flexibleprogram system to perform such calculations for theinitial cores up to the equilibrium core of a distinctcore design or reload strategy.

The modular program system ZIRKUS (Feltes,1993) developed by Framatome ANP GmbH was de-signed for the realization of various reactor physicscalculations for HTR cores with pebble fuel. Themain parts of ZIRKUS are function modules, a gen-eral data base and a control module for control of bothexecution of single modules or sequences of modules.An important feature of ZIRKUS is the data exchangebetween the modules via a general data base by themass storage archiving and retrieval system MARS.For every function module, a specific input can begenerated and stored before execution. By means ofa special command the execution of a single module

0029-5493/03/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved.doi:10.1016/S0029-5493(03)00036-0

332 W. Bernnat, W. Feltes / Nuclear Engineering and Design 222 (2003) 331–347

can be started via the control module. The results ofthis execution can be put on output device but alsoon the general data base for other function modules.Successive executions of function modules (chainsor modular sequences) can be formulated and identi-fied by an arbitrary identifier. ZIRKUS is therefore aflexible tool for calculation of important integral anddifferential parameters. Furthermore, it can be used toprepare a cross-section data base for transient calcu-lations by representing the few group cross-sectionsas a function of different parameters like fuel temper-ature, moderator temperature, reflector temperature,Xe-density, H-density (if water ingress is expected)and control rod positions.

2. Description of the reactor physics modules forstationary calculations

The main modules used in ZIRKUS and their tasksare listed inTable 1. They are mainly used for follow-ing tasks:

• design of the first core;• design of the interim (transition) core;• design of the equilibrium core;• preparation of cross-section data for transient cal-

culation;• preparation of afterheat distribution in the core for

transient thermal hydraulics calculations; e.g. lossof coolant or loss of forced circulation accident.

The principal ZIRKUS flow chart for executionof one reload step is shown inFig. 1. To realize

Table 1Main modules in program system ZIRKUS for HTR physics calculations

Module Task

KUGEL Specification of fresh fuel for every fuel typeNIVERM Refueling and transport of pebbles for next time stepNEWA Calculation of Dancoff factors for double heterogeneous fuelMICROX Microscopic few group cross-sections for spectral zonesMAGRU Macroscopic cross-sectionsHBLOCK Solution of multigroup 2D diffusion equationVORNEK Calculation of power distribution, from HBLOCK resultsBUCK Calculation of bucklings for spectral zonesSBURN Solving of burn-up equations for burn-up zones, calculation of number densitiesNZW Calculation of afterheat distribution as a function of time after shutdownTHERMIX/KONVEK Calculation of fuel and moderator temperatures

the pebble flow, the core is radially subdivided intoflow channels with individual flow velocities of thepebbles. At every reload step the pebbles will betransported from its present axial fuel zone (burn-upzone) to the corresponding zone below. Every radialchannel therefore is subdivided into a number of axialzones with identical volume. The number of zonesdepends from relative velocity of pebble in the radialchannels. The module NIVERM manages all load,reload, transport and withdrawal of pebbles for an ar-bitrary number of passes through the core. For everyburn-up zone and for every fuel cycle there are threeisotope vectors, one for the upper limit of the burn-upzone, one for the bottom limit of the burn-up zoneand one corresponding to the average values of theburn-up zone. These concentration records are thenused for the calculus of cross-sections in the followingdiffusion module, while the first two isotopes vectorspass through the burn-up module for every cycle andare subsequently transferred back to NIVERM. Theisotopes contained in a generic cell are burnt with theneutron flux associated to that cell starting from theupper limit of the burn-up zone.

The GGA Code MICROX (Wälti and Koch, 1972)calculates for a two zone model the fast slowing downflux density spectrum and the thermal flux densityspectrum. In every spectral zone the code solves theneutron slowing down and the thermalization equa-tion on a detailed energy grid of a lattice cell, where itconsiders two regions: one representing the fuel grainswith coating and binder, and the other representing themoderator. The fluxes in the two regions are then cou-pled by collision probabilities based on the flat flux

W. Bernnat, W. Feltes / Nuclear Engineering and Design 222 (2003) 331–347 333

Fig. 1. Flow chart for performing coupled neutronics, thermal hydraulics and burn-up calculations by program system ZIRKUS.

approximation. A second level of heterogeneity canbe treated, i.e. the fuel region may have grain struc-ture up to two different types of fuel particles. Thecoupling between the single fuel elements is realisedwith the Dancoff-Ginsburg factor for grained spheresin a pebble bed calculated by the module MEWA. TheMICROX cross-section data are available for three en-ergy ranges. The fast and epithermal energy range issubdivided into 99 fine groups in the energy zone from14.9 MeV to 0.414 MeV, the thermal energy region isrepresented by 101 energy points up to 2.38 eV. To takeinto account the scattering behaviour of the carbon,the fast/thermal energy boundary is chosen to 2.38 eV.For the absorbers in the resonance region (like Th-232,U-238, Pu-240) there are further data with Dopplerbroadened resonance cross-sections for the resolvedresonance range between 0.4 and 3.5 keV, representedby 8500 energy points. For this superfine energy gridthe slowing down equation is solved and the corre-sponding cross-sections are condensed to the groupstructure of the 99 group library (GAM library). Thesemethod allows the consideration of overlapping of res-onances from all nuclides present in the fuel zone.The macroscopic and microscopic groups constantsare condensed in the spectrum determined each timeand for every spectral zone from 93 fast and 101 ther-mal groups respectively to a few group cross-sectionset. The spectrum is calculated by means of BN-theoryusing bucklings from the 2D diffusion calculation toaccount for the leakage in the corresponding spectralzone. It is proven that this method allows the use ofcomparable few energy groups for the correct solutionof the diffusion equation for the full core if there is

an (buckling) iteration between spectral calculation inMICROX and the 2D diffusion code HBLOCK pro-vided that the spectral zones were properly chosen.Therefore, for most calculations only four or sevenenergy groups were used.

Due to the modular structure of ZIRKUS thereis a separate module: MAGRU for calculating themacroscopic cross-sections for the burn-up zones us-ing number densities calculated by the reload moduleNIVERM and the burn-up module SBURN and themicroscopic group constants for the spectral zonescalculated by the module MICROX. To regard thestreaming effects in the pebble bed core, the diffusionconstant is corrected to take into account the void vol-ume between the fuel elements in the core by meansof the so called Behrens correction, (Behrens, 1949;Lieberoth and Stojadinovic, 1980). By this correctionthe diffusion constant is increased by about 8%, forenergy values over 0.1 MeV, and by 16% for energyvalues below 0.1 MeV.

The diffusion code HBLOCK (Lieberoth, 1977)calculates the neutrons flux distribution in the coreand the eigenvaluekeff . It is a coarse mesh method,characterised as following:

The differential OperatordivDgrad is formulatedas usual in a five points difference notation. It formsa linear equation system for discrete flux values withnodal points on aR–Z grid of the core fine mesh.Each node can be a vertex of up to for four materi-als (original equations system and original mesh). Bytransferring to the coarse mesh equations, the mostpart of the original equations are in general omittedand auxiliary assumptions are made to enable solvabil-


ity of the remaining equations. The transversal leak-age is here determined through a spatial linear inter-polation from the respective leakage of each nodalpoint of the “big lines”. The cavity over the core issimulated with an effective diffusion constant, depen-dent on the direction. The void is treated as a diffu-sion zone with vanishing reaction cross-sections. Thediffusion cross-sections are synthetic values only de-pendent on radius and height (Gerwin and Scherer,1979).

The VORNEK module is used for the calculationof the power density distribution (averaged over allthe fuel elements at each point). The distributionof the power density can also be axially smoothed,i.e. discontinuity of the fission cross-sections at thelimit of the burn-up zones can be approximatedwith the method of the least squared errors and asfission cross-sections are assigned at each case thecross-sections values in the middle of the zone. Themodule does not consider the power delivered by thegamma irradiation in the zones of the graphite reflec-tor: Such heat sources have to be taken into accountseparately by coupled neutron gamma transport cal-culations. The BUCK module calculates bucklingsaccording to diffusion approximation for the spectralzones for use in the MICROX code. The SBURNmodule calculates the burn-up of heavy metal andbuild up of fission products for the burn-up zones forevery reload step. Explicitly regarded in SBURN are16 actinides and 69 fission products. The remainingabsorption due to all not explicitly treated fissionproducts is taken into account by means of fourpseudo fission products.

Additionally to the ZIRKUS calculations also 1Dand 2D transport calculations by the SN programsANISN (Engle, 1967) and DORT (Rhoades, 1993) forthe homogenisation of effective cross-sections for thereflector with inserted control rods or small absorberspheres (SAS) and 3D Monte Carlo calculations withthe programs MOCCA (Lieberoth, 1968; Lieberoth,1984; Feltes, 1996), KENO (Hollenbach et al., 1999)or MCNP (Briesmeister, 1997) for accurate determi-nation of reactivity effects can be performed. Thiscalculations will be performed outside the ZIRKUSregime, the results, however can be integrated into thedata base of ZIRKUS and used from the correspondingmodules. Furthermore, transport effects which cannotbe solved by diffusion theory can be treaded by means

of a coupling of diffusion and transport theory via re-sponse matrices (Neumann et al., 1987). Especiallythe treatment of the neutron streaming in the cavitybetween the pebble bed core and the upper reflectorcan be solved accurately by this method (Emendörfer,1967; Bernnat et al., 1990).

3. Reactor physics modules for instationarycalculations

For the simulation of reactivity transients in HTRsthe program RZKIND was developed from Fram-atome, ANP GmbH. The description of the basicphysics, the derived equations and method of theirsolution can be found in (Kindt and Kohtz, 1993). Forthe verification of the RZKIND code experimentalresults measured at the AVR high temperature reac-tor were compared with corresponding calculations(Kindt, 1986).

The KIND codes work on the basis of macroscopicone group cross-sections, which are implementedin the associated libraries as functions of feedbackparameters in polynomial representations. The codeconsists mainly of three parts, which are executedsequentially within a time step:

• neutronic part to calculate the neutron flux densityand the power density in the reactor core using◦ one-group neutron diffusion equation;◦ equations for the delayed neutrons in the usual

representation with six groups;◦ equations for the fission product poisoning

through Xe-135 (two isotopes) and throughSm-149 (chain with six isotopes);

◦ special treatment of the decay heat (so calledpseudo-emitters);

• thermal hydraulic part to calculate the temperaturesof fuel elements (solid material) and coolant gas(helium) in the pebble bed (core) and in the case ofRZKIND the temperatures in the reflector regions.The determination of the helium temperatures in thepebble bed assumes isolated channels with forcedstreaming;

• part for the characterisation of the neutronic/thermo-hydraulic feedback which enter in the form of modi-fied cross-sections into the neutronic part. The mainparameters are the fuel and moderator temperatures


Fig. 2. Infinite multiplication factor for HTR pebble fuel cell as a function of U load calculated with the Monte Carlo code MCNP, basedon the data evaluations JEF-2.2, JENDL-3.2 and ENDF/B-VI.5.

Fig. 3. Comparison of the infinite multiplication factor calculated by Monte Carlo code MCNP for a HTR cell as a function of U load.The calculations were based on JEF-2.2 (reference value), JENDL3.2 and ENDF/B-VI.5.


in the pebble bed, the distribution of the xenon con-centration in the fuel elements, the distribution ofthe water steam concentration in the coolant (acci-dental water ingress) as well as the position of thecontrol and shutdown elements.

The cooling gas passing the pebble bed is treatedas flowing in independent radial channels with equalmass flow densities. Furthermore, only convectiveheat transfer at the side reflector is considered. Thiscalculation model permits flow-rates down to 10%of the nominal mass flow. As an alternative, thethermal hydraulic part can be calculated by THER-MIX/KONVEK.

There is a special (1D version of RZKIND) whichis able to simulate the detailed transient heat up of fuelin the coated particles. This version can be used for

Fig. 4. Distribution of the epithermal neutron flux density for the HTR-MODUL (equilibrium cycle) calculated by ZIRKUS.

investigation of integrity of fuel during hypotheticalfast reactivity transient (Feltes et al., 1993).

All necessary nuclear and geometrical data forRZKIND are strongly related to the results of cor-responding pre-calculated ZIRKUS results. Thesedata are stored as polynomial functions of a varietyof parameters (fuel and moderator temperature, re-flector temperature, xenon concentration, control rodinsertion, etc.) in a special prepared library.

4. Thermal hydraulics calculations

The neutron spectrum and the effective cross-sectiondepend on temperature of moderator and fuel. There-fore, the neutronics calculations, also for stationary


cases, must be coupled with thermal hydraulics calcu-lations. In ZIRKUS this can be performed by a veryfast running code NECKAR or the 2D program THER-MIX/KONVEK. THERMIX/KONVEK ( Breitbach,1979; Petersen, 1984; Verforndern, 1984) is a specialtool for thermal hydraulic safety assessment studiesfor pebble-bed high-temperature reactors (HTR) espe-cially the HTR-MODUL of Framatome ANP (Reutlerand Lohnert, 1982). THERMIX/KONVEK simulatesfluid flow along with the temperature distribution influid and pebble bed/conducting solids. The fluid flowis modelled by the Euler-equations as a steady stateflow with no friction. The friction and pressure dropdue to the pebble bed is modelled by KTA-rule 3102.3with an additional term in the momentum equation.The temperature distribution in fluid and solid ismodelled with two temperature equations. Fluid andsolid are interacting by the additional friction andby heat transfer from pebble bed/solid to fluid. Theproperties of the fluid are implemented in accordanceto KTA-rule 3102.1. In total, the fluid flow and heat

Fig. 5. Comparison of the control rod reactivity as a function of insertion of all six control rods into reflector of the HTR-MODUL(equilibrium cycle) calculated with ZIRKUS and with the Monte Carlo code MOCA.

transfer in the system is then described by the massconservation equation, two momentum equations fortwo directions and two energy equations for fluidand solid. The pressure drop caused by the pebblebed is modelled in accordance to KTA-rule 3102.3.The convective heat transport from pebble and fluidis calculated by heat transfer coefficients defined byKTA-rule 3102.2. The NECKAR module is a verysimplified method for calculating the temperature dis-tribution in moderator and fuel for the case of forcedconvection. For more accurate solutions the THER-MIX/KONVEK module is preferred. The thermalhydraulics calculations can be performed also by thecode FRECON developed at IKE (Rieger, 1994) andthe 3D heat convection module HEATING (Childs,2000).

The afterheat distribution in core due to the ir-radiation of fuel is calculated by means of theZIRKUS module NZW. This module calculates thisdistribution as well as the U-239 and NP-239 num-ber density as a function of time for the simulated


power history (Feltes and Kindt, 1992). The cal-culation scheme is according to DIN 25485E. Ituses data calculated from NIVERM and SBURNas well as data pre-calculated from ORIGEN2 with

Fig. 6. Neutron flux density as a function of lethargy in a spectral zone of HTR-MODUL.

a special cross-section library condensed over corespectra. The afterheat distribution is used for thetransient calculations in THERMIX/KONVEK andRZKIND.


Fig. 7. Axial profile of the thermal neutron flux in the middle of the core of the HTR-MODUL (equilibrium cycle).


Fig. 8. Radial profile of the thermal neutron flux density at the position of axial power maximum in the HTR-MODUL (equilibrium cycle).


5. Nuclear data libraries

The nuclear data libraries used in MICROX arebased partly of ENDF/B-IV or JEF according to theavailability of nuclear data evaluations at time of de-veloping of ZIRKUS. Today, new libraries are avail-able from JEF-2.2, JEFF-3, ENDF/B-VI, JENDL-3.2and JENDL-3.3. The impact of different nuclear li-braries on reactivity was investigated for a HTR cellproblem. For the cell the U load of a sphere was variedand the infinite multiplication factor was calculatedthen for the spherical cell with standard coated parti-cles by the MCNP code taking into account the doubleheterogeneity by a regular cubical grain lattice. Theresults are shown inFigs. 2–3, respectively.Fig. 2shows the infinite multiplication factor calculated forthe three evaluations as a function of U load.Fig. 3shows the difference ofk-infinite for ENDF/B-VI andJENDL-3.2 compared to JEF-2.2. Whilst JENDL-3.2compares good with JEF-2.2, ENDF/B-VI (revision5) tends to strong under-estimation for high U load

Fig. 9. Distribution of the thermal flux density in a PBMR ring shaped core (equilibrium cycle) for a six pass reload strategy.

due to the increased U-235 capture cross-sectionof revision VI.5. This effect was also observed forunder-moderated LWR systems. The problem is al-ready under investigation by international nucleardata evaluation groups. For normal load from 7 to9 g U/pebble, however the U-235 effect is not toodistinct so that all three libraries can be applied forHTR calculations. Since with the newer (JEF-2.2)data libraries good results were achieved e.g. for thePROTEUS experiments with HTR fuel, it is plannedto use these data for further HTR calculations withZIRKUS by updating the MICROX libraries.

6. Applications of ZIRKUS for calculatingequilibrium cycle

For the design of HTR cores the burn-up, buildupand decay of isotopes, the flow of pebbles, the neutronflux distribution, the power distribution, the tempera-ture distribution of fuel and moderator of mixed fuel


elements with different burn-up have to be determinedfor the core under consideration of various reflectorand control conditions.

An example of ZIRKUS calculations will be givenfor the 200 MWth HTR-MODUL as designed byINTERATOM/SIEMENS/FRAMATOME (Lohnert,1992). The main data of the reactor are listed inTables 2 and 3, respectively. The core was subdividedinto eight radial channels with different pebble flowvelocities. The total number of burn-up zones was 72,the number of spectral zones was 10. The volume ofthe zones in every radial channel are proportional tothe pebble flow velocity in the channel. The completecalculation model regards the pebble bed core, thetop and bottom reflector, the cavity between pebblebed and top reflector and the radial side reflector. Dueto the rotational symmetry of the core the geometryis treated in 2D cylindrical coordinates (R, Z). The

Fig. 10. Maximum fuel temperature as a function of time after depressurisation for different recycle passes for HTR-MODUL (equilibriumcycle). The upper curve represents 5 passes, the lowest curve 15 passes.

Table 2Main data of the HTR-MODUL fuel element

Particle radius 0.25 cmThickness of the 1 (coating/density) 0.0095 cm/1.05 g/cm3

Thickness of the 2 (coating/density) 0.004 cm/1.90 g/cm3

Thickness of the 3 (coating/density) (SiC) 0.0035 cm/3.18 g/cm3

Thickness of the 4 (coating/density) 0.004 cm/1.90 g/cm3

External radius of the matrix zone 2.5 cmFuel element radius 3 cmHeavy metal content per fuel element 7 gU-235 share in uranium 8.0%

burn-up zones (1,. . . , 72) are the so called burn-upzones with burn-up dependent average number den-sities. For simulation of the pebble flow the isotopescontained in an axial zone of every radial channelwill be shifted after a finite irradiation interval intothe axial zone below. In the first axial zone (top ofcore) of every radial channel fresh fuel together with


Table 3Main data for the HTR-MODUL

Main dataThermal power 200 MWAverage power density 3 MW/m3

Core diameter 3 mAverage core height 9.4 mPrimary pressure 60 barPrimary coolant temperature (inlet/outlet) 250/700◦C

Nuclear data for the equilibrium coreNumber of radial enrichment zones 1Number of fuel element passes 15Heavy metal loading 7 g/FENumber of fuel spheres 360 000Enrichment 8 wt.%Target burn-up 80 000 MWd/MgU

Fuel inventoryHeavy metal 2396 kgFissile material 107 kg

FE, fuel element.

Fig. 11. Correlation between the maximum DLOCA accident temperature and the number of passes for HTR-MODUL (equilibrium cycle)for nominal power and 110% power.

irradiated fuel of 1, 2,. . . , N−1 passes through thecore will be inserted.N is the total number of passes.If N = 1 a once through then out (OTTO) core canbe simulated. Results of calculations for the describedmodel are shown in theFigs. 10–12. For calculationsup to the equilibrium state some hundreds of modulechains according toFig. 1 were run to reach equilib-rium at 80 MWd/kg HM with 7 g heavy metal load perfuel element and 1006 days residence time in core. Asexamples of the results the flux density distributionis drawn for group 3 (epithermal) of four groups inFig. 4. The control rod reactivity was calculated bymeans of several HBLOCK runs with different controlrod positions. The result is shown inFig. 5 togetherwith a Monte Carlo result as a reference solution. InFig. 6, the typical neutron spectrum in a spectral zoneis shown. InFigs. 7–8, the axial and radial thermalflux distributions in the core center and in the axialflux maximum are shown. For HTRs with extended


power there must be an inner fuel free zone if themaximum temperature of fuel under DLOCA condi-tions will be limited. The PBMR concept with higherpower than 200 MWth regards such an inner fuel freecolumn consisting of moderator elements or of solidgraphite. Corresponding fuel cycle calculations can beperformed with an extended NIVERM version, whichregards channel wise reloading of an arbitrary mix offuel and moderator elements. An example of a typi-cal thermal flux distribution is shown inFig. 9 with atypical very high thermal flux density in the center ofthe fuel free region of the core.

7. Safety related calculations

For the 200 MWth MODUL design the maximumfuel temperature after a depressurisation accidentDLOCA was analysed for a different number of fuelelement passes through the core. For every numberof passes from 5 to 15 the equilibrium state was cal-

Fig. 12. Correlation between the peak factor of power distribution at nominal conditions of HTR-MODUL (equilibrium cycle) as a functionof fuel element passes.

culated by ZIRKUS. Then the afterheat distributioncalculated by module NZW of ZIRKUS was passedto the transient heat conducting program HEATING-7of the SCALE system. It was conservatively assumedthat there was a prompt depressurisation. The prop-agation of maximum fuel temperature with time isshown inFig. 10. From this figure, one can see theadvantage of the MODUL concept since the max-imum fuel temperature even after depressurisationis limited. This maximum temperature, however isdependent from the number of fuel element passes.In Fig. 11, the maximum fuel temperature after aDLOCA accident as a function of fuel element passesis shown. The larger the number of passes the lower isthe maximum temperature. This fact can be used foroptimisation since the reactor nominal power can beincreased if the number of passes is increased withoutincrease of maximum fuel temperature compared to areload strategy with fewer passes. InFig. 12, the peakfactor of power distribution is shown as a function offuel element passes.


8. Transient neutron physics calculations

The Code RZKIND with a nuclear data base pre-pared by ZIRKUS can be used for a variety of tran-sients. As an example the hypothetical withdrawalof all control rods (excess reactivity 1.21%) fromMODUL reactor in equilibrium state was calculated.Following accident scenario was postulated:

• the rods are withdrawn at maximum withdrawalspeed (1 cm/s),

• the first scram signal (relative neutron flux≥ 1.2)of the reactor protection system fails

Fig. 13. Relative power response after withdrawal of all control rods with 1 cm/s. Dashed curves show first scram (flux density> 120%)and second scram (average He outlet temperature> 750◦C). The solid line assumes second scram but further withdrawal of control rods.

• the second scram signal (average helium outlettemperature≥750◦C) initiates only the trip of theblower.

Furthermore, it was postulated that, although theblower is shutdown after initiation of the scram, therods do not drop but continue to withdraw. The powerresponse of the core for this beyond-design-basic ac-cident is given inFig. 13, the corresponding tempera-ture inFig. 14. The reactor power increases up to ca.190% of the initial value, which is the point at whichthe reactivity insertion rate due to rod withdrawalis compensated by fuel and moderator temperature


Fig. 14. Maximum fuel element temperature for reactivity insertion of 1.2% by withdrawal of all control rods with 1 cm/s even aftersecond scram signal for HTR-MODUL (equilibrium cycle) at nominal power.

increase due to the strong negative temperature coef-ficients. As a consequence of the blower trip initiatedby the scram after a 2 min period of excess power thefuel element temperatures are still rising and the reac-tor power drops again to the level of decay heat withinfurther 5 min. The maximum fuel element tempera-tures resulting from this power excursion reach valuesof about 1000◦C.

9. Conclusions

The ZIRKUS program system together with thethermal hydraulics module THERMIX/KONVEKand the transient neutronics code RZKIND is able toperform all kind of design calculations for HTR coreswith pebble fuel. The modular concept allows the reli-able maintenance of the system and implementation ofupdates. The programs are verified by re-calculationof experiments and AVR operating data as well as

by comparison with other calculations and referencesolutions. Most of models used in these programs areproven for the usual design calculations. Extendedmodels and the intensified use of Monte Carlo pro-grams for detailed calculation of transport effects willcomplete the tool for HTR physics calculations.

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