25th Symposium of AER on VVER Reactor Physics and Reactor Safety

Review of AER Working Group B Meeting at Plze? – Hotel ?U Pramen, Czech Republic is
given.
Regular meeting of Core Design Group was organized by ?KODA JS a.s. and held at the
Hotel ?U Pramen in Plze? on April 20-22, 2015, together with Working Group A.
Presented papers (see List of papers and List of participants) covered topics as follows.

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SHUT?DOWN?BORIC?ACID?CONCENTRATION?
FOR?DIFFERENT?FUEL?LOADING?PATTERNS?
?
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Martin?B?rta?
CEZ?Inc.,?Dukovany?NPP?
Czech?Republic?
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ABSTRACT?
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The? purpose? of? this? paper ? is? to? show? different? approaches? to? calculations? of? shut?down? boric?
acid? concentration? and? to? show? problems? connected? with?this?type?of?calculation.?Attention ?is?
also? paid? on? subcriticality? calculations? during? the? fuel? rearrangement?in?the?reactor?core.?This?
issue? was? opened? due? to? the? requirement? for? revision? of? the?definition?of?the?shut?down?boric?
acid?concentration?on?the?Dukovany?NPP?in?the?Czech?republic.?
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?
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1.??SHUT?DOWN?BORIC?ACID?CONCENTRATION?
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Correct? calculation? of? the? shut?down? boric? acid? concentration? is? one? of? the? most? important?
safety? calculations? used? on? NPP.? It? allows? to? reach? sufficient? subcriticality? during?the?reactor?
outage.?Since?1985?the?definition?used?on?Dukovany?NPP?is?worded?as?follows:?
?
?
Shutdown? boric? acid? concentration? ?the? critical? H3BO3? concentration? of?the?cold?(20?C),?
is?
un?poisoned? reactor ? with? zero? power? and? with? all? control? rods? fully? extended? from? the ? core,?
incremented?by?1?g/kg.?
?
?
Shutdown? boric? acid? concentration? for? refueling? ?the? shutdown? boric? acid? concentration?
is?
for? the? parameters? of? the? core? after? completed? refueling.? The? minimum? value? is? 12? g/kg?
H? 3?
BO?
.?
3?
?
?
In? spring? 2015? appeared? the? new? proposal? of? the? prescription? for? the? boric? acid? shutdown?
concentration? calculation? from? the? State? Office.? The?main?difference?is,?that?there?are?specific?
values?of?k?
,?which?have?to?be?reached:?
eff?
?
?

In Paks NPP 4.7%-enriched, Gd-containing fuel assemblies had to be introduced for the
realization of 15-month long fuel cycles. The geometrical structure of these assemblies is the
same as the 4.2%-enriched ones. The above mentioned fuel assemblies differ from each other
in the enrichment and the enrichment distribution of fuel pins and in the number and the
position of fuel pins with Gd burnable absorber.
In fall of 2014 12 of such 4.7% enriched fresh assemblies (test assemblies) ? along with
4.2% enriched fresh ones ? were placed into the core of the 3rd unit, so that their
reactorphysical and thermalhydraulical behaviour during the fuel cycle could be checked.
Thermocouple and SPN detector measurement signals of 4.7% enriched FAs were compared
to the calculated values, and the differences were evaluated statistically. Based on these
investigations we gained some invaluable experience which can be used in the future for
planning C15 reload patterns.
This August 48 of 4.7%-enriched fresh FAs along with 54 of 4.2%-enriched fresh ones were
placed into the core of the 2nd unit. Reactorphysical parameters which were measured during
the physical startup tests were in good agreement with the calculated ones, and the unit can be
operated on 100% power level since startup without any problem. The evaluation of
thermocouple and SPN detector measurements vs. calculation is continuous.
Results of the above mentioned investigations will be presented in this paper and during the
symposium.

During the 70? of the last century 12 units of Russian VVER-440 type of reactors were
started to build on the territory of Czechoslovakia (now on the territory of the Czech and
Slovak Republic). Nowadays 2 units were already shutdown in Slovakia, 4+4 units are
operates in both countries and 2 units are still under finalizing in Slovakia. During these units
operation period, wide range of modifications and upgrades were performed to strengthen the
nuclear safety and reactors operability.
In scope of strengthening the reactor?s core monitoring and surveillance, the original VK3
system was completely replaced with advanced computer based core monitoring and
surveillance system SCORPIO-VVER. Since 1999 up to today the SCORPIO-VVER system
were installed on four units of Dukovany NPP (Czech Republic), on two units of Bohunice
NPP (Slovak Republic) and on the full scale plant training simulator for EBO V2 plant. The
system is a valuable tool for the reactor operators and reactor physicists and was licensed by
both Czech and Slovak Nuclear Regulatory Bodies as a Plant Technical Specification
Surveillance Tool.
The development of SCORPIO-VVER core monitoring system continues along with the
changes in VVER reactors operation. Within the planned upgrades the system is being
adapted according the utility needs. Between the most significant upgrades belongs the
modifications in connection with implementation of a new digital I&C system, adaptation of
the system to up-rated unit conditions, loading of the Gd2M+ fuel assemblies, improvements
in the area of core design (neutron physics, core thermal hydraulics and fuel thermal
mechanics), in design and methodology of the limit and technical specifications checking (online shutdown margin calculation) and improvements in the predictive part of the system
(Strategy Generator).
Since the first installation the SCORPIO-VVER system has a remarkable operating history and
experience. More than 16 years of experiences in 6 units of VVER-440 type of reactors, from
two different NPPs, in two different countries helps the SCORPIO-VVER Developer?s Team
to put the system to a very high level of quality and reliability.

Some years ago an OECD NEA benchmark for Kalinin-3 VVER-1000 NPP was set up.
Recently the Kalinin-3 benchmark has been merged into the OECD NEA UAM benchmark.
The objective of the OECD NEA Uncertainty Analysis in Best-Estimate Modeling (UAM)
LWR benchmark is to determine the uncertainties of the coupled reactor physics/thermal
hydraulics LWR calculations at all stages. At the final stage, one of the problems to be
analyzed is the Kalinin-3 benchmark problem from the point of view of the uncertainties in
case of VVER reactors.
In this paper the uncertainties of the KIKO3D-ATHLET calculations at core level are
presented using the Kalinin-3 (Phase II) benchmark data, although only the neutronic
uncertainties are considered and further simplifications are applied and discussed.
In the first part of the paper, the uncertainties (empirical standard deviations and correlations)
of the effective multiplication factor, the assembly-wise radial power distribution, the axial
power distribution, the rod worth, etc. are presented at steady-state. After that the
uncertainties of the transient calculations are discussed for the considered switch-off of one
MCP type transient.
1. INTRODUCTION
The OECD NEA Kalinin-3 benchmark ¹ is about a switch-off of one Main Circulation
Pump (MCP) at nominal power and for this real transient measured data are also available.
This benchmark is calculated by the KIKO3D-ATHLET coupled code at MTA EK (for phase
II see e.g. ²) and it was discussed by other participants of AER during the last years, see e.g.
[3, 4], as well.
Recently the Kalinin-3 benchmark has been merged into the OECD NEA UAM benchmark
⁵. The objective of the OECD NEA Uncertainty Analysis in Best-Estimate Modeling
(UAM) LWR benchmark is to determine the uncertainties of the coupled reactor
physics/thermal hydraulics LWR calculations at all stages. At the final stage, one of the
problems to be analyzed is the Kalinin-3 benchmark problem from the point of view of the
uncertainties in case of VVER reactors.

The goal of the ALLEGRO Project is to design, build and operate the first Gas cooled Fast
Reactor (GFR) Demonstrator. The GFR belongs to the 4th generation of nuclear reactors.
Prototype of the gas cooled reactor ALLEGRO is a subject of common interest of association
of countries France, Slovakia, the Czech Republic and Hungary with the goal to deploy
prototype of the reactor in Central Europe and present its functionality. Nuclear research
institutions of the four Visegrad countries (V4) agreed on establishment of “V4G4 Centre of
Excellence” on July 18, 2013, for performing common R&D in the area of Generation IV
reactors. The agreement allows participants to join their resources for development of
Generation IV reactors and thus contribute to meeting the goal of sustainability of nuclear
energy while maintaining the highest safety standards.
OBJECTIVE AND MISSION
An ALLEGRO demonstrator is an essential step to establish confidence in the innovative Gas
Cooled Fast Reactor (GFR) technology. The proposed demonstrator, would be the first ever
gas cooled fast reactor to be constructed. The objectives of ALLEGRO are to demonstrate the
viability and to qualify specific GFR technologies such as fuel, the fuel elements, heliumrelated technologies and specific safety systems. In particular, the decay heat removal
function, together with demonstration that these features can be integrated successfully into a
representative system ¹ is of great interest.
The attractive GFR concept aims to combine the benefits of fast spectrum and high output
temperature (up to 850 ?C), using helium as a coolant.
The high coolant temperature allows targeting high energy conversion efficiency (43-48 %)
and opens the possibilities for new application of nuclear energy, such as heat intensive
processes (metallurgy, hydrogen or synthetic hydrocarbon fuel production?). The GFR
concept aims to provide these new potentialities by affording a sustainable energy supply in
the long term.
In comparison with sodium, gas coolants have the following advantages for fast reactor
applications:
? Chemical compatibility with water, obviating the need of an intermediate coolant loop,
and generally good chemical compatibility with structural materials.
? Negligible activation of coolant.
? Optical transparent, simplifying fuel shuffling operations and inspection.

Demonstrator Allegro is a gas cooled fast reactor in the design stage. Its reactivity control
system consists mainly of control rods filled with enriched boron carbide as an absorber. The
boron enrichment of 70% is needed to ensure enough worth of the control rods. This paper
deals with searching for other possible absorbing materials that could be used in the design in
order to lower the boron enrichment needed while increasing the control rod worth and
keeping the safety margin. The worth of the control rods filled with known absorbing
materials is compared using the transport Monte-Carlo code SERPENT in a computational
supercell. A possible benefit of a neutron trap concept is explored as well. It is shown that the
best absorbers and the usable moderating materials for the neutron trap are compounds
containing hydrogen (HfH2 and ZrH2, respectively). The worth of the control rods containing
the selected materials (B4C, EuB6, ReB2) has also been calculated by SERPENT using the full
model of the Allegro reactor including the radial reflector and the radial absorber. The
corresponding integral characteristics are presented.

Preparation of first files at interpolation cross section library of dynamic macrocode DYN3D,
suitable for calculation of gas cooled fast reactor, is described at this paper. Spectral code
HELIOS was used for very first library files preparation. DYN3D-MG was chosen as target
macrocode because of its excellent characteristics. Input of cross sections in the format of
interpolation tables was preferred for GFR calculations. First macrocode results with new
library were compared with results of spectral codes HELIOS and SERPENT. Good
functionality of first library version was concluded.
1. INTRODUCTION
Dynamic macrocode DYN3D-MG was accepted for ALLEGRO reactor macro-calculations.
Suitable cross section library that enables burnup calculations is needed for core and reactor
analyses. Cross section interpolation tables were selected for this task performance.
Spectral code HELIOS is used regularly for preparation of LWR cross section libraries for
DYN3D-MG and other macrocodes. It was shown by comparison with general MC code
SERPENT, that HELIOS accuracy is acceptable also for ALLEGRO calculations.
Preparation of cross section data sets for VVER-440 and ALLEGRO reactors and its
transformation into cross section libraries by developed library code is described at this
report.
2. TARGET LIBRARY FORMAT
Dynamic macrocode DYN3D-MG contains various possibilities for cross section input.
Choice ?IWQS = 22? was selected as alternative for VVER-440 burnup calculations ¹.
This type of library is characterised by multi-dimensional tables of data records, in which all
possible combinations of parameter variation are considered. The accuracy of this method
increases with the density of ?data points?, calculated by the cell-code calculations. To avoid
huge tables and consequently immense computing times it make sense to choose the datapoint density in a way that matches the accuracy of both cell code and diffusion code
(DYN3D at this case).
Spectral code HELIOS was selected for generation of multi-dimensional-table library ². It is
used at DYN3D-MG with linear multi-dimensional interpolation. In general, five
?dimensions? = operation parameters are used as follows:
? Burn-up
? Coolant density D
? Boron concentration Cb
? Fuel temperature Tf
? Coolant temperature Tm

The most ambitious aim of experimental reactor operation in ALLEGRO project includes
qualification of carbide fuel. The first irradiation of carbide assemblies (UPuC) will be
provided with the MOX fuel combination. Using of both fuel types is associated with storage
of fresh as well as spent fuel assemblies. The research activities are therefore designed also to
ensure subcriticality of the storage and possibly for its handling.
The aim of the research is to design material and geometric configuration of storage space to
ensure subcriticality of fuel stored in accordance with national and international requirements
in all operational situations.
INTRODUCTION
During the storage and transport of nuclear fuel is necessary to provide sub-criticality of
storage and transport equipment. The computer programs used to calculate must be
sufficiently precise. Accuracy programs are verified by comparing the calculated k coefficient
with measurements. Measurements of criticality in the world are provided by the critical
experiments in an experimental reactor. The results are published in the International
Handbook of Evaluated Criticality Safety Benchmark Experiments? ¹⁶.
SCALE 6.1.2 SYSTEM
SCALE 6.1.2 ⁶ includes two modules for criticality calculation: elder and simple KENO V
module and newer KENO VI. Elder module doesn?t provide analyses of hexagonal geometry
such as ALLEGRO. New KENO VI are able to model hexagonal geometries.
Control module of criticality calculation is CSAS6 module which continuously calls
executive modules:
?
BONAMI ? self-shielding calculation based on Bondarenko method
?
CENTRM/PMC/WORKER ? library evaluation based on (?continuous energy? CE)
?
KENO VI ? 3D code for keff calculation by Monte Carlo method
Basic equation, which describes neutron balance, is Boltzman transport equation. Numerical
solution of this equation by Monte Carlo method is based on collision probability method
where is used P0 and P1 Legender polynomials. Weighted function is determined by Russian
roulette method.

SERPENT 2.1.21 code, continuous-energy Monte Carlo calculation, was used for verificati
on of CEA ALLEGRO reactor concept. ESNII+ ¹ international benchmark was a motivation
to evaluate the SERPENT core model. The position of control devices was set in the way that
the starting state was equal to the critical state. At burnup of 18.8 MWd/kgHM were evaluated
the power distribution on the assemblies of ALLEGRO reactor core and power distribution on
the pins around CSD rod. In the article is also studied the distribution of some uranus,
transuranus and fission products in the core assemblies at the end of the MOX lifetime. There
are analysed the processes of homogenous transmutation evenly dispersed minor actinides
(MA) in the fuel and heterogeneous transmutation of MA in inert and UO2 matrix located in
the central pin of three assemblies in the zone.

Recently the VUJE performed large scope analytical study, dedicated to the technological
demonstrator of the Allegro, the fast gas cooled reactor. The main objective of the study was
to investigate what are the foreseen characteristics of the facility. One of the work packages
was focussed to severe accidents up to core damage and reactor pressure vessel failure. The
aim of the work package was to propose, at the level of technical concept, a set of
countermeasures and systems which would allow prevention of accidents with fuel damage or
which would contribute to mitigation of accident consequences.
The paper briefly describes content and extent of the work package, presents summarization
of the main results, conclusions and recommendations.

Joint AER Working Group A on ?Improvement, extension and validation of
parameterized few-group libraries for VVER-440 and VVER-1000? and AER Working
Group B on ?Core design? twenty fourth meeting was hosted by ?KODA JS a.s. in Pilsen,
the Czech Republic, during the period of April 20 – 22, 2015.

MCU code make it possible to tally the sets of functionals, which can be interpreted
as an average cross-sections and diffusion coefficients over choosen subvolumes of reactor
core. Finite-difference calculations with these sets of cell characteristics can be then compared
with benchmark Monte Carlo ones, thus producing reliable information on operative code
quality. As an example of analysis of the kind Monte Carlo results are compared with 1-, 2and 4- groups 2D mesh calculations of VVER-1000 core. Surrounding of the core, such as
baffle, vessel and the like is covered by one row of fictitious fuel assemblies to avoid usage
of rather artificial boundary condition as neutron flux logarithmic derivative. The attempt also
was made to calculate with mesh algoritm equilibrium xenon distribution throughout the
core.

Preparation of first files at interpolation cross section library of dynamic macrocode DYN3D,
suitable for VVER-440 calculations, is described at this paper. Spectral code HELIOS was
used for very first library files preparation. Mochovce NPP first fuel cycle calculations were
used for comparison with standard BIPR7 code results. Good functionality of first library
version was concluded.
1. INTRODUCTION
Dynamic macrocode DYN3D-MG is used widely for VVER-440 calculations. Its
performance can be improved by suitable cross section library that enables accurate enough
burnup calculations and is needed for core and reactor analyses. Cross section interpolation
tables were selected for this task performance.
Spectral code HELIOS is used regularly for preparation of LWR cross section libraries for
DYN3D-MG and other macrocodes. Preparation of cross section data sets for VVER-440
reactor and its transformation into cross section library by developed library code is described
at this report.
2. TARGET LIBRARY FORMAT
Dynamic macrocode DYN3D-MG contains various possibilities for cross section input.
Choice ?IWQS = 22? was selected as alternative for VVER-440 burnup calculations ¹.
This type of library is characterised by multi-dimensional tables of data records, in which all
possible combinations of parameter variation are considered. The accuracy of this method
increases with the density of ?data points?, calculated by the cell-code calculations. To avoid
huge tables and consequently immense computing times it make sense to choose the datapoint density in a way that matches the accuracy of both cell code and diffusion code
(DYN3D at this case).
Spectral code HELIOS was selected for generation of multi-dimensional-table library ². It is
used at DYN3D-MG with linear multi-dimensional interpolation. In general, five
?dimensions? = operation parameters are used as follows:
? Burn-up
? Coolant density D
? Boron concentration Cb
? Fuel temperature Tf
? Coolant temperature Tm

Importance of SPND in in-core measurements (especially VVER-1000) is quite
evident, but validation of their accuracy is difficult.

The impact of rod and assembly bowing on rod-wise fission powers was studied using the
Monte Carlo reactor physics code Serpent and the 2D lattice code CASMO-4E. The rod
bowing was simulated with Serpent by changing the positioning of the fuel pins. In other
words, the simulations were carried out in an irregular pin lattice. The effect of assembly
bowing was studied with CASMO-4E by changing the water gap size between the assemblies.
In both Serpent and CASMO-4E analyses, the considered deviations were chosen in a
conservative manner on the basis of pool-side inspections results.

EVALUATION OF FUEL ASSEMBLY COOLANT OUTLET TEMPERATURES OF KALININ-3 BENCHMARK Jan HdekJV Rez, a. s., Hlavn?? 130, 250 68 Husinec-Rez, Czech Republicjan.hadek@ujv.czABSTRACT The OECD Kalinin-3 benchmark problem is connected with investigation of transient behavior in Kalinin-3 nuclear power plant (VVER-1000). The benchmark simulation problem is the reactor coolant pump No. 1 switching off at the nominal power when the other three reactor coolant pumps are in operation during the experiment. Overall, the benchmark consists of four exercises. Exercise 1 describes the plant simulation with point kinetics model. Exercise 2 is devoted to the benchmark solution with using of stand-alone 3D reactor dynamic codes. The time-dependent thermal-hydraulic boundary conditions at the inlet of the reactor core are given in this task. Exercise 3 describes the solution of the problem by the coupled 3D reactor dynamic codes and the plant system codes. Exercise 4 is devoted to the uncertainty analysis. Two different macroscopic cross section libraries are used. The paper is focused on evaluation of fuel assembly coolant outlet temperatures received during the solution of Exercises 2 and 3. The solution of Exercise 2 and 3 was performed by the code DYN3D and the coupled codes DYN3D/ATHLET. The calculation results obtained by both cross section libraries are compared with experimental values. The differences between calculated and measured fuel assembly coolant outlet temperatures are discussed. The results of similar comparison from Temeln NPP are briefly presented.1. INTRODUCTIONThe OECD benchmark Kalinin-3 (VVER-1000) benchmark was defined as a reactor coolant pump No. 1 switching off at the nominal power when the other three reactor coolant pumps are in operation during the experiment ¹. The basic reactor core geometric and material parameters were given. The Penn State – Risk Engineering Ltd. (PSU-REL) macroscopic cross section library was distributed by benchmark organizers. Using of this library was highly recommended by benchmark team. As a second option, the macroscopic cross section library created at the Kurchatov Institute (KI) was used. The benchmark participants have to use also their own plant input data decks developed according to the needs of their own VVER-1000 NPP system codes. ??JV Rez, a. s. has been participated in solving of Exercises 1 to 3 of this benchmark. Some results of Kalinin-3 benchmark were presented at the 24th Symposium of AER in Sochi ². In this paper, the main attention is focused on the comparison of the calculated and experimental fuel assemblies coolant outlet temperatures. It may also be understood as a contribution to the validation of three-dimensional reactor dynamic code DYN3D and its coupling with thermal-hydraulic system code ATHLET.EXERCISE 2Exercise 2 is focused on the evaluation of the three-dimensional reactor dynamic core model response ¹. The time-dependent boundary condition at the inlet and outlet of reactor core were given by benchmark organizers. They were prepared on the basis of coupled BIPR/ATHLET code calculation. Including of Exercise 2 to the analysis of fuel assemblies coolant outlet temperature has its own importance. Using uniform time-dependent boundary conditions, we can compare Exercise 2 results with the results of the next Exercise 3 and, if necessary, we can fine tune our Exercise 3 input deck.2.1 Computer code usedThe reactor dynamic code DYN3D is used as a tool for Exercise 2 calculation. DYN3D is a 3-D core model for dynamic and depletion calculations in LWR cores with hexagonal or quadratic fuel assembly geometry ³, ⁴ developed by Helmholtz Zentrum Dresden ? Rossendorf (HZDR). The neutron-kinetic model is based on the solution of the 3-D two-group neutron diffusion equation by nodal expansion methods. Different methods are used for hexagonal and quadratic fuel assembly geometry. It is assumed that the macroscopic cross sections are spatially constant in a node being the part of a fuel assembly. In the case of hexagonal fuel assemblies, the diffusion equation in the node is transformed into a 2-D equation in the hexagonal plane and 1-D equation in the axial direction. The two equations are coupled by the transverse leakage terms, which are approximated by polynomials up to the second order. Considering the 2-D equation in the hexagonal-plane, the side averaged values (HEXNEM1) or the side averaged and the corner point values (HEXNEM2) of flux and current are used for the approximate solution of the diffusion equation. In the case of Cartesian geometry, the 3-D diffusion equation of each node is transformed into 1-D equations in each direction x, y, z by transverse integrations. The equations are coupled by the transverse leakage term. In each energy group, the 1-D equations are solved with the help of flux expansions in polynomials up to second order and exponential functions being the solutions of the homogeneous equation. The fission source in the fast group and the scattering source in the thermal group as well as the leakage terms are approximated by the polynomials. In the steady state, the homogeneous eigenvalue problem or the heterogeneous problem with a given source is solved. Inner and outer iteration strategy is applied. The outer iteration (fission source iteration) is accelerated by Chebychev extrapolation. The steady-state iteration technique is applied for the calculation of the initial critical state, the depletion calculations, and the Xe and Sm dynamics. Concerning reactivity transients an implicit difference scheme with exponential transformation is used for the time integration over the neutronic time step. The exponents in each node are calculated from the previous time step during the iteration process. The precursor equations are analytically solved, assuming that the fission rate behaves exponentially over the time step. The heterogeneous equations obtained for each step are solved by inner and outer iteration techniques similar to the steady state.In addition, the thermal-hydraulic model of the reactor core and the fuel rod model are implemented in the FLOCAL module ⁴, which is a part of DYN3D. The reactor core is modeled by parallel coolant channels, which are coupled hydraulically by the condition of equal pressure drop over all core channels. Thermal-hydraulic boundary conditions for the core like coolant inlet temperature, pressure, and coolant mass flow rate or pressure drop must be given as input for DYN3D. FLOCAL comprises a one- or two-phase coolant flow model on the basis of four differential balance equations for mass, energy, and momentum of two-phase mixture and the mass balance for the vapor phase allowing the description of thermodynamic nonequilibrium between the phases, a heat transfer regime map from one-phase liquid up to postcritical heat transfer regimes an superheated steam. A fuel rod model for the calculation of fuel and cladding temperatures is implemented. A thermomechanical fuel rod model allows the estimation of relevant heat transfer behavior of the gas gap during transients and the determination of some parameters for fuel rod failure estimation.2.2 Reactor core modelThe reactor core model is fully described by the code DYN3D. It consists of 163 parallel coolant channels where each from them corresponds to one fuel assembly. The reactor core is surrounded by the band of artificial reflector assemblies. It means that it consists from 211 assemblies. The reactor core is divided into 12 axial layers (one layer for lower axial reflector, 10 layers for heated part of the core, one layer for upper axial reflector). The zero flux boundary conditions are applied for outer surface of axial reflector. Figure 1 shows the numbering of fuel assemblies in DYN3D core model in 60 degree rotational and full core symmetry and also the distribution of materials contained in PSU-REL cross section library. Locations of control rods (control clusters) in reactor core model are shown in Figure 2.Fig. 1 Numbering of fuel assemblies and their typesFig. 2 Numbering of fuel assemblies and location of control rods2.3 Cross section librariesTwo-group homogenized macroscopic cross sections and kinetic parameters for composition of each assembly were provided in nemtab format which was used also in previous OECD/NEA benchmark V1000-CT1 ⁵. Two sets of tables were available. One for unrodded (nemtab) and other for rodded assembly nodal compositions (nemtabr). Two types of nemtabr cross section data (for dysprosium and boron absorbers) were given for fuel assemblies with inserted control clusters during the transient. Reflector compositions were defined for lower and upper reflector and for one radial reflector. The parameterization of macroscopic cross sections and kinetic parameters within the nemtab format (for fuel temperature, moderator density and moderator temperature) was done in three-dimensional space ¹. The burn-up was taken into account in the composition of each axial node.Two types of cross-section libraries were provided. The first library was prepared on the basis of cooperation between Penn State and Risk Engineering Ltd. (PSU-REL X-S) ⁶. It contains a total of 973 materials in nemtab format. The PSU-REL X-S library takes into account the symmetry of materials arrangement in the reactor core model. The second library was prepared at the Kurchatov Institute (KI X-S) ⁷. It contains a total of 1761 materials and it is prepared in a different nemtab format. This library was prepared for the whole reactor core model.2.5 HFP initial steady-state conditionsThe HFP initial steady-state conditions are given in Table 1. Table 1 Exercise 2 ? HFP initial stead-state conditionsParameterValueInitial reactor core parametersReactor power, [MW]2965Cycle status, [EFPD]130.6Primary pressure, [MPa]15.52Reactor mass flow rate, [m3/h]88073Moderator inlet temperature [K], ( [oC])560.94 (287.79)Boron acid concentration [g H3BO3/kg H2O]3.60Control rod group 1-9 position [cm]369.25Control rod group 10 position [cm]309.252.6 Time dependent boundary conditionsThe time dependent boundary conditions were provided by benchmark organizers. They are shown in Figures 3 to 6. Fuel assembly inlet mass flow rates, fuel assembly inlet temperatures were obtained on the basis of calculations with coupled code BIPR/ATHLET ¹. Core outlet pressure and control rod positions were taken from experimental data. Fig. 3 Fuel assembly inlet mass flow ratesFig. 4 Fuel assembly inlet temperaturesFig. 5 Core outlet pressureFig. 6 Control rod positions2.7 Calculated vs experimental resultsComparison of calculated and experimental nuclear powers can be seen in Figure 7. The calculated time-dependent nuclear powers are at a lower level in comparison with experiment. This is valid for both used cross-section libraries; simultaneously the KI X-S library gives a higher level of nuclear power at the end of transient. Figures 8 to 15 show the comparison of calculated as well as experimental fuel assembly coolant outlet temperatures. The PSU-REL X-S library gives higher fuel assembly coolant outlet temperatures at the beginning of transient. At the end of transient, we can observe the opposite phenomenon where fuel assembly coolant outlet temperatures received with KI X-S library are higher. It can be seen in Figures 12 to 15. However, we can say that the calculated temperatures obtained with using of both libraries are in reasonable agreement. Another observed phenomenon is that the calculation results are systematically overestimated in comparison with experiment. The maximum deviation is about 10 oC at the beginning of transient. The minimum deviation is approximately 2 oC when the control rods of group No. 9 and 10 are in lower positions. It is shown in Figures 12 and 14. Fig. 7 Nuclear powersFig. 8 Fuel assembly coolant outlet temperature PSU-REL X-SFig. 9 Fuel assembly coolant outlet temperature KI X-SFig. 10 Fuel assembly coolant outlet temperature KI X-S vs PSU-REL X-SFig. 11 Fuel assembly coolant outlet temperature KI X-S vs PSU-REL X-S vs experimentFig. 12 Fuel assembly coolant outlet temperature t = 0 sFig. 13 Fuel assembly coolant outlet temperature t = 45 sFig. 14 Fuel assembly coolant outlet temperature t = 71 sFig. 15 Fuel assembly coolant outlet temperature t = 300 sEXERCISE 3Exercise 3 is focused on the best-estimate coupled code plant transient modeling ¹. Using of three-dimensional reactor dynamic code coupled with system plant thermal-hydraulic code enables fully simulate the system plant response.3.1 Computer code usedThe coupled code DYN3D/ATHLET is used as a tool for solution of Exercise 3. The thermal-hydraulic computer code ATHLET (Analysis of Thermal Hydraulics of LEaks and Transients) was developed by the Gesellschaft fuer Anlagen- und Reaktorsicherheit (GRS) mbH for the analysis of anticipated and abnormal plant transients, small and intermediate leaks as well as large breaks in LWR ⁸. The main code features are advanced thermal hydraulic, modular code architecture, separation between physical models and numerical methods, preprocessing and postprocessing tools, and portability. ATHLET offers the possibility of choosing between models for the simulation of fluid dynamics. The first option is five-equation model with separate conservation equations for liquid and vapor mass and energy, and a mixture momentum equation, accounting for the thermal and mechanical nonequilibrium, and including a mixture level tracking capability. Further, a complete two-fluid model with separate conservation equations for liquid and vapor mass, energy, and momentum is available. Additional mass conservation equation can be included for the description of boron transport within a coolant system. The time integration of the thermal fluid dynamics is performed with a general solver for ordinary differential equations called FEBE (Forward-Euler, Backward-Euler).For the simulation of heat conduction, a one-dimensional (1-D) heat conductor module is available. This model can simulate the 1-D temperature profile and heat conduction in plates, hollow and full cylinders in radial direction. A heat transfer package that covers a wide range of single-phase-flow and two-phase-flow conditions is available inside the module. Correlations for critical heat flux and minimum film boiling temperature are included; evaporation and condensation directly at heating surface are calculated. A quench front model for bottom and top reflooding is also available.The code development is accompanied by a systematic and comprehensive validation program. A large number of integral experiments and separate effects tests have been calculated by GRS and by independent organizations. The range of applicability has been extended to the Russian reactor types VVER and RBMK in cooperation with foreign partner organizations. ATHLET is being applied by numerous institutions in Germany and abroad.The model of external coupling of the 3-D reactor dynamic code DYN3D with the system code ATHLET was used ⁹. The whole reactor core model is removed from the ATHLET plant model and the core is completely substituted by the DYN3D core model. The thermal hydraulics of the whole NPP is split into two parts: the first part describes the thermal-hydraulic of the reactor and the second solves the thermal-hydraulics of the rest of the NPP system. The interfaces between them are located at the bottom and the top of the core. The pressures, mass flow rates, enthalpies, and boron acid concentrations are transferred at the interfaces. The parameters exchange is performed by the GCSM (General Control Simulation Module) of system code ATHLET ⁸. The SATM (Self Adapting Turbulent Mixing) model for lower and upper plenum was implemented in the DYN3D code ¹⁰. 3.2 Reactor core model and nodalization schemesThe reactor core model is identical to the model used for Exercise 2. Locations of coolant channels in reactor core model and their connection with primary system coolant loops are shown in Figure 16. The standard ATHLET input deck for VVER-1000 was used. All four loops of reactor coolant system are fully modeled as well as the pressurizer system. The pressurizer surge line is connected to the hot leg of the fourth loop; the spray line is connected with the cold leg of the first loop. The reactor upper plenum was modeled on three levels with four parallel volumes with cross-connections. The space under the reactor pressure vessel head was created by one volume. The lower plenum was modeled as four parallel channels. The core bypass was simulated by the DYN3D code.The secondary circuit modeling corresponds to the primary circuit. There are fully modeled steam generator (SG) secondary side, main steam system (main steam lines (MSL), main steam header (MSH)), and feedwater (FW) system lines. The simplified scheme of coolant loop No. 1 nodalization is given in Figure 17.1762696843166Hot leg00Hot leg992198828218Hot leg00Hot leg7848602071847Lower plenum00Lower plenum7372351278255Upper plenum00Upper plenum329608392014Pressurizer00Pressurizer1068121659078Pressurizer surge line00Pressurizer surge line25280131087650MCP00MCP18564971595120Downcommer00Downcommer2391985130036Steam generator00Steam generator9399041745615Core bypass00Core bypass14255051565813Core 00Core 27203401854835Cold leg00Cold legFig. 16 Fuel assemblies numbering and location of coolant loopsFig. 17 Reactor vessel and primary circuit nodalizationTwo-group homogenized macroscopic cross-section libraries are identical to those that are used in Exercise 2 – i.e. PSU-REL X-S and KI X-S libraries.3.4 HFP initial steady-state conditionsThe HFP initial steady-state conditions are given in Table 1. 3.5 Time dependent boundary conditionsThe time dependent boundary conditions for control rod group No. 9 and No. 10 positions, main steam header pressure, feedwater mass flow rates and temperatures were taken from experimental data. They are shown in Figure 6 and in Figures 18 to 20. Fig. 18 Main steam header pressureFig. 19 Steam generator feedwater mass flow rateFig. 20 Steam generator feedwater temperature3.6 Calculated vs experimental resultsThe main events during the transient are given in Table 2.Table 2 Transient description-sequence of main eventsTime [s]Event-150Start of zerotransient calculation, stabilization of system parameters0Start of transient calculation, E-motor of MCP1 pump switched off3Start of CR group No. 10 movement down from start position of 309.25 cm59Start of CR group No. 9 movement down from start position of 369.25 cm71Reactor power: 1889.04 MW = 62.97 % of Nnom (PSU-REL X-S) 2001.74 MW = 66.01 % of Nnom (KI X-S)72CR group No. 9 in constant position73CR group No. 10 in constant position180Start of CR group No. 9 movement up192CR group No. 9 in upper end position, start of CR group No. 10 movement up193CR group No. 10 in constant position206Start of CR group No. 10 movement up208CR group No. 10 in constant position300End of calculationReactor power: 1940.66 MW = 64.69 % of Nnom (PSU-REL X-S) 2037.38 MW = 67.91 % of Nnom (KI X-S)Comparison of calculated and experimental nuclear powers can be seen in Figure 21. In the case of PSU-REL X-S library the calculated nuclear power coincides practically with the experimental value at the end of transient. The KI X-S library gives a slightly higher power at the final stage of the transient. Fig. 21 Nuclear powerFig. 22 Coolant loop flow rate Fig. 23 Hot leg temperature Fig. 23 Hot leg temperature Comparison of imported calculated and experimental parameters of primary circuit is given Figures 22 through 24. Figures 25 through 32 present the comparison of calculated as well as experimental fuel assembly coolant outlet temperatures. The PSU-REL X-S library gives higher fuel assembly coolant outlet temperatures at the beginning of transient. At the end of transient, we can observe the opposite phenomenon, where fuel assembly coolant outlet temperatures received with KI X-S library are higher. It can be seen in Figures 29 to 32. However, we can say that the calculated temperatures obtained with using of both libraries are in very good agreement especially in the initial phase of transient. Another observed phenomenon is that the calculation results are again, as in Exercise 2, systematically overestimated in comparison with experiment. The maximum deviation is about 10 to 11 oC at the beginning and end of transient. The minimum deviation is approximately 1 oC when the control rods of group No. 9 and 10 are in lower positions. It is shown in Figures 29 through 32. Fig. 25 Fuel assembly coolant outlet temperaturePSU-REL X-SFig. 26 Fuel assembly coolant outlet temperature KI X-SFig. 27 Fuel assembly coolant outlet temperatureKI X-S vs PSU-REL X-SFig. 28 Fuel assembly coolant outlet temperatureKI X-S vs PSU-REL X-S vs experimentFig. 29 Fuel assembly coolant outlet temperaturet = 0 sFig. 30 Fuel assembly coolant outlet temperaturet = 45 sFig. 31 Fuel assembly coolant outlet temperaturet = 71 sFig. 32 Fuel assembly coolant outlet temperaturet = 300 sTemelin NPP – opening of steam dump to atmosphere test exampleThe other experimental transient which can be used for evaluation of fuel assembly coolant outlet temperatures at the NPP with VVER-1000/320 is the steam dump to atmosphere (SDA) test realized at Temelin NPP Unit 2 (Czech Republic). A detailed description of this test and comparison of calculated and experimental results is given in the literature ¹¹ and ¹². Only a brief description of the test and used computation tools and neutronic libraries is mentioned here. The main emphasis is placed on the evaluation of fuel assembly coolant outlet temperatures.Transient scenarioTemelin NPP consists from two units VVER-1000/320 type built according original Russian project. The control system was realized by Westinghouse Company (WEC) tools. The fuel assemblies were also of WEC origin at the time of experiment.The experimental test was performed at the beginning of the second fuel cycle of Temelin NPP Unit 2 in April 4, 2004. The reactor power was approximately 20 % of Nnom. All main circulations pumps (MCPs) were in operation. Control rod (CR) groups No. 1 to 9 were in their upper positions. CR group No. 10 was inserted in the core.At the beginning of experimental transient, the main steam header (MSH) pressure was increased with a trend of 1.7 MPa/h (0.028 MPa/min). The increasing or decreasing of MSH pressure was realized with using of steam dump to condenser (SDC). When the steam generator No.1 (SG1) pressure was equal to 6.9 MPa, then the steam dump to atmosphere on the first main steam line (SDA1) was opened. When the SG1 pressure was lower than 6.8 MPa, then the regime of SG1 pressure regulation with constant value of 6.5 MPa (with accuracy of 0.15 MPa) was started. After measurement termination, the final MSH pressure of 6.15 MPa was reached with a trend of -2.5 MPa/h (-0.04 MPa/min). The following thermal-hydraulic phenomena can be observed during the test: SDA opening causes an extensive steam release from affected main steam line with subsequent decreasing of steam temperature and pressure. It leads to decreasing of coolant temperature in attached coolant loop with consequent increasing of reactor power. The unsymmetrical cooling of the reactor causes non-uniform distribution of the power in the core due to the coolant temperature feedback.Computer code usedThe coupled code DYN3D/ATHLET was used for calculation solution of this transient. For the detailed description see Chapters 2.1 and 3.1 as well as references ¹¹ and ¹².Reactor core model and nodalization schemesThe reactor core model is fully described by the code DYN3D. It consists of 163 parallel coolant channels where each from them corresponds to one fuel assembly. The reactor core is divided into 27 axial layers (two layers for lower axial reflector, 24 layers for heated part of the core, one layer for upper axial reflector). The zero flux boundary conditions are applied for outer surface of axial reflector. The albedo boundary conditions are specified at radial boundaries of the reactor. Locations of coolant channels in reactor core model and their connection with primary system coolant loops are shown in Figure 33.The standard ATHLET input deck for VVER-1000 Temelin was used. All four loops of reactor coolant system are fully modeled as well as the pressurizer system. The pressurizer surge line is connected to the hot leg of the fourth loop; the spray line is connected with the cold leg of the first loop. The reactor upper plenum was modeled on three levels with four parallel volumes with cross-connections. The space under the reactor pressure vessel head was created by one volume. The lower plenum was modeled as four parallel channels. The core bypass was simulated by the ATHLET code. The secondary circuit modeling corresponds to the primary circuit. There are fully modeled steam generator (SG) secondary side, main steam system (main steam lines (MSL), main steam header (MSH)), and feedwater (FW) system lines.The simplified scheme of reactor vessel, coolant loop No. 1 nodalization and corresponding secondary side is given in Figures 34 to 36.303339532385 DYN3D CORE00 DYN3D CORE Fig. 33 Coolant channels location in the reactor core model Fig. 34 Nodalization of reactor vessel 30581605334000-15213509400 Fig. 35 Coolant loop 1 nodalization Fig. 36 SG1 steam system nodalization4.4 Cross section librariesTwo-group neutronic library ETEWH06 created by ??JV Rez a. s. ? division Energoprojekt Prague was prepared by the help of lattice code HELIOS ¹³. It contains node-homogenized cross sections and kinetic parameters of fuel assemblies (FA), FA with control clusters, and reflectors. 4.5 Calculated vs experimental resultsResults of simulation of selected global parameters and their comparison with experimental are given in Figures 37 to 40.Fig. 37 Main steam header pressure, calculation vs experimentFig. 38 Steam generator outlet pressure, calculation vs experimentFig. 39 Cold leg temperature, calculation vs experimentFig. 40 Hot leg temperature, calculation vs experimentFigure 41 presents comparison of calculated vs experimental coolant outlet temperatures from different fuel assemblies. The graphs show behavior of outlet temperatures in the reactor core region, which is connected with affected coolant loop No. 1, and in neighboring sectors. Figures 42 through 45 present the comparison of fuel assembly coolant outlet temperatures at the selected time intervals of the transient. The calculation results are systematically lightly overestimated in comparison with experiment. The maximum deviation is about 1.5 to 2 oC mainly at the beginning of transient (see Figure 42). Fig. 41 Fuel assembly coolant outlet temperature, calculation vs experimentFig. 42 Fuel assembly coolant outlet temperature, calculation vs experiment, t = 0 sFig. 43 Fuel assembly coolant outlet temperature, calculation vs experiment, t = 542 sFig. 44 Fuel assembly coolant outlet temperature, calculation vs experiment, t = 1000 sFig. 45 Fuel assembly coolant outlet temperature, calculation vs experiment, t = 1500 sCOnclusionsThe paper presents the calculation of OECD Kalinin-3 benchmark problem with using of stand-alone code DYN3D and externally coupled codes DYN3D/ATHLET. Two different cross-section libraries ? PSU-REL and KI were used. The trends of main calculated parameters (nuclear powers, coolant loops flow rates, coolant loops temperatures) and experimental results are in acceptable agreement ? influence of different X-S libraries can be observed. Differences between calculated fuel assembly coolant outlet temperatures (PSU-REL X-S versus KI X-S library) may be seen. Their ratio is changing during the simulation. Generally we can say that calculated fuel assembly coolant outlet temperatures are higher than experimental values.A question arises. Is the DYN3D and externally coupled codes DYN3D/ATHEL suitable for detailed modeling of coolant outlet distribution in thermocouples location? The clear answer cannot be given in the case of Kalinin-3 benchmark. The thermocouples are located in upper head of fuel assemblies. They are simply modeled as a part of upper axial reflector in the DYN3D model. The same approach is used in the external DYN3D/ATHLET coupling in contrast to detailed modeling used in BIPR/ATHLET coupled codes ¹⁴. We can say, that DYN3D and DYN3D/ATHLET fuel assemblies outlet temperatures better reflect the results of thermal balance (t = P/(m c), where P: initial reactor power, m: core mass flow rate, c: mean specific heat, t = 2900000000[W]/163 110[kg/s] 5600 [J/kgoC] 29 oC, tout = tin t = 288 29 = 317 oC, where tout (tin): mean coolant outlet (inlet) temperature at the beginning of transient) than experimental values.The results of SDA test show on a very good agreement of calculated and experimental fuel assembly coolant outlet temperatures. Here we can say that DYN3D/ATHLET external coupling is sufficiently suitable for modeling of this transient. ACKNOWLEDGMENTAuthor would like to thank colleagues from HZDR – Dr. Y. Kozmenkov and Dr. S. Kliem for friendly and valuable consultations during Kalinin-3 Benchmark problem solving. My thanks also to my colleague from JV Rez, a. s. – Dr. Radim Meca for valuable advice in modeling of Temelin NPP SDA test.NOMENCLATURE1-Done-dimensional3-Dthree-dimensionalAERAtomic Energy ResearchATHLETthermal-hydraulic system codeBIPR/ATHLETcoupled code CRcontrol rodFAfuel assemblyDYN3Dreactor dynamic codeGRSGesellschaft fuer Anlagen ?und Reaktor SicherheitHFPhot full powerHPKmain steam headerHSKupper plenumHVShot legHVSKOLhot leg collectorHZDRHelmholtz-Zentrum Dresden-RossendorfKIKurchatov InstituteLPlower plenumLWRlight water reactorMCPmain circulation pumpMSHmain steam headerMSLmain steam lineNnomnominal powerNPP Nuclear Power PlantOECDOrganization for Economic Co-operation and DevelopmentPGsteam generatorPG-PARmain steam linePG-TRsteam generator pipesPSU-RELPenn State University ? Risk Engineering Ltd.PVpressure vesselREFcore bypassRBMKRussian type of reactorSDAsteam dump to atmosphereSDCsteam dump to condenserSGsteam generatorSSRreactor downcomerSVScold legSVSCOLcold leg collectorUPupper plenumVRCHLIKupper headJVstav jadernho vzkumu Rez, a. s. (Nuclear Research Institute Rez, plc.)VVERRussian type of pressurized water reactorWECWestinghouse CompanyX-Scross sectionREFERENCES¹V. A. Tereshonok, S. P. Nikonov, M. P. Lizorkin, K. Velkov, A. Pautz, K. Ivanov: Kalinin-3 Coolant Transient Benchmark- Switching-Off of One of the Four Operating Main Circulation Pumps at Nominal Reactor Power, Specification ? First Edition 2008,NEA/NSC/DOC (2009)5² J. Hdek: Solution of the Kalinin-3 Benchmark ? Exercise 2 and 3,24th Symposium of AER on VVER Reactor Physics and Reactor Safety, Sochi, Russian Federation, October 14-18, 2014³U. Grundmann, S. Mittag, U. Rohde and S. Kliem: DYN3D Version 3.2 (FORTRAN90), Code for Calculation of Transients in Light Water Reactors (LWR) with Hexagonal or Quadratic Fuel Elements, Code Manual and Input Data Description for Release, Forschungszentrum Dresden-Rossendorf e.V., December 2009.⁴U. Grundmann, U. Rohde, S. Mittag, S. Kliem: DYN3D Version 3.2, Code for d Verifikation Calculation of Transients in Light Water Reactors (LWR) with Hexagonal or Quadratic Fuel Elements, Description of Models and Methods, Forschungszentrum Rossendorf, Institute of Safety Research, August 2005. ⁵B. Ivanov, K. Ivanov, P. Groudev, M. Pavlova, V. Hadjiev: VVER-1000 Coolant Transient Benchmark, PHASE 1(V1000CT-1), Vol. I.: Main Coolant Pump (MCP) Switching On ? Final Specification, NEA/NSC/DOC (2002)6, 2002 ⁶K. Ivanov: Kalinin-3 libraries, K-3_July11_update, E-mail from 31. 1. 2012 ⁷I. Pasichnyk: KI X-S library for Kalinin-3 benchmark, lib_sept2012, E-mail from 30. 5. 2013⁸ATHLET Mod2.2 Cycle A, User?s manual, GRS-P-1/ Vol.1, Rev. 4, July 2009⁹U. Grundmann, D. Lucas, U. Rohde: Coupling of the Thermohydraulic Code Athlet with the Neutron Kinetic Core Model DYN3D, In: Proceedings of the International Conference on Mathematics and Computations, Physics and Environmental Analysis,Portland, Oregon, USA, May 1995, Vol. 1, pp. 179-191.¹⁰S. Kliem, Y. Kozmenkov, T. Hhne, U. Rohde: Analyses of the V1000CT-1 Benchmark with the DYN3D/ATHLET and DYN3D/RELAP Coupled Code Systems Including a Coolant Mixing Model Validated Against CFD Calculations, Progress in Nuclear Energy, Vol. 48 (2006), pp. 830-848¹¹J. Hdek, J. Macek, R. Meca: Validation of Thermal-Hydraulic Computing Model of VVER-1000/320 Temelin NPP for Calculation with Coupled DYN3D/ATHLET Codes, AER Working Group D Meeting on VVER Reactor Safety Analysis, Hotel Vltava, Rez, Czech Republic, May 18-29, 2009¹²J. Hdek, R. Meca, J. Macek: Validation of Thermal-Hydraulic Computing Model of VVER-1000 Temelin NPP for Coupled DYN3D/ATHLET Codes, Proceedings of ICONE19, 19th International Conference on Nuclear Engineering, Chiba, Japan, May 16-19, 2011¹³J. J. Casal, R. J. J. Stammler, E. A. Villarino, A. A. Feri: HELIOS: Geometric Capabilities of a New Fuel Assembly Program, Proceedings of the International Topical Meeting on Advances in Mathematics, Computation, and Reactor Physics, Pittsburgh, PA, USA, April 28 ? May 2, 1991, Vol. 2, pp. 102-113.¹⁴I. Pasichnyk, K. Velkov, S. Nikonov: Coolant Temperature Distribution in the Fuel Assembly Head of VVER-1000, OECD Kaninin-3 Benchmark, 3rd Workshop, Stockholm, 2011

The Apros simulation environment has currently two different three-dimensional neutronics
models available for use. The original model is based on the method of finite-differences and
has been a part of Apros since the beginning. A new neutronics model based on advanced
nodal codes HEXTRAN and HEXBU-3D has been under implementation since 2008. The
implementation of the model is now practically complete, but some small improvements and
validation calculations still remain to be done. This work concentrates on the validation part
of the new neutronics model. For the purpose of validation, the calculated results were
compared against measured data of a MCP coast-down transient performed at the Kozloduy
NPP in 1991-1992. The fact that no validation calculations against measured VVER-1000
data have yet been made with the new Apros neutronics model makes the transient case be
very convenient for the purpose of this work. In addition, the same transient has been
calculated by HEXTRAN as a part of an international code benchmark. It is convenient to be
able to compare these results with Apros. Comparisons are made with the results calculated
by the finite-difference model of Apros as well. This work presents the main results obtained
in the comparisons and makes conclusions based on them.

Evaluation has been performed for the extended mathematical benchmark described in the
Atomic Energy Research (AER) association devoted to the VVER physics, using the models of
the KARATE code system and MCNP. The main task of the benchmark is to test the assembly
averaged and pin by pin power distribution predicted by codes that are used for reactor physical
calculation in the engineering practice. The calculated power distribution especially in assemblies
and pins next to the reflector strongly depends on the modelling choice. In case of a VVER-440
core high power peakings can be observed in the vicinity of control assembly, too.
In the paper the linear pin power calculation methodology of KARATE near the reflector
and control assembly will be presented and our results will be shown.