Evaluation of the Full Core VVER-440 Benchmarks Using the KARATE and MCNP Code Systems

Transcription

1 NENE 2015 September PORTOROŽ SLOVENIA 24th International Conference Nuclear Energy for New Europe Evaluation of the Full Core VVER-440 Benchmarks Using the KARATE and MCNP Code Systems György Hegyi Hungarian Academy of Sciences, Centre for Energy Research Konkoly Thege Miklós út H-1121, Budapest, Hungary Gábor Hordósy, Csaba Maráczy, Emese Temesvári Hungarian Academy of Sciences, Centre for Energy Research Konkoly Thege Miklós út H-1121, Budapest, Hungary {gabor.hordosy; csaba.maraczy; ABSTRACT Evaluations have been performed for two 2D calculational benchmarks 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 these benchmarks is to test the assembly averaged and pin by pin power distribution predicted by codes that are used for reactorphysical 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 similar difficulty can be observed in the vicinity of control assembly, too. This is the subject of the second benchmark. In the paper the two benchmarks will be outlined, the linear pin power calculation methodology of KARATE near the reflector and control assembly will be presented and our results prepared by the two different code systems will be shown and compared to the reference solutions. 1 INTRODUCTION The important reactor design and safety parameters must be determined with a high degree of accuracy and reliability. In generally the calculation methods for power reactors use simplified methods for cell or assembly calculations and the few group diffusion theory for the final calculations of the detailed power distribution. Corresponding reactor physics calculations therefore should be validated on representative experiments and operational data. An extension to ranges not covered by experiments or operational data may cause large uncertainties. Because the pinwise power distribution cannot be measured directly by the core monitoring system, a benchmark of this kind has been outlined. For such cases, an independent and validated method compared to the design methods should be available for the verification. Applications of the Monte Carlo Method which enables a pin by pin description of all assemblies in the core together with a detailed description of their inhomogeneity were chosen

2 408.2 Both the new, second generation Russian fuel which is profiled and contains gadolinium pins and the uprated core power make necessary a new, careful investigation for the detailed power distribution in the VVER-440 core. Due to the relatively narrow water gaps between the fuel and vessel wall makes the simulation more complicated.to study these phenomena, two mathematical benchmarks were defined by ŠKODA JS a.s. in the frame of the Atomic Energy Research (AER) association devoted to the VVER physics [1-2]. The proposal of the first benchmark was presented at the 21st Symposium of AER in 2011.It is a 2D calculation benchmark based on the VVER-440 reactor core cold state. The core consists of fresh second generation Russian fuel assemblies with 3 different enrichments.the goal of The Full-Core calculation benchmark for VVER-440 reactor was to verify the calculated pin power distribution especially in assemblies and pins next to the reflector, where the effect of modelling choice is very sensitive. In case of a VVER-440 core similar strong perturbation can be observed in the vicinity of the control assembly (CA), too. That is why the benchmark was extended such a way that the working group was inserted to the core. The reference solutions have been calculated by the MCNP code [2-3]. In the paper the two benchmarks will be outlined, the reference solutions prepared by MCNP code using our different input decks will be shown and compared to the published reference. The linear pin power calculation methodology of the Hungarian code system KARATE near the reflector and CA will be presented and the different solutions will be compared. 2 OUTLINE OF THE BENCHMARKS A short description of the 2D mathematical benchmarks is presented below. The horizontal cross section of the benchmark problems is hexagonal and it is restricted only on a one sixth part of the core with the basket due to its 30 degree symmetry (see in Figure 1.). Figure 1: Sixty degree symmetry sector of the VVER-440/213 vessel, its surrounding structures and the loading pattern (3 different enrichments marked by different colours) The core segment consists of 59 fresh fuel assemblies (FA s) with 3 different enrichments marked by different colours and names which correspond to their average

3 408.3 enrichment. Only the enrichment of the individual fuel pins of FA type 4.25 is presented in Figure 2 as in the case of the other two FA s the structure is similar and the pins are uniform. The second task differs from the first in the loading. In that case two assemblies (1 and 7) correspond to the control group 6 were changed to the absorber assembly, of which geometry is given in Figure 3.These assemblies are signed by fat curve in Figure 1. The two exercises called as all rods out (ARO) and +6th group in (6GI) case. Figure 2: Fuel assembly type 4.25 Figure 3: Horizontal cut of CA The further details about core basket, the geometry of explicit radial reflector and material compositions are given in paper [1-2]. The outer edge of the reactor vessel presents the boundary of the model in the radial direction. The reflection boundary conditions are used on the azimuthal surfaces of the cylindrical sector while the total absorption boundary condition (leakage to the vacuum) is used on its outer boundary (Figure 1). Reflection boundary conditions are used in axial directions. The measures of the structure are based on the cold state geometry of the VVER-440 reactor vessel, however the temperature of the FA s and the coolant is K, the pressure is 12.3 MPa. The results to be reported: The eigenvalue of the system (k eff ), the integral fission power distribution of FA (Kq) and the pin by pin power distributions in FAs (normalized for the assembly (Kk): an average relative pin powers equal 1 in each FA s). 3 COMPUTER CODES USED FOR THE INVESTIGATIONS Generally, a reactor physical problem can be analysed by deterministic and Monte Carlo methods. The KARATE code system based on deterministic methods obtains the solutions of the approximated representation of the model (energy, spatial and angular discretizations). In contrast, Monte Carlo Methods solve the exact representation of the model statistically (approximately; with statistic deviations) however they involve vast computational time compared to deterministic methods. That is why it is used to generate the numerical reference for verification and validation meanwhile the deterministic calculations are used for industrial calculations. 3.1 The Monte Carlo method The MCNP5 (Monte-Carlo N-Particle) code [5], is an advanced version of a flexible 3- D Monte Carlo code with provision to compute accurate detailed analysis of complex reactor

4 408.4 configurations. The publicly available MCNP5 code has been utilized at HAS CER for the purposes of research. The version of MCNP used in the presented research was MCNP5 release The ENDF/B-IV library was used (.14c for uranium isotopes,.62c and.66c for the others) for the most isotopes but for the Fe, Co and Ni isotopes the ENDF/B-V data were chosen. Possible source convergence problems were checked by increasing the number of active and passive cycles as well as the number of neutrons per cycles. The limitations of the publicly available codes based on Monte Carlo method have some limitations which should be taken into account in case of calculation of in criticality problems. In criticality problems the transport equation can be written in the form of eigenvalue problem where the reciprocal of the first (highest) eigenvalue is the k eff. This equation is solved by power iteration in Monte Carlo process. It is known from literature [6], that in this case the estimated value of k eff and reaction rates has a bias due to the renormalization of neutron numbers in each cycles and the estimated standard deviation of k eff and reaction rates has a bias due to the inter-cycle correlation. The bias in the estimated values is proportional with 1/N where N is the number of neutrons per cycle, so it can be reduced by using large number of neutrons per cycle. The bias in the estimated standard deviations is independent from the number of neutrons per cycle and from number of cycles. It depends only, via the correlation coefficient, on the dominance ratio of the system. The dominance ratio is the ratio of the first and second eigenvalue of the transport operator. If the dominance ratio is close to one, which is typical for large systems such as reactor core, the correlation is strong. In the publicly available codes, such as MCNP or KENO, this correlation is neglected, which results the underestimation of the standard deviations. According the experience, this underestimation may be significant for the standard deviation of the reaction rates and has only minor impact on the standard deviation of the k eff. The true values of the standard deviations can be determined only by repeated calculations using different random number sequences. This procedure was applied to the first benchmark problem. Due to its large computer time requirement, only the assembly-wise power distribution was examined. The core calculation was repeated 65 times using identical initial source, input files and libraries but using different random number sequences. The random number sequence was controlled changing the "seed" parameter on the "rand" card. The initial source was taken from a previous calculation neutrons per cycle, 350 active and 20 passive cycles was used. (The initial source was developed in the previous calculation.) The multiplication factor and the fission power density in each assembly were determined from each run. The real standard deviation of these quantities was then estimated using the 65 calculated values. Denoting by σe the real standard deviation and by σmc the standard deviation from a single Monte Carlo run, the results can be summarized, as follows: For the multiplication factor: σe /σmc =1.2. This is only a minor correction, and has small practical impact because the value of σmc is quite low for k eff. In the case of assembly power density, the value of σe /σmc averaged for the 59 assemblies is 3.6, its minimal and maximal value is 2.04 and For the assembly No. 27, 34 and 40 which were chosen by the benchmark team for detailed investigation the σe /σmc ratio is 3.6, 3.4 and 3.7. This is a significant correction which could cover the deviations between the Monte Carlo and deterministic calculation, but these results will not be used in the following intercomparisons. Similar investigation for the pin power distribution has not been completed, yet.

5 The KARATE code system The KARATE code system (version 5.1) has been developed, maintained and continuously enhanced at Hungarian Academy of Sciences Centre for Energy Research (the former Atomic Energy Research Institute, AEKI). The code system involves all the libraries and computer programs needed to perform fuel cycle calculations and design. It works properly for many years [7]. The libraries of the recent version are based on ENDF/B-VI data (Release 6). KARATE-440 has been extensively tested, the test problems range from mathematical tests and zero reactor experiments to nuclear power plant operational data. Its computational levels are the following: 1. level: 70 group, 2D transport calculation for an assembly, or an assembly with surroundings. Generate few group constants for higher levels, MULTICELL module calculate the composition for 176 isotopes. 2. level: 4-group, 2D fine mesh reflector albedo calculations for the further levels, with detailed reflector geometry. 3. level: 2-group, 2D fine-mesh diffusion calculations for one assembly and its surroundings (SADR module). 4. level: 2-group, nodal calculations for the core (in a sixty degree symmetrical part: GLOBUSKA module or for the full core: GLOBUS36). There is consistent, bi-directional connection between levels via parameterization. Core calculations are made with the GLOBUSKA nodal code using the homogenized few group cross sections of assemblies, then as a result of the core calculations (with flux boundary conditions) inhomogeneous type fine mesh diffusion calculations are carried out for the assembly and its vicinity with the SADR code. Figure 4 presents an example of the calculated domain in case of pin by pin power distribution. Figure 4: Pin-wise calculation domain in the KARATE code system (the vicinity of reflector core basket and CA) As the goal of the work is the validation of the KARATE-440 code system concerning the linear pin power calculation near the strongly inhomogeneous regions of the core (basket and CA), in solving the test case we applied the same methods and procedures as in case of routine power plant calculations. The sources of the difficulties of the calculations in these regions are their very complicated structure (geometry and composition data).complicated spectral and 3D spatial effects of the neutron transport have to be solved. The diffusion approximation in the very heterogeneous region is not satisfactory without some special treatment. 3D effects must be taken into account. Meanwhile core design calculations are

6 408.6 based on the few-group diffusion approximation. Fine mesh calculations taking into account the flux-tilt caused by the environment of the calculated region is usually two-dimensional. In KARATE, the reflector parts and the CA regions are excluded from the diffusion type calculations and represented by albedo matrices. The elements of the albedo matrices [ά gg' ] are the reflection probabilities for neutrons entering the excluded region in group g' and returning to the fuel assemblies in group g, can be expressed as 2 J g = ggj g' (1) g' 1 According to the results of the methodological investigations, the reflector albedo matrix elements can be considered as a function of the soluble boric acid concentration [C B ] the moderator density [ρ m ] and the position of the edge. gg = gg(c B, m ) (2) In case of CA the reflector albedo matrix elements can be considered as a function of the soluble boric acid concentration [C B ] the moderator density [ρ m ] and the composition of the axial layer: gg' gg' X, CB, m (3) X plays role only in cases where the axial layer contains boron steel or Hafnium. X=C Bsteel is the boron concentration of the boron steel, which is burnt out. One axial layer of the CA contains Hf. The burnout of the Hf isotopes is characterised by the time integral of the incoming partial current X=F Hf at the proper surface of the CA assembly. In the KARATE calculations, first 1D multigroup transport calculations of the different coupler regions of CA and reflector and the neighbour assemblies are performed by using the COLA module, and the obtained two-group albedo matrices are parameterized. Finally a correction factor D is determined by using MCNP 3D results: J MCNP DC ( po ) JMCNP (4) * Where J MCNP is the partial current calculated by MCNP with given p 0 parameters, c (p o ) is the albedo matrix with given p 0 parameters calculated with the COLA code and D is the diagonal correction matrix for each albedo type. 4 CALCULATIONAL RESULTS Even though the reference solutions were offered by SKODA with using MCNP method and different nuclear libraries, our own Monte Carlo calculations were performed also, simply to investigate some differences originated from the different nuclear data set. The effective multiplication factors given by the benchmark team is summarised in Table 1 Table 1: Reference Monte Carlo Calculations of Benchmark team [3] Monte Carlo code MCNP4B MCNP5 1.4 MCNP4B Used Libraries, excl. steel: ENDF/B-V (.50c and.55c) Precision of calculation n. per cycle, 30 cycle non active ENDF/B-VI (.60c) Jeff 3.1 (.34c) ENDF/B-VI (.68c) 1430 cycles 1030 cycles 1030 cycles (ARO) k eff < ) (6GI) k eff < )

7 408.7 The effective multiplication factor for the two cases determined by our institute (HAS EK) is the following: (ARO) k eff (MCNP): (ARO) k eff (KARATE): (6GI) k eff (MCNP): (6GI) k eff (KARATE): (= ) (= ) By additional analysis of our MCNP calculations in ARO case, there was observed that the differences within ENDF/B-VI libraries may be up to due to the option selection. The remainder can be accounted for the parametrization error of cross sections. Concerning the details of the reference (made by the benchmark team) and our auxiliary calculations one can state, that the difference in relative power of FA's not higher than 1 % (See on Figure 5-6). Due to some technical reasons, the reference solution for ARO case originated from the benchmark team, while in the other case it is based on our calculations in the following text. Figure 5: Kq calculated by our MCNP input and its relative difference from reference in case of ARO Figure 6: Kq reference solution and its relative difference from our MCNP result in case of 6GI In this text the relative deviations (_x) and standard deviation (SD) estimated by the equation 5 and 6: i i x _ C xref i i xref *100 2 _ X i N SD N 1 x (5) The assembly integrated power distribution (Kq) was calculated by KARATE for both cases. Our results and the differences to the reference solutions made by MCNP can be seen on Figure 7 and 8. The highest discrepancies can be found near the basket in both cases. Even the two cases quite differ from each other due to the insertion of CA's the nodal solution shows same behaviour comparing to the Monte Carlo solution: the KARATE calculations underestimate the power at the peripheral assemblies. The difference among the (6)

8 408.8 assembly integrated power distribution is less than 3.6%; the standard deviation is about 1.5%. Figure 7: Kq, calculated by KARATE and its relative difference from reference in case of ARO Figure 8: Kq, calculated by KARATE and its relative difference from reference in case of 6GI Comparison between fine mesh solution (Kk) and reference MC solution was also provided. Instead of the detailed results, which can be found in [3-4] some statistics of these results are presented here. In case of ARO, the assemblies were divided into 2 groups. Peripheral assemblies near the reflector and the others so called inner assemblies. The frequency of the relative deviation for these two cases can be seen on Figures One can see that the deviation is much wider in the group of peripheral assemblies. In case of 6GI, the assemblies were divided into 3 groups. Peripheral assemblies are the same as above. The inner assemblies were divided further to two groups: assemblies in the vicinity of insered CA belong to the third group. The frequency of the relative deviation for these groups can be seen on Figure 11, 12 and 13. In case of inner assemblies and peripheral assemblies the error distribution is rather similar to each other meanwhile the third group of 6GI case is similar to the group of inner assemblies. Pin by pin power distribution and its deviation from our MCNP calculations can be seen on Figures The first pictures (assembly No 6) present the power distribution near the inserted control group. Larger differences can be observed at the edge next to the absorber regions.the second one shows the assembly No 41 where the largest deviation was found in both benchmark cases. It is worth to see that the discrepancy alters along the edge of the peripheral assembly and is rather constant in the other case. Finally, assuming 1485 MW total power for all the pins in the benchmark, the pin powers were calculated for the assembly 41 in which we have got the largest (17.5%) relative deviation in one corner pin (ARO case, see in [3]). The corresponding value is 14.5 % in the 6GI case (see in Figure 15). The absolute deviation was found to be less than 1.52 kw, which is in accordance with the 7.4 kw uncertainty of KARATE-SADR corresponding to 3σ.

9 Frequency Relative deviation in % Frequency Relative deviations in % Figure 9: The frequency of the relative deviations in % for the assemblies far from the reflector in the 30-degree part of the core. The range of deviation: %, standard deviation is 1.4 % Figure 10: The frequency of the relative deviations in % for the assemblies next to the reflector in the 30-degree part of the core. The range of deviation: %, standard deviation is 2.75 %. Frequency Relative deviations in % Figure 11: The frequency of the relative deviations in % for the assemblies far from the reflector in the 30-degree part of the core. The range of deviation: %, standard deviation is 1.0% Frequency Relative deviations in % Figure 12: The frequency of the relative deviations in % for the assemblies next to the reflector in the 30-degree part of the core. The range of deviation: %, standard deviation is 2.4 %. Frequency Relative deviations in % Figure 13: The frequency of the relative deviations in % for the 3 rd group. The range of deviation: %, standard deviation is 1.0%.

10 Figure 14: Pin wise power distribution calculated by SADR for FA 6 (left) and its relative deviationfrom reference MCNP result in 6GI case Figure 15: Pin wise power distribution calculated by SADR for FA 41 (left) and its relative deviation from reference MCNP result in 6GI case 5 CONCLUSIONS The two parts of the Full-Core VVER-440 pin power distribution calculation benchmark seem to be very useful for engineering code validation. The problems have been investigated by the KARATE code system and also MCNP. The relative deviations from the reference were determined. An underestimation of the standard deviations in MCNP for large systems was presented, on the basis of a set of MCNP calculations for this benchmark. A significant correction was found which covers the deviations between the Monte Carlo and deterministic calculation. Similar investigation for the pin power distribution has not been performed. Taking into account the differences between nuclear data libraries the results of the eigenvalues of nodal code and our MCNP calculations are in a relatively good agreement with the reference results. Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 14 17, 2015

11 The calculated fuel assembly wise power distributions are also in good agreement with reference solution, however the underestimation in the vicinity of reflector is unambiguous. It is not the case around the CA s. The results of SADR module of the KARATE code system show good agreement in the pin by pin power distribution in the central part of the core. This accordance is decreasing with closing to the edge of the core. The underestimation changes along the edge and the worst agreement is found in the outer corner of the FA close to the reflector. Similar effect can not be seen beside of CA. REFERENCES [1] V. Krýsl, P. Mikoláš, D. Sprinzl, J. Švarný, 'Full-Core' VVER-440 Pin Power Distribution Calculation Benchmark, Proceedings of the 21st Symposium of AERon VVER Reactor Physics and Reactor Safety, Dresden, Germany, September 19-23,2011. pp [2] V.Krýsl, P.Mikoláš, D.Sprinzl, J.Švarný, 'Full-Core' VVER-440 Benchmark extension, Proceedings of the 24th Symposium of AERon VVER Reactor Physics and Reactor Safety Sochi, Russia, October 14-18, 2014, pp [3] V. Krýsl, P. Mikoláš, D. Sprinzl, J. Švarný, E Temesvári, I. Pós& L. Heraltová, Full- Core VVER-440 Calculation Benchmark,Kerntechnik Vol 79, No. 4,Aug. 2014, pp [4] V.Krýsl, P. Mikoláš, D. Sprinzl, J. Švarný, 'Full-Core' VVER-440 Pin Power Distribution Calculation Benchmark, Proceedings of the 22 nd Symposium of AER on VVER Reactor Physics and Reactor Safety, Pruhonice, Czech Republic, October 1-5, pp [5] MCNP - A General Monte Carlo N-Particle Transport Code, Version 4C, Judith F. Breismeister (Editor), LA M, Los Alamos National Laboratory, 2000 [6] Forrest B. Brown: A Review of Monte Carlo Criticality Calculations - Convergence, Bias, Statistics; LA-UR [7] Cs. Hegedűs, Gy. Hegyi, G. Hordósy, A. Keresztúri, M. Makai, Cs. Maráczy, F. Telbisz, E. Temesvári, P.Vértes, The KARATE Program System, PHYSOR 2002, Seoul, Korea, October 7-10, 2002