2-D Reflector Modelling for VENUS-2 MOX Core Benchmark

Transcription

1 2-D Reflector Modelling for VENUS-2 MOX Core Benchmark Dušan Ćalić ZEL-EN d.o.o. Vrbina , Krsko, Slovenia ABSTRACT The choice of the reflector model is an important issue in full core calculations. In 2015 new approach was developed where the existent WIMSD code for lattice cell calculations was replaced with the Monte Carlo code Serpent 2. Newly developed calculational tool Serpent-GNOMER is used to obtain a reference result for full core calculation. However the Serpent-GNOMER simulation code uses simplified 1-D reflector model. In this paper new approach is presented. Based on a VENUS-2 benchmark new 2-D reflector model is proposed. The results of the power distribution using Serpent- GNOMER code are compared to Monte Carlo results. 1 INTRODUCTION Due to the differences of neutronics properties between the core and the reflector regions a special treatment of the reflector in reactor analysis is required. This is a challenging task due to geometry complexity, material and structural heterogeneity of radial and axial reflectors. The correct modelling of the reflector is important for accurate predictions of power core distribution especially in regions close to the reflector. WIMSD-GNOMER sequence is used for core design calculations of pressurized water reactors. Full core simulation [1] starts with the lattice cell calculation with homogenized group constants produced by using deterministic code WIMSD [2]. Constants are then used as an input for fuel assembly calculation with nodal diffusion method using GNOMER code [3] and finally full core calculations is preformed solving two group diffusion equation using GNOMER code. In this calculational scheme, reflector constants are generated with effective diffusion homogenization method (EDH) using 1-D geometry where an analytical solution of the diffusion equation can be used with some additional assumptions. Recently, the deterministic group constant generator in lattice cell calculations was replaced by Serpent 2 code using the Monte Carlo (MC) method [1]. This newly developed sequence Serpent- GNOMER calculates the reflector constants using 1-D model that is used in WIMSD-GNOMER sequence. Before we were unable to model 2-D reflector model with the WIMSD code but there are no restrictions with the Serpent 2 code since the geometry can be modelled explicitly. In this paper, the validation of 3-D VENUS-2 benchmark using Serpent 2 code is presented since the VENUS-2 benchmark is very sensitive to the reflector model and can be regarded as a perfect test to develop a better reflector model for Serpent-GNOMER sequence

2 DESCRIPTION OF THE VENUS-2 REACTOR VENUS-2 benchmark is an international benchmark used for validation of codes for MOX fuel system. It was a subject of many verifications where different codes and nuclear data sets were used ([4], [5]). In the first part of this paper, the results of VENUS-2 benchmark using Serpent 2 code are compared to those of the Monte Carlo code MCNP and to measured experimental data. Calculations are performed using Serpent 2 code, version , together with nuclear data based on ENDF/BVII.0 evaluation. Those results are used as a reference for the validation of the Serpent-GNOMER calculations using 2-D reflector model, which is presented in the second part of this paper. 2.1 Computational model The VENUS critical facility is a zero power critical reactor located at SCK-CEN in Mol, Belgium. The core consists of U O2 fuel pins (central part) and MOX fuel pins (core periphery). A complete specification of the VENUS-2 geometry, composition and experimental results are given in [5]. For this analysis a detailed VENUS-2 Serpent model was constructed. The horizontal overview is shown in Figure 1 while the Figure 2 shows a vertical cross-section of the core. As you can se in Figure 1, fuel pins are marked with different colours representing different fuel enrichments while the red colour pins are used in pin power distribution in 1/8 of the core calculation. Figure 1: Radial view of the VENUS-2 benchmark using Serpent 2 code. Proceedings of the International Conference Nuclear Energy for New Europe, Portoroz, Slovenia, September 5-8, 2016

3 316.3 Figure 2: Axial view of the VENUS-2 benchmark using Serpent 2 code. 3 COMPUTATIONAL MONTE CARLO RESULTS In the first part, the Monte Carlo calculations were performed for each type of the unit cell. In the second part, the full core results are presented. 3.1 Unit Cell Calculations Results For each type of fuel cell (3.3 wt. % UO 2, 4.0 wt. % UO 2, and 2.0/2.7 wt. % MOX), the k calculations were performed. The results are shown in Table 1. Also the comparison to MCNP results, version 6.1.1b, using the same ENDFB/VII.0 library, and the comparison to the benchmark average k values [5] are given. Table 1: Multiplication factor (k ) results of cell calculations using Serpent, MCNP and benchmark average (Avg.) together with deviations ( k(pcm*). Serpent MCNP k MCNP Avg. k Avg. 3.3 UO ± ± ± UO ± ± ± MOX ± ± ± *1 pcm = 10 5 The k results using Serpent code are in excellent agreement with MCNP results since both codes use the same nuclear data. Higher discrepancies are observed with the benchmark average

4 316.4 values. Some reasons for those discrepancies are due to the different nuclear data and were already investigated in [5] and [4]. 3.2 Full Core Calculations Results As we can see in Figure 2, the core was modelled in three dimensional geometry, where all fuel and Pyrex rods were modelled in detail. For this paper the multiplication factor for full core calculation (k eff ) and normalised radial fission rate distribution at 325 fuel pin positions pins are presented Multiplication factor results The calculated k eff value using Serpent 2 code is presented in Table 2. Also, discrepancies to the calculated value of the MCNP [6] and experimental value (k eff = 1) [5] are presented. All calculations were performed using ENDF/B-VII.0 library. Table 2: k eff core calculations using ENDF/B-VII.0 library k eff k eff (MCNP) k eff (Measurements) ± pcm pcm As it can be seen from Table 2, all calculated k eff are in good agreement with the experimental value. In this study only one type of library was used, ENDF/B-VII.0. As it was already discussed in [6] and [5] the discrepancies due to the chosen nuclear library can be of order of 1000 pcm Pin power distribution results The relative comparison, C/E-1 [%], of calculated results against experimental results for the pin power distribution in 1/8 of the core are presented in Figure 3. Also, in the first row the coordinates of the fuel pin positions are given in x-axis and in the first column the co-ordinates in y-axis with respect to the core centre are given. The results of pin power distribution are well consistent with the experimental data. Around 5 % of the values are above 5 % deviation and almost 60 % of the values are within 2% of the experimental results. The results for two types of UO 2 fuel rods are in excellent agreement with the experimental results. In the case of 3.3 wt. % UO 2 fuel an average deviation from the measurements is 1.74 % ± 1.18 % and 2.31 % ± 1.52 % for 4.0 wt. % UO 2 fuel. The average deviation with the experimental data for the MOX fuel is increased and in some cases it can reach more than 6.0 %. An average deviation is around 3.36 % ± 1.81 %, mainly due to the fuel pins in the region near the 4.0 wt. % UO 2 fuel. Similar results were obtained using MCNP code [6]. It can be seen that there is a systematic trend in the discrepancies, as the calculated fission rates are under estimated in the regions near the reflector. If we only consider the power distribution in the pins near the reflector (first row near the reflector is considered) for each of the fuel types than in the case of 3.3 wt. % UO 2 fuel only one fuel pin is relevant (x:-18.27, y:18.27) with the deviation of 2.91

5 316.5 Figure 3: Relative comparison of calculated Serpent 2 and experimental results (in units of % ). %. For the 4.0 wt. % UO 2 fuel we have seven fuel pins near the reflector with an average deviation 2.51 % and finally for the MOX region an average deviation is around 3.81 % (22 fuel pins). 4 SERPENT-GNOMER SIMULATION In the following section the development of 2-D reflector model for Serpent-GNOMER simulation is presented. In the existent Serpent-GNOMER simulation the cross-section homogenization method EDH is used to generate the reflector constants using 1-dimensional geometry shown in Figure 4. Figure 4: Fuel reflector 1-D model. Fuel reflector model presented in Figure 4 is 1-D color set reflector model that contains the fuel

6 316.6 region (left) which is further divided into fuel pellet, gap, cladding, spacer grids and coolant and the reflector region (right) that contains baffle, reflector water (volume fraction of stainless steel in water), and barrel region. In this case the partial currents only on the internal boundary (fuel-reflector) are conserved, while on the external boundary the zero-flux condition is imposed. For a VENUS-2 benchmark four different 1-D reflector cells are considered. All reflector cells use the same baffle thickness, while the effective water thickness is changed to preserve the ratio between the water and steel for each reflector cell. 2-D radial reflector modelling underwent various changes of development. Finally, a full sized VENUS-2 benchmark model was considered. Four different reflector cells were considered: R1, R2, R3 and R4 (Figure 5). As we can see from Figure 5 each of the reflector cell is explicitly defined. For each of the new reflector cells the homogenized cross-sections are calculated. Together with the homogenized cross-sections obtained for each different fuel cell fuel cross-sections constants are then used in a nodal GNOMER code for core power distribution calculation. To verify the accuracy of the 2-D methodology, the following model is tested against the Serpent Monte Carlo results presented in section The results are presented in the following subsection. Figure 5: 2-D reflector model. 4.1 Serpent-GNOMER results For the Serpent-GNOMER core calculations, Serpent produced homogenized 4-group crosssections using the EDH method. The core calculations was performed by using the nodal diffusion code GNOMER. The results of the pin power distribution in 1/8 of the core were investigated. The relative comparison, C(MC)/C(SG)-1 [%], of calculated Serpent Monte Carlo (MC) results against Serpent-GNOMER (SG) using 2-D reflector model are at this stage not really satisfactory. Biggest deviations are in the MOX region, around 10%. Results are in better agreement for two types of UO 2 fuel rods. In the case of 3.3 wt. % UO 2 fuel an average deviation from the (MC) is 2.63% and 2.85 % for 4.0 wt. % UO 2 fuel. The average deviation for the MOX fuel is around 6.37 %.

7 CONCLUSIONS The Monte Carlo Serpent 2 results of criticality and power distribution are presented and compared to MCNP and experimental results. The criticality results for the benchmark model are within the uncertainties. The calculated results of reaction rates are almost completely consistent with the MCNP results and in very good agreement with the experimental results. This means that the geometry and the material properties are modelled very well. In regions near the reflector the core power distribution is slightly underestimated, especially in the MOX region and overestimated in the 4.0 wt. % UO 2 fuel region. Average deviations near the reflector are higher. In general, the results from the analysis confirm that Serpent 2 can adequately perform Venus-2 benchmark, which is known to be highly sensitive to the reflector model. The Serpent code is to be used to refine the reflector model used in the Serpent-GNOMER sequence for global core calculation, where the current reflector model is given in planar geometry with additional assumptions. The results of the Serpent-GNOMER simulation using 2-D reflector model shows poor agreement with Monte Carlo results, especially in the MOX region. Thus, further investigation is needed on this subject. REFERENCES [1] D. Ćalić, A. Trkov, M. Kromar, L. Snoj, Use of Effective Diffusion Homogenization method with the Monte Carlo code for light water reactor. Ann. Nucl. Energy., 94, pp , [2] A. R. Askew, F. J. Fyers, P. B. Kemshell, A General Description of the Code WIMS, J. Br. Nucl. Energy Soc., 5, p. 564, [3] A. Trkov, GNOMER - Multigroup 3-Dimensional Neutron Diffusion Nodal Code with Thermohydraulic Feedbacks, Institute Jožef Stefan, Ljubljana, Slovenia, IJS-DP-6688, Rev.1, Mar.1994, NEA-Data Bank, ID:IAEA [4] Byung-Chan Na, N. Messaoudi, Benchmark on the VENUS-2 MOX Core Measurements, OECD/NEA report, NEA/NSC/DOC(2000)7., ISBN , [5] Byung-Chan Na, N. Messaoudi, Benchmark on the Three-dimensional VENUS-2 MOX Core Measurements, Final Report,NEA/NSC/DOC(2003)5, ISBN , [6] R. Bizjak, Primerjava determinističnih in Monte Carlo metod za izračun porazdelitve gostote moči na eksperimentu VENUS-2, diplomsko delo (slovene language), 2010.