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Serpent2-SUBCHANFLOW pin-by-pin modelling capabilities for VVER geometries
Annals of Nuclear Energy 135 (2020) 106955
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Serpent2-SUBCHANFLOW pin-by-pin modelling capabilities for VVER geometries Manuel García a,⇑, Diego Ferraro a, Ville Valtavirta b, Riku Tuominen b, Uwe Imke a, Jaakko Leppänen b, Victor Sanchez-Espinoza a a b
Karlsruhe Institute of Technology, Institute of Neutron Physics and Reactor Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany VTT Technical Research Centre of Finland Ltd., Tietotie 3, Espoo FI-02044 VTT, Finland
a r t i c l e
i n f o
Article history: Received 24 May 2019 Received in revised form 19 July 2019 Accepted 22 July 2019
Keywords: Serpent2 SUBCHANFLOW VVER Multiphysics
a b s t r a c t In the framework of the EU Horizon 2020 McSAFE project, a Serpent2-SUBCHANFLOW coupling has been developed with the aim at performing large-scale pin-by-pin depletion and transient calculations in Light Water Reactors. While this tool is not tied to a specific type of geometry, a set of capabilities have been developed to generate the pin-level hexagonal models corresponding to VVER reactors. The handling of VVER geometries is based on the use of nested hexagonal regular meshes in Serpent2, pin-level subchannel models in SUBCHANFLOW and unstructured meshes for feedback exchange and interpolation. In this work, these features are explained in detail and illustrated in a VVER-1000 fuel assembly. For this test case, an in-depth analysis is made regarding the modelling considerations in SUBCHANFLOW and their impact on the neutronic solution. In particular, the use of coolant- and fuel-centered subchannels and the explicit modelling of stiffener plates is discussed. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Driven by the growing interest in high-fidelity reactor physics analysis in the nuclear industry, the EU Horizon 2020 McSAFE project (Mercatali et al., 2018) was set to develop multiphysics tools based on Monte Carlo neutron transport, subchannel thermalhydraulics and fuel-performance analysis. The final objective is to be able to tackle large-scale problems in PWR and VVER reactors, such as full-core pin-by-pin depletion and transient scenarios. McSAFE is a continuation of two lines of work investigated in previous European projects: HPMC (HPMC, 2019), devoted to highperformance Monte Carlo methods, and NURESAFE (Nuresafe, 2019), dealing with core-level multiphysics calculations. A central component of the McSAFE project is the development of a coupling scheme for Serpent2 (Leppänen et al., 2015), a Monte Carlo particle transport code, and SUBCHANFLOW (Imke et al., 2012), a subchannel analysis code, suitable for large-scale simulations in High Performance Computing (HPC) environments. This coupled tool is to be used in steady-state, depletion and transient calculations. In addition, the coupling of Serpent2SUBCHANFLOW with TRANSURANUS (Lassmann, 1992), a
⇑ Corresponding author. E-mail address: [email protected] (M. García). https://doi.org/10.1016/j.anucene.2019.106955 0306-4549/Ó 2019 Elsevier Ltd. All rights reserved.
fuel-performance code, and its application to depletion problems, is foreseen. In this context, a flexible Serpent2-SUBCHANFLOW coupling was developed (García et al., 2019) and its results verified for high-fidelity PWR calculations (Ferraro et al., 2019). This tool is based on an object-oriented design and on the exchange of feedback between codes using unstructured meshes. The coupling scheme is problem-independent and any reactor type that can be modelled with Serpent2 and SUBCHANFLOW can be simulated with the coupled system. The application of Serpent2SUBCHANFLOW to different LWR types is therefore a matter of building the corresponding models. The objective of this work is to show the capabilities developed in the McSAFE project for the simulation of VVER geometries in Serpent2-SUBCHANFLOW, which are presented in Section 3. Given that the geometry and modelling approach in Serpent2 is extremely flexible and VVER reactors can be readily simulated, the focus is put on the exchange and interpolation of feedback variables and on the SUBCHANFLOW models in the specific case of VVER cores. The feedback exchange is explained through Sections 2 and 3. Section 4 presents and discusses the results for different SUBCHANFLOW models and their impact on the Serpent2 calculation. The use of coolant- and fuel-centered subchannels is analyzed, as well as the modelling of stiffener plates, present in most modern VVER fuel-assembly designs.
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It is important to note that no comparison is made here with other tools or with experimental results, but the general modelling approach is shown and assessed. This is due to the fact that to the knowledge of the authors no proper high-quality benchmarks with pin-level solutions for VVER reactors are currently available in the literature. The validation of Serpent2-SUBCHANFLOW with VVER experimental data provided by industry partners is foreseen for subsequent stages of the McSAFE project. 2. Serpent2-SUBCHANFLOW coupling The Serpent2-SUBCHANFLOW coupling used in this work is based on an object-oriented methodology (García et al., 2019) in which both codes are restructured as solver classes that are then used in a supervisor program to perform the calculation. The exchange and interpolation of feedback fields is done using unstructured meshes superimposed to the geometry of each code. The traditional iterative scheme for neutronic-thermalhydraulic coupling is used. This methodology is described in detail in this section, starting with a brief description of each code with a focus on the aspects relevant to the coupling scheme.
Fig. 1. Object-oriented coupling.
libraries are then wrapped into C++ classes derived from a common base class, masking the particular language of each code and defining a uniform interface. This base class represents a generic code with multiphysics capabilities, and is defined by the Interface for Code Coupling (ICoCo) from the SALOME open-source platform (CEA/DEN, EDF R&D, OPEN CASCADE, 2019a). The iterative coupling scheme is then implemented in a C++ program that manages the calculation objects that represent both codes.
2.1. Serpent2
2.4. Feedback-field exchange
Serpent2 (Leppänen et al., 2015) is a continuous-energy Monte Carlo particle transport code. The problem geometry is most often modelled using the Constructive Solid Geometry (CSG) technique, which makes the definition of virtually any core geometry possible. Serpent2 also supports unstructured meshes and stereolithography- (STL) based geometries to build the model. All relevant components of a reactor core can be modelled explicitly virtually without restrictions. One key feature of Serpent2 for its use in multiphysics simulations is the ability to superimpose meshes to the geometry to define density and temperature distributions and to tally the power, without linking these distributions to the geometry used for particle tracking. Each mesh is specified in an interface file and is associated to one or more materials, for which the thermalhydraulic conditions are given. The transfer of feedback fields to and from Serpent2 is based on this capability (Valtavirta, 2017).
The exchange of feedback fields is done using the same format for both codes and relies on the MEDCoupling library from the SALOME platform (CEA/DEN, EDF R&D, OPEN CASCADE, 2019b). This library provides classes that represent unstructured meshes and fields defined on them, as well as advanced interpolation methods, and input and output capabilities. In Serpent2, each multiphysics interface represents a mesh superimposed to the geometry. In the work presented here, Serpent2 uses regular hexagonal meshes, while Cartesian meshes are used in the same way for PWR-type geometries. With the aim at full-core PWR and VVER models however, a newlydeveloped structure of nested regular meshes is being used. This method is based on filling the cells of a regular mesh with another regular mesh, to create a multilevel structure that works essentially in the same way as the universe-based CSG geometry, i. e. given a position the density and temperature can be found starting in the outermost mesh and going down nested levels. To exchange feedback fields and perform interpolation, this multi-level meshes are represented as unstructured meshes with the actual physical shape resulting from the nested meshes. This is clearly illustrated with an example in Section 3.2. Two meshes can be used in SUBCHANFLOW, one for the fuel and one for the coolant. The fuel mesh defines the rod structure and can be used to extract fuel variables such as temperature, claddingcoolant heat transfer coefficient and Departure from Nucleate Boiling Ratio (DNBR) and to input a power distribution. The coolant mesh gives the shape of the subchannels and can be used to get coolant variables, e. g. temperature, density and pressure. Given that neither Serpent2 nor SUBCHANFLOW use meshes for their internal calculation schemes and that in both cases building a mesh from the geometrical model is not straight forward, the meshes are built with a preprocessor and given to the codes as part of the input. The feedback exchange for all fields works in the exact same way, and can be summarized as:
2.2. Subchanflow SUBCHANFLOW (Imke et al., 2012) is a subchannel-level thermalhydraulic code for steady-state and transient analysis of Light Water Reactors. The flow solver consists of three conservation equations in the axial direction, namely for mass, energy and momentum, plus a simplified model for cross-flow based on momentum conservation in the lateral direction. The geometry is defined as a set of channels and rods with given hydraulic parameters and connectivities in a flexible manner, i. e. without assuming a particular geometry type such as square or hexagonal. As in the case of Serpent2, meshes can be superimposed to the geometry to exchange coolant and fuel feedback fields. These meshes are not used in the internal calculation at all, but only to define the exact shape of the subchannels and the rod structure, which can’t be inferred from the model used in the calculation. This is further explained with an example in Section 3.3. 2.3. Object-oriented coupling The object-oriented coupling approach is depicted in Fig. 1. Both codes are first restructured as libraries which provide the features needed to implement a multiphysics scheme, i. e. initialization, calculation, feedback exchange and termination. These
1. Get the field from the code that calculated it with its associated mesh. 2. Get a template of the field in the second code with its associated mesh. 3. Interpolate the field from the source mesh to the target mesh.
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4. Set the interpolated field to the second code. In this scheme the classes that define the fields and meshes, as well as the interpolation methods, are provided by the MEDCoupling library. 2.5. Iterative scheme The multiphysics scheme used for the Serpent2SUBCHANFLOW coupling is the traditional Picard iteration method. The pin power calculated by Serpent2 is used in SUBCHANFLOW, which in turn calculates the subchannel-level thermalhydraulic state to feedback the neutronics. The evaluation of the convergence is based on the error in L2 or L1 norm between iterations for the feedback fields and on the change in the multiplication factor, with the exact criteria defined by the user. For iteration k, the convergence norms for a field v k with N discrete values fv ki g are defined as
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P k k1 2 Þ i ðv i v i Lk2 ¼ N jg: Lk1 ¼ maxfjv ki v k1 i i
ð1Þ ð2Þ
Fig. 2. Serpent2 model for sections without spacers.
3. VVER modelling capabilities This section describes the Serpent2-SUBCHANFLOW modelling capabilities specific to VVER reactors. A VVER-1000 fuel assembly is used to show these capabilities and to evaluate different modelling decisions. Given that no reference solutions are available for this problem, comparisons are made between different modelling approaches. 3.1. Test problem The VVER case considered is the 30AV5 fuel-assembly type from the TVSA benchmark for VVER core burnup calculations (Lötsch et al., 2010). It consists of a VVER-1000 fuel assembly at Beginning of Life (BOL) and Hot Full Power (HFP). The geometry is comprised of 303 regular fuel pins (UO2 with 2.99% weight enrichment), 9 fuel pins with burnable poison (UO2 with 2.4% weight enrichment, 5% Gd2O3 mass fraction), both with a central hole, 18 guide tubes and a single instrumentation tube. The fuel assembly has 15 spacer grids, 13 of them within the active length of the core, and stiffening angle plates. This problem represents a typical VVER geometry, and illustrates the relevant modelling features. The Serpent2 and SUBCHANFLOW models for this fuel assembly are described in the following sections.
Fig. 3. Serpent2 model for sections with spacers.
3.2. Serpent2 models As mentioned before, the CSG methodology used in Serpent2 allows for the explicit modelling of any component of the reactor. In this case, the active length consists of two types of sections, namely with and without grid spacers, which are shown in Figs. 2 and 3. The spacers are simulated in such a way as to maintain their mass and volume, and the stiffeners in the corners are modelled explicitly. In addition, three reflector layers are included in the top and in the bottom of the fuel assembly, as described in the benchmark definition. Reflective boundary conditions are used in all directions except axially, where vacuum conditions are used. The thermalhydraulic state for this case is given in a superimposed mesh that consists on a regular y-type hexagonal pin-level
mesh inside an x-type fuel-assembly-level mesh, as shown in Fig. 4. As mentioned before, this mesh is represented as a multilevel mesh inside Serpent2, and as an unstructured mesh for feedback and interpolation. 3.3. SUBCHANFLOW models Due to the fact that the SUBCHANFLOW geometry is given as a set of channels and rods with prescribed hydraulic parameters, no changes to the code have to be made to model VVER reactors. Instead, the subchannel-level hexagonal models are built with the same preprocessor used to construct the feedback meshes.
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Fig. 4. Serpent2 mesh.
Fig. 6. SUBCHANFLOW fuel-centered model.
Fig. 5. SUBCHANFLOW coolant-centered model.
Two types of VVER subchannel models can be used in SUBCHANFLOW, namely coolant- and fuel-centered. Both models for the VVER test case are shown in Figs. 5 and 6. It is important to note that the exact shape of the subchannels is not represented in SUBCHANFLOW, which only considers their hydraulic parameters. The standard approach in subchannel analysis is to use coolantcentered channels (Moorthi et al., 2018), as they represent the physical subchannels defined by the rods and are clear from the physical point of view, in particular to model the cross-flow between subchannels. Fuel-centered subchannels are not as clear from the physical point of view, and an ad hoc method to calculate the cross-flow parameters has been formulated (García et al., 2019). This new approach has been analyzed in detail in SUBCHANFLOW standalone simulations and it was concluded that the differences in the results from the thermalhydraulic point of view, in particular for VVER reactors but also for PWR cases, are not significant considering the general accuracy of subchannel codes (García
et al., 2019). The impact on the neutronic simulation has not been studied until now however, and a quantification of the potential differences is needed to asses the use of these models in highfidelity neutronics. This is done in Section 4.2. The motivation for the use of fuel-centered subchannels in multiphysics simulations is the fact that the mapping to the neutronic model is straight forward, since subchannels and rods in the thermalhydraulic calculation are mapped one-to-one to pins in the neutronics. This is also the case for couplings involving a fuelperformance code, since the coolant boundary conditions for each pin can be readily obtained. Regarding the structural parts in the active length of the core, both spacer grids and stiffeners can be simulated. Spacer grids are accounted for as local pressure drops with a fixed loss coefficient, in this case 1.0. Stiffeners can be included as part of the hydraulic model, as shown in Fig. 7. The stiffener plates have two effects in the subchannel model: an increase in the wetted perimeter and therefore in the friction at the channels in contact with it, and the elimination of the cross-flow between channels in the corners in models with more than one fuel assembly. The impact of modelling the stiffeners is analyzed in Section 4.3. As previously stated, the exchange of feedback fields is done superimposing two unstructured meshes to the SUBCHANFLOW model, one to define the shape of the subchannels and another one to give the rod structure. The subchannel mesh for the coolant-centered model is shown in Fig. 8, where it can be seen that the cells have the shapes shown in Fig. 5. The fuel mesh, which is identical for the coolant- and fuel-centered models, is shown in Fig. 9, where it is clear that the actual shape of the rods is not considered, but rather cells containing the rods are defined. The rod geometry is considered through the flow area and the hydraulic and heated perimeters that define the subchannels used for the flow calculation, as well as in the heat-conduction solver for the fuel. The fuel variables are represented as scalars in this cells, and in particular the fuel temperature, for which a radial profile
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is calculated, is condensed into an effective Doppler temperature for each cell. This radial average is calculated using either a volume average or an empirical formula of the form T Doppler ¼ wT s þ ð1 wÞT c using the fuel surface and centerline temperatures T s and T c and a weight w, for which several models exist (Grandi et al., 2010). 4. Results
Fig. 7. SUBCHANFLOW coolant-centered model with stiffeners.
This section presents the results obtained with Serpent2SUBCHANFLOW for the selected test case, as well as an analysis of the impact of the SUBCHANFLOW modelling approach in the overall solution. In particular, the choice of coolant- or fuelcentered subchannels and the explicit modelling of the stiffener plates is discussed in Sections 4.2 and 4.3 respectively. All simulations were performed using 2000 active cycles with 1.105 particles per cycle for each Monte Carlo iteration. This results in a local statistical uncertainty lower than 1% in the power distribution. The fission source for the first iteration was calculated with 250 inactive cycles and corrected with 50 inactive cycles in each subsequent iteration. For the convergence of the iterative coupled solution the stochastic approximation method (Dufek et al., 2006), a type of relaxation, is used. Since the Monte Carlo statistical uncertainty in the power distribution is affected by the relaxation, the uncertainty from the last iteration is taken as an upper boundary of the error. The convergence criteria for the iterative solution over the multiplication factor keff , the coolant density qcool , the fuel temperature T fuel and the power P are:
keff : 10 pcm.
qcool : 0.1% in L1 norm. T fuel : 0.1% in L1 norm. P: 0.5% in L1 norm.
With these calculation parameters, the average running time per iteration was 1.1 h, in a 48-core node with Intel(R) Xeon(R) E5-2697 v2 (2.70 GHz) processors. Each simulation required 9 iterations to reach a converged solution. Most of the running time was spent on the Monte Carlo solution, as the SUBCHANFLOW calculations and the feedback exchange, including interpolation, consumed less than 0.01% of the total computing time. For the comparison of local axial profiles, the subchannels and rods shown in Fig. 10 are considered. Fig. 8. SUBCHANFLOW mesh for the subchannels.
Fig. 9. SUBCHANFLOW mesh for the fuel rods.
Fig. 10. Subchannels and rods for comparison.
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~ ~ Absolute differences dabs x ðrÞ at position r for variable x are calculated as
~ ~ ~ dabs x ðrÞ ¼ xSCFCC ðrÞ xðrÞ;
ð3Þ
where xSCFCC ð~ rÞ is the value calculated with the coolant-centered SUBCHANFLOW model and xð~ rÞ is the value for either the fuelcentered model or considering the stiffeners. Relative differences ~ drel x ðrÞ are defined as
~ drel x ðrÞ ¼
~ dabs x ðrÞ : xSCFCC ð~ rÞ
ð4Þ
4.1. Serpent2-SUBCHANFLOW Figs. 11 and 12 show the coolant temperature and power distributions obtained with Serpent2-SUBCHANFLOW with coolantcentered subchannels. A decrease in power is observed in the zones with spacer grids, as well as in the pins with burnable poison. The multiplication factor keff is 1.132000.00004. This solution is taken as reference to compare other models. 4.2. Subchannel types This section presents the results obtained with fuel-centered subchannels and their differences with respect to the coolantcentered model. To make this comparison, the results for the coolant are interpolated to the mesh with coolant-centered subchannels using the capabilities of the MEDCoupling library. Table 1 shows the maximum and average differences in the results using a fuel-centered model with respect with the Fig. 12. Power for the coolant-centered SUBCHANFLOW model.
Table 1 Global differences between SUBCHANFLOW models. Variable
qcool
kg m3
T cool (K) T fuel (K) P (W)
Fig. 11. Coolant temperature for the coolant-centered SUBCHANFLOW model.
Max. diff., abs. (rel.)
Av. diff., abs. (rel.)
10.69 (1.54%)
1.96 (0.28%)
4.33 (0.74%) 3.75 (0.42%) 14.34 (1.62%)
0.83 (0.14%) 0.78 (0.09%) 2.38 (0.23%)
coolant-centered ones. The deviation in the results for the coolant is clearly negligible considering the general accuracy of subchannel methods. The maximum relative difference in the power is 1.62%, which is noticeable but within the range of accuracy of highfidelity Monte Carlo simulations (García et al., 2019), while the average difference is quite small. The multiplication factor is 1.132030.00004, equivalent to the reference simulation within the statistical accuracy. Fig. 13 shows the differences in the coolant temperature for the whole fuel assembly. The largest differences are located in the edges, where the temperature calculated with the fuel-centered model is larger than for the coolant-centered model. This is due to the fact that in the coolant-centered model the additional coolant flow area around the fuel-assembly contributes to the edge subchannels, that hence have a larger mass flux resulting in lower heat-up. In the fuel-centered model, the relative increase of flow area near the assembly boundary is less pronounced, and therefore the effect is not as strong (García et al., 2019). Relatively large differences in the coolant temperature are also located around the fuel rods with burnable poisons. The reason for this is that fuel-centered models tend to reduce the diffusion of the
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Fig. 14. Coolant temperature in the subchannel with the largest differences (1 in Figure 10).
Fig. 13. Differences in the coolant temperature between SUBCHANFLOW models.
power in the coolant compared to coolant-centered subchannels, producing stronger hot and cold spots in the coolant. This is a known issue in fuel-centered models, and is due to the fact that each rod is associated to a single subchannel, so a higher or lower power in the rod is translated directly to a higher subchannel temperature and only convective and turbulent cross-flow allow for heat diffusion. In coolant-centered models each rod is linked to more than one subchannel (5 or 6 in this VVER case) and each subchannel receives power from more than one rod, which results in much stronger mixing, which is generally considered more realistic. In this case this effect produces lower coolant temperatures around the fuel rods with burnable poisons for the fuel-centered subchannels. This is more significant in the three rods located near the center of the assembly, and less pronounced in the six rods in the periphery, likely due to the combined effect of the edge subchannels. The coolant temperature for the subchannel with the largest differences (1 in Fig. 10) is shown in Fig. 14. The maximum difference between models is reached near the top of the active length. Fig. 15 shows the differences in the radial power distribution for the fuel assembly, integrated axially. In addition to the differences due to the stochastic nature of the result, a shift of the power towards the center is clearly observed and can be attributed to the heating of the edge subchannels. The differences are below 0.2% everywhere however, and the effect does not seem to be significant. Figs. 16 and 17 show the axial power profile for the fuel assembly and for the pin with the largest differences (A in Fig. 10), respectively. A slight shift of the power towards the bottom is observed for the fuel-centered subchannels, but here again the effect is essentially negligible.
Fig. 15. Differences in the integrated pin power distribution between SUBCHANFLOW models.
Fig. 16. Axial power profile integrated pin-wise.
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To summarize, this results show that fuel-centered subchannel models can be used in Serpent2-SUBCHANFLOW without a significant impact on the solution. For analyses focused on the regions with larger deviations, i. e. close to the edges, the differences quantified here should be taken into account.
4.3. Stiffener plates
Fig. 17. Power in the pin with the largest differences (A in Fig. 10). The statistical uncertainty is lower than 1% for all points.
This section analyses the effect of including stiffeners in the SUBCHANFLOW model. The global differences in the results comparing coolantcentered models with and without stiffeners are shown in Table 2. The deviations are of the same order as the ones observed when using fuel-centered subchannels. The multiplication factor is 1.13198 ± 0.00004, again within the statistical range of the reference solution. As can be seen in Fig. 18, the differences in the coolant temperature due to the stiffeners are concentrated in the corners of the fuel assembly. The increase in the loss of pressure due to the
Table 2 Global differences due to the stiffeners. Variable
qcool
kg m3
T cool (K) T fuel (K) P (W)
Max. diff., abs. (rel.)
Av. diff., abs. (rel.)
3.69 (0.52%)
0.37 (0.05%)
1.64 (0.28%) 3.34 (0.36%) 16.34 (1.97%)
0.16 (0.03%) 0.67 (0.08%) 2.76 (0.25%)
Fig. 19. Coolant temperature in the subchannel with the largest differences (2 in Figure 10).
Fig. 18. Differences in the coolant temperature due to the stiffeners.
Fig. 20. Differences in the integrated pin power distribution due to the stiffeners.
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greater friction leads to less coolant flow and hence to a larger heat up in the subchannels near the stiffeners. In turn, some subchannels near the edges get cooled down due to the cross flow coming from the corners. The coolant temperature for a corner subchannel (2 in Fig. 10) is shown in Fig. 19. The differences in the axially integrated radial power distribution for the fuel assembly are shown in Fig. 20. A shift of the power away from the corners can be observed, its magnitude (less than 0.15% for all pins) is clearly negligible. To conclude, the explicit modelling of stiffeners in the thermalhydraulic model is largely irrelevant, except when focusing on the subchannels in the direct vicinity of the plates.
Acknowledgments
5. Conclusions
CEA/DEN, EDF R&D, OPEN CASCADE, SALOME Platform Documentation: Documentation of the Interface for Code Coupling (ICoCo), https://docs. salome-platform.org/latest/extra/Interface_for_Code_Coupling.pdf, accessed: 2019/04/26. CEA/DEN, EDF R&D, OPEN CASCADE, SALOME Platform Documentation: MEDCoupling User’s Guide, https://docs.salome-platform.org/7/dev/ MEDCoupling/index.html, accessed: 2019/04/26. Dufek, J. et al., 2006. Stochastic approximation for monte carlo calculation of steady-state conditions in thermal reactors. Nucl. Sci. Eng. Ferraro, D. et al., 2019. Serpent/SCF pin-level multiphysics solutions for the VERA Fuel Assembly benchmark. Ann. Nucl. Energy 128, 102–114. García, M., et. al. 2019. Advanced Modelling Capabilities for Pin-level Subchannel Analysis of PWR and VVER Reactors, submitted to the 18th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-18), Portland, Oregon, USA, August 18–23, 2019. M. García, et. al., 2019. Development of an Object-oriented Serpent2SUBCHANFLOW Coupling and Verification with Problem 6 of the VERA Core Physics Benchmark, submitted to the International Conference on Mathematics and Computational Methods applied to Nuclear Science and Engineering (M&C 2019), Portland, Oregon, USA, August 25-29, 2019. Grandi, G., et. al. 2010, Effect of CASMO-5 Cross-section Data and Doppler Temperature Definitions on LWR Reactivity Initiated Accidents. In: The International Congress on Advances in Nuclear Power Plants (ICAPP-2017), Pittsburgh, Pennsylvania, USA, May 9-14, 2010. HPMC – An FP7 Euratom Project, http://www.fp7-hpmc.eu, accessed: 2019/05/21. Imke, U. et al., 2012. Validation of the Subchannel Code SUBCHANFLOW using the NUPEC PWR Tests (PSBT). Sci. Technol. Nucl. Installations. Lassmann, K., 1992. TRANSURANUS: a fuel rod analysis code ready for use. J. Nucl. Mater. 188, 295–302. Leppänen, J. et al., 2015. The Serpent Monte Carlo code: Status, development and applications in 2013. Ann. Nucl. Energy 82, 142–150. Lötsch, T. et al., 2010. In: Corrections and Additions to the Proposal of a Benchmark for Core Burnup Calculations for a VVER-1000 Reactor, Proceedings of the Twentieth Symposium of Atomic Energy Research, Hungary, Kiadja and KFKI. Atomenergia Kutatointezet. Mercatali, L. et al. 2018. The EC McSAFE Project: High Performance Monte Carlo Methods for Safety Demonstration - Status and Perspectives, International Multi-Physics Validation Workshop, North Carolina State University, Raleigh, USA, June 14–15, 2018. Moorthi, A. et al., 2018. A review of sub-channel thermal hydraulic codes for nuclear reactor core and future directions. Nucl. Eng. Des. 332, 329–344. Nuresafe: NUclear REactor SAFEty simulation platform, http://www.nuresafe.eu, accessed: 2019/05/21. Valtavirta, V., 2017. Development and Applications of Multiphysics Capabilities in a Continuous Energy Monte Carlo Neutron Transport Code Ph.D. thesis. Aalto University, School of Science, Department of Applied Physics, Finland.
The main features of Serpent2-SUBCHANFLOW for the modelling of VVER reactors have been presented. The treatment of the geometry is based on nested regular meshes in Serpent2 and on pin-by-pin subchannel models in SUBCHANFLOW. In both cases, the exchange of feedback fields in multiphysics simulations is done using unstructured meshes from the MEDCoupling library, which features advanced interpolation methods and visualization capabilities. The use of fuel-centered subchannels in SUBCHANFLOW has been described and its impact on the overall solution analyzed and compared with a coolant-centered model for a VVER-1000 fuel assembly. Differences of the order of 4 K in the coolant temperature were observed for channels in the edges of the fuel assembly, resulting on a shift of less than 0.2% in the radial power distribution. It was concluded that fuel-centered models are in principle suitable for this type of high-fidelity simulations. It is important to note however, that for operating conditions that result in subcooled boiling or low margins to saturated boiling, the use of fuel-centered models is discouraged, as they tend to localize local power peaks, leading to large errors in the calculation of the void fraction, which can produce large effects on the neutronic calculation, in addition to numerical instability. The impact of modelling the stiffener plates in the thermalhydraulic calculation was quantified as well. In this case the effects are only seen in the subchannels in the immediate vicinity of the angles, where the temperature increases less than 2 K with respect to the solution without stiffeners. The impact on the power distribution is negligible. This work serves as a demonstration of the VVER modelling capabilities for steady state developed within the McSAFE project. Further work includes the application of Serpent2-SUBCHANFLOW to single-fuel-assembly pin-level-depletion and full-core steadystate problems, with the final objective of tackling full-core pinby-pin depletion. The final stage will be the validation of this tool using experimental data provided by industry partners. Declaration of Competing Interest The authors declare no conflict of interest.
This work was done within the McSAFE project which is receiving funding from the Euratom research and training programme 2014–2018 under grant agreement No 755097. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, athttps://doi.org/10.1016/j.anucene.2019. 106955. References
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Serpent2-SUBCHANFLOW pin-by-pin modelling capabilities for VVER geometries Manuel García a,⇑, Diego Ferraro a, Ville Valtavirta b, Riku Tuominen b, Uwe Imke a, Jaakko Leppänen b, Victor Sanchez-Espinoza a a b
Karlsruhe Institute of Technology, Institute of Neutron Physics and Reactor Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany VTT Technical Research Centre of Finland Ltd., Tietotie 3, Espoo FI-02044 VTT, Finland
a r t i c l e
i n f o
Article history: Received 24 May 2019 Received in revised form 19 July 2019 Accepted 22 July 2019
Keywords: Serpent2 SUBCHANFLOW VVER Multiphysics
a b s t r a c t In the framework of the EU Horizon 2020 McSAFE project, a Serpent2-SUBCHANFLOW coupling has been developed with the aim at performing large-scale pin-by-pin depletion and transient calculations in Light Water Reactors. While this tool is not tied to a specific type of geometry, a set of capabilities have been developed to generate the pin-level hexagonal models corresponding to VVER reactors. The handling of VVER geometries is based on the use of nested hexagonal regular meshes in Serpent2, pin-level subchannel models in SUBCHANFLOW and unstructured meshes for feedback exchange and interpolation. In this work, these features are explained in detail and illustrated in a VVER-1000 fuel assembly. For this test case, an in-depth analysis is made regarding the modelling considerations in SUBCHANFLOW and their impact on the neutronic solution. In particular, the use of coolant- and fuel-centered subchannels and the explicit modelling of stiffener plates is discussed. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Driven by the growing interest in high-fidelity reactor physics analysis in the nuclear industry, the EU Horizon 2020 McSAFE project (Mercatali et al., 2018) was set to develop multiphysics tools based on Monte Carlo neutron transport, subchannel thermalhydraulics and fuel-performance analysis. The final objective is to be able to tackle large-scale problems in PWR and VVER reactors, such as full-core pin-by-pin depletion and transient scenarios. McSAFE is a continuation of two lines of work investigated in previous European projects: HPMC (HPMC, 2019), devoted to highperformance Monte Carlo methods, and NURESAFE (Nuresafe, 2019), dealing with core-level multiphysics calculations. A central component of the McSAFE project is the development of a coupling scheme for Serpent2 (Leppänen et al., 2015), a Monte Carlo particle transport code, and SUBCHANFLOW (Imke et al., 2012), a subchannel analysis code, suitable for large-scale simulations in High Performance Computing (HPC) environments. This coupled tool is to be used in steady-state, depletion and transient calculations. In addition, the coupling of Serpent2SUBCHANFLOW with TRANSURANUS (Lassmann, 1992), a
⇑ Corresponding author. E-mail address: [email protected] (M. García). https://doi.org/10.1016/j.anucene.2019.106955 0306-4549/Ó 2019 Elsevier Ltd. All rights reserved.
fuel-performance code, and its application to depletion problems, is foreseen. In this context, a flexible Serpent2-SUBCHANFLOW coupling was developed (García et al., 2019) and its results verified for high-fidelity PWR calculations (Ferraro et al., 2019). This tool is based on an object-oriented design and on the exchange of feedback between codes using unstructured meshes. The coupling scheme is problem-independent and any reactor type that can be modelled with Serpent2 and SUBCHANFLOW can be simulated with the coupled system. The application of Serpent2SUBCHANFLOW to different LWR types is therefore a matter of building the corresponding models. The objective of this work is to show the capabilities developed in the McSAFE project for the simulation of VVER geometries in Serpent2-SUBCHANFLOW, which are presented in Section 3. Given that the geometry and modelling approach in Serpent2 is extremely flexible and VVER reactors can be readily simulated, the focus is put on the exchange and interpolation of feedback variables and on the SUBCHANFLOW models in the specific case of VVER cores. The feedback exchange is explained through Sections 2 and 3. Section 4 presents and discusses the results for different SUBCHANFLOW models and their impact on the Serpent2 calculation. The use of coolant- and fuel-centered subchannels is analyzed, as well as the modelling of stiffener plates, present in most modern VVER fuel-assembly designs.
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It is important to note that no comparison is made here with other tools or with experimental results, but the general modelling approach is shown and assessed. This is due to the fact that to the knowledge of the authors no proper high-quality benchmarks with pin-level solutions for VVER reactors are currently available in the literature. The validation of Serpent2-SUBCHANFLOW with VVER experimental data provided by industry partners is foreseen for subsequent stages of the McSAFE project. 2. Serpent2-SUBCHANFLOW coupling The Serpent2-SUBCHANFLOW coupling used in this work is based on an object-oriented methodology (García et al., 2019) in which both codes are restructured as solver classes that are then used in a supervisor program to perform the calculation. The exchange and interpolation of feedback fields is done using unstructured meshes superimposed to the geometry of each code. The traditional iterative scheme for neutronic-thermalhydraulic coupling is used. This methodology is described in detail in this section, starting with a brief description of each code with a focus on the aspects relevant to the coupling scheme.
Fig. 1. Object-oriented coupling.
libraries are then wrapped into C++ classes derived from a common base class, masking the particular language of each code and defining a uniform interface. This base class represents a generic code with multiphysics capabilities, and is defined by the Interface for Code Coupling (ICoCo) from the SALOME open-source platform (CEA/DEN, EDF R&D, OPEN CASCADE, 2019a). The iterative coupling scheme is then implemented in a C++ program that manages the calculation objects that represent both codes.
2.1. Serpent2
2.4. Feedback-field exchange
Serpent2 (Leppänen et al., 2015) is a continuous-energy Monte Carlo particle transport code. The problem geometry is most often modelled using the Constructive Solid Geometry (CSG) technique, which makes the definition of virtually any core geometry possible. Serpent2 also supports unstructured meshes and stereolithography- (STL) based geometries to build the model. All relevant components of a reactor core can be modelled explicitly virtually without restrictions. One key feature of Serpent2 for its use in multiphysics simulations is the ability to superimpose meshes to the geometry to define density and temperature distributions and to tally the power, without linking these distributions to the geometry used for particle tracking. Each mesh is specified in an interface file and is associated to one or more materials, for which the thermalhydraulic conditions are given. The transfer of feedback fields to and from Serpent2 is based on this capability (Valtavirta, 2017).
The exchange of feedback fields is done using the same format for both codes and relies on the MEDCoupling library from the SALOME platform (CEA/DEN, EDF R&D, OPEN CASCADE, 2019b). This library provides classes that represent unstructured meshes and fields defined on them, as well as advanced interpolation methods, and input and output capabilities. In Serpent2, each multiphysics interface represents a mesh superimposed to the geometry. In the work presented here, Serpent2 uses regular hexagonal meshes, while Cartesian meshes are used in the same way for PWR-type geometries. With the aim at full-core PWR and VVER models however, a newlydeveloped structure of nested regular meshes is being used. This method is based on filling the cells of a regular mesh with another regular mesh, to create a multilevel structure that works essentially in the same way as the universe-based CSG geometry, i. e. given a position the density and temperature can be found starting in the outermost mesh and going down nested levels. To exchange feedback fields and perform interpolation, this multi-level meshes are represented as unstructured meshes with the actual physical shape resulting from the nested meshes. This is clearly illustrated with an example in Section 3.2. Two meshes can be used in SUBCHANFLOW, one for the fuel and one for the coolant. The fuel mesh defines the rod structure and can be used to extract fuel variables such as temperature, claddingcoolant heat transfer coefficient and Departure from Nucleate Boiling Ratio (DNBR) and to input a power distribution. The coolant mesh gives the shape of the subchannels and can be used to get coolant variables, e. g. temperature, density and pressure. Given that neither Serpent2 nor SUBCHANFLOW use meshes for their internal calculation schemes and that in both cases building a mesh from the geometrical model is not straight forward, the meshes are built with a preprocessor and given to the codes as part of the input. The feedback exchange for all fields works in the exact same way, and can be summarized as:
2.2. Subchanflow SUBCHANFLOW (Imke et al., 2012) is a subchannel-level thermalhydraulic code for steady-state and transient analysis of Light Water Reactors. The flow solver consists of three conservation equations in the axial direction, namely for mass, energy and momentum, plus a simplified model for cross-flow based on momentum conservation in the lateral direction. The geometry is defined as a set of channels and rods with given hydraulic parameters and connectivities in a flexible manner, i. e. without assuming a particular geometry type such as square or hexagonal. As in the case of Serpent2, meshes can be superimposed to the geometry to exchange coolant and fuel feedback fields. These meshes are not used in the internal calculation at all, but only to define the exact shape of the subchannels and the rod structure, which can’t be inferred from the model used in the calculation. This is further explained with an example in Section 3.3. 2.3. Object-oriented coupling The object-oriented coupling approach is depicted in Fig. 1. Both codes are first restructured as libraries which provide the features needed to implement a multiphysics scheme, i. e. initialization, calculation, feedback exchange and termination. These
1. Get the field from the code that calculated it with its associated mesh. 2. Get a template of the field in the second code with its associated mesh. 3. Interpolate the field from the source mesh to the target mesh.
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4. Set the interpolated field to the second code. In this scheme the classes that define the fields and meshes, as well as the interpolation methods, are provided by the MEDCoupling library. 2.5. Iterative scheme The multiphysics scheme used for the Serpent2SUBCHANFLOW coupling is the traditional Picard iteration method. The pin power calculated by Serpent2 is used in SUBCHANFLOW, which in turn calculates the subchannel-level thermalhydraulic state to feedback the neutronics. The evaluation of the convergence is based on the error in L2 or L1 norm between iterations for the feedback fields and on the change in the multiplication factor, with the exact criteria defined by the user. For iteration k, the convergence norms for a field v k with N discrete values fv ki g are defined as
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P k k1 2 Þ i ðv i v i Lk2 ¼ N jg: Lk1 ¼ maxfjv ki v k1 i i
ð1Þ ð2Þ
Fig. 2. Serpent2 model for sections without spacers.
3. VVER modelling capabilities This section describes the Serpent2-SUBCHANFLOW modelling capabilities specific to VVER reactors. A VVER-1000 fuel assembly is used to show these capabilities and to evaluate different modelling decisions. Given that no reference solutions are available for this problem, comparisons are made between different modelling approaches. 3.1. Test problem The VVER case considered is the 30AV5 fuel-assembly type from the TVSA benchmark for VVER core burnup calculations (Lötsch et al., 2010). It consists of a VVER-1000 fuel assembly at Beginning of Life (BOL) and Hot Full Power (HFP). The geometry is comprised of 303 regular fuel pins (UO2 with 2.99% weight enrichment), 9 fuel pins with burnable poison (UO2 with 2.4% weight enrichment, 5% Gd2O3 mass fraction), both with a central hole, 18 guide tubes and a single instrumentation tube. The fuel assembly has 15 spacer grids, 13 of them within the active length of the core, and stiffening angle plates. This problem represents a typical VVER geometry, and illustrates the relevant modelling features. The Serpent2 and SUBCHANFLOW models for this fuel assembly are described in the following sections.
Fig. 3. Serpent2 model for sections with spacers.
3.2. Serpent2 models As mentioned before, the CSG methodology used in Serpent2 allows for the explicit modelling of any component of the reactor. In this case, the active length consists of two types of sections, namely with and without grid spacers, which are shown in Figs. 2 and 3. The spacers are simulated in such a way as to maintain their mass and volume, and the stiffeners in the corners are modelled explicitly. In addition, three reflector layers are included in the top and in the bottom of the fuel assembly, as described in the benchmark definition. Reflective boundary conditions are used in all directions except axially, where vacuum conditions are used. The thermalhydraulic state for this case is given in a superimposed mesh that consists on a regular y-type hexagonal pin-level
mesh inside an x-type fuel-assembly-level mesh, as shown in Fig. 4. As mentioned before, this mesh is represented as a multilevel mesh inside Serpent2, and as an unstructured mesh for feedback and interpolation. 3.3. SUBCHANFLOW models Due to the fact that the SUBCHANFLOW geometry is given as a set of channels and rods with prescribed hydraulic parameters, no changes to the code have to be made to model VVER reactors. Instead, the subchannel-level hexagonal models are built with the same preprocessor used to construct the feedback meshes.
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Fig. 4. Serpent2 mesh.
Fig. 6. SUBCHANFLOW fuel-centered model.
Fig. 5. SUBCHANFLOW coolant-centered model.
Two types of VVER subchannel models can be used in SUBCHANFLOW, namely coolant- and fuel-centered. Both models for the VVER test case are shown in Figs. 5 and 6. It is important to note that the exact shape of the subchannels is not represented in SUBCHANFLOW, which only considers their hydraulic parameters. The standard approach in subchannel analysis is to use coolantcentered channels (Moorthi et al., 2018), as they represent the physical subchannels defined by the rods and are clear from the physical point of view, in particular to model the cross-flow between subchannels. Fuel-centered subchannels are not as clear from the physical point of view, and an ad hoc method to calculate the cross-flow parameters has been formulated (García et al., 2019). This new approach has been analyzed in detail in SUBCHANFLOW standalone simulations and it was concluded that the differences in the results from the thermalhydraulic point of view, in particular for VVER reactors but also for PWR cases, are not significant considering the general accuracy of subchannel codes (García
et al., 2019). The impact on the neutronic simulation has not been studied until now however, and a quantification of the potential differences is needed to asses the use of these models in highfidelity neutronics. This is done in Section 4.2. The motivation for the use of fuel-centered subchannels in multiphysics simulations is the fact that the mapping to the neutronic model is straight forward, since subchannels and rods in the thermalhydraulic calculation are mapped one-to-one to pins in the neutronics. This is also the case for couplings involving a fuelperformance code, since the coolant boundary conditions for each pin can be readily obtained. Regarding the structural parts in the active length of the core, both spacer grids and stiffeners can be simulated. Spacer grids are accounted for as local pressure drops with a fixed loss coefficient, in this case 1.0. Stiffeners can be included as part of the hydraulic model, as shown in Fig. 7. The stiffener plates have two effects in the subchannel model: an increase in the wetted perimeter and therefore in the friction at the channels in contact with it, and the elimination of the cross-flow between channels in the corners in models with more than one fuel assembly. The impact of modelling the stiffeners is analyzed in Section 4.3. As previously stated, the exchange of feedback fields is done superimposing two unstructured meshes to the SUBCHANFLOW model, one to define the shape of the subchannels and another one to give the rod structure. The subchannel mesh for the coolant-centered model is shown in Fig. 8, where it can be seen that the cells have the shapes shown in Fig. 5. The fuel mesh, which is identical for the coolant- and fuel-centered models, is shown in Fig. 9, where it is clear that the actual shape of the rods is not considered, but rather cells containing the rods are defined. The rod geometry is considered through the flow area and the hydraulic and heated perimeters that define the subchannels used for the flow calculation, as well as in the heat-conduction solver for the fuel. The fuel variables are represented as scalars in this cells, and in particular the fuel temperature, for which a radial profile
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is calculated, is condensed into an effective Doppler temperature for each cell. This radial average is calculated using either a volume average or an empirical formula of the form T Doppler ¼ wT s þ ð1 wÞT c using the fuel surface and centerline temperatures T s and T c and a weight w, for which several models exist (Grandi et al., 2010). 4. Results
Fig. 7. SUBCHANFLOW coolant-centered model with stiffeners.
This section presents the results obtained with Serpent2SUBCHANFLOW for the selected test case, as well as an analysis of the impact of the SUBCHANFLOW modelling approach in the overall solution. In particular, the choice of coolant- or fuelcentered subchannels and the explicit modelling of the stiffener plates is discussed in Sections 4.2 and 4.3 respectively. All simulations were performed using 2000 active cycles with 1.105 particles per cycle for each Monte Carlo iteration. This results in a local statistical uncertainty lower than 1% in the power distribution. The fission source for the first iteration was calculated with 250 inactive cycles and corrected with 50 inactive cycles in each subsequent iteration. For the convergence of the iterative coupled solution the stochastic approximation method (Dufek et al., 2006), a type of relaxation, is used. Since the Monte Carlo statistical uncertainty in the power distribution is affected by the relaxation, the uncertainty from the last iteration is taken as an upper boundary of the error. The convergence criteria for the iterative solution over the multiplication factor keff , the coolant density qcool , the fuel temperature T fuel and the power P are:
keff : 10 pcm.
qcool : 0.1% in L1 norm. T fuel : 0.1% in L1 norm. P: 0.5% in L1 norm.
With these calculation parameters, the average running time per iteration was 1.1 h, in a 48-core node with Intel(R) Xeon(R) E5-2697 v2 (2.70 GHz) processors. Each simulation required 9 iterations to reach a converged solution. Most of the running time was spent on the Monte Carlo solution, as the SUBCHANFLOW calculations and the feedback exchange, including interpolation, consumed less than 0.01% of the total computing time. For the comparison of local axial profiles, the subchannels and rods shown in Fig. 10 are considered. Fig. 8. SUBCHANFLOW mesh for the subchannels.
Fig. 9. SUBCHANFLOW mesh for the fuel rods.
Fig. 10. Subchannels and rods for comparison.
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~ ~ Absolute differences dabs x ðrÞ at position r for variable x are calculated as
~ ~ ~ dabs x ðrÞ ¼ xSCFCC ðrÞ xðrÞ;
ð3Þ
where xSCFCC ð~ rÞ is the value calculated with the coolant-centered SUBCHANFLOW model and xð~ rÞ is the value for either the fuelcentered model or considering the stiffeners. Relative differences ~ drel x ðrÞ are defined as
~ drel x ðrÞ ¼
~ dabs x ðrÞ : xSCFCC ð~ rÞ
ð4Þ
4.1. Serpent2-SUBCHANFLOW Figs. 11 and 12 show the coolant temperature and power distributions obtained with Serpent2-SUBCHANFLOW with coolantcentered subchannels. A decrease in power is observed in the zones with spacer grids, as well as in the pins with burnable poison. The multiplication factor keff is 1.132000.00004. This solution is taken as reference to compare other models. 4.2. Subchannel types This section presents the results obtained with fuel-centered subchannels and their differences with respect to the coolantcentered model. To make this comparison, the results for the coolant are interpolated to the mesh with coolant-centered subchannels using the capabilities of the MEDCoupling library. Table 1 shows the maximum and average differences in the results using a fuel-centered model with respect with the Fig. 12. Power for the coolant-centered SUBCHANFLOW model.
Table 1 Global differences between SUBCHANFLOW models. Variable
qcool
kg m3
T cool (K) T fuel (K) P (W)
Fig. 11. Coolant temperature for the coolant-centered SUBCHANFLOW model.
Max. diff., abs. (rel.)
Av. diff., abs. (rel.)
10.69 (1.54%)
1.96 (0.28%)
4.33 (0.74%) 3.75 (0.42%) 14.34 (1.62%)
0.83 (0.14%) 0.78 (0.09%) 2.38 (0.23%)
coolant-centered ones. The deviation in the results for the coolant is clearly negligible considering the general accuracy of subchannel methods. The maximum relative difference in the power is 1.62%, which is noticeable but within the range of accuracy of highfidelity Monte Carlo simulations (García et al., 2019), while the average difference is quite small. The multiplication factor is 1.132030.00004, equivalent to the reference simulation within the statistical accuracy. Fig. 13 shows the differences in the coolant temperature for the whole fuel assembly. The largest differences are located in the edges, where the temperature calculated with the fuel-centered model is larger than for the coolant-centered model. This is due to the fact that in the coolant-centered model the additional coolant flow area around the fuel-assembly contributes to the edge subchannels, that hence have a larger mass flux resulting in lower heat-up. In the fuel-centered model, the relative increase of flow area near the assembly boundary is less pronounced, and therefore the effect is not as strong (García et al., 2019). Relatively large differences in the coolant temperature are also located around the fuel rods with burnable poisons. The reason for this is that fuel-centered models tend to reduce the diffusion of the
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Fig. 14. Coolant temperature in the subchannel with the largest differences (1 in Figure 10).
Fig. 13. Differences in the coolant temperature between SUBCHANFLOW models.
power in the coolant compared to coolant-centered subchannels, producing stronger hot and cold spots in the coolant. This is a known issue in fuel-centered models, and is due to the fact that each rod is associated to a single subchannel, so a higher or lower power in the rod is translated directly to a higher subchannel temperature and only convective and turbulent cross-flow allow for heat diffusion. In coolant-centered models each rod is linked to more than one subchannel (5 or 6 in this VVER case) and each subchannel receives power from more than one rod, which results in much stronger mixing, which is generally considered more realistic. In this case this effect produces lower coolant temperatures around the fuel rods with burnable poisons for the fuel-centered subchannels. This is more significant in the three rods located near the center of the assembly, and less pronounced in the six rods in the periphery, likely due to the combined effect of the edge subchannels. The coolant temperature for the subchannel with the largest differences (1 in Fig. 10) is shown in Fig. 14. The maximum difference between models is reached near the top of the active length. Fig. 15 shows the differences in the radial power distribution for the fuel assembly, integrated axially. In addition to the differences due to the stochastic nature of the result, a shift of the power towards the center is clearly observed and can be attributed to the heating of the edge subchannels. The differences are below 0.2% everywhere however, and the effect does not seem to be significant. Figs. 16 and 17 show the axial power profile for the fuel assembly and for the pin with the largest differences (A in Fig. 10), respectively. A slight shift of the power towards the bottom is observed for the fuel-centered subchannels, but here again the effect is essentially negligible.
Fig. 15. Differences in the integrated pin power distribution between SUBCHANFLOW models.
Fig. 16. Axial power profile integrated pin-wise.
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To summarize, this results show that fuel-centered subchannel models can be used in Serpent2-SUBCHANFLOW without a significant impact on the solution. For analyses focused on the regions with larger deviations, i. e. close to the edges, the differences quantified here should be taken into account.
4.3. Stiffener plates
Fig. 17. Power in the pin with the largest differences (A in Fig. 10). The statistical uncertainty is lower than 1% for all points.
This section analyses the effect of including stiffeners in the SUBCHANFLOW model. The global differences in the results comparing coolantcentered models with and without stiffeners are shown in Table 2. The deviations are of the same order as the ones observed when using fuel-centered subchannels. The multiplication factor is 1.13198 ± 0.00004, again within the statistical range of the reference solution. As can be seen in Fig. 18, the differences in the coolant temperature due to the stiffeners are concentrated in the corners of the fuel assembly. The increase in the loss of pressure due to the
Table 2 Global differences due to the stiffeners. Variable
qcool
kg m3
T cool (K) T fuel (K) P (W)
Max. diff., abs. (rel.)
Av. diff., abs. (rel.)
3.69 (0.52%)
0.37 (0.05%)
1.64 (0.28%) 3.34 (0.36%) 16.34 (1.97%)
0.16 (0.03%) 0.67 (0.08%) 2.76 (0.25%)
Fig. 19. Coolant temperature in the subchannel with the largest differences (2 in Figure 10).
Fig. 18. Differences in the coolant temperature due to the stiffeners.
Fig. 20. Differences in the integrated pin power distribution due to the stiffeners.
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greater friction leads to less coolant flow and hence to a larger heat up in the subchannels near the stiffeners. In turn, some subchannels near the edges get cooled down due to the cross flow coming from the corners. The coolant temperature for a corner subchannel (2 in Fig. 10) is shown in Fig. 19. The differences in the axially integrated radial power distribution for the fuel assembly are shown in Fig. 20. A shift of the power away from the corners can be observed, its magnitude (less than 0.15% for all pins) is clearly negligible. To conclude, the explicit modelling of stiffeners in the thermalhydraulic model is largely irrelevant, except when focusing on the subchannels in the direct vicinity of the plates.
Acknowledgments
5. Conclusions
CEA/DEN, EDF R&D, OPEN CASCADE, SALOME Platform Documentation: Documentation of the Interface for Code Coupling (ICoCo), https://docs. salome-platform.org/latest/extra/Interface_for_Code_Coupling.pdf, accessed: 2019/04/26. CEA/DEN, EDF R&D, OPEN CASCADE, SALOME Platform Documentation: MEDCoupling User’s Guide, https://docs.salome-platform.org/7/dev/ MEDCoupling/index.html, accessed: 2019/04/26. Dufek, J. et al., 2006. Stochastic approximation for monte carlo calculation of steady-state conditions in thermal reactors. Nucl. Sci. Eng. Ferraro, D. et al., 2019. Serpent/SCF pin-level multiphysics solutions for the VERA Fuel Assembly benchmark. Ann. Nucl. Energy 128, 102–114. García, M., et. al. 2019. Advanced Modelling Capabilities for Pin-level Subchannel Analysis of PWR and VVER Reactors, submitted to the 18th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-18), Portland, Oregon, USA, August 18–23, 2019. M. García, et. al., 2019. Development of an Object-oriented Serpent2SUBCHANFLOW Coupling and Verification with Problem 6 of the VERA Core Physics Benchmark, submitted to the International Conference on Mathematics and Computational Methods applied to Nuclear Science and Engineering (M&C 2019), Portland, Oregon, USA, August 25-29, 2019. Grandi, G., et. al. 2010, Effect of CASMO-5 Cross-section Data and Doppler Temperature Definitions on LWR Reactivity Initiated Accidents. In: The International Congress on Advances in Nuclear Power Plants (ICAPP-2017), Pittsburgh, Pennsylvania, USA, May 9-14, 2010. HPMC – An FP7 Euratom Project, http://www.fp7-hpmc.eu, accessed: 2019/05/21. Imke, U. et al., 2012. Validation of the Subchannel Code SUBCHANFLOW using the NUPEC PWR Tests (PSBT). Sci. Technol. Nucl. Installations. Lassmann, K., 1992. TRANSURANUS: a fuel rod analysis code ready for use. J. Nucl. Mater. 188, 295–302. Leppänen, J. et al., 2015. The Serpent Monte Carlo code: Status, development and applications in 2013. Ann. Nucl. Energy 82, 142–150. Lötsch, T. et al., 2010. In: Corrections and Additions to the Proposal of a Benchmark for Core Burnup Calculations for a VVER-1000 Reactor, Proceedings of the Twentieth Symposium of Atomic Energy Research, Hungary, Kiadja and KFKI. Atomenergia Kutatointezet. Mercatali, L. et al. 2018. The EC McSAFE Project: High Performance Monte Carlo Methods for Safety Demonstration - Status and Perspectives, International Multi-Physics Validation Workshop, North Carolina State University, Raleigh, USA, June 14–15, 2018. Moorthi, A. et al., 2018. A review of sub-channel thermal hydraulic codes for nuclear reactor core and future directions. Nucl. Eng. Des. 332, 329–344. Nuresafe: NUclear REactor SAFEty simulation platform, http://www.nuresafe.eu, accessed: 2019/05/21. Valtavirta, V., 2017. Development and Applications of Multiphysics Capabilities in a Continuous Energy Monte Carlo Neutron Transport Code Ph.D. thesis. Aalto University, School of Science, Department of Applied Physics, Finland.
The main features of Serpent2-SUBCHANFLOW for the modelling of VVER reactors have been presented. The treatment of the geometry is based on nested regular meshes in Serpent2 and on pin-by-pin subchannel models in SUBCHANFLOW. In both cases, the exchange of feedback fields in multiphysics simulations is done using unstructured meshes from the MEDCoupling library, which features advanced interpolation methods and visualization capabilities. The use of fuel-centered subchannels in SUBCHANFLOW has been described and its impact on the overall solution analyzed and compared with a coolant-centered model for a VVER-1000 fuel assembly. Differences of the order of 4 K in the coolant temperature were observed for channels in the edges of the fuel assembly, resulting on a shift of less than 0.2% in the radial power distribution. It was concluded that fuel-centered models are in principle suitable for this type of high-fidelity simulations. It is important to note however, that for operating conditions that result in subcooled boiling or low margins to saturated boiling, the use of fuel-centered models is discouraged, as they tend to localize local power peaks, leading to large errors in the calculation of the void fraction, which can produce large effects on the neutronic calculation, in addition to numerical instability. The impact of modelling the stiffener plates in the thermalhydraulic calculation was quantified as well. In this case the effects are only seen in the subchannels in the immediate vicinity of the angles, where the temperature increases less than 2 K with respect to the solution without stiffeners. The impact on the power distribution is negligible. This work serves as a demonstration of the VVER modelling capabilities for steady state developed within the McSAFE project. Further work includes the application of Serpent2-SUBCHANFLOW to single-fuel-assembly pin-level-depletion and full-core steadystate problems, with the final objective of tackling full-core pinby-pin depletion. The final stage will be the validation of this tool using experimental data provided by industry partners. Declaration of Competing Interest The authors declare no conflict of interest.
This work was done within the McSAFE project which is receiving funding from the Euratom research and training programme 2014–2018 under grant agreement No 755097. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, athttps://doi.org/10.1016/j.anucene.2019. 106955. References