LWR MULTI-PHYSICS DEVELOPMENTS AND APPLICATIONS WITHIN THE FRAMEWORK OF THE NURESIM EUROPEAN PROJECT

Transcription

1 Supercomputing in Nuclear Applications (M&C + SNA 2007) Monterey, California, April 15-19, 2007, on CD-ROM, American Nuclear Society, LaGrange Park, IL (2007) LWR MULTI-PHYSICS DEVELOPMENTS AND APPLICATIONS WITHIN THE FRAMEWORK OF THE NURESIM EUROPEAN PROJECT O. Zerkak, P. Coddington Laboratory for Reactor Physics and Systems Behavior Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland omar.zerkak@psi.ch; paul.coddington@psi.ch N. Crouzet, E. Royer Département de Modélisation des Systèmes et des Structures (DM2S) Direction de l Energie Nucléaire (DEN) Commissariat à l Energie Atomique (CEA), Saclay, Gif sur Yvette, France nicolas.crouzet@cea.fr; eric.royer@cea.fr J. Jimenez, D. Cuervo Department of Nuclear Engineering Polytechnic University of Madrid, c/ José G. Abascal 2, Madrid, Spain jimenez@din.upm.es; d.cuervo@upm.es ABSTRACT The overall objective of the NURESIM Multi-Physics subproject (NURESIM-MP) activities is to integrate the simulation tools developed within the NURESIM Core Physics subproject (NURESIM-CP), with the simulation tools developed within the NURESIM Thermal-Hydraulics subproject (NURESIM-TH), to complete the European software platform and enable coupled neutron-kinetics/thermal-hydraulics transient simulations of operational and design basis accident conditions for existing LWR s (PWR, BWR, VVER). The first NURESIM-MP developments are described and the first, proof-of-principle, applications to multi-physics and multi-scale problems using the European codes CRONOS2, FLICA4 and COBAYA3 are presented and discussed. Thus, a coupled N/TH application using the CEA codes CRONOS2 and FLICA4 was developed using the advanced multi-physics functionalities of the SALOME software, on which the architecture of the European platform will be based. The coupling application includes a mesh-to-mesh interpolation tool that was developed in order to allow coupling N and TH solvers using non identical three-dimensional meshing schemes. A generic Application Programming Interface was also developed to allow for a flexible manipulation and coupling of different solvers, which is a prerequisite for the development of complex multi-physics calculation routes. The first exercise applies a N/TH coupling of CRONOS2 and FLICA4 inside the SALOME-based platform for the analysis of a test case derived from the NEA-OECD PWR MSLB Benchmark. The second exercise applies the COBAYA3 core 3D fine-mesh multi-group neutron diffusion solver using a domain decomposition method, which allows for an efficient parallel implementation in memory distributed multi-processors. Key Words: Numerical reactor simulation, multi-physics, neutronics, thermal-hydraulics, coupling. Corresponding author

2 O. Zerkak, P. Coddington, N. Crouzet, E. Royer, J. Jimenez, D. Cuervo 1. INTRODUCTION The European Project NURESIM (Numerical Reactor Simulation) [1], a project sponsored by the European Union which started in February 2005, includes a subproject Multi-Physics (NURESIM-MP) that aims at further developing dynamic coupling techniques for LWR simulations requiring the application of neutronics (N) and thermal-hydraulics (TH) solvers together. In the project, the development and the qualification of advanced N and TH solvers are carried out by the NURESIM Core Physics (NURESIM-CP) and NURESIM Thermal-Hydraulics (NURESIM-TH) subprojects, while the mission of NURESIM-MP is to develop and qualify the necessary functionalities and applications that allow for a consistent coupling of the solvers from the different disciplines, both in the space and time domains, inside one common simulation platform, whose architecture is supported by the SALOME software. This software is briefly described in the next chapter. In the context of the establishment of a common LWR simulation platform applying solvers from different disciplines and at different scales, one important task is to develop a set of functionalities allowing for a consistent and efficient communication between the different solvers that need to be coupled for one multi-physics analysis. In particular, when the solvers are derived from existing legacy codes, it is important to ensure a consistent relationship between the input data specified to the different codes. When the coupled simulation requires the development of a complex calculation scheme (in time and space), the different solvers need to be parameterized in the form of components that can be readily manipulated and, if necessary, interchanged. Also, when the solvers use different meshing schemes of the simulation domain, there is the need for establishing a consistent set of interpolation-averaging tools for the data transfer between the solvers. Some of the developments made in relation to these aspects and first verification of the tools, using the French codes CRONOS2 and FLICA4, are described in the third and fourth chapters. In respect to the more specific issue of the coupling of N and TH solvers at different scales, the steady-state or transient analysis of a complete LWR core at the cell-subchannel scale (pin-level) is still a challenge. In particular, the size of the coupled N/TH problems is so large when simulated at the pin-level that a robust convergence method would be very difficult to establish, and a multi-scale approach will certainly need to be considered as part of the solution method. The issue then consists in establishing a consistent relationship in the analysis between the assembly level and the pin level. In the framework of the NURESIM-MP subproject, this type of problem is being investigated using the new code COBAYA3, a core 3D fine-mesh multi-group neutron diffusion solver using a domain decomposition method, which allows for an efficient parallel implementation in memory distributed multi-processors. The characteristics and the first, proof of principle, applications of the code are presented in the last part of the paper. 2/22

3 LWR Multi-physics developments and applications within the framework of the NURESIM European Project 2. THE SALOME SOFTWARE SALOME is an open source software that provides a generic and modular platform for pre and post-processing for numerical simulation. It is based on an open and flexible architecture made of reusable components available as free software. Different types of computer programs, such as scientific computation codes for instance, can be integrated in the platform in order to build advanced computation applications (or other types of applications) taking advantage of all the native functionalities of the software. SALOME is composed of modules. The initial version of the platform includes 5 main modules (i.e. the native modules of the software), as indicated with the five different colors of the boxes described in Fig. 1. Theses modules propose the main general services that are needed in the context of scientific computation (in particular: pre-processing tools for CAD models development, meshing algorithms, modular model for the manipulation of physical properties assigned to geometrical elements, 2D and 3D graphical post-processing, functionalities for parallelization of applications, functionalities for creation and persistence of complex applications, functionalities for the development and the supervision of advanced calculation routes using different solvers) [2]. CAD Systems CAD Interface, CAD Modeling & Cleaning Meshing Properties Supervision Codes & Solvers Visualization Post- Processing Figure 1. Main functionalities of the SALOME software. One important characteristic of SALOME is that the data exchange between different scientific solvers and/or other types of applications (pre-processors, post-processors, etc.) is based on a common data exchange model called MED (French acronym for Modélisation et Échange de Données ). The MED structure is based on the notion of variable fields attached to a meshing. The MED data model defines in a logical and object-oriented manner the data structures exchanged by codes (Fig. 2). The modeled data concern meshes (structured and unstructured) and the associated fields (e.g. power, thermal-hydraulic temperatures and density, and fuel temperatures for the simulation of a LWR core) that can be defined on nodes, elements or Gauss points of meshes. MED supports eight element shapes: point, line, triangle, quadrangle, tetrahedron, pyramid, hexahedron, polygon and polyhedron. The data exchange can be operated through files or memory. A library of functions and procedures is also included (MED-library), so that a variety of operations can be 3/22

4 O. Zerkak, P. Coddington, N. Crouzet, E. Royer, J. Jimenez, D. Cuervo made, like for instance arithmetical operations with fields, search of extremum values (min/max) or localization of points within a meshed geometrical domain. The structure of MED includes all the prerequisite specifications for the development of consistent interpolation and averaging methods in the space domain. For instance, one can mention the possibility of affecting the values of a field at the Gauss points of a meshing scheme, which are important for the coupling of solvers using finite-element methods, as these points are necessary to calculate averaged values inside or at the interface of a mesh. In addition, a Python command language interpreter is included in SALOME, in order to allow piloting the execution of the different codes. Finally, one can recall the SUPERVISION module of SALOME, which allows using a GUI for the development of complex (multi-physics) calculation routes, while the possibility of using scripts (Python-based) is preserved through appropriate conversion tools.!! % #!" " # $ # Figure 2. Data exchange model (MED) of SALOME. 3. MULTI-PHYSICS DEVELOPMENTS IN THE NURESIM PLATFORM 3.1. Input data pre-processing The best solution to reduce the risk of inconsistencies during the input data preparation is certainly to derive automatically input data of the different solvers using the same source of information. The procedure should then consist in defining a pre-processing tool that would read the actual information from a common database and generate those parts of the input data files of 4/22

5 LWR Multi-physics developments and applications within the framework of the NURESIM European Project the N and TH solvers that need to match up. Therefore, one can envisage developing a more generic pre-processing tool using some of the SALOME features, and that could also be applied to all the N and TH solvers that would be integrated in the European platform. Such preprocessing implicitly assumes that a common data model could be defined for any type of code or solver to be integrated in the platform. This set of common information should include, as a minimum: The geometry (core layout, assembly layout, fuel pins, etc.), The material properties (heat conductivity, specific heat, viscosity, etc.), The initial conditions, The boundary conditions. One could also consider adding the assumptions associated to the physical closure laws or the numerics of the solvers for instance. But the specification of a common data model would then become extremely challenging, given the specificities of each type of code. The best solution would be to have an evolutive data model, based on an initial common model covering the main set of input information and could be then further supplemented with new types of data depending on the specific needs of each solver. The development of such an evolutive type of pre-processing tool can be envisaged in the NURESIM platform by using the XDATA module of SALOME, which allows parameterizing any set of data other than geometry or mesh-related information (referred as physical properties in the context of SALOME) that are associated to a numerical simulation. XDATA allows for the description of Python classes in order to integrate them in SALOME and to interact dynamically with the set of information through the GUI. As a preliminary step, a prototype of common data model has been developed using XDATA and has been interfaced with the French codes CRONOS2 and FLICA4 using Python, which is the scripting language of SALOME. The interfacing work consisted in writing the application that reads the data from the XDATA-based common data model and converts it into the input data format required for the two codes. Actually, the interface application has to be re-developed for each new code or solver to be integrated into SALOME. Once the interfacing work has been done, any new solver in the platform should be then able to consistently share input data with any other similar solver of the platform. The resulting tool consists of a GUI application including the set of common input information (i.e. the physical properties ) of CRONOS2 and FLICA4. The different data can be dynamically customized by the user inside the SALOME environment according to the specificity of the study. As illustrated in Fig. 3, the application has been successfully tested for the preparation of the steady-state input data files of CRONOS2 and FLICA4 corresponding to a case derived on the geometry and the specifications of the NEA-OECD PWR MSLB Benchmark [3]. 5/22

6 O. Zerkak, P. Coddington, N. Crouzet, E. Royer, J. Jimenez, D. Cuervo Figure 3. Common input data model for CRONOS2 and FLICA4 using XDATA. In particular, one can note that not only the geometry can be consistently modified with this tool, but also some parameters relevant to the parametric coupling, like for instance the Rowland coefficient that is used to determine the effective fuel temperature for the determination of the Doppler feedback, or the direct moderator heating fraction Mesh-to-mesh interpolation component The coupling of the geometry is an essential necessary step before the determination and the specification of the N and TH parameters to be exchanged by the two codes (parametric coupling). The geometry coupling consists in comparing the calculation domains and the meshing schemes associated to the N solver and the TH solver respectively, since the data to be exchanged should be consistent in space. Some TH codes are very flexible in terms of spatial meshing, thus allowing a description of the calculation domain combining fuel-assembly-sized channels with pin-sized sub-channels. The N diffusion codes presents less possibilities and it is in general recommended to apply the codes with an homogeneous meshing scheme (assembly-sized radial meshes or pin-sized radial meshes). As a consequence, the resulting meshing applied to the coupled N and TH codes are not necessarily the same, and one mesh of one code calculation domain can have an intersection with one or more meshes of the other code calculation domain. 6/22

7 LWR Multi-physics developments and applications within the framework of the NURESIM European Project Thus, the purpose of the geometry coupling is to identify for each mesh of one code calculation domain (the target mesh), the number of meshes in the other code calculation domain with a nonzero intersection volume (the source meshes). Then for this group of source meshes, one needs to calculate the corresponding intersection volumes with the target mesh and other additional information that will be necessary to compute the different source mesh contributions for the parametric coupling. In the NURESIM platform, the geometric coupling is to be made using a dedicated interpolation tool developed in SALOME. The interpolation tool has been integrated in SALOME as an individual component (INTERP_2_5D). The object of this component is to derive the data transfer weighting factors from the N meshing to the TH meshing, and vice-versa. The externalization of that functionality from the two codes to be coupled presents the substantial advantage of allowing a re-utilization of the tool for the coupling new codes and solvers that will be integrated in SALOME. The principle and the procedure followed by this interpolation tool are described below. Principle The basic idea is to exchange data fields associated with two different three-dimensional nonregular meshing schemes. The first meshing scheme is called the Source (S) and the second one is called the Target (T). Thus, one code/solver calculates the field on the meshing Source, while the other code/solver uses the field defined on the meshing Target as a boundary condition in order to proceed with the simulation. The distinction between the two codes in terms of Source and Target depends on the type of field to be transferred, and the two codes can be alternatively Source and Target during the calculation. A simple (two-dimensional) example of the coupling of two non-regular meshing schemes is showed in Fig. 4. Figure 4. Coupling and field projection between two overlapping meshing schemes. 7/22

8 O. Zerkak, P. Coddington, N. Crouzet, E. Royer, J. Jimenez, D. Cuervo One can see that the target mesh T_it (subscript it stands for i target ) has an intersection with many meshes of the meshing Source, precisely meshes S_1, S_2 and S_3 in the figure. The issue is then to ensure a consistent data transfer from the meshing Source to the meshing Target. In the case where the two codes use a finite-volume numerical method, the field quantity in one mesh is assumed to be homogenously distributed inside this mesh. A consistent transfer of the field on mesh T_it necessitates then to weight the contribution from the three source meshes in proportion with their respective intersection volume with mesh T_it, as illustrated in Fig. 4. Thus, based on the notations of the figure, assuming any field f calculated in the meshing Source, the consistent value in mesh T_it of the projected field should be: 3 n= 1 ( n) it f n V n= 1 F it = (1) 3 it V ( n) In order to perform this consistent interpolation of the field f, one should first determine the different intersections volumes (V) for all the meshes of two coupled meshing schemes. That actually is the main purpose of the interpolation component. Procedure The interpolation method is applicable to any three-dimensional meshing scheme that can be described as a 2D (radial) non-regular meshing scheme extruded in the third 1D (axial) direction. This type of meshing scheme extruded in one direction is sometimes referred as a 2.5D meshing scheme, as a specific subfamily of 3D meshing schemes. The Source and Target meshes need all to be convex (that is the case for the meshing schemes of LWR core simulations using homogenization methods). The interpolation is implemented using the MED structure of SALOME and takes advantage of the associated MED-library of procedures and tools, which allow for the use of a variety of elementary mesh shapes. The method consists first in decomposing the three-dimensional source and target meshing schemes into an axial one-dimensional part and a radial two-dimensional part. The two parts are obtained by projecting the meshing schemes on one axis and on the corresponding perpendicular radial plane as illustrated by the example in Fig. 5. When the axis coincides with the extrusion direction of the two meshing schemes (i.e. the vertical direction for a typical LWR core analysis), the intersection volume of one target mesh with one source mesh can be rewritten as the intersection area (A) of the axial projections of the two meshes, multiplied by the intersection length (L) of the radial projections of the two meshes: V t s t s t s ( mi m j ) = A( mi m j ) L( mi m j ), (2) x, y x, y The problem can then be decomposed in two separate parts, namely the determination of the axial intersection lengths and the determination of the radial intersection areas. z z 8/22

9 LWR Multi-physics developments and applications within the framework of the NURESIM European Project m s j z m t i z m s j x, y Figure 5. Axial and radial projections of the meshing schemes. In the axial direction, the operation consists in comparing the coordinates of the different pairs of intersecting meshes from the 1D projected meshing schemes and then deriving the different intersection lengths. The pairs of intersecting meshes can be directly identified by comparing the elevations of the respective bottom and top nodes of the two meshes. Thus, using notations consistent with Fig. 5, the axial intersection length between one target mesh i and the source mesh j can be expressed with the following equation: t s t t s s t s ( mi m j ) = min( zi + zi, z j + δz j ) max( zi z j ) L δ, (3) z z a) Triangulation On the radial plane, the projected meshes can be of different shapes, such as triangles, quadrangles, or any other types of polygons. In order to reduce the complexity of the problem, the two projected radial meshing schemes are first triangulated. Three different triangulation options were used, depending on the shape of the original mesh: triangle, quadrangle and polygon (with more than 4 edges). For a triangular mesh (axial projection of a 6-node pentahedral), the shape is kept as it is: 9/22

10 O. Zerkak, P. Coddington, N. Crouzet, E. Royer, J. Jimenez, D. Cuervo For a quadrangular mesh (axial projection of an 8-node hexahedral), the shape is divided into two triangles by connecting two non-consecutive nodes: For a polygon with more than 4 edges, an additional node is formed at the barycenter (center of mass) of the polygon, and the triangles are constructed by connecting the barycentric node to all the pairs of two consecutive nodes of the polygon: As a result of the triangulation, two new radial meshing schemes are formed only composed of triangles. b) Localization At this stage, the objective is to superimpose the two triangulated meshing schemes and to calculate the intersection area for all the pairs of intersecting Source and Target triangles. But a preliminary work is necessary in order to identify all the pairs of intersecting triangles of the two triangulated mesh schemes. Hence, for any selected triangle it in the triangulated meshing Target, the procedure is first to localize in the triangulated meshing Source one source triangle that has a non-zero intersection with triangle it and then to determine by a propagation algorithm all the other intersecting source triangles. Two methods for the localization of the first intersecting source triangle are applied. The first method consists in finding the source triangle that contains the barycenter Git of the target triangle it (Fig. 6). The search takes advantage of the MED-library, which includes a procedure to localize the mesh that encloses one given point. The procedure is based on a predecomposition of the three-dimensional meshing domain into a series of cubes, where each cube is sub-divided into 8 other cubes recursively. The resulting structure ( octree ) is then used for a dichotomic search. This procedure is computationally more efficient than a non-ordered list search procedure, since the size of the problem corresponding to the latter increases linearly with the number of meshes whereas the increase is logarithmic for the MED procedure. The second localization method is used as a second attempt when the first one is not successful. That is the case when the Source and the Target simulation domains do not fully overlap and the barycenter of some peripheral target triangles can then be partially or completely outside of the Source simulation domain. The second localization is also based on the MED-library search tools, and consists in finding the source nodes that are the closest to the barycenter Git or to the summits of the triangle it, and to localize the corresponding source triangles by connectivity. 10/22

11 LWR Multi-physics developments and applications within the framework of the NURESIM European Project!"# $ Figure 6. Localization method in the triangulated radial meshing schemes. c) Propagation Once the target triangle it has been localized inside the triangulated meshing scheme Source, all the source triangles that intersect with this triangle are found by a propagation algorithm starting form the first source triangle(s) already identified. The algorithm consists in iteratively generating layers of source triangles around the already identified group of triangles intersecting with triangle it. The propagation algorithm stops when the sum of all the calculated intersection areas equals the total area of triangle it, or when all the intersection area of a new layer are zero (the second test is necessary for cases when a target triangle is only partially included in the meshing scheme Source). d) Reconstruction As a result of the triangulation and the propagation procedures, the total area intersection between one target radial mesh and one source radial mesh can be reconstructed from the intersection areas (a) of the nt triangles obtained from the triangulation, and the ns sets of triangles identified with the localization and the propagation procedures: nt( i ) ns( it ) t s t s ( i m j ) = a[ triangle( it mi ) triangle( js, m j )] A m x, y x, y it= 1 js= 1, (4) x, y x, y 11/22

12 O. Zerkak, P. Coddington, N. Crouzet, E. Royer, J. Jimenez, D. Cuervo The total radial intersection areas are then multiplied by the corresponding axial intersection lengths, which are calculated with equation (3), in order to obtain the actual mesh-to-mesh intersection volumes of the two coupled mesh schemes. The localization and propagation procedure allows for a significant reduction of the number of source meshes to be tested for each target triangle. That was made possible through the use of the MED-library. This permitted to reduce the size of the problem and to achieve a time complexity of (n ln(n)) theoretically. Actually, a series of tests showed that the CPU time necessary to perform a complete search was increasing linearly with the size of the meshing scheme (verification made for up to 1'000'000 meshes) High-level API for the N and TH solvers A high-level Application Programming Interface (API) was developed for the coupling of N and TH solvers in the platform. The main advantage of a high-level API is to create a standardized layer between the user and the solvers, so that the part of the study that consists in defining and executing the calculation route can be performed by using the standard tools and features of SALOME, including the possibility of using the a GUI interface to develop graphically the chaining of the calculation (use of the SUPERVISION module). The API also offers the possibility of manipulating the solvers and their associated components using a common scripting language (Python), in order to allow a re-usability of the scripts to any other solver of the NURESIM platform that would be provided with the same (or a similar) API structure. In this way the specific command language of each solver can become completely transparent to the analyst through the use of the API, which could be very useful for nonadvanced users or beginners or when the application is to be used as a production tool. One can also note that different coupling operations associated with the independent interpolation tool (i.e. the component INTERP_2_5D) were also included in the API. The first task was to determine and categorize the different operational steps that are required to set up a calculation route and to execute the coupled calculation. As a starting point, only the solvers applying solution methods in the time domain were considered (in opposition to the frequency domain). The different elementary blocks that were identified for the N and TH components in the platform are given here: Initialization of the solvers: This includes starting the components inside the platform, by allocating the memory and specifying the location of the input and output directories in particular. Specification of the application: This includes the specification of the sets of input data files of the two solvers for the actual analysis to be performed (geometry, boundary conditions, XS libraries, etc.). Establishment of the coupling: 12/22

13 LWR Multi-physics developments and applications within the framework of the NURESIM European Project This includes the calculation of the interpolation/averaging coefficient between the simulation domains (meshing schemes) of the two solvers, and the specification of the coupled parameters (power, reactivity feedback parameters). Evaluation of the exchange parameters from the N to the TH and vice-versa: This consists in retrieving and when necessary processing the parameters calculated by the N solver (power) or the TH (reactivity feedback parameters). Establishment of the steady-state step: This consists of the establishment of a converged steady-state for the two solvers. This means that a virtual time-step is processed in order to reach a converged steady-state. Transient time step: This consists of the calculation with one solver of one transient time-step. These different elementary blocks were kept as generic as possible, in order to allow reusing the API for new N and TH solvers in the platform, but even solvers form new disciplines (TH system, Fuel mechanics, etc.). 4. COUPLED N/TH ANALYSIS IN SALOME USING CRONOS2 AND FLICA4 As a proof of principle of the operability of the different multi-physics functionalities developed for the platform, the two French codes CRONOS2 [4] and FLICA4 [5] were integrated in SALOME and used for a coupled N/TH steady-state and transient analysis of a PWR core. Actually, the integration consists first in creating an interface between the internal data model of a code and the MED format. The second part is to encapsulate the code inside SALOME as a solver component, in order to allow the solver using the different multi-physics applications (e.g. interpolation tool, High-level API) and dynamically exchanging information with other solvers in SALOME. The integration of the two codes took approximately 4-5 months of work in total. This time is given just as an indication, since it depends on the internal structure of the code. In order to verify the global coupling between the CRONOS2, FLICA4 and INTERP_2_5D components in the platform, simplified test cases were developed. The input geometry and the nodal neutronic XS libraries were derived from the exact specifications of the NEA-OECD PWR MSLB Benchmark [3]. The interpolation tool and the SUPERVISION module of SALOME were used to derive both the steady-state and transient calculation routes. First, the steady-state for initial conditions of the benchmark was computed, i.e. the conditions of the reactor at Hot Full Power with one control rod partially inserted. This test case demonstrated the correct convergence of the coupling (Fig. 7). 13/22

14 O. Zerkak, P. Coddington, N. Crouzet, E. Royer, J. Jimenez, D. Cuervo Figure 7. HZP steady-state calculated with CRONOS2 and FLICA4 in SALOME Figure 8. Radial power distribution after 1s of transient 14/22

15 LWR Multi-physics developments and applications within the framework of the NURESIM European Project Then, to verify the coupling for transient conditions, two scenarii were defined: i) a control rod insertion (neutronic perturbation) and ii) a core inlet cooling (TH perturbation). The latter case was the most interesting one, since it results in significant multi-dimensional effects. The core inlet boundary conditions were defined such as the cooling affects only a limited number of fuel assemblies (35 out of 177) located in one peripheral region of the core. In Fig. 8, one can see the calculated radial power distribution following the transitory decrease of the local core inlet water temperature. The overcooling reached 20% after 1s. One can also see in the top part of the figure, the transient calculation route of the analysis developed with the SUPERVISION module of SALOME, and where each box corresponds to one of the elementary blocks of the High-level API described in the previous chapter. 5. INVESTIGATIONS OF N/TH COUPLING AT THE PIN LEVEL Advanced multi-scale N/TH coupling schemes require a consistent exchange of neutronic and thermal-hydraulic data at both of the two scales: 1) at the nodal and channel scale for the whole core, and 2) at the fuel rods and sub-channels scale corresponding to the pin-cells fine-mesh diffusion calculations, for each 3D sub-domain of the whole core height. In the framework of the NURESIM-MP subproject, this type of problem is being investigated using the new code COBAYA3 code [6], which code is based on the successful performance of the previous UPM codes for PWR core simulation: COBAYA for 2D (X-Y), 2-group fine-mesh diffusion and SIMTRAN for 2-group diffusion in 3D rectangular geometry, coupled with a TH sub-channel code and a plant system code [7]. The UPM advanced schemes being implemented in COBAYA3 include: a Domain Decomposition by alternate core dissections for the local 3D fine-mesh problems (i.e. assemblies or color-sets), and the ANDES analytical nodal diffusion solver in 3-D and multi-groups [8, 9]. The ANDES nodal solver has been integrated into the DESCARTES code, within the NURESIM Core Physics subproject Domain decomposition and alternate core dissections Domain decomposition consists in the division of the whole 3D core domain in sub-domains, fuel assemblies or color-sets, where the N/TH problems can be solved in parallel. Initially the boundary conditions (BC) for each sub-domain, which are the current to flux ratios for the N and the energy and momentum transport terms due to turbulent and diversion cross-flows for the TH, are supplied by interpolation from a nodal solution of the whole domain. In order to converge quickly to the true detailed solution, avoiding the errors introduced by the interpolation or by the matching with the neighboring sub-domains, four different dissections for the domain decomposition are defined, where the sub-domains are characterized by the way they overlap each other. The more obvious ones are the fuel assemblies and the color-sets but also half of two different assemblies in two different directions can be used. Every kind of domains decomposition of the core is called an alternate core dissection. 15/22

16 O. Zerkak, P. Coddington, N. Crouzet, E. Royer, J. Jimenez, D. Cuervo After solving within each sub-domain, the N and TH variables distributions at the central planes become the detailed boundary conditions to the other alternate dissections, what reduces the error introduced by the approximate BC in just few iterations. Once the problems have converged to the desired tolerance, the detailed internal fields and BC at the central and borders planes are averaged and supplied to the nodal solution. The nodal-local iterations are alternated up to reaching the convergence of the whole domain. This approach is optimal to parallelize the solution method, since each sub-domain can be solved independently from the other sub-domains and the information stream can be processed in a decentralized manner to a neighbour processor for the next iteration, thus getting the best of a distributed memory parallel multi-processor. Another of the main advantages of the domain decomposition is that it allows accelerating the whole core calculation convergence in the long wavelength effects by a consistent high-order analytic nodal solution performed by the ANDES solver, after each sweep over all the 3D sub-domains. A brief introduction of how the coupling is performed at the pin-cells fine mesh scale is given in the next paragraph. The pin-wise power solution is passed to the TH code, which combines it with the geometrical and material descriptions of rods and sub-channels and with the iteratively updated boundary conditions on each sub-domain, namely the cross flows between the sub-channels, in order to calculate the fuel and coolant properties, and to pass it back to the neutronic solver until iterative convergence is reached in each sub-domain. Fig. 9 illustrates for a typical PWR assembly, with 17x17 rods, how the boundary conditions for the next dissection are computed on the center planes of the sub-domain, thus reducing significantly the numerical errors on the iteratively updated boundary conditions. Figure 9. Thermal-Hydraulics domain decomposition by alternate dissections. 16/22

17 LWR Multi-physics developments and applications within the framework of the NURESIM European Project At the local fine mesh scale, the coupling scheme is programmed for each sub-domain, i.e. full fuel assemblies or four quarters of assemblies (color-sets). It is essential to include the whole axial core domain in each local sub-domain, since the TH phenomena evolve mainly in the axial direction due to the dominant coolant flow Coupling interfaces The work done within the project NURESIM-MP has been the development and implementation of new coupling interfaces that will help very much future integration and coupling of TH and N codes. These interfaces are an evolution of the traditional coupling methods via shared common memory between both codes. Now it could be done through the MED format inside SALOME. At coarse mesh, the neutronic nodes (quarters of assemblies) can be mapped one-to-one to average channels and fuel rods. This is the top part of the scheme shown in Fig. 10. At the low part there are the local fine-mesh neutronic and TH solvers, with one fuel pin per cell and one sub-channel per four quarters of fuel rods. For the TH solver, it is essential to include the whole axial core domain in each local box, since the axial flow is very high and dominant in the TH solution. In COBAYA3 the information exchange is done at the level of the TH mesh, because this requires normally a minimum of data. The mesh transformations are included in the COBAYA3 part, which requires extra input data to define the TH mesh, if different from the neutronic mesh. Figure 10. Multi-scale and Multi-physics Neutronics/TH coupling through SALOME or memory commons. 17/22

18 O. Zerkak, P. Coddington, N. Crouzet, E. Royer, J. Jimenez, D. Cuervo The N/TH coupling can be done at both scales, nodal and local, and the nodal-channel solutions must be fully consistent with the local cell/sub-channel solutions. This requires further investigation for the TH multi-scale solvers, while is now of routine use in neutronics. The steady-state or transient analysis of a complete LWR core at the cell-sub-channel scale (pinlevel) is still a challenge. In particular, the size of the coupled N/TH problems is so large when simulated at the pin-level that a robust convergence method would be very difficult to establish, and a multi-scale approach has certainly to be considered as part of the solution method. The issue would then consist in establishing a consistent relationship between the assembly level and the pin level of the analysis. In the framework of the NURESIM-MP subproject, this type of problem can be considered and investigated using the COBAYA3 code, in which the two scales of simulation can be used COBAYA3 results The multi-physics N/TH coupling of COBAYA3, at the nodal-channel scale, has been verified running several NEA-OECD benchmarks exercises (UOX-1 rod ejection and MOX rod ejection) using as TH code COBRAIIIc/MIT-2. In Table I some steady states results are presented at HFP of the benchmark UOX-1. As it is shown, the results fit very well with the reference ones. Table I. UOX-1 steady state results of COBAYA3 at nodal-channel scale Case F xy F Q TF Dop-ave (ºC) TF max-center (ºC) Rod worth (pcm) K eff UOX-1 A2 Reference COBAYA UOX-1 B2 Reference COBAYA UOX-1 C2 Reference COBAYA In Table II, some others steady states results of COBAYA3 are given. The cases correspond to the MOX benchmark part 2, at HFP-ARO and COBAYA3 has been executed using 2g/4g and 1/4 nodes per assembly. 18/22

19 LWR Multi-physics developments and applications within the framework of the NURESIM European Project Energy groups Table II. MOX critical HZP results of COBAYA3 at nodal-channel scale Radial nodes per assembly Critical Boron (ppm) TF Dop-ave (ºC) TF max-center (ºC) 2g 1x g 2x g 1x g 2x F xy F Q As a first proof of principle verification for the local scale, isolated assemblies and color-sets have been computed with reflective boundary conditions with the same kind of material that represents an axially homogeneous and infinite reactor core. The 8g heterogeneous cell averaged cross sections library of the UOX+MOX benchmark and the TH boundary conditions correspond to an assembly at nominal conditions have been used. The numerical tests that have been performed to show that the coupling at that scale runs correctly are as follows: Proof of principle for the alternate core dissection. It means reflective boundary conditions in the neutronics and consistent modelization hypothesis in TH. The calculations taking an assembly dissection give the same results as when the color-set dissection are used, so the routines that perform the domain decomposition have been verified in this numerical test. Proof of principle of the multi-scale approach. Exercise developed to show the importance of the fine mesh solution in the TH side. Solutions using either detailed 3D distributions of TH parameters in fuel assembly or radial averaged ones (1 channel per assembly) have been compared. Taking an assembly dissection, two solutions were calculated: a) A local solution with complete 3D properties feedback (the same as in the previous test) b) A semi-nodal solution that uses the same neutronic model than the local solution but an average channel model for the TH response. It is done by averaging the detailed properties field (TH output) at each axial level before giving the field to the XS feedback module A brief outline of the test cases modelization and input data is given next. The total number of axial cells is 304 (8 N cells per subchannel). The power deposited in the assembly is 20 MW and the average power error for convergence is only 1 W. The water inside the guide tubes is taken into account for the TH averaging. 19/22

20 O. Zerkak, P. Coddington, N. Crouzet, E. Royer, J. Jimenez, D. Cuervo Table III. COBAYA3 results at local scale Numerical test Averaging TH properties ASSEMBLY COLORSET ASSEMBLY COLORSET K eff TF Dop-ave (ºC) TF max-center (ºC) F H F z F Q The results obtained are shown in Table III. It can be seen that when a detailed neutronic calculation (8g, XS heterogeneous) is performed it is also necessary to perform a detailed termalhydraulic solution because there could be an error of up to 85 pcm in K eff against the average channel calculations, just for taking into account the heterogeneity of the TH problem (guide tubes). 6. CONCLUSIONS AND OUTLOOK In order to establish a multi-physics LWR simulation platform open to different codes with different level of maturity, there is need for developing consistent interpolation and averaging methods for the data transfer from one discipline to another or, within one given discipline, from one scale to another. Another issue that was also discussed is the need for ensuring coherence between the input data models of the codes/solvers of the different disciplines and at the different scales of simulation. A third and not less important aspect, is the need for developing numerically robust and computationally efficient simulation methods applying and combining at different scales the codes/solvers from the different disciplines (e.g. assembly level and pin level homogenization methods for the N solvers, assembly and sub-channel discretization levels for the coarse-volume-averaged TH solvers). A first step in the direction of addressing these problems was proposed in the more focused area of the coupled N/TH analysis of LWR cores. First, a coupled N/TH application using the CEA codes CRONOS2 and FLICA4 was developed using advanced multi-physics functionalities that were developed in SALOME. A mesh-to-mesh interpolation tool was developed in order to allow coupling N and TH solvers using non identical meshing schemes both in the radial and the vertical directions. A generic Application Programming Interface was developed to allow for a flexible manipulation and coupling of different solvers, which is a prerequisite for the development of complex multi-physics calculation routes. Finally, an application based on the XDATA module of SALOME, allowed regrouping some of the input data that are common to 20/22

21 LWR Multi-physics developments and applications within the framework of the NURESIM European Project CRONOS2 and FLICA4 (fuel assembly geometry and TH and power boundary conditions, in particular). A first simple test case derived from the specifications of the NEA-OECD PWR MSLB problem was successfully executed using the codes CRONOS2 and FLICA2 integrated and coupled in the platform, thus showing the operability of the different multi-physic functionalities developed. Further verification of this coupled application in SALOME is still needed, in particular for situations where the respective meshing schemes used by the two codes present significant dissimilarity (overlapping of meshes in both the radial and the axial direction). This work will be performed during the next phase of the project. The application will be also applied to the NEA- OECD PB2TT benchmark exercise, in order to verify the applicability of the tools to a BWR system. In respect to the development of advanced multi-scale calculation methods, a solution scheme materialized by the UPM code COBAYA3, which is being developed in collaboration with the NURESIM-CP subproject, was presented. In this code the core 3D fine-mesh multi-group neutron diffusion problem is solved using a domain decomposition method, which allows for an efficient parallel implementation in memory distributed multi-processors through alternate dissections in the 4 possible sets of 4 neighboring quarters of assemblies in the radial direction, and using a high-order analytic nodal solvers (ANDES) for accelerating the calculation convergence over the whole core domain. First, proof of principle, coupled N/TH applications at the nodal level based on the specifications of NEA-OECD benchmark exercises already showed the good performance of COBAYA3 and emphasized the need for a detailed TH solution. In the third phase of the NURESIM project, the COBAYA3 will be integrated in SALOME. In a longer term, a coupling with FLICA4 is considered, in order to test and further develop the multi-physics functionalities of the platform and also to better evaluate the importance of the TH feedback at the sub-assembly scale. This work should also give the opportunity of testing and validating the possibilities of SALOME for parallelization of applications on different processors. ACKNOWLEDGMENTS This work is partially funded by the European Commission under the 6 th EURATOM Framework Programme, within the RTD Integrated Project NURESIM European Platform for Nuclear Reactor Simulations, contract n (FI6O). The work of one of the authors (J. Jimenez) is also supported by the Consejo de Seguridad Nuclear (Spain). We would like also to thank Anthony Geay and Jérôme Roy (CEA) for their efficient technical support, and Audrey Arthaud Berthet and Annelise Gauclin for their excellent work during their traineeship at CEA. 21/22

22 O. Zerkak, P. Coddington, N. Crouzet, E. Royer, J. Jimenez, D. Cuervo REFERENCES 1. D.G. Cacuci, J.M. Aragonés, D. Bestion, P. Coddington, L. Dada, C. Chauliac, NURESIM: A European Platform for Nuclear Reactor Simulation, in 2006 FISA Conference on the 6th Framework Euratom Research Program, European Commission, Luxembourg, (2006). 2. Salome Platform: general presentation (February 2007). 3. K.N. Ivanov, T.M. Beam, A.J. Baratta. Pressurized Water Reactor Main Steam Line Break (MSLB) Benchmark. Volume I: Final Specifications, NEA/NSC/DOC(99)8, (2005). 4. A.M. Baudron, J.J. Lautard, D. Schneider, Mixed dual Methods for Neutronic Reactor Core Calculations in the CRONOS SYSTEM, in Mathematical Methods and Supercomputing in Nuclear Applications, Madrid, Spain, April (1999). 5. S. Aniel et al, FLICA4: Status of Numerical and Physical Models and Overview of Applications, in Int. Topical Meeting on Nuclear Thermal-Hydraulics (NURETH-11), Avignon, France, October 2-6, (2005). 6. J.J. Herrero, C. Ahnert, J.M. Aragonés, 3D Whole Core fine Mesh Multigroup Diffusion Calculations by Domain Decomposition through Alternate dissections, submitted to M&C/SNA-2007, Monterey (this Conference), (2006). 7. J.M. Aragonés, C. Ahnert, N. García-Herranz, O. Cabellos, V. Aragonés-Ahnert, Methods and Results for the MSLB NEA Benchmark using SIMTRAN and RELAP-5, Nuclear Technology, 146, 29 (2004). 8. J.M. Aragonés, C. Ahnert, N. García-Herranz, The Analytic Coarse-Mesh Finite-Difference Method for Multigroup and Multidimensional Diffusion Calculations, in Mathematics and Computation, Supercomputing, Reactor Physics and Nuclear and Biological Applications (MC-2005), Am. Nucl. Soc., Avignon, p. 194 (2005). 9. J.A. Lozano, J.M. Aragonés, N. García-Herranz, Development and Performance of the Analytic Nodal Diffusion Solver ANDES in Multigroups for 3D Rectangular Geometry, submitted to M&C/SNA-2007, Monterey (this Conference), (2006). 22/22