3. DESCRIPTION OF PROGRAM OR FUNCTION
The European Reactor ANalysis Optimized calculation System, ERANOS, has been developed and validated with the aim of providing a suitable basis for reliable neutronic calculations of current as well as advanced fast reactor cores. It consists of data libraries, deterministic codes and calculation procedures which have been developed within the European Collaboration on Fast Reactors over the past 20 years or so, in order to answer the needs of both industrial and R&D organisations. The whole system counts roughly 250 functions and 3000 subroutines totalling 450000 lines of FORTRAN-77 and ESOPE instructions.
ERANOS is written using the ALOS software which requires only standard FORTRAN compilers and includes advanced programming features. A modular structure was adopted for easier evolution and incorporation of new functionalities. Blocks of data (SETs) can be created or used by the modules themselves or by the user via the LU control language. Programming, and dynamic memory allocation, are performed by means of the ESOPE language. External temporary storage and permanent storage capabilities are provided by the GEMAT and ARCHIVE functions, respectively. ESOPE, LU, GEMAT and ARCHIVE are all part of the ALOS software. This modular structure allows different modules to be linked together in procedures corresponding to recommended calculation routes ranging from fast-running and moderately-accurate 'routine' procedures to slow-running but highly-accurate 'reference' procedures.
The main contents of the ERANOS-2.0 package are: nuclear data libraries (multigroup cross-sections from the JEF-2.2 evaluated nuclear data file, and other specific data files), a cell and lattice code (ECCO), reactor flux solvers (diffusion, Sn transport, nodal variational transport), a burn-up module, various processing modules (material and neutron balance, breeding gains,...), tools related to perturbation theory and sens
itivity analysis, core follow-up modules (connected in the PROJERIX procedures), a fine burn-up analysis subset named MECCYCO (mass balances, activities, decay heat, dose rates). Coupled neutron/gamma calculations are also possible using specific libraries.
Nuclear data libraries:
The ECCO/ERANOS 2.0 code package contains four neutron cross section libraries derived from the JEF-2.2 nuclear data evaluated files. They are:
- a 1968-group library (41 main nuclides)
- a 33-group library (246 nuclides, including pseudo fission products)
- a 175-group library (VITAMIN-J energy group scheme)
- a 172-group library (XMAS energy group scheme, 246 nuclides, including pseudo-FP).
These libraries were obtained by processing the JEF-2.2 files with the NJOY and CALENDF codes. Probability tables are included for the main 37 resonant nuclides. The 172-group library (XMAS energy scheme) may be used for thermal spectrum calculations. The 175-group library (some cross-sections in P5, but no probability tables) is used for shielding calculations only.
Other nuclear data (fission yields and energies, decay constants, gamma production and interaction libraries, etc.) are provided in separate files.
Cell/lattice calculations:
The ECCO cell/lattice code in the ERANOS-2.0 package uses the subgroup method to treat resonance self-shielding effects. This method is particularly suitable for calculations involving complex heterogeneous structures. ECCO prepares self-shielded cross sections and matrices by combining a slowing-down treatment in many groups (1968 groups) with the subgroup method within each fine group. The subgroup method takes into account the resonance structure of cross-sections by means of probability tables and by assuming that the neutron source is uniform in lethargy within a given fine group. Flux calculations in heterogeneous geometry are performed by means of the collision probability method.
In the reference calculation s
cheme, ECCO treats the heterogeneous geometry in fine groups (1968) for the most important nuclides while broad group libraries (33 or 172 groups) are used for the less important nuclides. These calculations are very accurate as the fine group plus sub-group scheme have been set up to represent accurately the reaction thresholds and the resonances in any situation, narrow or wide. One usually distinguishes wide and narrow resonances depending on their width compared to the neutron energy loss by scattering, which is smallest for scattering by heavy nuclides. Translated into lethargy gain, the value for U238 is almost constant and is equal to 0.008. This compares well with the fine group width of 1/120 = 0.0083 and explains the fact that 3/4 of the neutrons having a collision in a given fine group escape from that group. Wide resonances are treated explicitly, the resonances in that case having a width larger than the fine group width. On the other hand, narrow resonances are represented by probability tables, and hence use of the subgroup method can be applied in a very accurate way.
Self-shielded cross sections and matrices are condensed and smeared to provide effective cross sections and matrices in the user required broad group scheme. The neutron balance is preserved in ECCO after condensation and smearing. The effective cross-sections and matrices produced by ECCO are subsequently used in full-core ERANOS calculations.
Many types of geometries are available within the ECCO code: 1D (plane or cylindrical: exact collision probabilities), 2D (rectangular lattice of cylindrical and/or square pins within a square tube, hexagonal lattice of cylindrical pins within an hexagonal wrapper: approximate collision probabilities by Roth and double step methods), 3-D (slab with the sides of the boxes and the tube described explicitly: approximate collision probabilities).
The user can chain several calculation steps so as to produce desig
n (less accurate, faster) or reference (more accurate, slower) calculations, or even to use specific capabilities, according to the needs of a given study.
Flux solvers:
Three main classes of flux solvers are available. In each case, external sources, up-scattering and adjoint calculations can be addressed. Anisotropic scattering is available for transport calculations.
Finite difference diffusion solvers can be used in any geometry: 1D (plane, cylindrical, spherical), 2D (RZ, R-theta, rectangular lattice XY, hexagonal lattice), and 3D (rectangular lattice XYZ, hexagonal-Z). An efficient solution of the diffusion equation is obtained by using either the successive line over-relaxation method (SLOR), the alternating direction implicit method (ADI) or the strongly implicit method (SIM).
Finite difference Sn transport calculations are performed by the BISTRO code, using a highly efficient convergence algorithm. It can be used in 1D geometry (plane, cylindrical, spherical) and some 2D geometries (RZ, XY). Different algorithms (step, diamond and "theta-weighted") and a negative flux fix-up capability exist. The inner iterations are accelerated by the DSA method using the source correction scheme.
The OECD version of the variational nodal method developed for the VARIANT code has been used in ERANOS-2.0 as the TGV/VARIANT module. This method is based on the second-order form of the even-parity transport equation. A solution is searched in form of expansions for the even and odd parity fluxes in pre-computed angular and spatial basis functions with unknown coefficients. These basis functions are orthogonal polynomials for the spatial variables and spherical harmonics for the angular variables. Scattering anisotropy can be taken in to account as Pn moments up to the order N of the Legendre expansion of the flux. Both Cartesian (XY or XYZ) and hexagonal (Hex or Hex-Z) geometries are available with TGV/VARIANT. A 'simplified transpo
rt' option exists, in which the angular developments both within the nodes and at the node boundaries are truncated by neglecting high-order cross terms. This option is rather accurate in practice (large reactors), and less time and memory consuming.
Burn-up calculations:
Calculation of isotopic concentration evolution is possible in the ERANOS system for actinides as well as fission and activation products. The Bateman equations governing the time dependence of concentrations are solved with various techniques related to the type of nuclide (actinide, fission product or activation product). Burn-up can be performed at the full core scale, with suitable 'burnable zones' subdividing the fuel and fertile regions, or in elementary cells/lattices.
Result-processing modules.
Besides the modules related to basic data preparation (creation of medium, geometry, and burn-up chain SETs, modelling of operating conditions, etc.), a variety of modules computes and/or extracts specific information from the code output (fluxes, concentrations, etc.). Here is a non-exhaustive sample of such modules:
- Traverse extraction and processing
- Mass and atom balances by region
- Neutron balance by region, reaction and energy group
- Integrated reaction rate processing
- Equivalence coefficients and Breeding gain
- Beta effective
- Linear and bilinear integrals (with respect to the forward and possibly adjoint fluxes)
Perturbation theory and sensitivity analysis.
The reactor physicist is often interested in the breakdown of the variation (or of the first order derivative) of integral parameters such as the multiplication factor, reaction rates and more generally ratios of bilinear integrals, nuclide concentrations, reactivity coefficients, etc., with respect to input data such as multigroup cross-sections, decay constants, or initial concentrations. This can be readily obtained through the use of adjoint (standard or generalized) flux calculati
ons and the computation of suitable bilinear integrals. Several modules of ERANOS are available for a modular processing of such problems : calculation of perturbation integrals, of cross-section variations, sensitivity analysis, perturbation analysis.
As a matter of fact, sensitivity analyses, and first-order or exact perturbation analyses can be performed for the multiplication factor (standard perturbation theory, SPT), ratios of linear or bilinear integrals (generalized perturbation theory, GPT), and reactivity effects (equivalent generalized perturbation theory, EGPT). If a dispersion (variance/covariance) matrix is provided, a specific module can be used to perform uncertainty and representativeness calculations.
Core follow-up:
Specific ERANOS modules and appropriate complex subroutines written in the LU user's language (the PROJERIX package) are available to perform a detailed core follow-up. Each individual sub-assembly can be followed through its entire life (moves during shuffles and batch reloadings, time spent in internal storage, etc.).
Fine burn-up:
For sub-assemblies burnt in significant flux gradients (e.g. fertile sub-assemblies) a detailed burn-up capability is available through specific ERANOS modules.
Other topics:
Several other features are available:
- Coupled neutron/gamma Sn transport calculations (with specific libraries)
- Detailed treatment of damage and kerma (with specific libraries)
- Detailed burn-up with computation of decay (alpha, beta, gamma and neutron particles) activities, energies, energy spectra of emitted particles, dose rates (for simple geometries), decay heat (the MECCYCO package, with specific libraries).