Andreas Pautz

DORT-TD: A transient neutron transport code with fully implicit time integration

Abstract A new neutron transport code for time-dependent analyses of nuclear systems has been developed. The code DORT-TD is based on the well-known Discrete Ordinates code DORT, which solves the steady-state neutron transport equation in two dimensions for an arbitrary number of energy groups and standard regular geometries. For the implementation of time-dependence, a fully implicit, unconditionally stable time integration scheme was employed to minimize errors due to temporal discretization. This requires several modifications to the transport equation and the extensive use of sophisticated acceleration mechanisms. The convergence criteria for fluxes and fission densities had to be strongly tightened to ensure the reliability of results. We also allowed for cross sections varying with time to couple neutronics and thermal hydraulics calculations. The neutronics code was finally applied to a research reactor to show its capabilities for both slow and fast transients.

FUEL ASSEMBLY CALCULATIONS USING THE METHOD OF DISCRETE ORDINATES

Abstract The discrete ordinates code DORT is employed to treat pin cell and fuel assembly configurations in two spatial dimensions. Despite DORT’s restriction to regular (i.e., Cartesian) coordinates, we demonstrate its ability to calculate accurate pin power distributions and eigenvalues of typical reactor fuel lattices. Several numerical experiments have been performed to investigate the effects of spatial, angular, and energy discretization and to quantify their impact on the results. DORT is also used to homogenize and collapse cross-section sets within the framework of the coupled transport/burnup code system KENOREST.

Coupling of time-dependent neutron transport theory with the thermal hydraulics code ATHLET and application to the research reactor FRM-II

Abstract We introduce a new coupled neutronics/thermal hydraulics code system for analyzing transients of nuclear power plants and research reactors, based on a neutron transport theory approach. For the neutron kinetics, we have developed the code DORT-TD, a time-dependent extension of the well-known discrete ordinates code DORT. DORT-TD uses a fully implicit time integration scheme and is coupled via a general interface to the thermal hydraulics system code ATHLET, a generally applicable code for the analyses of LWR accident scenarios. Feedback is accounted for by interpolating multigroup cross sections from precalculated libraries, which are generated in advance for user-specified, discrete sets of thermal hydraulic parameters, e.g., fuel and coolant temperature. The coupled code system is applied to the high-flux research reactor FRM-II (Germany). Several design basis accidents are considered, namely the unintended control rod withdrawal, the loss of offsite power, and the loss of the secondary heat sink as well as a hypothetical transient with large reactivity insertion.

Application of Time-Dependent Neutron Transport Theory to High-Temperature Reactors of Pebble Bed Type

Abstract We introduce a new coupled neutronics/thermal-hydraulics code system for analyzing transients of high-temperature gas-cooled reactors (HTGRs), based on a neutron transport theory approach. At the heart of the coupled code system resides the DORT-TD code, a time-dependent extension of the well-known DORT discrete ordinates code. DORT-TD uses a fully implicit time integration scheme and is coupled via its generalized thermal-hydraulics interface to the THERMIX-DIREKT code, an HTGR-specific heat conduction/convection code for pebble bed-type reactor cores. Feedback is accounted for by interpolating multigroup cross sections from libraries pregenerated with appropriate spectral codes. These libraries are structured for user-specified discrete sets of thermal-hydraulic parameters, e.g., fuel and moderator temperatures. The coupled code system is applied to a pebble bed HTGR model case, i.e., the PBMR 268 MW design. Steady-state studies are performed, and several design-basis and beyond-design-basis transients are simulated in an effort to assess the adequacy of using neutron diffusion theory against the more accurate but yet computationally more expensive neutron transport approach. Relatively small but significant differences arise from using either theoretical approach, from which it is concluded that transport theory as the more versatile tool should be used as reference to quantify the effects of the approximations inherent in diffusion and to gain confidence in its predictive power, especially in safety analyses. In an effort to validate the DORT-TD/THERMIX code system, the neutronics stand-alone solver is benchmarked against available transient benchmark exercises, and the coupled code system is applied to the Organisation for Economic Co-operation and Development/Nuclear Energy Agency/Nuclear Science Committee PBMR 400 MW Coupled Neutronics Thermal Hydraulics Transient Benchmark, demonstrating its remarkable viability for a wide range of safety cases. The final product is a high-fidelity, highly flexible, and well-validated state-of-the-art computer code system, with multiple capabilities to analyze HTGR safety-related transients in an accurate and efficient manner.

Advanced calculation methodology for manufacturing and technological parameters" uncertainties propagation at arbitrary level of lattice elements grouping

A new methodology, referred to as manufacturing and technological parameters uncertainty quantification (MTUQ), is under development at Paul Scherrer Institut (PSI). Based on uncertainty and global sensitivity analysis methods, MTUQ aims at advancing state-of-the-art for the treatment of geometrical/material uncertainties in light water reactor computations, using the MCNPX Monte Carlo neutron transport code. The development is currently focused primarily on criticality safety evaluations (CSE). In that context, the key components are a dedicated modular interface with the MCNPX code and a user-friendly interface to model functional relationship between system variables. A unique feature is an automatic capability to parameterize variables belonging to so-called “repeated structures” such as to allow for perturbations of each individual element of a given system modelled with MCNPX. Concerning the statistical analysis capabilities, these are currently implemented through an interface with the ROOT platform to handle the random sampling design. This paper presents the current status of the MTUQ methodology development and a first assessment of an ongoing organisation for economic cooperation and development/nuclear energy agency benchmark dedicated to uncertainty analyses for CSE. The presented results illustrate the overall capabilities of MTUQ and underline its relevance in predicting more realistic results compared to a methodology previously applied at PSI for this particular benchmark.

A Two-Step Approach to Uncertainty Quantification of Core Simulators

For the multiple sources of error introduced into the standard computational regime for simulating reactor cores, rigorous uncertainty analysis methods are available primarily to quantify the effects of cross section uncertainties. Two methods for propagating cross section uncertainties through core simulators are the XSUSA statistical approach and the “two-step” method. The XSUSA approach, which is based on the SUSA code package, is fundamentally a stochastic sampling method. Alternatively, the two-step method utilizes generalized perturbation theory in the first step and stochastic sampling in the second step. The consistency of these two methods in quantifying uncertainties in the multiplication factor and in the core power distribution was examined in the framework of phase I-3 of the OECD Uncertainty Analysis in Modeling benchmark. With the Three Mile Island Unit 1 core as a base model for analysis, the XSUSA and two-step methods were applied with certain limitations, and the results were compared to those produced by other stochastic sampling-based codes. Based on the uncertainty analysis results, conclusions were drawn as to the method that is currently more viable for computing uncertainties in burnup and transient calculations.

Testing the Sampling-Based NUSS-RF Tool for the Nuclear Data—Related Global Sensitivity Analysis with Monte Carlo Neutronics Calculations

Abstract NUSS-RF is a tool for nuclear data uncertainty propagation through neutronics calculations with continuous-energy Monte Carlo codes and ACE-formatted nuclear data libraries. Many existing codes, including the original version of NUSS (Nuclear data Uncertainty Stochastic Sampling), are based on simple random sampling algorithms. The NUSS-RF extension now uses a frequency-based sampling algorithm, called the random balance design (RBD), to analyze individual nuclear data uncertainty contributions in regard to the total output (e.g., keff) uncertainty. The implementation of the RBD method into NUSS-RF is initially verified by comparing the computed individual input variance contributions with analytical solutions for two analytical test cases. As well, it is assessed against the alternative approach based on the use of correlation coefficients. NUSS-RF is then used for an analysis of the Jezebel and Godiva fast-spectrum criticality benchmarks: in a first step, the overall effect of the 239Pu(n,f) and 235U(n,f) cross-section uncertainties on keff is evaluated, while in a second step, the contributions from the individual energy groups are quantified. As an additional verification, the NUSS-RF results are assessed against sensitivity and uncertainty analysis based on perturbation theory, showing good agreement between the two solutions. Finally, the capability of NUSS-RF is demonstrated for ranking the input parameters with respect to their influence on the total uncertainty of the output parameters, taking into account possible correlations between input parameters. Possible future improvements for the current computational scheme are discussed in the conclusions.

FUTURE EXPERIMENTAL PROGRAMMES IN THE CROCUS REACTOR

CROCUS is a teaching and research zero-power reactor operated by the Laboratory for Reactor Physics and Systems Behaviour (LRS) at the Swiss Federal Institute of Technology (EPFL). Three new experimental programmes are scheduled for the forthcoming years. The first programme consists in an experimental investigation of mechanical noise induced by fuel rods vibrations. An in-core device has been designed for allowing the displacement of up to 18 uranium metal fuel rods in the core periphery. The vibration amplitude will be 6 mm in the radial direction (±3 mm around the central position), while the frequency can be tuned between 0.1 and 5 Hz. The experiments will be used to validate computational dynamic tools currently under development, which are based on DORT-TD and CASMO/S3K code systems. The second programme concerns the measurement of in-core neutron noise for axial void profile reconstruction. Simulations performed at Chalmers University have shown how the void fraction and velocity profiles can be reconstructed from noise measurements. The motivation of these experiments is to develop an experimental setup to validate in-core the method in partnership with Chalmers University. The third experimental programme aims at continuing the validation effort on the nuclear data required in the calculation of GEN-III PWR reactors with heavy steel reflectors. This is a collaboration with CEA Cadarache that extends the results of the PERLE experiments carried out in the EOLE reactor at CEA. Scattering cross sections at around 1 MeV will be studied separately by replacing successively the water reflector by sheets of stainless steel alloy and pure metals – iron, nickel, and chromium. Data will be extracted from the measured flux attenuation using foils in the metal reflector and from the criticality effects of these reflectors. In parallel to the three reactor experiments, we develop in-core detectors and measurement systems. Following the last development of a neutron noise measurement station in pulse mode, a second neutron noise station in current mode is being designed. In current mode the reactor can be used at higher power without dead time effects. It allows faster measurement time or lower results uncertainties. Finally, a joint development of a full new detection system based on chemical vapour deposited (sCVD) diamond has been started with the CIVIDEC instrumentation start-up company. A first prototype has been tested in November 2015 in CROCUS. One of the main purposes is to work on the discrimination of gammas, thermal and fast neutrons for demonstrating the interest of this detector type in a mixed neutron-gamma field.

Methods and Models for the Coupled Neutronics and Thermal-Hydraulics Analysis of the CROCUS Reactor at EFPL

In order to analyze the steady state and transient behavior of the CROCUS reactor, several methods and models need to be developed in the areas of reactor physics, thermal-hydraulics, and multiphysics coupling. The long-term objectives of this project are to work towards the development of a modern method for the safety analysis of research reactors and to update the Final Safety Analysis Report of the CROCUS reactor. A first part of the paper deals with generation of a core simulator nuclear data library for the CROCUS reactor using the Serpent 2 Monte Carlo code and also with reactor core modeling using the PARCS code. PARCS eigenvalue, radial power distribution, and control rod reactivity worth results were benchmarked against Serpent 2 full-core model results. Using the Serpent 2 model as reference, PARCS eigenvalue predictions were within 240 pcm, radial power was within 3% in the central region of the core, and control rod reactivity worth was within 2%. A second part reviews the current methodology used for the safety analysis of the CROCUS reactor and presents the envisioned approach for the multiphysics modeling of the reactor.

NUSS-RF: stochastic sampling-based tool for nuclear data sensitivity and uncertainty quantification

The “blackbox” approach of stochastic sampling (SS) methods for simultaneous nuclear data uncertainty quantification is powerful except it reveals little of the individual uncertainty contributions. In this work, the SS-based tool “NUSS” (nuclear data uncertainty stochastic sampling) developed at PSI is updated to “NUSS- RF” which estimates individual nuclear data uncertainty contributions to the total output uncertainty. The new capability is based on the Random balance design and Fourier amplitude sensitivity testing methods, both belonging to the so-called global sensitivity analysis. First, the implementation of NUSS-RF is tested using a mathematical function, followed by the sensitivity and uncertainty analysis for 235U(n,γ) and 238U(n,γ) cross sections in Godiva and BWR pincell benchmarks, respectively. The results are compared to the deterministic sensitivity/uncertainty “Sandwich Rule” approach which is local. For uncorrelated inputs, both methods have the equivalent interpretation of the input uncertainty contribution (in terms of variance fraction and sensitivity index), hence producing good agreement in the results. For correlated inputs, the discrepancy between the two methods broadens with the extent of the correlations.