Deterministic Code Research Articles

MAPPING OF SODIUM VOID EFFECT AND DOPPLER CONSTANT IN ESFR-SMART CORE WITH MONTE CARLO CODE SERPENT AND DETERMINISTIC CODE ERANOS

The Sodium Fast Reactor is one of the most technologically developed Gen-IV reactors, which can close the nuclear fuel cycle. Its criticality safety directly depends on the sodium void effect and Doppler constant. Hence the knowledge of their local distribution is important. These coefficients can be mapped by deterministic or Monte Carlo codes, where the latter provide higher modeling accuracy, but are also strongly computer demanding and subject to stochastic noise issues. In this study, the void effect and Doppler constant have been enumerated for the ESFR core by Serpent2 and ERANOS2 codes, preserving a six-batch operation scheme. The Serpent code was coupled to the Python script BBP to simulate batch-wise operation in a radially infinite inner core configuration; the ERANOS code was applied to the whole core geometry and the batch-wise operation was simulated by the EQL3D routine. Sodium void effect and Doppler constant spatial maps with different levels of refinement were produced, as well as the time evolution of the integral coefficients during the transition from initial cycle to equilibrium cycle. Both codes indicate deterioration of these coefficients during the transition. The equilibrium cycle performance of the inner core zone from the ERANOS calculation was compared with Serpent results and they showed reasonable agreement. For very fine mapping, the Monte Carlo method employed was computationally very demanding and the enumerated effect was lower than the stochastic noise. In general, the Serpent model practically excludes modeling assumptions and produces reliable results for reasonably sized maps, which can be combined if needed with the high spatial resolution results obtained by ERANOS simulations.

ANALYSIS OF THE SUPERPHENIX START-UP TESTS WITH APOLLO-3: FROM ZERO POWER ISOTHERMAL CONDITIONS TO DYNAMIC POWER TRANSIENT ANALYSIS

Sodium-cooled Fast Reactors (SFRs) remain a potential candidate to meet future energy needs. In addition, the SFRs experimental feedback is considerable, for instance, the French research program has considered experimental facilities including the Superphénix which has emerged as a transition to commercial deployment. In this paper a set of tests from the Superphénix start-up are reanalyzed with new tools, considering APOLLO-3 and TRIPOLI-4 (respectively deterministic and stochastic codes) for neutron physics evaluation, GERMINAL-V2 for the fuel irradiation behavior and CATHARE-3 for the thermal-hydraulics modelling. Neutron physics evaluations are performed for the main control rod worth and the Doppler Effect, both measured under isothermal conditions at Superphénix start-up. A good agreement is obtained for these tests, which were purely neutronic tests. Next, the core temperature distribution is evaluated at nominal conditions, where larger discrepancies are observed. However, these deviations are related to the measurement of the fuel assemblies, which have a larger than expected uncertainty. Finally a transient, consisting of a negative reactivity insertion, is analyzed to assess the dynamic core behavior. A good agreement is obtained during the reactivity insertion, however the thermal-hydraulic model has to be improved, namely the vessel model, which is considered as a 0-D volume.

MACROSCOPIC CROSS SECTIONS GENERATION BY MONTE CARLO CODE MCS FOR FAST REACTOR ANALYSIS

Recent researches have become more interested in the feasibility of using Monte Carlo (MC) code to generate multi-group (MG) cross sections (XSs) for fast reactor analysis using nodal diffusion codes. The current study, therefore, presents a brief methodology for MG XSs generation by the in-house UNIST MC code MCS, which can be compatibly utilized in nodal diffusion codes, PARCS and RAST-K. The applicability of the methodology is quantified on the sodium fast reactor (SFR) ABR-1000 design with a metallic fuel from the OECD/NEA SRF benchmark. The few-group XSs generated by MCS with a two-dimensional (2D) fuel assembly geometry are well consistent with those of SERPENT 2. Furthermore, the simulation of beginning-of-cycle (BOC) steady-state three-dimensional (3D) whole-core problem with PARCS and RAST-K is conducted using the generated 24-group XSs by MCS. The nodal diffusion solutions, including the core keff, power profiles and various of reactivity parameters, are compared to reference whole-core results obtained by MC code MCS. Overall, the code-to-code comparison indicates a reasonable agreement between deterministic and stochastic codes, with the difference in keff less than 100 pcm and the root-mean-square (RMS) error in assembly power less than 1.15%. Therefore, it is successfully demonstrated that the employment of the MG XSs generation by MCS for nodal diffusion codes is feasible to accurately perform analyses for fast reactors.

3-D COUPLED SIMULATION OF A VVER 1000 WITH PARCS/ATHLET

A new OECD/NEA benchmark entitled “Reactivity compensation with diluted boron by stepwise insertion of control rod cluster” is starting. This benchmark, based on high quality measurements performed at the NPP Rostov Unit 2, aims to validate and assess high fidelity multi-physics simulation code capabilities. The Benchmark is divided in two phases: assembly wise and pin-by-pin resolution of steady-state and transient multi-physics problems. Multi-physics simulation requires the generation of parametrized few-group cross-sections. This task used to be done with deterministic (2-D) lattice codes, but in the past few years the Monte-Carlo code SERPENT has demonstrate its ability to generate accurate few-group homogenized cross-section without approximations, neither on the geometry nor in the nuclear data. Since the whole core SERPENT models for production of such cross-section libraries would be computationally costly (and the standard 2-D approach may introduce unnecessary large approximations), 3-D models of each assembly type in infinite radial lattice configurations have been created. These cross-sections are then used to evaluate effective multiplication factors for different core configurations with the diffusion code PARCS. The results are compared with the reference SERPENT calculations. In the next step, a thermal-hydraulic model with the system code ATHLET applying an assembly-wise description of the core (i.e. one channel per fuel assembly) has been developed for coupled PARCS/ATHLET transient test calculations. This paper describes in detail the models and techniques used for the generation of the few-group parameterized cross section libraries, the PARCS model and the ATHLET model. Additionally, a simple exercise with coupled code system PARCS/ATHLET is presented and analysed.

SENSITIVITY ANALYSIS OF PWR SPENT FUEL DUE TO MODELLING PARAMETER UNCERTAINTIES USING SURROGATE MODELS

In the BEPU (Best Estimate Plus Uncertainty) framework, uncertainty quantification (UQ) is a requirement to improve confidence and reliability of code predictions. Over the years, a lot of works have been done to quantify uncertainties in code predictions of spent nuclear fuel (SNF) characteristics due to nuclear data uncertainties. The purpose of this study is to quantify the uncertainty in pressurized water reactor (PWR) fuel assembly radiation source terms (isotopic inventory, activity, decay heat, neutron and gamma source) due to uncertainties in modeling parameters. The deterministic code STREAM is used to predict the source terms of a typical PWR fuel assembly following realistic and detailed irradiation history. For the sensitivity analysis (SA) and UQ, surrogate models are developed based on polynomial chaos expansion (PCE) and variance-based global sensitivity indices (i.e., Sobol’ indices) are employed. The global SA identifies the less important uncertain parameters, showing that the number of uncertain input parameters can be reduced. The surrogate model offers a significantly reduced computational burden even with large number of samples required for the SA/UQ of the model response.

ZERO POWER CRITICALITY BENCHMARK EVALUATION OF THE MSRE IN WIMS

This paper discusses work done to benchmark the deterministic code WIMS [1] against the Monte Carlo code Serpent [2] and experiment. Comparison is made against the Molten Salt Reactor Experiment at Oak Ridge National Laboratory as well as a Serpent model produced at the University of California, Berkeley. Producing a model for an MSR is possible thanks to the development of the next version of WIMS, WIMS11. The structure of the WIMS model built is discussed, and the final predicted criticality value for the MSR is given. This compares favourably with the Serpent model; however, both codes predict values considerably different to those expected. Potential reasons for this are suggested. However, it is concluded that WIMS has successfully been benchmarked against the current state of the art. This provides confirmation that this is a valid approach for molten salt reactor research analysis.

NEUTRONIC BENCHMARK ON HOLOS-QUAD MICRO-REACTOR CONCEPT

The Holos-Quad micro-reactor concept is proposed by HolosGen LLC for civilian applications to generate 22 MWt with a lifetime of approximately 8 effective full power years (EFPYs). The design is based on a very innovative high-temperature gas-cooled reactor concept using four Subcritical Power Modules (SPMs) that fit into one commercial 40-foot transport ISO container. Neutronics benchmarks were developed based on a preliminary version of the Holos-Quad design to confirm feasibility of the neutronics design of this non-traditional high temperature gas-cooled (HTGR)-type micro-reactor concept. Calculations were performed using Monte Carlo codes (SERPENT and OpenMC) as well as the PROTEUS high-fidelity deterministic code for two exercises based on a unit cell model and a full core model. The results obtained showed good agreement with all of the evaluated parameters for the unit cell problem and the full core problem. SERPENT and OpenMC display consistently good agreement in eigenvalue within 150 pcm for the unit cell benchmark and less than 270 pcm for the full core benchmark. PROTEUS eigenvalues showed relatively larger differences but still reasonable agreement with the SERPENT solutions. For the depletion benchmark, the observed eigenvalue differences between SERPENT and OpenMC were within 300 pcm throughout the depletion up to 100 GWd/MT, ensuring that the two codes used equivalent input parameters such as the recoverable heat values for fission reactions. This benchmark exercise confirms the neutronic feasibility and core performance of the preliminary Holos-Quad design.

MAXIMISING DISCHARGE BURNUP IN AN OPEN CYCLE MOLTEN SALT REACTOR

This paper discusses work done to find an estimate of the maximum achievable discharge burnup in an open cycle molten salt reactor (MSR). An in-development deterministic code (WIMS11) is used to create a model of a simple generic MSR, and the methodology employed is discussed. Some experimentation is done with regards to the internal set-up of the ‘unit cells’ within the core, which shows there is a strong link between this geometry and the achievable burnup. Work is done to quantify the effects of removing volatile fission products and implementing a two-batch refuelling scheme. Finally, an optimization process is carried out whereby the optimal proportion of graphite moderator within the core is found which balances power across the regions while maximising discharge burnup. Two fuels are tested, one which carries only 235U and 238U, and another which also carries 232Th. It is found that the maximum achievable discharge burnup is approximately 155 MWd/kg, which is considerably higher than modern PWRs, despite a lower enrichment and only two batches of fuel being used.

NUMERICAL BENCHMARK OF STRONGLY TO LOOSELY COUPLED ASSEMBLIES USING THE TRANSIENT FISSION MATRIX METHOD

Advances in computational methods have given rise to the study and simulation of different aspects of reactor behavior. As such, topics associated with high computational costs become feasible candidates for further investigation and one of them is reactor space-time kinetics (STK). Until recently, STK simulation and point kinetics approximation were limited to deterministic codes, with Monte Carlo codes being too costly to start with. However, recent developments in this area have allowed the use of certain methods in stochastic codes. One such technique is based on the Transient Fission Matrix (TFM) model, a hybrid method that uses a system response obtained through Monte Carlo and stored in fission and time matrices as input for deterministic calculations. The result enables a view of the STK in terms of neutron propagation probability and propagation time across the system. The TFM method was applied to a simple coupled core configuration to generate a numerical benchmark. The Serpent 2 Monte Carlo code was used for the stochastic part of the calculation. The configuration consists of two fuel assemblies placed in a light water tank, with a water blade of varying width between them. TFM, flux and fission results were obtained for varying water blade widths, ranging between 0 cm and 20 cm. The data is then used to analyze the behavior of the system, as well as the effects of the coupling between the two assemblies. As the assemblies move further apart, the system slowly transitions from two tightly coupled assemblies that essentially form a single core, to two almost independent cores. This study enables to produce a benchmark for future calculations and predefine an innovative way of designing high dominant ratio configurations, required for tackling Monte Carlo residual problems. An actual experimental program could be led in ad hoc zero power reactor (ZPR), such as the KUCA reactor of Kyoto University.

Approaching the full configuration interaction ground state from an arbitrary wavefunction with gradient descent and quasi-Newton algorithms.

We consider gradient descent and quasi-Newton algorithms to optimize the full configuration interaction (FCI) ground state wavefunction starting from an arbitrary reference state |0⟩. We show that the energies obtained along the optimization path can be evaluated in terms of expectation values of |0⟩, thus avoiding explicit storage of intermediate wavefunctions. This allows us to find the energies after the first few steps of the FCI algorithm for systems much larger than what standard deterministic FCI codes can handle at present. We show an application of the algorithm with reference wavefunctions constructed as linear combinations of non-orthogonal determinants.

Verification of the current coupling collision probability method with orthogonal flux expansion for the assembly calculations

The operation of nuclear reactors requires detailed knowledge of important safety parameters, such as the spatial power distribution, control rod worth, margin to departure from nucleate boiling (DNB), fuel pin burnup etc. To obtain a detailed analysis of all of the safety parameters requires a full core pin-by-pin coupled neutronics and thermal-hydraulics simulations which are too computationally expensive even for modern high-performance computer clusters. Therefore, the industrial standard approach in design and safety calculations are coupled neutronics and thermal-hydraulics codes for the steady state and transient simulations. In these codes, the neutronics calculations are typically performed at a nodal level using the diffusion approximation and assembly-homogenised sets of cross-sections while the thermal hydraulics relies on a channel model with fuel assembly sized channels. However, for determining safety limits, which are based on local pin-based parameters, the knowledge of the power and temperature distribution on a nodal level is not sufficient. Therefore, novel new approaches are required to resolve this multiscale and multiphysics problem to resolve the power distribution within the zones of interest. Pin-wise calculations, in this case, are performed by applying a transport solver using the heterogeneous fuel assembly geometry on an unstructured mesh with boundary conditions extracted from the 3D full core nodal diffusion solution. This combined nodal-transport approach will provide the detailed power distribution on the pin-level and perform coupled multiphysics simulations within reasonable simulation time limits, which is important for industry.To follow this strategy, a transport solver is required which can be used for the flux reconstruction on the pin level. Current coupling collision probability (CCCP) method seems to be a good choice for the development of such a solver.In this study, the developed transport solver utilising CCCP method with orthogonal flux expansion is tested and verified on the set of the benchmark problems. The results of simulations are compared with the results of Monte Carlo and deterministic code. The expansion of the flux by orthogonal polynomials allows us to avoid discretisation of the calculation regions while keeping the accuracy of the calculations to an acceptable level. The results of the calculations demonstrate good agreement with the results of Monte Carlo calculations. The comparison of the new method with the flat flux (today's industry standard approach) approximation demonstrates either an improved quality of the result for identical cell discretisation or reduced computational time to achieve the identical solution.

Modeling and neutronic analysis of pin-cell comprising nuclear fuel with different chemical composition and neutron moderator using Monte Carlo code OpenMC

Selection of a perfect nuclear reactor fuel demands the neutronic analysis of the available fuel materials in particular reactor environment. This paper summarizes the pin-cell analysis of eight (08) models considering five (05) different chemical compositions of nuclear fuel, three (03) different neutron moderator and two (02) types of cladding materials using the open-source Monte-Carlo code OpenMC. The fuel element includes UO2, UN, UC2, MOX, and Thorium fuel, whereas light water, heavy water, and graphite were considered as moderator. The effective multiplication factor (keff) was calculated for all the models and validated by the deterministic code Dragon. It was found that, while keeping the dimensions fixed, the graphite and heavy water moderated fuel pin-cells did not reach criticality. So, an appropriate pitch was found where these two cells reached criticality. Depletion and production of different fissionable materials, as well as neutron poison, were studied. Effect of enrichment, moderator to fuel ratio, and boron concentration on the keff in a typical water-moderated UO2 with zircalloy-4 clad pin-cell were also presented.

A Preliminary Study on the Use of the Linear Regression Method for Multigroup Cross-Section Interpretation

Computational modeling and simulations are widely used for evaluation of the performance and safety features of innovative nuclear reactor designs. Multigroup-based deterministic neutronics codes are often employed in these reactor design calculations because they can provide fast predictions of the neutron flux distribution and other neutronics characteristic parameters. Nevertheless, providing accurate multigroup cross sections for deterministic codes is an onerous job, which makes establishing an exhaustive cross-section library computationally prohibitive. Partly because of these reasons, multigroup neutron cross sections are normally stored only at certainty state points in the data library of these deterministic codes, and linear interpolation methodology is commonly utilized to estimate the cross sections at unknown states. However, the applicability of linear interpolation is limited, and the precision of its results is moderate. In this paper, we discuss a preliminary feasibility study that we performed on providing more precise multigroup cross sections for deterministic neutronics codes by using the linear regression methodology. Compared to the traditional linear interpolation method, the linear regression approach principally showed improved computational efficiency considering the use of more data in the cross-section library, and constructed hypothesis functions for the responses of interest with a higher order of accuracy. In this study, a case study on Lightbridge Corporation’s metallic fuel element was carried out to demonstrate the feasibility and advantages of linear regression in multigroup cross-section interpretation. A reference cross-section library was established through calculations conducted with the Monte Carlo neutronic code Serpent. Because of the preliminary nature of this feasibility study, only the macroscopic total cross section is considered. Linear interpolation and linear regression were both used to estimate cross sections at unknown states based on the data available in the library. By comparing the performance of both methodologies, we demonstrated that the linear regression methodology achieved wider applicability and better precision in cross-section interpretation. Moreover, the linear regression process was finished within 15 s using a single processor core, which indicated that the additional computational burden brought by the implementation of linear regression methodology in the task was acceptable.

Lossless Source Coding in the Point-to-Point, Multiple Access, and Random Access Scenarios

This work studies point-to-point, multiple access, and random access lossless source coding in the finite-blocklength regime. In each scenario, a random coding technique is developed and used to analyze third-order coding performance. Asymptotic results include a third-order characterization of the Slepian-Wolf rate region with an improved converse that relies on a connection to composite hypothesis testing. For dependent sources, the result implies that the independent encoders used by Slepian-Wolf codes can achieve the same third-order-optimal performance as a single joint encoder. The concept of random access source coding is introduced to generalize multiple access (Slepian-Wolf) source coding to the case where encoders decide independently whether or not to participate and the set of participating encoders is unknown {\em a priori} to both the encoders and the decoder. The proposed random access source coding strategy employs rateless coding with scheduled feedback. A random coding argument proves the existence of a single deterministic code of this structure that simultaneously achieves the third-order-optimal Slepian-Wolf performance for each possible active encoder set.

Computational burnup analysis of the TRIGA Mark II research reactor fuel

In this study, analysis of the complete operational history of the “Jožef Stefan” Institute (JSI) TRIGA reactor was performed. Reactor power changes, core configurations and weekly excess reactivity measurements were analysed to obtain the needed data for fuel burnup calculations. More than 50 years of reactor operation was simulated using deterministic code TRIGLAV and stochastic code Serpent-2. The calculated core reactivities are in good agreement compared with the excess reactivity measurements. Code-to-code comparison is presented. Clear agreement is observed when comparing changes in core excess reactivity, and discrepancies are observed in the comparison of individual fuel element burnup and its isotopic composition. The Serpent-2 results are in better agreement with the measurements compared to the TRIGLAV code; nevertheless, a conclusion can be made that the TRIGLAV code is viable for TRIGA fuel management and burnup analysis. A three-dimensional (3D) burnup study was conducted, where individual fuel elements were further divided into multiple angular and axial depletion zones. Notable burnup effects were observed, and an explanation using surrounding water distance is presented.

Composite grid designs for adaptive computer experiments with fast inference

Summary Experiments are often used to produce emulators of deterministic computer code. This article introduces composite grid experimental designs and a sequential method for building the designs for accurate emulation. Computational methods are developed that enable fast and exact Gaussian process inference even with large sample sizes. We demonstrate that the proposed approach can produce emulators that are orders of magnitude more accurate than current approximations at a comparable computational cost.

Comparison of Deterministic and Stochastic Depletions in Graphite-Filled MOX Fuel Assembly Design

A comparison between stochastic and deterministic depletion calculations based on a graphite-filled MOX fuel assembly configuration is presented in this paper. The infinite multiplication factors and isotope inventory changes as a function of burnup obtained by Monte Carlo method module SCALE/KENO and deterministic method module SCALE/NEWT are compared with those obtained by deterministic code HELIOS. The impact in calculation results by using different nuclear data library is also investigated. The SCALE/KENO results show a good agreement with SCALE/NEWT results in the eigenvalue as a function of burnup (less than 0.1%). However, the absolute difference in the initial k¥ between SCALE/KENO and NEWT modules and HELIOS results is quite large (around 1.1%) and the isotope inventory changes show quite differently at the end of cycle. The uranium and plutonium depletion rates calculated by SCALE/KENO and SCALE/NEWT have quite good agreement. By using the same data library, the good agreement between stochastic and deterministic code’s results were confirmed.

Deterministic and stochastic modeling of rarefied gas flows in fusion particle exhaust systems

In the present work, a deterministic approach is applied for the first time ever to simulate the rarefied gas flow in the particle exhaust system of a nuclear fusion device. As an example of such a system, the pumping area of the DEMO (DEMOnstration Fusion Power Plant) fusion reactor is considered, which is characterized by high geometrical complexity and strong gradients of macroscopic quantities. The Knudsen number in this system may vary from free molecular up to the slip regime and the flow behavior must be described by the Boltzmann equation. In the present work, the Boltzmann equation is approximated by the well-known Bhatnagar–Gross–Krook and Shakhov kinetic models supplemented with the deterministic discrete velocity method. In addition, in order to assess the capabilities of the deterministic modeling, the problem has also been studied by solving the Boltzmann equation with the stochastic direct simulation Monte Carlo (DSMC) method. Extended comparisons between the deterministic and stochastic methods in terms of all macroscopic quantities of practical interest, namely, pressure, number density, temperature, and pumping fluxes, are performed and remarks about the effectiveness of the implemented deterministic approach have been drawn. Results are obtained by assuming He and D2 gas flows, various values of the capture coefficient at the pumping opening, and two different scenarios of the inlet gas temperature. In all examined cases, the deterministic results are in very good agreement with the DSMC ones, with the maximum relative deviation being less than 4%. The nonlinear deterministic code is significantly faster than the stochastic DSMC code for acceptable noise levels. The pumping fluxes and the pressure values in the vicinity of the pumping opening, both quantities useful for pumping system evaluation, have been calculated in terms of the capture coefficient. The present work may support decision making on the suitability of the pumping technology of DEMO and the design of the pumping system.

ВЕРИФИКАЦИЯ ГРУППОВОГО ФИЗИЧЕСКОГО МОДУЛЯ В ПРОГРАММЕ РАСЧЕТА НЕЙТРОННОЙ КИНЕТИКИ КИР2 НА ОСНОВЕ БЕНЧМАРК-ТЕСТА С5G7

Describes the software used in the calculation, according to the KIR2 program and the algorithms developed by the MAGMA group module (Group modulus taking into account anisotropic scattering). The results of the verification stage of the KIR2 program with a group physical module are presented. For verification, we used the C5G7 mathematical benchmark test, in which the energy field is divided into 7 groups. The results of comparison with the MCNP benchmark program on the effective breeding coefficient, confidence intervals and deviations from the benchmark program are presented. A comparison with other programs based on the Monte Carlo method (VIM and UNKMK and other independent calculations using the MCNP program) is also given. In addition, the use of the calculated data of the KIR2 program with high statistics as reference data for deterministic class codes (ATTILA, MCCG3D, CRX, PARTISN, UNKGRO) and programs based on the Monte Carlo method is presented. The analysis of the effectiveness of using comparison methods by deviations and confidence intervals is presented. The results of the verification phase of the KIR2 program with the MAGMA group module are summarized.

Safety analysis of the DONES primary heat removal system

Abstract The development of a neutron source able to reproduce the irradiation conditions typical of a nuclear fusion reactor, in order to test candidate structural materials, is the main goal of the Work Package Early Neutron Source (WPENS) of the EUROfusion action. This source, named Demo Oriented NEutron Source (DONES), is a facility where neutrons are produced by means of D-Li interactions. More in detail, a beam of 125 mA deuterium ions at the energy of 40 MeV strikes a lithium jet flowing in a purposely shaped channel in order to obtain an intense and stable neutron flux for the irradiation of material samples. In the framework of these activities, safety analyses are a key aspect in the DONES design and development. Among the postulated initiating events identified during the preliminary Failure Mode Analysis, the Loss of Flow Accident (LOFA) in the Primary Heat Removal System of the lithium loop, due to a trip of the electro-magnetic pump, is one of the most severe. In fact, the loss of lithium flow, combined with the failed stop of the accelerator, could lead to the destruction of the lithium flow channel in correspondence of the component named Back-Plate. For this reason, it has been chosen to investigate the LOFA adopting the deterministic system code RELAP5-3D. Results, obtained from this analysis, are critically discussed and compared with those obtained by a similar calculation carried out with MELCOR 1.8.6 code, in order to assess the RELAP5-3D capability of describing systems adopting lithium as working fluid.