Lattice Code Research Articles

Few-group diffusion theory parameters from lattice calculations using leakage corrected collision probabilities

The paper describes a new method for lattice calculations for obtaining the leakage corrected neutron distribution and spectrum and few group diffusion theory parameters therefrom. The leakage correction is carried out, with the help of leakage corrected collision probabilities, during the lattice calculation of the heterogeneous medium and not after homogenisation following a lattice calculation. Expressions are derived for axial and radial leakage corrected collision probabilities using a method similar to the one used in an earlier paper for obtaining homogenised axial diffusion coefficients. These expressions have been coded in the LWR lattice code BOXER3 for calculation of the leakage corrected flux distribution and few group diffusion theory parameters. Comparisons of the results of core calculations using parameters obtained by the proposed method (i.e. using leakage corrected flux spectrum and distribution) and by standard P1 and B1 methods with Monte Carlo results are presented.

INTERFACING OF WIND ENERGY CONVERSION SYSTEM WITH SOLID STATE TRANSFORMER FOR SEAMLESS FAULT RIDE THROUGH OPERATION

In wind vitality change frameworks, the major recurrence venture up transformer goes about as a key interface between the breeze turbine and the lattice. As of late, there have been endeavors to supplant this transformer by propelled control hardware based strong state transformer (SST). This paper proposes a setup that consolidates the doubly bolstered enlistment generator-based breeze turbine and SST activity. The primary target of the proposed design is to interface the turbine with the lattice while giving upgraded task and execution. In this paper, SST controls the dynamic capacity to/from the rotor side converter, accordingly, wiping out the network side converter. The proposed framework meets the ongoing lattice code prerequisites of wind turbine activity under blame conditions. Also, it can supply receptive power tothe framework when the breeze age isn't up to its appraised esteem. An itemized reenactment examine is directed to approve the execution of the proposed setup.

Defeating Lattice-Based Data Hiding Code Via Decoding Security Hole

Lattice code has been widely used for data hiding. It can provide security for data hiding by randomly translating its codebook with a secret dither. However, besides the secret dither, there are an infinite amount of points that are near the secret dither and can also be used for perfect decoding in the noiseless scenario. This means that lattice-based data hiding has a serious security hole, named decoding security hole (DSH) in this paper. After a theoretical analysis of DSH, we find that these points form a convex polytope and the centroid of this convex polytope is the secret dither. Based on this finding, a simple yet effective attack method is presented to estimate the secret dither of lattice-based data hiding. Extensive experimental results show that the proposed method significantly outperforms state-of-the-art attack methods, especially when the number of observations is small or the document-to-watermark ratio changes over a wide range.

Study of PHWR and BWR lattice benchmark problems with multigroup multidimensional neutron transport code dragon

Neutron transport codes are an integral part of reactor physics calculation. The freely available lattice code DRAGON results from an effort to unify inside a single computer code various well-established numerical techniques and calculation methodologies which are commonly used to solve the neutron transport equation. It is of utmost importance for the user community, both from safety and operation point of view, that the codes being utilised for neutronic calculations maintain a high degree of confidence in their predictions. Benchmark problems are designed to test the capability of a neutronic code by comparing the results obtained from the code with well-established results, either from experimentation or from other validated neutronic codes. After PWRs, BWRs, and PHWRs are two of the most popular types of nuclear reactors currently in use worldwide. Consequently, the ability to perform accurate neutronic calculation involving these lattice types can be deemed as a necessary requirement in most modern lattice codes. In this work, we will study two benchmark problems based on the aforementioned reactor lattice types. Using the lattice code DRAGON and subsequently comparing the results with available published solutions, we aim to ascertain the capability of DRAGON to effectively simulate both of these two types of lattices with fresh and burnt fuel.

An Approximation of Theta Functions with Applications to Communications

Computing the theta series of an arbitrary lattice, and more specifically a related quantity known as the flatness factor, has been recently shown to be important for lattice code design in various...

Modelling and analysis of fuel assembly vibrational modes in PWRs using SIMULATE-3K

Some of the KWU pre-KONVOI PWRs operating across Europe saw a systematic increase in the neutron noise levels over several cycles in the last decade, and subsequently, core internals’ movements, especially vibrations of fuel assemblies with specific designs were identified as one of the plausible causes. Therefore, it is important to develop computational methods that can allow to investigate and predict the reactor noise response to fuel assemblies vibrations. To this aim, the 3D nodal reactor dynamics code SIMULATE-3K is used at PSI with a special module called the ‘assembly vibration model’ that imitates time-dependent motions of fuel assemblies by dynamically modifying the water-gaps surrounding the laterally moving fuel assemblies. The varying water-gaps are represented by the variation in the corresponding two-group macroscopic cross sections generated using the lattice code CASMO-5 in 2D. The studies conducted so far to assess the methodology for full core noise simulations were based on assuming vibrations of a clamped-free cluster of fuel assemblies that are unsupported from both ends. However, as this represents a non-physical movement, further developments were made at PSI to allow simulating more realistic movements of fuel assemblies such as the cantilevered mode vibration. The updated methodology, along with evaluations of the simulated noise response to realistic vibration modes, is presented in this paper. Results show that, as expected, the radial and axial neutron noise behaviour follow the vibration pattern of the imposed time-dependent axial functions corresponding to the natural oscillation modes of the fuel assemblies, thereby providing confidence in the application of the developed methodology for numerical neutron noise analyses of the PWR cores.

Neutronic study of the 2-MW TRIGA MARK-II research reactor by the deterministic codes DRAGON5 & DONJON5

The main objective of this work is to perform a neutronic study of the 2 MW TRIGA MARK-II research reactor of the National Centre of Sciences, Energy and Nuclear Techniques (CNESTEN), Rabat, Morocco and then validate the results by comparing the experimental values and those published for an ordinary 2 MW TRIGA MARK II research reactor. The core diffusion code DONJON5 and the lattice code DRAGON5 were coupled to perform a full model of the TRIGA core and their consistency and accuracy were established by benchmarking the TRIGA experiments. In this study, the nuclear data libraries ENDF/B-VII.1 and JEFF3.1 based on 172 energy groups were used. The group constants of all the reactor components were generated using DRAGON5 code and the collision probability method. These group constants were used then in the DONJON5 core code to calculate the multiplication factor, core excess reactivity, total and integral control rods worth as well as power peaking factors. Good agreement found between the calculated and measured results.

Energy group search engine based on surrogate models constructed with the RAVEN/NEWT/PHISICS sequence

Transient calculations with nodal neutronics codes entail few-group energy structures. In systems other than LWRs, significant efforts are devoted to obtain satisfying group structures. The energy cut-offs available in the literature do not always match the energy boundaries available in lattice codes. This paper demonstrates an automated sequence that searches for suitable coarse-group configurations. The sequence couples the lattice code T-XSEC/NEWT for cross section generation and collapsing, the nodal code PHISICS for core calculations and the software RAVEN for variable sampling and analytical purposes. T-XSEC/NEWT receives an energy group configuration from RAVEN to generate microscopic self-shielded cross sections in a coarse format. PHISICS provides the core solution using the microscopic libraries. The performances of the group structures in the core model are stored to train a Reduced Order Model (ROM) built on-the-fly. The ROM spares the necessity to survey the large input space of all possible energy group structures, or expert judgements. The solution provided by RAVEN is a Limit Surface of group structures fitting success criteria. The approach is tested on a simplified two-dimensional HTTR core model. The Limit Surface obtained by RAVEN derives a few six-group structures fitting the HTTR model.

Extended development of a Monte Carlo code OpenMC for fuel cycle simulation of molten salt reactor

Adopting liquid fuel and on-line reprocessing scenario are the unique features of molten salt reactor (MSR). Considering lattice code for thermal reactor is not suitable for MSR calculation, batch-wise fuel salt reprocessing scheme and “two-step” deterministic calculations cause some approximations in simulation of MSR on-line continuous fuel reprocessing, this study focuses on the development of a direct calculation method for MSR fuel cycle simulation based on an open source Monte Carlo code OpenMC. A fictitious decay constant and an external source term were introduced into traditional burnup equation for accurate simulation of on-line fuel reprocessing. Finally, a MSR fuel cycle simulation code OpenMCB-MSR was developed by coupling OpenMC and burnup code with Python script. Two pressurized water reactor (PWR) pin cell benchmarks without considering fuel on-line reprocessing, and one actual MSFR fuel cycle benchmark considering fuel on-line reprocessing were used for verification of OpenMCB-MSR. By comparison with reference results, the maximum differences of kinf calculated by OpenMCB-MSR are no more than 400 pcm both for two PWR pin cell benchmarks. Moreover, apart from isotopes with small absolute nuclide number density, all the other isotopes' nuclide number densities show a difference of less than 10%. For MSFR benchmark, the reactivity coefficients, isotope mass evolutions during fuel cycle process, mass evolution of fission products in core and breeding ratio calculated by OpenMCB-MSR show a good agreement with reference results. At equilibrium state, apart from isotopes with very small absolute mass, the differences of other isotopes' mass are no more than 5.0% in comparison with reference results. Benchmark verification results indicate that the method of MSR fuel cycle simulation based on OpenMC code is correct, and OpenMCB-MSR has capability of MSR fuel cycle analysis.

Verification of the TIGRSP Computer Code as Applied to a 19-Rod Fuel Assembly Using CFD Computations

For assessing the core critical heat flux ratio in VVER-type nuclear reactors, the lattice computation code TIGRSP (steady-state thermal and hydraulic analysis of parameters in fuel rod bundles) is used. Despite the fact that quite a large amount of verification studies has been accomplished and that the code has passed the certification procedure, work on improving the code capabilities is still being continued. One of the modern tendencies is the wide-scale involvement of CFD codes for studying local parameters in fuel assemblies (FAs). Along with comparison with experimental data, it is advisable to carry out cross verification of lattice codes with the results of 3D thermal-hydraulic computations for conditions for which experimental data are either lacking or limited for some or other reasons. This article considers thermal-hydraulic processes during coolant flow in a 19-rod assembly with parameters close to the nominal conditions in the FAs of a VVER-1000 reactor. The 3D model is verified with respect to empirical formulas and experimental data. Based on the results of test and verification computations, we determined the mesh and turbulence model parameters using the ANSYS CFX code by means of which it is possible to obtain reliable results in estimating the hydraulic characteristics of FAs fitted with spacer grids, heat transfer in the single-phase region, and coolant flow distribution over the FA cross section. The CFD computation of coolant flow for the 19-rod assembly is carried out, and the coolant mass velocity and temperature in different sections over the length and corresponding cells of the TIGRSP code are calculated. The TIGRSP code has been verified against experimental data and taking into account the CFD simulation of the 19-rod FA, and a software module for graphically visualizing the lattice code output results has been developed. The presented data can be used for verification of thermal-hydraulic codes and in elaborating the design of FAs for VVER-type reactors.

A review of history parameters in PWR core analysis

We present a review of the methodologies for history effect modelling with few-group cross sections for PWR fuel assemblies. Different depletion conditions with varying moderator density, fuel temperature and protracted control rod insertion are considered where the exposure history can show significant changes in the local isotopic inventory and in the neutron spectra. Cross sections are homogenized over a classical PWR-type UO2 fuel assembly provided by the Burn-up Credit Criticality Benchmark NEA-6227 and condensed in two energy groups by the lattice code APOLLO2.8. The methodologies are analyzed in view of their capability to improve the error in microscopic and macroscopic cross sections, and the associated multiplication factor and the spectral index in the infinite homogeneous medium.

Numerical Simulation and Sensitivity Study of the Rhodium Self-Powered Neutron Detector Used in PWR

Focusing on the specific self-powered neutron detector (SPND) using rhodium as the emitter material, this paper performs the numerical simulation and sensitivity study for SPNDs used in a typical pressurized water reactor (PWR). The computational model was developed based on a PWR lattice code bamboo lattice and a Monte Carlo code Geant4. In order to validate the model, the neutron sensitivities with single-energy incident neutrons are calculated and compared against the experimental results. Influences of the incident neutron energy spectrum and the emitter burnup to the neutron sensitivity of the SPND are analyzed. Bamboo lattice is used to calculate the incident neutron energy spectrum and the emitter nucleus densities which are the environment of the SPND. Numerical results show that the neutron sensitivity decreases due to the increase of the enrichment, the assembly average burnup, the boron concentration, the moderator temperature, and the burnable poison rods. The increase in the emitter burnup will lead to the decrease of the neutron sensitivity. Taking the incident neutron energy spectrum and the nucleus density into account together, the neutron sensitivity decreases with the increase in the assembly average burnup.

RISMC industry application #1 (ECCS/LOCA): Core characterization automation: Lattice codes interface for PHISICS/RELAP5-3D

The United States Nuclear Regulatory Commission (U.S. NRC) is currently proposing rule-making “10 CFR 50.46c” to revise the loss-of-coolant-accident (LOCA) and emergency core cooling system (ECCS) acceptance criteria to include the effects of higher burn-up on cladding performance. The key implications of this proposition are that the cladding performance cannot be evaluated anymore as separated from other disciplines, but needs to be evaluated in a coupled manner with other physics. The Risk-Informed Safety Margin Characterization (RISMC) Pathway initiated several programs at Idaho National Laboratory (INL) to support the industry in the transition to the new rule. One of these programs is the Industry Application #1 (IA1). IA1’s goal is to develop an Integrated Evaluation Model (IEM) called LOCA Toolkit for the US (LOTUS). This tool connects five major disciplines involved in LOCA analysis, among them is (automated) core design (CD-A). This paper focuses solely on the design of LOTUS' CD-A module as well as a demonstration application of the CD-A module to a generic Pressurized Water Reactor (PWR). The demonstration of the other LOTUS disciplines together with a demonstration example of the final risk-informed safety margin analysis is published in a separate paper. LOTUS is meant to provide the methodology framework into which the user can plug his established tools and codes. With the CD-A, the plant owner/operator will characterize his core design with the tools he has. He will then integrate his tools/methods into the LOTUS framework for the downstream safety analysis. For the current CD-A demonstration, the tools used are the already coupled codes PHISICS and RELAP5-3D, while cross section generation is done using the Studsvik lattice code HELIOS-2.

Fast-adaptive color-collaborative constellation designs for multicolor multiple-input multiple-output visible light communications systems.

A fast-adaptive color-collaborative signal constellation (CCSC) is proposed for chromaticity-changeable multicolor multiple-input multiple-output (MIMO) visible light communications (VLC) systems. The design of CCSC aims at developing the constellation to minimize the average optical power with shaping-based lattice code. For multicolor VLC signals, we arrive at the fact that the optimum shape of the constellation bounding region is an inequilateral N-D simplex. With the densest lattice-packing structure, detailed design steps of CCSC are fully elaborated by lattice construction, effective point selection, and chromaticity adjustment. As CCSC has a low complexity, its constellation structure can adapt quickly to changeable chromaticity demands. Simulation results show that the performance of CCSC is better than enhanced standard color shift keying (CSK) and is close to iterative CSK modulation based on numerical search.

A leakage correction with SPH factors for two-group constants in GET-based pin-by-pin reactor analyses

In this paper, a new leakage correction method called GET plus SPH (GPS) method is introduced. First, both GET-based and SPH-based two-step pin-by-pin methods are applied to a small PWR benchmark to evaluate their limited accuracy. In order to improve the accuracy in the two-step method, we introduced the cross-section (XS) dependent SPH factors, which are parameterized as a function of the integrated pin-wise albedo information, i.e., current-to-flux ratio (CFR). For the functionalization of the XS-dependent SPH factor, small color-set problems are modeled to obtain the relationship between the CFR information and the SPH factors. The color-set problems are comprised of several fuel assemblies (FAs) to obtain physically meaningful perturbations in pin-wise CFR values relative to the single-assembly CFR values. The GPS functions are separately determined for each region in FA to consider their position-dependent characteristics. In this work, both the color-sets and whole core problems are solved by the DeCART2D code, which is a 2-D method of characteristic based lattice code. The GPS method is implemented to an in-house pin-wise diffusion analyzer based on a pin-wise CMFD method. To test the performance of the GPS method, a small PWR benchmark is considered in this study. In addition, the same GPS functions are applied to its small and large variants to demonstrate that the GPS functions can be reliably utilized regardless of the different core configurations. The results of this work show that the GPS method can improve substantially the accuracy of the pin-wise reactor analyses with a small additional computational cost.

Modeling and simulation of a TRIGA MARK-II research reactor using WIMSD-5B and CITATION codes

The main objective of this study is to analyse neutronic safety parameters of the Moroccan TRIGA Mark-II research reactor using the WIMSD-5B and CITATION computer codes. New 172-group libraries of multi-group constants for the lattice code WIMSD-5B have been generated for all isotopes presented in the TRIGA reactor core by processing nuclear data from ENDFB-VII.1, JENDL-4.0 and JEFF-3.1.1 using NJOY99. The lattice code WIMSD-5B was employed to generate multi-group cross sections in the suitable format that will be used by the 3-dimensional diffusion code CITATION. This later was used to calculate various neutronic safety parameters of the TRIGA Mark-II research reactor, such as reactivity excess and neutron fluxes profiles. The results of these calculations are compared to the results of Monte Carlo calculation based on MCNP code. A good agreement is achieved and the current computation scheme will be adopted for our further coupling neutronic/thermal-hydraulic study of the Moroccan TRIGA reactor.

Blind Integer-Forcing Interference Alignment for Downlink Cellular Networks

A novel blind interference alignment (IA) scheme in conjunction with interference decoding by virtue of integer forcing is proposed for downlink cellular networks without channel state information at the base station. In the proposed scheme, inter-user interference at each mobile user is aligned in blind manner, and by employing the same lattice code for all users, each user directly decodes integer-linear combinations of interfering codewords from the aligned interference signals in contrast to the previous works that simply null out the aligned interference by zero forcing. Numerical simulations demonstrate that the proposed scheme significantly improves the sum rate compared with the previous blind IA schemes.

Development and verification of a model for generation of MSFR few-group homogenized cross-sections based on a Monte Carlo code OpenMC

A concept of molten salt fast reactor (MSFR) was proposed in EVOL to burn transuranium element discharged from pressurized water reactors. MSFR is featured by fast spectrum and using liquid fuel salt containing UF4 or ThF4. Some issues are presented, for instance, global material arrangement affects the local neutron spectrum due to long neutron free path, and fluoride salt (LiF-BeF2) has nonnegligible thermal neutron scattering effect. Thus, lattice code prepared for thermal-spectrum reactor is not suitable for MSFR calculation. In this study, “two-step” calculation scheme combining Monte Carlo method and deterministic method was prepared for MSFR calculation. A tool named TRANS was developed to transfer tally data from an open source Monte Carlo code OpenMC into few-group homogenized cross-sections, and one benchmark based on pressurized water reactor and two types of model based on MSFR were used for verification. Besides, the applicability of few-group parameters generated by different model to MSFR whole-core calculation was analyzed. Finally, MSFR neutronics characteristics at steady-state were calculated using MOREL. The results show that the few-group parameters generated by one-dimension (1D) and two-dimension (2D) model are correct, and it is feasible to use OpenMC to generate few-group parameters. In case of 1D homogenization model, few-group parameters by 1D model (b) can give more accurate results both for eigenvalue and flux distribution. In MSFR whole-core calculation, using few-group cross-sections generated by 2D model has better accuracy in flux distribution, however, using few-group cross-sections generated by 1D model has better accuracy in keff calculation. Moreover, the neutronics parameters of MSFR calculated by MOREL code agree well with that by other institutes.

Depletion chain optimization of lattice code STREAM for LWR fuel assembly burnup analysis

A depletion chain simplification method is applied to UNIST lattice code STREAM (Steady state and Transient REactor Analysis code with Method of Characteristics) in this paper to alleviate the computational burden of depletion calculation associated with a large depletion matrix. A simplified burnup matrix (burnup chain) of 464 nuclides and 10,638 transitions is thus created from a large detailed burnup matrix containing 3,837 nuclides and 43,416 transitions from ENDF/B-VII.0 nuclear decay data. The simplified burnup matrix is optimized for the purpose of calculating effective neutron multiplication factors (keff) and power distributions with reduced computation time and memory usage. The nuclide selection method relies on the Generalized Perturbation Theory (GPT): by exploiting the adjoint function of nuclide number densities as derived with GPT, a set of nuclides which must be included in the simplified chain (nuclides with important contribution to reactivity) is determined. Numerical verification of the simplified burnup chain is conducted using the deterministic neutron transport analysis code STREAM, developed to perform whole light water reactor (LWR) core calculations with the direct transport analysis method and the two-step method. The simplified burnup chain is tested on the 16 LWR fuel assembly depletion problems from the Virtual Environment for Reactor Application (VERA) benchmarks, including burnable poison (BP) pin cells commonly used in nuclear reactor design such as gadolinia, Pyrex, AIC, B4C and IFBA, and one OPR-1000 fuel assembly with gadolinium bearing fuel depletion problem. For burnup up to 80 MWd/kg and 235U enrichment ranging from 2.1 w/o to 4.6 w/o, the calculations with the simplified burnup chain predict the keff variations within 10 pcm and identical power distributions, with a speed-up factor from 20 to 40 in depletion calculation and a reduction factor by 3–4 of the total simulation time compared to the ones with the detailed burnup chain.

A study of the impact of mixed mode of fuel salt in plenum on steady-state performance of channel-type molten salt reactor

In this study, a coupled neutronics and thermal-hydraulics (THs) code named MOREL2.0, based on multi-group diffusion theory and multi-channel THs model, was employed to analyze a channel-type molten salt reactor TMSR-LF and the impact of different fuel mix mode in plenum on its steady-state performance was also discussed. MOREL2.0 adopts “two-step” calculation scheme, in which few-group homogenized parameters are generated by lattice code PIJ, and diffusion equation considering the drift of delayed neutron precursors is coupled with multi-channel THs model, and the least square method is implemented for cross-section feedback in coupling scheme. The numerical results indicate that TMSR-LF has negative reactivity coefficients in term of inlet fuel temperature and core power level, and the response of keff to mass flow is different for cases of nominal power and zero power, and keff decreases with the rise of time of fuel salt spent in external loop and gradually tends to steady. Different mix mode in plenum have a greater impact on the mass flow distribution and delayed neutron precursors distribution, but less impact on core lumped parameter such as keff and effective delayed neutron fraction.