Thermal-hydraulic Feedback Research Articles

VALIDATION OF WIMS11 FOR SMALL MODULAR REACTOR ANALYSIS

The WIMS (Winfrith Improved Multigroup Scheme) reactor physics code is actively being developed for whole core modelling of a range of Small Modular Reactor types including the Pressurized Water Reactor (PWR), High Temperature Reactor (HTR), and Liquid Metal Cooled Fast reactor (LMFR). These developments include the capability for whole core multiphysics modelling with neutronics and thermal hydraulic feedback, as well as methods to determine the power deposition from neutron and gamma heating. Flux solutions are obtained using a wide variety of deterministic methods including diffusion theory, SP3, and full transport with the method of characteristics and Sn discrete ordinates methods, as well as multi-group Monte Carlo methods. The SP3 method allows both steady state and time dependent transient solutions by solving the time dependent SP3 equations. A wide variety of nuclear data libraries are available with WIMS including data from the JEF3.3, ENDF/B-VII.0 and CENDL3.1 nuclear data evaluations. This paper presents validation of the latest version of the WIMS code, WIMS11, for PWR and HTR systems. Comparisons are made against physics data obtained from the OECD/NEA PWR Watts Bar multi-physics benchmark and the IAEA HTR-10 benchmark, as well as neutron and gamma heating experiments that took place on the NESSUS reactor at Winfrith in the United Kingdom. In each case, validation of WIMS has been obtained by comparison either against measured data, or results provided by other benchmark participants that have been obtained with alternative deterministic or Monte Carlo methods.

DEVELOPMENT OF A COUPLED SUBPLANE CAPABILITY IN MPACT

Recent efforts in the development of the deterministic transport code MPACT have been devoted to preparing the 2D/1D subplane method to be a production-level capability, as well as leveraging a multilevel coarse mesh finite difference (CMFD) approach to substantially reduce the runtime of target problems. For example, as compared to the previous default 2D/1D solver in MPACT on a standard quarter core model, the new solver reduces in core-hour requirements by ~5–6×. Previous work focused solely on cases without multiphysics feedback, which is obviously important for analyzing the more realistic problems of operating reactors. The work presented in this article focuses on efforts to incorporate thermal hydraulics (TH) coupling through CTF by leveraging what are termed as subgrid solvers, which effectively treat material heterogeneities within subplane regions. Previous efforts have targeted using subgrid solvers for control rods and spacer grids; in this work, they are applied to account for the material property heterogeneities with regards to temperature/density distributions. This will allow the fidelity of coupling to be maintained while still reaping the performance benefits. These new developments are demonstrated on two problems: (1) a single assembly case with feedback, known as Progression Problem 6a, and (2) a 3×3 cluster of assemblies with feedback based on Progression Problem 4a. The results demonstrate notable performance improvement potential for cases with TH feedback, but this approach is more dependent on the iteration process.

MULTI-PHYSICS TRANSIENT SIMULATIONS WITH TRIPOLI-4®

In this work, we present the first dynamic calculations performed with the Monte Carlo neutron transport code TRIPOLI-4R with thermal-hydraulics feedback. For this purpose, the Monte Carlo code was extended for multi-physics capabilities and coupled to the thermal-hydraulics subchannel code SUBCHANFLOW. As a test case for the verification of transient simulation capabilities, a 3x3-assembly mini-core benchmark based on the TMI-1 reactor is considered with a pin-by-pin description. Two reactivity excursion scenarios initiated by control-rod movement are simulated starting from a critical state and compared to analogous simulations performed using the Serpent 2 Monte-Carlo code. The time evolution of the neutron power, fuel temperature, coolant temperature and coolant density are analysed to assess the multi-physics capabilities of TRIPOLI-4. The stabilizing e_ects of thermal-hydraulics on the neutron power appear to be well taken into account. The computational requirements for massively parallel calculations are also discussed.

ON THE FLY PREDICTION OF TH-DEPENDENT SPATIAL MACROSCOPIC CROSS-SECTIONS USING FFT

Monte Carlo (MC) codes can accurately model neutron transport in nuclear reactors. However, the efficient inclusion of thermal-hydraulic (TH) feedback within the MC calculation sequence is still an open problem, particularly when burnup’s time-evolution must be included in the analysis. For this reason, deterministic codes, leveraging the use of macroscopic cross-sections generated with higher order methods from 2D lattice calculations, are still widely used to perform reduced-order multiphysics analyses. However, traditional cross-sections generation procedures typically decompose the large core problem into multiple assembly-level problems; thus not having the ability to capture inter-nodal effects. Moreover, the pre-generation procedure requires additional pre-computational time to perturb/branch the problem for various operational conditions (e.g. fuel temperature), which, again, is decoupled from the core. In this paper, we propose a new method leveraging the use of Fourier transfer functions to predict the cross-sections distribution due to a variation in TH conditions. The method was tested against a 3D BWR unit-cell problem with realistic density profile and axial fuel heterogeneity. The method was able to compute the mono-energetic cross-sections distribution with maximum error lower than 2%. Insights on the influence of the statistics used to generate the cross-sections on the accuracy of the results is also provided.

CONTRIBUTION OF THERMAL-HYDRAULICS SIMULATION TO CRITICALITY ANALYSIS OF A DEBRIS BED NUMERICAL MOCK-UP

In this work, we evaluate the impact of simulating the thermal-hydraulics feedback in criticality risk assessment in a benchmark configuration corresponding to a simplified debris bed. We have recently discussed the coupling of the multi-phase thermal-hydraulics code MC3D with a reactivity evaluation scheme based on multi-point kinetics, which paves the way towards the assessment of the system behavior in terms of energy release. In this work, we analyze the system reactivity as a function of the thermal-hydraulics state of the system. For our investigation, we have considered a simplified cylindrical region and assumed that the fuel particles in the mixture consist of spheres of small diameter. The power has been adjusted to be representative of nuclear decay heat. For most of the examined configurations, the maximum reactivity lies below zero, which shows that the occurrence of a criticality event is likely to be excluded, thanks to the contribution of the decay heat of the fuel.

Improved MPACT energy deposition and explicit heat generation coupling with CTF

The CASL neutronics code MPACT assumes local energy deposition with equilibrium delayed energy for steady-state and transient calculations. These approximations limit the accurate representation of the heat generation in space and its variations over time, both of which are essential for power distribution and thermal–hydraulic coupling analyses. This paper presents an explicit energy deposition model considering the neutron and gamma heating of all regions and the time-dependent delayed energy. The MPACT/CTF interfaces are updated to transfer the explicit heat sources. The new model agrees well with MCNP for problems without thermal–hydraulic feedback. The MPACT/CTF coupled calculation for a hot-full-power quarter-core case using the new model exhibits a reduction of peak pin power by 2.3% and fuel centerline temperature by 17 K. The new model also shows a keff difference up to −100 pcm in depletion and a 30 K peak fuel temperature reduction in a reactivity-initiated-accident problem.

Modelling nuclear fuel assembly with thermal-hydraulic feedback and burnup using WIMS-PANTHER-Serpent

State-of-the-art deterministic code sequence WIMS-PANTHER and Monte Carlo particle transport code Serpent are employed in this work for computationally modelling the UK EPR nuclear reactor core’s fuel assembly with and without thermal-hydraulic feedback, the results of which targets the government energy policymakers and wider academic community.

Nonlinear stability analysis of a self-pressurized, natural circulation integral reactor via the Lyapunov's second method

The non-linear stability of a small modular self-pressurized reactor is assessed here by means of a direct Lyapunov function. The trial and error method is analyzed by applying an appropriate dynamical model for this type of reactors. A function containing all the states of the system which has conditions of a direct Lyapunov function is presented. This continuous function is positive definite and its derivative is negative semi-definite. The results indicate that the primary coolant is asymptotically global stable over its entire power range. Also, we assess the effects of neutronic and thermal hydraulic feedbacks on the system stability. Its been found that in the presence of these feedbacks, the system is stable in the entire power range.

Neutronic Simulation of Fuel Assembly Vibrations in a Nuclear Reactor

The mechanical vibrations of core internals such as fuel assemblies (FAs) cause oscillations in the neutron flux that require in some circumstances nuclear power plants to operate at a reduced power level. This work simulates and analyzes the changes of the neutron flux throughout a nuclear core due to the oscillation of a single FA without considering thermal-hydraulic feedback. The amplitude of the FA vibration is bounded to a few millimeters, and this implies the use of fine meshes and accurate numerical solvers due to the different scales of the problem. The results of the simulations show a main oscillation of the neutron flux with the same frequency as the FA vibration along with other harmonics at multiples of the vibration frequency much smaller in amplitude. Also, this work compares time domain analysis and frequency domain analysis of the mechanical vibrations. Numerical results show a close match between these two approaches for the fundamental frequency.

A Serpent/OpenFOAM coupling for 3D burnup analysis

In nuclear reactor analysis, a relevant challenge is to achieve a suitable global description of nuclear systems through the coupling between neutronics and thermal hydraulics. Indeed, a multi-physics approach improves the reactor safety analysis and the design of different types of nuclear systems; in addition, it allows the investigation of physical effects at different scales of time and space. In this context, a challenging task is the development of multi-physics tools to study the fuel cycle. This paper presents a modelling approach for 3D burnup analysis with the Serpent Monte Carlo code that implements an external interface for the coupling with OpenFOAM, importing material temperatures and density field. We adopt CFD to simulate thermal hydraulics for its high flexibility that simplifies the management of input data. In addition, the coupling with a Monte Carlo code assures a natural description of the different physics phenomena of nuclear reactors. We carry out the burnup calculations for one year of burnup of a PWR fuel cell, composed of an $$\hbox {UO}_{2}$$ pin surrounded by water. We compare the results to those obtained from simulations that adopt uniform temperature and density distributions. The results show that thermal hydraulics feedback influences the spatial distribution of the reaction rates over the time, leading to a remarkable effect on the nuclide density field along the radial and axial direction. In future works, we plan to extend the analysis for fuel assembly design.

On the performance of nanofluids in APR 1400 PLUS7 assembly: Neutronics

The purpose of this work is to investigate the utilization of a set of nanofluids as a coolant/moderator for Pressurized Water Reactor (PWR) APR 1400 PLUS7 assembly design through modeling their effect on essential neutronics parameters and quantities of interest via SERPENT with simplistic thermal-hydraulics feedback. Various scenarios are discussed including fresh and burned conditions as well as the effect of nanoparticles crud deposition. Al2O3, TiO2, and CNT water-based nanofluids with a range of concentrations in the span of 0.001 wt%–0.3 wt% were chosen for the present case study. For each nanofluid/concentration combination; the effect on the assembly’s multiplication factor, Fuel Temperature Coefficient (FTC), Moderator Temperature Coefficient (MTC), and the discharge burnup are studied and highlighted. Moreover, the effect of a CRUD-like deposition of the nanoparticles on the axial power shifts is studied via SERPENT.

Neutronics and thermal-hydraulics coupling analysis in accelerator-driven subcritical system

Accelerator-driven subcritical system (ADS) is a new generation nuclear reactor with various highly coupled physical fields. A typical system is a liquid metal, lead-bismuth eutectic cooled subcritical reactor core coupled to a neutron spallation target. Therefore, ADS simulations require multi-physics coupling among the proton, neutronics, and thermal hydraulics. In this work, GEANT4, RMC, and FLUENT were used to simulate the multi-physics processes in MYRRHA. The GEANT4/RMC was used for the spallation process and the proton-neutron transport calculations, with the power distributions verified against the MCNP6 code with an average difference of about 1.85%. A hybrid RMC/FLUENT coupling scheme was used for the neutronics thermal-hydraulics calculations. The subcritical reactor was simplified using the porous media method for the FLUENT simulations to obtain the coolant temperature and density fields. A temperature-dependent thermal conductivity model used to calculate the temperature filed in typical fuel pellets gave consistent results with the FLUENT predictions within an absolute error of 3 K. The neutronics and thermal-hydraulics coupling took the temperature and the lead-bismuth eutectic density feedback into consideration. Simulations show that thermal-hydraulics feedback has a fairly small effect on the power distribution in the ADS reactor. In this case, the radial power difference between the coupling and coupling-free is within 5%. In addition, the mechanisms of neutronics/thermal-hydraulics are compared for lead-bismuth eutectic cooled reactors and water-cooled reactors. The feedback is much more significant in water-cooled reactors than in the Pb-Bi cooled reactor since the water moderation, and the water density is more sensitive to the temperature.

On-The-Fly Prediction of Macroscopic Cross-Section Spatial Response to TH Perturbations Through Transfer Functions: Theory and First Results

Monte Carlo (MC) codes are widely used for the accurate modeling of nuclear reactors. However, efficient inclusion of thermal-hydraulic (TH) feedback within the MC calculation sequence is still an open problem. The issue is emphasized when coupled MC-TH calculations are needed to model the burnup evolution using multiple depletion steps. Among the techniques proposed to solve this problem is the utilization of stabilized Picard iteration in conjunction with a low-order prediction step. The latter is composed of a prediction block for cross sections and a fast deterministic solver that uses the cross sections to obtain a prediction of the power profile. The predicted power is then used as an improved guess for the next MC calculation, therefore leading to faster convergence for the overall algorithm. In this paper, we propose a new prediction block in which one-group cross sections are calculated through convolution of the TH scalar fields with MC-generated generalized transfer functions (GTFs). First-order perturbation theory is then utilized to calculate the power profile from the updated cross sections. A version of this prediction block using a simple fast Fourier transform–based approximation of the GTF is tested against a boiling water reactor unit-cell with realistic density profile and axial reflectors. The analysis was limited to the feedback between neutronics and coolant density variation. Good agreement was observed for both the spatial power and the one-group macroscopic cross-section profiles, which were compared to the reference MC results. This agreement was also preserved near the boundary, where the spatial flux gradients are maximum due to proximity to the axial reflectors.

Coupled Neutronics–Thermal-Hydraulic Simulation of BEAVRS Cycle 1 Depletion by the MCS/CTF Code System

The coupled neutronics–thermal-hydraulic simulation of the Benchmark for Evaluation and Validation of Reactor Simulations (BEAVRS) Cycle 1 depletion has been performed by the Monte Carlo–based multiphysics coupling code system MCS/CTF. MCS/CTF is a cyclewise pi-card iteration-based inner-coupling code system that couples the subchannel thermal-hydraulic code CTF as a thermal-hydraulic solver in the Monte Carlo neutron transport code MCS. MCS has been developed by the Computational Reactor Physics and Experiment Lab group at the Ulsan National Institute of Science and Technology for the full-core analysis of large-scale commercial light water reactors with high fidelity at the engineering level. With the high-fidelity performance of MCS, the quarter-core pinwise depletion simulation for the BEAVRS Cycle 1 benchmark has been conducted with thermal-hydraulic feedback including fuel temperature, coolant temperature, and coolant density. Moreover, the MCS internal one-dimensional thermal-hydraulic solver TH1D (MCS/TH1D) has been utilized as the reference. On one hand, the simulated results of the criticality boron concentration and axially integrated assemblywise detector signals were compared with measured data. On the other hand, the comparisons of power, fuel temperature, coolant temperature, and density are also presented in this paper.

Solution of a new model of fractional telegraph point reactor kinetics using differential transformation method

A new model of fractional telegraph point reactor kinetics FTPRK is introduced to approximate the time dependent Boltzmann transport equation considering new terms that contain time derivative of the reactivity and fractional integral of the neutron density. Caputo fractional derivatives and fractional Leibniz rule are used for such derivation. Cattaneoequation is applied to overcome the flaw of infinite neutron velocity and to describe the anomalous transport. Effect of the new term on the neutron behaviour is discussed. The new model is applied to both TRIGA reactor and to commercial pressured water reactor of a Three Mile Island type reactor, TMI-type PWR. Results for step, ramp and sinusoidal excess reactivities with thermal hydraulic feedback are presented and discussed for different values of anomalous sub-diffusion exponent, the fractional order, 0 < µ ≤ 1. To maintain the reactor safe at start-up after insertion of step reactivity and based on the concept of prompt jump approximation, the FTPRK model is simplified and solved analytically by Mittag–Liffler function. Physical interpretations of the fractional order µ and relaxation time τ and their effects on the behaviour of the neutron population are discussed. Also, the effect of a small perturbation in the geometric buckling on the neutron behaviour is discussed for finite reactor core. The new model is solved numerically using the fractional order multi-step differential transform method MDTM. The MDTM constitutes an easy algorithm based on Taylor's formula and Caputo fractional derivative. Two theorems with their proofs are introduced to solve the fractional system. Two major disadvantages of the method about the choice of the fractional order values and the step size length are addressed. We present a procedure which enables us to solve the system with appropriate values of fraction orders.

Development and validation of reactor nuclear design code CORCA-3D

Abstract The advanced node core code CORCA-3D is one of the independent developed codes of NPIC for the nuclear reactor core design. CORCA-3D code can calculate the few-group cross section, solve the 3D diffusion equations, consider the thermal-hydraulic feedback, reconstruct the pin-by-pin power. It has lots of functions such as changing core status calculation, critical searching, control rod value calculation, coefficient calculation and so on. The main theory and functions of CORCA-3D code are introduced and validated with a lot of reactor measured data and the SCIENCE system. Now, CORCA-3D code has been applied in ACP type reactor nuclear cores design.

Non-linear, time dependent target accuracy assessment algorithm for multi-physics, high dimensional nuclear reactor calculations

Safety analysis and design optimization depend on the accurate prediction of various reactor core responses. Model predictions can be enhanced by reducing the uncertainty associated with the responses of interest. Accordingly, an inverse problem analysis can be designed to provide guidance to determine the optimum experimental program to reduce the uncertainties in model parameters, e.g. cross-sections and fuel pellet-clad thermal conductivity, so as to reduce the uncertainties in constrained reactor core responses. This process is referred to as target accuracy assessment. In this work a nonlinear algorithm to determine an optimum experimental program has been developed and tested.The algorithm is based on the construction of surrogate model to replace the original model used to predict the core responses and uncertainties, therefore, enabling the target accuracy assessment to treat non-linearity within reasonable computational cost. Subspace based projection techniques are used to identify the influential degrees of freedom, which are then used to construct the surrogate model. Once constructed, the new computationally efficient surrogate model is used to propagate uncertainties via Monte Carlo sampling. Moreover, this work replaces the classical objective function used for nuclear data target accuracy assessment with another that factors in the financial gains of the target accuracy assessment results and replaces [or can supplement] differential experiments with many times more readily available integral experiments.Finally, the proposed algorithm is applied on a 3-dimensional fuel assembly depletion problem with thermal-hydraulics feedback using the VERA-CS core simulator. Specifically, CASL Progression Problem Number 6 is the illustrative problem employed which resembles a pressurized water reactor fuel assembly.

Implementation of a dynamic Monte Carlo method for transients analysis with thermal-hydraulic feedbacks using MCNPX code

Transient analysis which is vital in safety analysis requires a reliable calculation method. Most valid tools use diffusion theory with many approximations by now. However, the Monte Carlo method inherently overcomes these approximations and accurately calculates the parameters of a reactor. In this paper, a new time-dependent transport approach is described to simulate the nuclear reactor dynamic correctly using the MCNPX code. In this approach the fundamental parameters of a nuclear reactor like multiplication factor (Keff) and mean generation time (tG) are calculated using MCNPX code. They are then employed in the formulas to compute neutron population, proportional to Keff, during a generation time as well as precursors are decayed. Based on the approach, a dynamic Monte Carlo code namely DMCNP (Dynamical MCNPX code) is developed for a time-dependent simulation of particle tracking in an arbitrary geometry, considering the thermal-hydraulic feedbacks. The effects of temperature on cross section and density are applied at each time steps. Several test problems such as TWIGL, LMW, LRA and C5G7 are examined to assess the performance of the method.

Qualification of the ANET Code for Spallation Neutron Yield and Core Criticality in the KUCA ADS

Innovative nuclear reactor concepts such as the Accelerator Driven Systems (ADSs) have imposed extra requirements of simulation capabilities on the existing stochastic neutronics codes. The combination of an accelerator and a nuclear reactor in the ADS requires the simulation of both subsystems for an integrated system analysis. Therefore, a need arises for more advanced simulation tools, able to cover the broad neutron energy spectrum involved in these systems. ANET (Advanced Neutronics with Evolution and Thermal hydraulic feedback) is an under development stochastic code for simulating conventional and hybrid nuclear reactors. Successive testing applications performed throughout the ANET development have been utilized to verify and validate the new code capabilities. In this context, the ANET reliability in simulating the spallation reaction and the corresponding neutron yield as well as computing the multiplication factor of an operating ADS are here examined. More specifically, three cores of the Kyoto University Critical Assembly (KUCA) facility in Japan were analyzed focusing on the spallation neutron yield and the neutron multiplication factor. The ANET-produced results are compared with independent results obtained using the stochastic codes MCNP6.1 and MCNPX. Satisfactory agreement is found between the codes, confirming thus ANET’s capability to successfully estimate both the neutron yield of the spallation reaction and the keff of a realistic ADS.

A New Accurate Numerical Method Based on Shifted Chebyshev Series for Nuclear Reactor Dynamical Systems

A new method based on shifted Chebyshev series of the first kind is introduced to solve stiff linear/nonlinear systems of the point kinetics equations. The total time interval is divided into equal step sizes to provide approximate solutions. The approximate solutions require determination of the series coefficients at each step. These coefficients can be determined by equating the high derivatives of the Chebyshev series with those obtained by the given system. A new recurrence relation is introduced to determine the series coefficients. A special transformation is applied on the independent variable to map the classical range of the Chebyshev series from [-1,1] to [0,h]. The method deals with the Chebyshev series as a finite difference method not as a spectral method. Stability of the method is discussed and it has proved that the method has an exponential rate of convergence. The method is applied to solve different problems of the point kinetics equations including step, ramp, and sinusoidal reactivities. Also, when the reactivity is dependent on the neutron density and step insertion with Newtonian temperature feedback reactivity and thermal hydraulics feedback are tested. Comparisons with the analytical and numerical methods confirm the validity and accuracy of the method.