PWR Core Research Articles

Physics-informed Reinforcement Learning optimization of PWR core loading pattern

The nuclear sector represents the largest single source of carbon-free energy in the United States. Nevertheless, keeping existing nuclear assets competitive on the grid is key to their ability to continue to provide dispatchable clean energy along side renewable generation. Optimizing the fuel cycle cost through the optimization of core loading patterns is one approach to addressing this lack of competitiveness. However, this optimization task involves multiple objectives and constraints, resulting in a vast number of candidate solutions that cannot be explicitly solved. While stochastic optimization (SO) methodologies are utilized by various nuclear utilities and vendors for fuel cycle reload design, manual design remains the preferred approach. To advance the state-of-the-art in core reload patterns, we have developed methods based on Deep Reinforcement Learning for single and multi-objective optimization. Previous research has laid the groundwork for these approaches and demonstrated its ability to discover high-quality patterns within a reasonable timeframe. Moreover, RL methods have shown superiority against SO in the multi-objective settings. In this paper, we introduce an innovative paradigm by incorporating multi-objective RL, interpretable AI, and physics knowledge to further improve the performance of the algorithms. When the problem increases in complexity, the classical single-objective sometimes failed to even found feasible solutions. Leveraging physic-information becomes pivotal to find high-quality and more diverse solutions faster. These findings motivate incorporation of more physics to further aid in the quest of surpassing human intelligence. Future work will focus on scaling this method and addressing fuel performance and control rod limits to demonstrate that these new designs can be considered for a real reactor.

A PWR core power control using optimized PID controller with SQP based on control rod positioning and variable coolant flow rate

To ensure safety and stability, it is optimal for nuclear power plants to operate at their nominal power level. However, to meet the needs of power systems, NPPs must also be able to adjust their output for load-following purposes. This necessitates finding an effective control algorithmto maintain stable/safe operating conditions. The current study investigates the performance of PID controllersoptimized using Sequential Quadratic Programming algorithm and applied using two control techniques: control rod positioning and variable coolant flow rate. Simulation is done using model of four-loop Westinghouse PWR-1200 MW nuclear reactor. The proposed controller’s performance is evaluated in three scenarios:sudden control rod withdrawal, sudden change in coolant inlet temperature, and linear load tracking. The influences of model parametric uncertainty are also investigated. Simulation results revealed that the performance of the control algorithm applied using variable coolant flow rate was superior to the one usingcontrol rod positioning.

Neutronic Analysis of Accident-Tolerant Cladding Materials in 3D Full Core BEAVRS PWR Benchmark Using OpenMC Code

After the Fukushima Daiichi nuclear accident in 2011, the performance of nuclear fuel during accidents became a matter of great concern. To address this, a new type of fuel technology called accident-tolerant fuel (ATF) has been developed with the goal of enhancing the ability of light water reactors (LWRs) to withstand severe accident conditions. Iron-based alloys have been suggested as potential candidates for fuel cladding due to their favourable thermomechanical properties, lower reactivity with steam, and lower hydrogen generation. This study evaluates the neutronic performance of C26M (a 2nd generation nuclear grade FeCrAl alloy), APMT™, 310SS, and 304SS cladding materials by comparing them with Zircaloy-4 cladding in a 3D PWR core at the beginning of the cycle (BOC) using OpenMC code. The results revealed that the neutronic penalty varied for different alternative cladding materials where C26M exhibited the lowest neutronic penalty value of -12551 pcm, while 310SS demonstrated the highest with a value of -17855 pcm. Additionally, important parameters in the reactor core such as neutron spectrum, reactivity coefficients, boron worth, control rod bank worth, power distribution, and radial thermal neutron flux distribution are evaluated and discussed. The analysis results showed that C26M provided a significantly higher level of neutronic performance compared to APMT™, 304SS, and 310SS. Although this study primarily focused on the neutronic performance of PWRs at BOC, future research should encompass fuel depletion analysis to delve deeper into the potential of alternative cladding materials.

Multi-objective reinforcement learning-based approach for pressurized water reactor optimization

A novel method, the Pareto Envelope Augmented with Reinforcement Learning (PEARL), has been developed to address the challenges posed by multi-objective problems, particularly in the field of engineering where the evaluation of candidate solutions can be time-consuming. PEARL distinguishes itself from traditional policy-based multi-objective Reinforcement Learning methods by learning a single policy, eliminating the need for multiple neural networks to independently solve simpler sub-problems. Several versions inspired from deep learning and evolutionary techniques have been crafted, catering to both unconstrained and constrained problem domains. Curriculum Learning (CL) is harnessed to effectively manage constraints in these versions. PEARL’s performance is first evaluated on classical multi-objective benchmarks. Additionally, it is tested on two practical PWR core Loading Pattern (LP) optimization problems to showcase its real-world applicability. The first problem involves optimizing the Cycle length (LC) and the rod-integrated peaking factor (FΔh) as the primary objectives, while the second problem incorporates the mean average enrichment as an additional objective. Furthermore, PEARL addresses three types of constraints related to boron concentration (Cb), peak pin burnup (Bumax), and peak pin power (Fq). The results are systematically compared against conventional approaches from stochastic optimization. Notably, PEARL, specifically the PEAL-NdS ( ▪ ) variant, efficiently uncovers a Pareto front without necessitating additional efforts from the algorithm designer, as opposed to a single optimization with scaled objectives. It also outperforms the classical approach across multiple performance metrics, including the Hyper-volume. Future works will encompass a sensitivity analysis of hyper-parameters with statistical analysis to optimize the application of PEARL and extend it to more intricate problems.

Comparative analysis of different FeCrAl alloys in pressurized water reactors

Discussing and researching issues related to their safety is essential to guarantee the continuity of fission systems in generating energy for existing and new electrical matrices. Commercial fission reactors currently in operation have undergone a series of redesigns. One aspect much discussed in recent years is related to research about new fuels and cladding materials. Therefore, in this work, the feasibility of replacing Zircaloy-4 with FeCrAl-based alloys (C06M, C35M, C36M, Kanthal APMT) was evaluated considering these materials' physical–chemical, thermal, and neutronic properties. Moreover, thermal–hydraulic and neutronic simulations have been presented to compare the cladding behavior in a PWR core in steady state and transient operation conditions. The results showed, in a general way, that the analyzed alloys have equivalent properties from a physical–chemical and thermal point of view. Despite the similarity, the Kanthal APMT alloy presented the worst performance, and the C35M alloy showed more advantageous characteristics. Considering the similarities in the composition of the C06M, C35M, and C36M alloys, which have the same elements in their constitution, the alloy with the best thermal performance has the lowest aluminum content. Considering the neutronic behavior, the Kanthal APMT alloy, with more Cr percentile, presents the lowest neutron effective multiplication factor, keff. Axial and radial power distribution did not change significantly after the cladding replacement. Nevertheless, modifications must be made to keep the criticality during the fuel cycle burnup for all FeCrAl alloys.

A comprehensive examination of the linear and numerical stability aspects of the bubble collision model in the TRACE-1D two-fluid model applied to vertical disperse flow in a PWR core channel under loss of coolant accident conditions

The one-dimensional Two-Fluid concept uses an area-average approach to simplify the time and phase-averaged Two-Fluid conservation equations, making it more suitable for addressing difficulties at an industrial scale. Nevertheless, the mathematical framework has inherent weaknesses due to the loss of details throughout the averaging procedures. This limitation makes the conventional model inappropriate for some flow regimes, where short-wavelength perturbations experience uncontrolled amplification, leading to solutions that need to be physically accurate. The critical factor in resolving this problem is the integration of closure relations. These relationships play a crucial function in reintroducing essential physical characteristics, thus correcting the loss that occurs during averaging and guaranteeing the stability of the model. To improve the accuracy of predictions, it is essential to assess the stability and grid dependence of one-dimensional formulations, which are particularly affected by closure relations and numerical schemes. The current research presented in the text focuses on improving the well-posedness of the TFM, specifically within the TRACE code, which is widely utilized for nuclear reactor safety assessments. Incorporating a bubble collision model in the momentum equations is demonstrated to enhance the TFM's resilience, especially in scenarios with high void fractions where conventional TFMs may face challenges. The analysis presents a linear stability analysis performed for the transient one-dimensional Two-Fluid Model of system code TRACE within the framework of vertically dispersed flows. The main emphasis is on evaluating the stability characteristics of the model while also acknowledging its susceptibility to closure relations and numerical techniques.

PWR Core Loading Pattern Design Assisted by Artificial Intelligence

Core design is the a priori study of the behavior of a reactor core throughout a cycle between two fuel reloads. There is a growing interest in using Artificial Intelligence (AI) tools to accelerate this type of calculation. Coupled thermal-hydraulic/neutronic calculations allow access to many variables of special interest to develop a digital twin (metamodel), which can be used, for instance, for pattern optimization, since it presents restrictions from the point of economics, safety and licensing. This work presents a neural network (NN) trained to obtain a metamodel, which will be used to determine different optimal configurations of the fuel elements based on certain criteria.

PWR core calculation based on pin-cell homogenization in three-dimensional pin-by-pin geometry

For the pressurized water reactor two-step calculation, the traditional assembly homogenization and two-group neutron diffusion calculation have been widely used. When it comes to the core pin-by-pin simulation, many models and techniques are different and unsettled. In this paper, the homogenization methods based on the pin discontinuity factors and super homogenization factors are used to get the pin-cell homogenized parameters. The heterogeneous leakage model is applied to modify the infinite flux spectrum of the single assembly with reflective boundary condition and to determine the diffusion coefficients for the SP3 solver which is used in the core simulation. To reduce the environment effect of the single-assembly reflective boundary condition, the on-line method for the SPH factors updating is applied in this paper, and the functionalization of SPH factors based on the least-squares method will be pre-made alone with the table of the group constants. The fitting function will be used to update the thermal-group SPH factors with a whole-core pin-by-pin homogeneous solution on-line. The three-dimensional Watts Bar Nuclear Unit 1 (WBN1) problem was utilized to test the performance of pin-by-pin calculation. And numerical results have demonstrated that PWR pin-by-pin core calculation has more accurate results compared with the traditional assembly-homogenization scheme.

Fine-mesh homogenization and anisotropic SP3 calculation for PWR cores with plate-type fuel and strong absorbers

SP3 based pin-by-pin calculation has been proven to be efficient in improving the accuracy of PWR cores with a strong heterogeneity. In this work, it is renamed “fine-mesh transport calculation scheme” when applied to research reactors with plate-type fuel. However, despite that the introduction of strong absorbers has greatly enhanced the angular heterogeneity of the problem, the fine-mesh homogenization for isotropic SP3 calculation still cannot accurately capture the features. This work introduces a series of strategies aimed at enhancing the anisotropic effect for simulating plate-type fuel cores with strong absorbers. These strategies are based on the anisotropic SP3 equations, which are derived from high-order scattering. In addition, an adaptive generation method for the group constants is introduced to further optimize the process. To validate the effectiveness of these strategies, a series of tests, including those employing MTR and JRR-3M, are conducted, demonstrating the significant improvement brought about by the proposed methodology.To conclude, the method introduced in this paper facilitates the two-step method for calculating the reactors with a strong heterogeneity.

Modeling single-phase transverse flows in a PWR rod bundle at low Reynolds number

In normal functioning conditions, the primary component of the flow within the rod bundle of a PWR core is in the axial direction, along the rods. However, in accidental situations, such as the refilling or reflooding phase during a Loss of Coolant Accident, or a Steam Line Break accident, transverse flows may significantly affect thermal-hydraulic properties in the core. Such effects have received little attention in system codes such as CATHARE, particularly in anisotropic rod structures at low Reynolds numbers. Here, we develop macroscopic pressure drop models for flows spanning from the creeping regime to unsteady vortex shedding. The averaged model is a generalized Darcy–Forchheimer equation with an apparent permeability including a rotation matrix and a non-linear dimensionless coefficient. The constitutive relations for the intrinsic permeability matrix are derived from polynomial regressions based on results obtained from microscale numerical simulations at different flow directions and Reynolds numbers. We finally test our approach in a case where transverse flow is imposed through a differential of inlet velocities and validate by comparing results from CATHARE with those obtained from a finite element toolbox.

Fuel performance evaluation of two high burnup PWR core designs during normal operation, control rod withdrawal, and control rod ejection scenarios

There is interest among utilities to extend the current, 18-month operating cycle to 24 months. Economically, this extension would require greater than 5 % enrichment and peak rod average discharge burnup levels above 62 GWd/MTU. A notable challenge of increasing enrichment is the resulting additional excess reactivity encountered during the early stages of fuel life. To accommodate, burnable absorbers beyond soluble boron are introduced into the fuel system. In high burnup fuels, the possibilities of cladding lift-off and fuel melting increase due, in part, to increased rod internal pressures and limited fuel thermal conductivity, respectively. This work collaboratively employs PARCS, RELAP5-3D, and BISON to compare the fuel performance of two high burnup fuel candidates with higher than 5 % enrichment. The fuel performance parameters were compared to current NRC guidance. The results demonstrate an annular fuel design with homogenously blended gadolinium as a burnable absorber operates with greater safety margins during normal operation, allowing for additional operational flexibility. During normal operation, the core design utilizing Integral Fuel Burnable Absorber pins contained fuel pins which reached plenum pressures above 15.5 MPa by the end of the first fuel cycle and fuel pins experienced cladding hoop strains above 1 %. In the Gd core design, only two observed pins experienced plenum pressures above 15.5 MPa and no pins exceeded 1 % cladding hoop strain. During the control rod withdrawal scenario, plenum pressures for pins in both designs marginally exceeded system pressure, however neither experienced excessive hoop strain. The Gd core design experienced a maximum fuel temperature of 2418 K, which is significantly higher than the Integral Fuel Burnable Absorber design at 2157 K, but still within regulatory guidance. We predicted that the fuel in both could return to service after the CRW event. We also predicted that cladding would not fail during the Control Rod Ejection in either core design. Generally, the Integral Fuel Burnable Absorber core design performed with greater safety margin with regards to temperature during normal operation and the transient events. However, the Gd core design performed with greater safety margin regarding plenum pressure and hoop strain limits during normal operation and both transient events.

Neutronic investigation of enriched gadolinium, natural gadolinium and Zirconium-erbium as burnable poisons in the advanced PWR assemblies by MCNPX code

In Pressurized Water Reactors, burnable absorbers are implemented for controlling the excess reactivity and avoiding the high power peaking factor. A feasibility study was carried out for investigating the effect of enriched gadolinium (157Gd2O3), natural gadolinium (152 - 160Gd2O3) and Zirconium-Erbium (ZrEr2) as burnable absorbers on the safety parameters of advanced PWR assembly. Three poisoned assemblies are modeled and simulated by the well-known MCNPX code. To hold a fair comparison between these assemblies, the author adjusted the concentration of fissile materials and burnable absorbers in each assembly to provide approximately the same initial reactivity. The MCNPX simulation showed that the enriched gadolinium model achieved a number of advantages over Zirconium-Erbium as: 1) prolonging the fuel cycle length by 1.04%, 2) increasing the negativity of moderator temperature coefficient and fuel temperature coefficient by 10.3% and 9.3% at the BOL and this contributes to core safety, 3) minimizing residual reactivity penalty at the higher burnup steps and 4) more hardening of neutron spectrum at the BOL. On the other hand, the Zirconium – Erbium layer presented a number of benefits over enriched gadolinium as 1) reducing the peaking factor by 1.3%, 2.6% and 2% at 20, 30 and 50 GWd/ton, 2) increasing the reactivity worth by 1.6% at the BOL, 3) increasing the power flattening by 7.6% at the EOL, and this is considered an enormous economic benefit. Therefore, the modeling of enriched gadolinium and zirconium erbium in this study is suggested for improving the neutronic and safety parameters of PWR cores.

Mechanical interaction of bowed hexagonal fuel assemblies in PWR core

Due to the lateral and axial forces or irradiation growth, nuclear fuel assemblies (FAs) are prone to bowing during reactor operation. In some cases, FAs can even mutually contact. The paper focuses on the modelling of the bowed hexagonal FAs in mutual interaction considering complex operation conditions given by coolant pressure pulsations. The multi-stage modelling is used to describe the behaviour of the chosen FA in the reactor core. A possible contact between FA and reactor core–shell is also taken into account. All the analyses are performed with respect to the fuel burn-up that significantly influences FAs dynamic behaviour.

Semi-analytical fluid-structure model for the analysis of fuel assembly bow in full PWR cores

Fuel assembly bow is an intricate industrial issue occurring in PWR nuclear cores, which relies on multiphysics coupled phenomena based on mechanics, thermal hydraulics and neutronics.Amongst many causes, the hydraulic forces induced by in-core flow redistributions play an important role on the fuel assembly mechanical deflection.Because deformation spread out over days, weeks or months, fuel assembly bow is often studied as a quasistatic fluid-structure interaction with neutronics parameters as inputs only. In order to set up an efficient partitioned two-way coupling between mechanics and hydraulics representing a full PWR core, simplified models must be used.Regarding hydraulics, common strategies imply porous media, or even more time-saving 1D networks. In a previous study, we followed such a 1D approach to simulate the flow redistributions occurring near spacer grids, from fuel assemblies to the bypasses surrounding them or the other way around. In the current paper, we extend the latter local hydraulic networks to build up a full fuel assembly, which is then two-way coupled with an in-house CEA mechanical code. The simulations are compared with a CEA experiment. The lateral force exerting on spacer grids induced by the bypass-fuel assembly redistribution appears to play an important role on the shape of the fuel assembly.Finally, we propose further extensions to a row of fuel assemblies, and then to a whole core. Qualitative comparisons with the literature highlight proper bow patterns for the single row test case, with high sensitivity to the flow inlet and outlet conditions. At last, we demonstrate that hydraulic forces in a full core can indeed be estimated accurately through separated calculations on single rows in orthogonal directions, as suggested in the literature.

Implementation and optimization of WDT algorithm on IMPC-Neutron and comparison of efficiency of various algorithms

In Monte Carlo code, the use of Delta-tracking algorithm can greatly improve the computational efficiency, but the existence of virtual collision will waste computing resources because the virtual collision introduced by Delta-tracking algorithm does not make any contribution to the statistical results. The Weighted Delta-tracking algorithm makes the virtual collision contribute to the statistics and improves the efficiency of Delta-tracking algorithm. We implemented Weighted Delta-tracking algorithm into the IMPC-Neutron code, then we optimized the Weighted Delta-tracking algorithm to improve its computational efficiency, and analyzed the effects and limitations of Weighted Delta-tracking algorithm in different assemblies. The optimal parameters of Weighted Delta-tracking algorithm are tested in the full reactor models of PWR core and sub-critical fast reactor core. Finally, the calculation efficiency of various neutron transport methods is compared by using IMPC-Neutron.

Note on the performance of parametrization strategies to determine the decay heat of PWR fuel

The behavior of fuel assembly safety properties such as decay heat is often parametrized by a set of proxy variables such as burnup and by categorical variables like UOX or MOX. The standards ANS5.1 and DIN-25463 are examples of this strategy. They face the challenge to accurately approximate a wide range of possible fuel assembly states which occur in practice because they traditionally do not follow the nuclide vector evolution with a detailed microscopic model. While burnup is widely regarded as an important fuel parameter it is only an approximation or proxy for the physical relevant quantity which is the fuel nuclide vector. The performance of one of the latest and most advanced decay heat standards, DIN-25463-2014, is compared with Studsvik’s best-estimate code SSP SNF which uses a state-of-the-art microscopic model. Both the differences in initial nuclide vector after irradiation and the differences in decay heat between 1 s and 60 years are analyzed. Comparisons with realistic PWR core fuel inventories show that the margin between SSP SNF and DIN-25463-2014 varies in a range ±5% which is a manifestation of the challenge to accurately approximate the fuel state without detailed microscopic model. Given today’s small compute footprint of best-estimate codes for decay heat determination we conclude that parametrization strategies have little advantage except for applications like system codes used in transient analyses.

Development and validation of multiphysics PWR core simulator KANT

KANT (KAIST Advanced Nuclear Tachygraphy) is a PWR core simulator recently developed at Korea Advance Institute of Science and Technology, which solves three-dimensional steady-state and transient multigroup neutron diffusion equations under Cartesian geometries alongside the incorporation of thermal-hydraulics feedback effect for multi-physics calculation. It utilizes the standard Nodal Expansion Method (NEM) accelerated with various Coarse Mesh Finite Difference (CMFD) methods for neutronics calculation. For thermal-hydraulics (TH) calculation, a single-phase flow model and a one-dimensional cylindrical fuel rod heat conduction model are employed. The time-dependent neutronics and TH calculations are numerically solved through an implicit Euler scheme, where a detailed coupling strategy is presented in this paper alongside a description of nodal equivalence, macroscopic depletion, and pin power reconstruction. For validation of the steady, transient, and depletion calculation with pin power reconstruction capacity of KANT, solutions for various benchmark problems are presented. The IAEA 3-D PWR and 4-group KOEBERG problems were considered for the steady-state reactor benchmark problem. For transient calculations, LMW (Lagenbuch, Maurer and Werner) LWR and NEACRP 3-D PWR benchmarks were solved, where the latter problem includes thermal-hydraulics feedback. For macroscopic depletion with pin power reconstruction, a small PWR problem modified with KAIST benchmark model was solved. For validation of the multi-physics analysis capability of KANT concerning large-sized PWRs, the BEAVRS Cycle1 benchmark has been considered. It was found that KANT solutions are accurate and consistent compared to other published works.

CorTAF: A nuclear reactor core three-dimensional thermal-hydraulic characteristics analysis code based on OpenFOAM

In this paper, a thermal hydraulic analysis method based on open source CFD platform OpenFOAM was proposed. The models of coolant flow and heat transfer, fuel rod heat conduction and coupled heat transfer were established according to the bundle structure characteristics of PWR core, and then a nuclear reactor three-dimensional thermal–hydraulic characteristics analysis code CorTAF was developed based on finite volume method with the spatialresolution of subchannel level. The international benchmarks, including GE3 × 3, Weiss and PNL2 × 6 fuel assembly flow and heat transfer experiments, were selected to carry out the validation. The calculation results were basically consistent with the experimental data, illustrating that CorTAF is suitable for predicting the flow and heat transfer characteristics of coolant in the rod bundle fuel assembly. The thermal–hydraulic characteristics of fuel assembly and PWR core under full power operation and blockage accident conditions were simulated using CorTAF. The steady-state and transient spatial distribution of physical quantities in subchannel-scale including coolant and fuel rod temperature were obtained, and the influence of blockage condition on flow and heat transfer characteristics was analyzed. This work has reference significance for the development of core thermal hydraulic analysis tools for PWR.

Drag coefficient estimation in FSI for PWR fuel assembly bowing

Assembly bowing in a PWR core can be a serious problem for managing the power during normal operation or for periodical maintenance. One of the causes of this phenomenon is the transverse flow in the core, generated by the non-uniformity of the axial flow. Modelling the mechanical behaviour of a PWR core is made difficult by the complex geometry and the numerous friction points that lead to non-linearities. A simple but efficient way to deal with these issues is the porous medium model proposed by Ricciardi et al. (2009). In this model, the equations used at the fluid–structure interface require empirical parameters such as the added mass, or axial and normal drag coefficients. Using a new experimental setup at CEA, Eudore, which hosts 3 half-scale fuel assemblies in a line, the forces acting on the assembly by a non-uniform flow profile were measured. An analytical model to retrieve the normal drag coefficient was then proposed. This coefficient is then used in FSCORE, a numerical software based on the porous medium approach. The experimental and numerical results are presented and show good agreement.

Numerical simulation of Delayed-SPND response current in NECP-Bamboo

Self-Powered Neutron Detectors (SPNDs) are widely used in Gen-III commercial PWR cores to simultaneously and continuously measure the in-core neutron flux density. A response current simulation module has been designed, developed and validated in the NECP-Bamboo code for delayed-SPNDs. First, neutron transport and nuclide depletion simulation are carried out in Bamboo-Lattice to obtain the variation of nuclide composition and the few-group constants. Next, a Monte-Carlo code is employed to calculate the electron escape probability and gamma sensitivity of SPND for each depleted lattice. Finally, the electron escape probability, gamma sensitivity and the few-group constants are regarded as input parameters for the core simulation. The response current is calculated in the Bamboo-Core code during the simulation of core operation. The methodology and the code were verified against measured values on Vanadium and Rhodium SPND. In addition, the response current of Vanadium SPND in the AP1000 core was simulated and validated.