Pressurized Core Research Articles

Eigenvalue Solvers for Modeling Nuclear Reactors on Leadership Class Machines

Three complementary methods have been implemented in the code Denovo that accelerate neutral particle transport calculations with methods that use leadership-class computers fully and effectively: a multigroup block (MG) Krylov solver, a Rayleigh quotient iteration (RQI) eigenvalue solver, and a multigrid in energy (MGE) preconditioner. The MG Krylov solver converges more quickly than Gauss Seidel and enables energy decomposition such that Denovo can scale to hundreds of thousands of cores. RQI should converge in fewer iterations than power iteration (PI) for large and challenging problems. RQI creates shifted systems that would not be tractable without the MG Krylov solver. It also creates ill-conditioned matrices. The MGE preconditioner reduces iteration count significantly when used with RQI and takes advantage of the new energy decomposition such that it can scale efficiently. Each individual method has been described before, but this is the first time they have been demonstrated to work together effectively.The combination of solvers enables the RQI eigenvalue solver to work better than the other available solvers for large reactors problems on leadership-class machines. Using these methods together, RQI converged in fewer iterations and in less time than PI for a full pressurized water reactor core. These solvers also performed better than an Arnoldi eigenvalue solver for a reactor benchmark problem when energy decomposition is needed. The MG Krylov, MGE preconditioner, and RQI solver combination also scales well in energy. This solver set is a strong choice for very large and challenging problems.

Study of Fast Transient Pressure Drop in VVER-1000 Nuclear Reactor Using Acoustic Phenomenon

This article aims to simulate the sudden and fast pressure drop of VVER-1000 reactor core coolant, regarding acoustic phenomenon. It is used to acquire a more accurate method in order to simulate the various accidents of reactor core. Neutronic equations should be solved concurrently by means of DRAGON 4 and DONJON 4 coupling codes. The results of the developed package are compared with WIMS/CITATION and final safety analysis report of Bushehr VVER-1000 reactor (FSAR). Afterwards, time dependent thermal-hydraulic equations are answered by employing Single Heated Channel by Sectionalized Compressible Fluid method. Then, the obtained results were validated by the same transient simulation in a pressurized water reactor core. Then, thermal-hydraulic and neutronic modules are coupled concurrently by use of producing group constants regarding the thermal feedback effect. Results were compared to the mentioned transient simulation in RELAP5 computer code, which show that mass flux drop is sensed at the end of channel in several milliseconds which causes heat flux drop too. The thermal feedback resulted in production of some perturbations in the changes of these parameters. The achieved results for this very fast pressure drop represent accurate calculations of thermoneutronic parameters fast changes.

Application of CUPID for subchannel-scale thermal–hydraulic analysis of pressurized water reactor core under single-phase conditions

Abstract There have been recent efforts to establish methods for high-fidelity and multi-physics simulation with coupled thermal–hydraulic (T/H) and neutronics codes for the entire core of a light water reactor under accident conditions. Considering the computing power necessary for a pin-by-pin analysis of the entire core, subchannel-scale T/H analysis is considered appropriate to achieve acceptable accuracy in an optimal computational time. In the present study, the applicability of in-house code CUPID of the Korea Atomic Energy Research Institute was extended to the subchannel-scale T/H analysis. CUPID is a component-scale T/H analysis code, which uses three-dimensional two-fluid models with various closure models and incorporates a highly parallelized numerical solver. In this study, key models required for a subchannel-scale T/H analysis were implemented in CUPID. Afterward, the code was validated against four subchannel experiments under unheated and heated single-phase incompressible flow conditions. Thereafter, a subchannel-scale T/H analysis of the entire core for an Advanced Power Reactor 1400 reactor core was carried out. For the high-fidelity simulation, detailed geometrical features and individual rod power distributions were considered in this demonstration. In this study, CUPID shows its capability of reproducing key phenomena in a subchannel and dealing with the subchannel-scale whole core T/H analysis.

Multivariable modeling and nonlinear coordination control of nuclear reactor cores with/without xenon oscillation using H∞ loop shaping approach

This investigation is to achieve multivariable modeling for a pressurized water reactor core with/without iodine-xenon dynamics and design nonlinear core multivariable coordination control systems with stability analyses for simultaneous regulations of the core power and axial power difference during load following/transient load maneuvers. A two-point based multivariable model for this nonlinear core with iodine-xenon and that for the core without iodine-xenon are respectively built adopting the power regulating rod and the axial offset regulating rod as inputs and ignoring boron, and are then linearized. The H∞ loop shaping control with robustness is utilized to contrive a coordination controller of each linearized model and this controller is applied to the nonlinear model corresponding to the linear model. The nonlinear model with iodine-xenon and its coordination controller construct the nonlinear core load following coordination control system, and the nonlinear model without iodine-xenon and its coordination controller structure the nonlinear core transient load coordination control system. One stability theorem is deduced to analysis stability of the two nonlinear control systems. Eventually, the two nonlinear coordination control systems are simulated. Simulations show that the systems possess the desired decoupling control ability for coordination regulations of multi-parameter and good dynamic performance, and are effective.

A Three-Dimensional Variational Nodal Method for Pin-Resolved Neutron Transport Analysis of Pressurized Water Reactors

A three-dimensional variational nodal method (VNM) is presented for pressurized water reactor core calculations without fuel-moderator homogenization. The nodal functional is presented and discretized to obtain response matrix equations. Within the nodes, finite elements in the x-y plane and orthogonal polynomials in z are used to approximate the spatial flux distribution. On the lateral interfaces, orthogonal polynomials are employed. On the axial interfaces, the finite elements facilitate a spatially accurate current representation that has proven to be a challenge for the method of characteristics–based two-dimensional/one-dimensional approximations which typically rely on spatial homogenization. The angular discretization utilizes an even-parity integral method within the nodes, with the integrals evaluated using high-order Chebyshev-Legendre cubature. On the lateral and axial interfaces, low-order spherical harmonics (Pn) are augmented by high-order Pn expansions to which quasi-reflected conditions are applied. With quasi-reflected conditions, the solution converges to the high-order Pn solution for an infinite lattice of identical cells with no gradient, while the low-order Pn expansions handle global gradients in both the radial and axial directions. The method is implemented in the PANX code and applied first to a number of model problems to study convergence of the space-angle approximations and then to the C5G7 benchmark problems. Multigroup Monte Carlo solutions provide reference values for eigenvalues and pin-power distributions.

Thermal-Hydraulics analysis of pressurized water reactor core by using single heated channel model

Thermal hydraulics of nuclear reactor as a basis of reactor safety has a very important role in reactor design and control. The thermal-hydraulic analysis provides input data to the reactor-physics analysis, whereas the latter gives information about the distribution of heat sources, which is needed to perform the thermal-hydraulic analysis. In this study single heated channel model as a very fast model for predicting thermal hydraulics behavior of pressurized water reactor core has been developed. For verifying the results of this model, we used RELAP5 code as US nuclear regulatory approved thermal hydraulics code. The results of developed single heated channel model have been checked with RELAP5 results for WWER-1000. This comparison shows the capability of single heated channel model for predicting thermal hydraulics behavior of reactor core.

A Variational Nodal Approach to 2D/1D Pin Resolved Neutron Transport for Pressurized Water Reactors

A two-dimensional/one-dimensional (2D/1D) variational nodal approach is presented for pressurized water reactor core calculations without fuel-moderator homogenization. A 2D/1D approximation to the within-group neutron transport equation is derived and converted to an even-parity form. The corresponding nodal functional is presented and discretized to obtain response matrix equations. Within the nodes, finite elements in the x-y plane and orthogonal functions in z are used to approximate the spatial flux distribution. On the radial interfaces, orthogonal polynomials are employed; on the axial interfaces, piecewise constants corresponding to the finite elements eliminate the interface homogenization that has been a challenge for method of characteristics (MOC)–based 2D/1D approximations. The angular discretization utilizes an even-parity integral method within the nodes, and low-order spherical harmonics (PN) on the axial interfaces. The x-y surfaces are treated with high-order PN combined with quasi-reflected interface conditions. The method is applied to the C5G7 benchmark problems and compared to Monte Carlo reference calculations.

Comparative Study on Reactor Pressure Vessel Failure Behaviors With Various Geometric Discontinuities Under Severe Accident

The so-called “in-vessel retention (IVR)” is a basic strategy for severe accident (SA) mitigation of some advanced nuclear power plants (NPPs). The IVR strategy is to keep the reactor pressure vessel (RPV) intact under SA like core meltdown condition. During the IVR, the core melt (∼1327 °C) is collected in the lower head (LH) of the RPV, while the external surface of RPV is submerged in the water. Through external cooling of the RPV, the structural integrity is assumed to be maintained within a prescribed period of time. The maximum thermal loading is referred to critical heat flux (CHF) on the inside, while the external surface is considered to perform in the environment of the boiling crisis point (∼130 °C). Due to the high temperature gradients, the failure mechanisms of the RPV is found to span a wide range of structural behaviors across the wall thickness, such as melt-through, creep damage, plastic yielding as well as thermal expansion. Besides CHF, the pressurized core meltdown was another evident threat to the RPV integrity, as indicated in the Fukushima accident on 2011. In illustrating the effects of internal pressures and individual CHF on the failure behaviors, three typical RPVs with geometric discontinuity caused by local material melting were adopted for the comparative study. Through finite-element method (FEM), the RPV structural behaviors were investigated in terms of deformation, stress, plastic strain, creep, and damage. Finally, some important conclusions are summarized in the concluding remark. Such comparative study provides insight and better understanding for the RPV safety margin under the IVR condition.

Particle Filter Based Recursive Data fusion with Sensor Indexing for Large Core Neutron Flux Estimation

We introduce a sequential importance sampling particle filter (PF)-based multisensor multivariate nonlinear estimator for estimating the in-core neutron flux distribution for pressurized heavy water reactor core. Many critical applications such as reactor protection and control rely upon neutron flux information, and thus their reliability is of utmost importance. The point kinetic model based on neutron transport conveniently explains the dynamics of nuclear reactor. The neutron flux in the large core loosely coupled reactor is sensed by multiple sensors measuring point fluxes located at various locations inside the reactor core. The flux values are coupled to each other through diffusion equation. The coupling facilitates redundancy in the information. It is shown that multiple independent data about the localized flux can be fused together to enhance the estimation accuracy to a great extent. We also propose the sensor anomaly handling feature in multisensor PF to maintain the estimation process even when the sensor is faulty or generates data anomaly.

Simulating stress-dependent fluid flow in a fractured core sample using real-time X-ray CT data

Abstract. Various geoscientific applications require a fast prediction of fracture permeability for an optimal workflow. Hence, the objective of the current study is to introduce and validate a practical method to characterize and approximate single flow in fractures under different stress conditions by using a core-flooding apparatus, in situ X-ray computed tomography (CT) scans and a finite-volume method solving the Navier–Stokes–Brinkman equations. The permeability of the fractured sandstone sample was measured stepwise during a loading–unloading cycle (0.7 to 22.1 MPa and back) to validate the numerical results. Simultaneously, the pressurized core sample was imaged with a medical X-ray CT scanner with a voxel dimension of 0.5 × 0.5 × 1.0 mm3. Fracture geometries were obtained by CT images based on a modification of the simplified missing attenuation (MSMA) approach. Simulation results revealed both qualitative plausibility and a quantitative approximation of the experimentally derived permeabilities. The qualitative results indicate flow channeling along several preferential flow paths with less pronounced tortuosity. Significant changes in permeability can be assigned to temporal and permanent changes within the fracture due to applied stresses. The deviations of the quantitative results appear to be mainly caused by both local underestimation of hydraulic properties due to compositional matrix heterogeneities and the low CT resolution affecting the accurate capturing of sub-grid-scale features. Both affect the proper reproduction of the actual connectivity and therefore also the depiction of the expected permeability hysteresis. Furthermore, the threshold value CTmat (1862.6 HU) depicting the matrix material represents the most sensitive input parameter of the simulations. Small variations of CTmat can cause enormous changes in simulated permeability by up to a factor of 2.6 ± 0.1 and, thus, have to be defined with caution. Nevertheless, comparison with further CT-based flow simulations indicates that the proposed method represents a valuable method to approximate actual permeabilities, particularly for smooth fractures (< 35 µm). However, further systematic investigations concerning the applicability of the method are essential for future studies. Thus, some recommendations are compiled by also including suggestions of comparable studies.

Pressure retaining method based on phase change for coring of gas hydrate-bearing sediments in offshore drilling

Coring of gas hydrate-bearing sediment with situ-pressure retained is significant for both geophysics and geochemistry. However, the core recovery of current pressure corers is relatively low, which is attributed to the sensitivity of mechanical valves to solid particles and drilling cuttings. To improve the core recovery of the pressure corers, the pressure retaining method based on the phase change of situ drilling fluid has been used to seal the core tube mouth. The pressure retaining capacity of the ice valves made from seawater mixed with different mass concentrations of bentonite was tested; the influence of the ice valve length and freezing temperature on the pressure retaining capacity was also studied. Results show that the ice valve made from pure seawater could not retain pressure for the fissures caused by stress because of the temperature difference and the incompletely freezing of the ice valve caused by the concentrated inorganic salts in the core of the ice valve. The ice valve made from seawater mixed with 7% mass concentration of bentonite can sustain pressures of up to 47MPa. Both high ice valve length and low freezing temperature are beneficial for improving the pressure sustaining capacity of the ice valve. Results indicate that using the ice valve made from seawater mixed with bentonite to instead mechanical valves in the pressure corer can be a potential solution to improve the recovery of pressurized hydrate-bearing sediment core.

A Study on the Optimal Position for the Secondary Neutron Source in Pressurized Water Reactors

Abstract This paper presents a new and efficient scheme to determine the optimal neutron source position in a model near-equilibrium pressurized water reactor, which is based on the OPR1000 Hanul Unit 3 Cycle 7 configuration. The proposed scheme particularly assigns importance of source positions according to the local adjoint flux distribution. In this research, detailed pin-by-pin reactor adjoint fluxes are determined by using the Monte Carlo KENO-VI code from solutions of the reactor homogeneous critical adjoint transport equations. The adjoint fluxes at each allowable source position are subsequently ranked to yield four candidate positions with the four highest adjoint fluxes. The study next simulates ex-core detector responses using the Monte Carlo MAVRIC code by assuming a neutron source is installed in one of the four candidate positions. The calculation is repeated for all positions. These detector responses are later converted into an inverse count rate ratio curve for each candidate source position. The study confirms that the optimal source position is the one with very high adjoint fluxes and detector responses, which is interestingly the original source position in the OPR1000 core, as it yields an inverse count rate ratio curve closest to the traditional 1/M line. The current work also clearly demonstrates that the proposed adjoint flux-based approach can be used to efficiently determine the optimal geometry for a neutron source and a detector in a modern pressurized water reactor core.

Development of applicable ice valves for ice-valve-based pressure corer employed in offshore pressure coring of gas hydrate-bearing sediments

Because of sealing failures, less than 60% hydrate-bearing sediment pressure cores can be retrieved by pressure corers based on mechanical valves. The ice-valve-based pressure corer presents a promising solution to improve the recovery of pressurized hydrate-bearing sediment cores. This study aims to develop applicable ice valves for ice-valve-based pressure corer employed in offshore pressure coring of gas hydrate-bearing sediments. The pressure sustaining performance of the ice valves formed from both seawater and seawater mixed with bentonite were studied. Experimental results indicate that ice valves formed from pure seawater can sustain the pressure of only 3.2MPa, which is far from meeting the requirement of pressure coring. By analyzing the freezing-equilibrium relationships in seawater, it can be concluded that there was a unfrozen zone containing calcium and magnesium ions kept in the axial center of the ice valve, which was considered to be the primary reason for the poor pressure sustaining capacity of sea ice valves. In addition, pressurizing tests of the ice valves made from seawater with different mass concentration of bentonite added were carried out and results showed that the sustained pressure can be greater than 38MPa when the bentonite mass concentration was more than 5%, which was quite satisfactory for offshore pressure coring. Comprehensive analysis for the significant improvement of sustained pressure was also provided which reasonably and satisfactorily revealed the enhancement mechanism of bentonite on sea ice valves.

Effects of gas diffusion from fractures to coal matrix on the evolution of coal strains: Experimental observations

In this study, we investigate coal matrix swelling during the process of gas diffusion from cleats and its impact on the evolution of strain. We inject helium into both jacketed and unjacketed coal samples within a pressurized core holder. In the unjacketed experiment, the coal sample was exposed to hydrostatic gas pressure. In the jacketed experiment, the coal sample was constrained by fixed displacement at the two ends and by constant confining pressure laterally. In both experiments, strains were measured continuously both parallel/perpendicular to the bedding plane of the coal as internal pressure of helium is increased. For the unjacketed test the initial rapid compactive deformation of the sample rebounds to dilative at long term — attributed to the gas diffusion-induced swelling of the coal matrix. For the jacketed test both axial and circumferential coal strains are first dilative due to the decrease in effective stress with subsequent changes of coal strain induced by the gas diffusion closely associated with the specific boundary conditions. For a constant stress boundary, the circumferential strain first remains unchanged for some time and then gradually increases to steady state. Such a phenomenon suggests that when gas diffuses from the cleat to the matrix, the coal matrix-cleat system probably undergoes a transition from local swelling to macroswelling. In contrast, for a fixed displacement boundary, the axial strain first decreases and then reaches a steady state. It also indicates that the swelling of the matrix not only decreases the aperture of the fracture, but also expands the circumferential profile of the coal sample due to the Poisson effect. In addition, helium diffusion in the matrix is estimated by using the bidisperse diffusion model. The calculated effective diffusivity increases with pore pressure. This suggested that the gas diffusion coefficient is a pore pressure-dependent parameter. These results demonstrate that gas diffusion from the cleat to the matrix can cause the swelling of the coal matrix, change the aperture of the cleat, and in turn impact the evolution of the coal permeability.

A Reduced-Boron OPR1000 Core Based on the BigT Burnable Absorber

Reducing critical boron concentration in a commercial pressurized water reactor core offers many advantages in view of safety and economics. This paper presents a preliminary investigation of a reduced-boron pressurized water reactor core to achieve a clearly negative moderator temperature coefficient at hot zero power using the newly-proposed “Burnable absorber-Integrated Guide Thimble” (BigT) absorbers. The reference core is based on a commercial OPR1000 equilibrium configuration. The reduced-boron ORP1000 configuration was determined by simply replacing commercial gadolinia-based burnable absorbers with the optimized BigT-loaded design. The equilibrium cores in this study were directly searched via repetitive Monte Carlo depletion calculations until convergence. The results demonstrate that, with the same fuel management scheme as in the reference core, application of the BigT absorbers can effectively reduce the critical boron concentration at the beginning of cycle by about 65 ppm. More crucially, the analyses indicate promising potential of the reduced-boron OPR1000 core with the BigT absorbers, as its moderator temperature coefficient at the beginning of cycle is clearly more negative and all other vital neutronic parameters are within practical safety limits. All simulations were completed using the Monte Carlo Serpent code with the ENDF/B-VII.0 library.

Burnable absorber-integrated guide thimble (BigT) – II: application to 3D PWR core design

ABSTRACTThis paper is a companion to its immediate predecessor in the “Burnable absorber-integrated Guide Thimble” (BigT) series. It aims to demonstrate potential applications of the BigT concepts in a three-dimensional (3D) commercial pressurized water reactor core, which is based on the AP1000 first core design. The study specifically compares neutronic characteristics of the reference core against a BigT-loaded design. In this study, reactivity depletion patterns of nine fuel assembly lattices in the reference core were first evaluated. Corresponding sets of BigT-loaded assemblies that yield neutronically similar characteristics (i.e., initial reactivity suppression and depletion trend) with those of the reference assembly lattices were determined next. These BigT-loaded fuel assemblies were later loaded in place of the reference fuel assemblies for the subsequent high-fidelity 3D Monte Carlo core simulations. Results of the study clearly demonstrate that the BigT-loaded AP1000 first core performs as well as the reference core since all neutronic parameters are comparable, especially in terms of reactivity depletion, power peaking factors and shutdown margin. All simulations were completed using the Monte Carlo Serpent code with ENDF/B-VII.0 library.

Bias factor method using random sampling technique

ABSTRACTToward the practical use of the bias factor method for actual light water reactor core analyses, the bias factor method using the random sampling technique is newly proposed. The bias factor method is one of the correction methods using information of E/C values in existing measurable systems, to reduce biases and uncertainties of predicted core characteristics parameters. By the aid of the random sampling technique, our proposed bias factor method can be carried out using only forward calculations without any adjoint calculations, and can easily take into account burnup and thermal-hydraulic feedback effects, which are difficult points in the practical application to actual core analyses. Although the statistical error due to the random sampling technique is inevitable in the proposed method, the statistical error can be simply quantified by the resampling technique such as the bootstrap method. As one of the feasibility studies, effectiveness of the proposed method is verified through a numerical experiment which virtually simulates a typical equilibrium pressurized water reactor core. In this verification problem, it is clarified that E/C values of control rod worth at the beginning of cycle under the hot zero power condition are useful information to reduce biases and uncertainties of predicted assembly-wise power distributions during operation of hot full power.

Power-level regulation and simulation of nonlinear pressurized water reactor core with xenon oscillation using H-infinity loop shaping control

This investigation is to solve the power-level control issue of a nonlinear pressurized water reactor core with xenon oscillations. A nonlinear pressurized water reactor core is modeled using the lumped parameter method, and a linear model of the core is then obtained through the small perturbation linearization way. The H∞loop shapingcontrolis utilized to design a robust controller of the linearized core model.The calculated H∞loop shaping controller is applied to the nonlinear core model. The nonlinear core model and the H∞ loop shaping controller build the nonlinear core power-level H∞loop shaping control system.Finally, the nonlinear core power-level H∞loop shaping control system is simulatedconsidering two typical load processes that are a step load maneuver and a ramp load maneuver, and simulation results show that the nonlinear control system is effective.

Modeling and Simulation for Nonlinear Pressurized Water Reactor Cores Using Gap Metric and Fuzzy Model with Transfer Function

This investigation is to deal with the modeling issue for nonlinear pressurized water reactor cores. Nonlinearity measure with gap metric and T-S fuzzy modeling are exploited to build the fuzzy model of a nonlinear core which approximates this nonlinear core model. The gap metric of the core is proposed to quantify the core nonlinearity. The curve in the whole range of core power level that is solved adopting the gap metric is the core nonlinearity measure. In terms of the measure, six linearized core models at six power levels are selected as local models of the nonlinear core model. Based on the local models and the introduction of the triangle membership function, the core fuzzy model is achieved. The core fuzzy model and nonlinear core model are simulated. Simulation results show that the core fuzzy model can approximate and substitute the nonlinear core model.

Review on Application of Control Algorithms to Power Regulations of Reactor Cores

This research is to solve the stability analysis issue of nonlinear pressurized water reactor cores. On the basis of modeling a nonlinear pressurized water reactor core using the lumped parameter method, its linearized model is achieved via the small perturbation linearization way. Linearized models of the nonlinear core at six power levels are selected as local models of this core. The T-S fuzzy idea for the core is exploited to construct the T-S fuzzy model of the nonlinear core based on the local models and the triangle membership function, which approximates the nonlinear core model within the entire range of power level. This fuzzy model as a bridge is to cater to the stability analysis of the nonlinear core after defining its stability. One stability theorem is deduced to define the nonlinear core is globally asymptotically stable in the global range of power level. Finally, the simulation work and stability analyses are separately completed. Numerical simulations show that the fuzzy model can substitute the nonlinear core model; stability analyses verify the nonlinear core is globally asymptotically stable in the global range of power level.