Pressurized Water Reactor Core Research Articles

New strategies with multi-model, state-feedback control and stability analysis for load-follow PWR core

The objective of this study is to design a Pressurized Water Reactor (PWR) core load following control system for regulating the core power level and axial power difference and analyze the global stability of the system theoretically. On the basis of building a two-point based nonlinear PWR core model without boron and with the power rod and Axial Offset (AO) rod, the linearized single-variable (multi-variable) core model under Case 1 (Case 2) classified by two movable regions of power rod is constructed. For each case, by proposing the equilibrium manifold and the nonlinearity measure of the core to calculate the distribution situation of the core nonlinearity measure in the entire range of power level, linearized models of the core at ten power levels are chosen as local models of the core to substitute the nonlinear core model. Based on each local model, the state feedback control is implemented by utilizing the robust pole assignment method with an additional integrator for Case 1 and devising an integral decoupling control system with a dynamic controller for Case 2; a Kalman filter with robustness is designed as an observer for each case. The integration of the state feedback and the observer structures a local controller of the core of each case. For each case, a local model and a local controller at one of ten power levels compose a core load following control subsystem. The combination of core load following control subsystems at ten power levels is the core load following control system. The global stability theorem is deduced to define that the core load following control system for Case 1 (Case 2) is globally asymptotically stable within the whole range of power level. Finally, the core load following control system for each case is simulated and the simulation results show that the control system is effective.

Pressurized water reactor core thermal-hydraulics model for flow coastdown transient

The flow coastdown transient analysis is crucial for the design and safety analysis of a nuclear reactor because, in such an event, the core cooling depends upon flywheel inertia of reactor coolant pumps. In this paper, the results of real time flow coastdown transient initiated by power failure to the reactor coolant pumps on the CHASHMA Nuclear Power Plant Unit-2 (CHASNUPP-2) are presented. To examine the effect of thermal-hydraulics parameters, a mathematical model of core thermal-hydraulics for the flow of coastdown transient has been developed. The resulting equations are solved analytically for a pressurized water reactor. The accuracy of the model depends on the core time constant τ, which has been computed to be 9.28 s for CHASNUPP-2, the calculation methodology is described in the paper. The results are compared with the transient data, good agreement is found between the model prediction and the flow coastdown transient data. It is inferred that the coastdown flow rate is effective in removing the stored heat in the core.

Multi-recycling of transuranic elements in a PWR assembly with reduced fuel rod diameter

This paper examines the multi-recycling of transuranic (TRU) elements (Pu-Np-Am-Cm) in standard Pressurized Water Reactor (PWR) assemblies. The original feed of TRU comes from legacy spent UOX fuel. For all subsequent recycling passes, TRU elements from the previous generation are employed, supplemented by TRU from legacy UOX fuel, as needed. The design criteria include: 235U enrichment requirements to remain below 5 w/o, TRU loading limits to avoid return to criticality under voided conditions, and assembly power peaking factors. In order to carry out multiple recycling passes within the design envelope, additional neutron moderation is required and achieved by reducing the fuel pellet diameter by about 13%, thus keeping the assembly design compatible with current PWR core internals. TRU transmutation rates and long-term ingestion radiotoxicity results are presented for 15 recycling passes and compared to standard UOX and MOX once-through cycles. The results also show that TRU fuel isotopics and radiotoxicity tend towards an equilibrium, enabling further additional recycling passes.

Modeling and LQG/LTR control for power and axial power difference of load-follow PWR core

The task of this investigation is to design a nonlinear Pressurized Water Reactor (PWR) core load following control system for regulating the core power level and axial power difference. A two-point based nonlinear PWR core model without boron and with the power regulating rod and Axial Offset (AO) rod is built. The linearized single-input single-output (SISO) or multiple-input multiple-output (MIMO) core model under Case 1 or Case 2 classified by two movable regions of power regulating rod is constructed. The linear SISO or MIMO model is further augmented with additional integrators to cater to the control design. The Linear Quadratic Gaussian with Loop Transfer Recovery (LQG/LTR) robust optimal control is used to contrive a controller of the linear core model of each case. For Case 1 (Case 2), the nonlinear core model and the LQG/LTR SISO (MIMO) controller construct the nonlinear PWR core load following control system. Two stability theorems are deduced to define that the nonlinear core load following control system of each case is asymptotically stable. Finally, the control system of each case is simulated and the simulation results show that the control system is effective.

Extension for load-follow operation of PWR core by using single- or multi-variable control of state-feedback

The single- or multi-variable control of full-state feedback with a full-order observer is applied to design a nonlinear Pressurized Water Reactor (PWR) core load following control system for regulating the core power level and axial power shape. A two-point based nonlinear PWR core model without boron and with the power rod and Axial Offset (AO) rod is built. The linearized single-variable (multi-variable) core model under Case 1 (Case 2) classified by two movable regions of power rod is constructed. Based on a linearized core model, the state feedback control is implemented by utilizing the robust pole assignment method with an additional integrator for Case 1 and devising an integral decoupling control system with a dynamic controller for Case 2; a Kalman filter with robustness is designed as an observer for each case. The integration of the state feedback and the observer structures a controller of the nonlinear core model of each case. For Case 1 (Case 2), the nonlinear core model and the state feedback single-variable (multi-variable) control construct the nonlinear PWR core load following control system. Finally, the control system of each case is simulated and the simulation results show that the control system is effective.

Coupling of a Lumped Parameter and a Finite Difference Model for Estimation of a Reactivity-Induced Transient in a PWR with Annular Fuel Rods

This paper develops a finite difference and a semianalytical model to evaluate the thermal behavior of fuel rods during a hypothetical reactivity-induced transient (absorber rod ejection) in a pressurized water reactor (PWR). The calculations are carried out for two different reactor core designs, namely, for a typical PWR core with typical fuel rods and for a modified PWR core containing annular fuel rods. The overall dimensions of the core internals and fuel assemblies are unchanged, and the total number of fuel assemblies is the same in both designs. The finite difference code was verified on the results provided by the semianalytical model. In the calculations, two point models were used (neutron kinetics to compute the fission power of the reactor; power balance of coolant in the active core region). The point models were coupled to the one-dimensional, finite difference heat conductivity model to calculate the radial temperature profile in the solid and the annular cylindrical pellets (UO2). The latter are the constituent part of annular fuel rods cooled both on their external and internal surfaces. The fuel, cladding, and fluid temperatures were evaluated for the annular and the solid fuel design in the hot spot, where the maximum allowable power rating of rods is 2.5 times higher than the average one. It was assumed that before the transient, (a) the reactor with annular fuel runs continuously at higher nominal power (150%) and at higher nominal coolant flow rate (150%) at the core inlet than the reference reactor with solid fuel (100%) and (b) the modified and the reference reactors have the same coolant temperature at the core inlet and the same temperature rise of coolant along their core. These conditions correspond to a 150% power uprate of the reference reactor. The coupled models require limited computational resources only. The calculated results showed that during the transient, in the annular fuel pellet, the temperatures peaked at considerably lower values, even at 150% power, than in the solid pellets at 100% power. These evaluations show that in the case of the reactivity-induced transient analyzed, the annular fuel cooled from both sides has a better safety performance than the solid fuel cooled only on its external surface.

Bond graph representation of nuclear reactor point kinetics and nearly incompressible thermal hydraulics

This work presents a simplified 1D model for a pressurized water reactor core, suitable for very rapid transients like control rod ejection. The model is represented using the bond graph formalism, a technique for modeling engineering systems as combinations of connected elements. Bond graphs are a flexible way of presenting coupled physics problems by automating the computer science aspects of modeling and letting the modelers focus on the physics; they were introduced in earlier work.To help leverage the flexibility of bond graph representations of physical systems, a new bond graph processing code, BGSolver, is introduced. BGSolver has been developed by the authors over the past several years, and is now released as open source software.A rapid rod ejection benchmark is solved with both BGSolver and RELAP5-3D; BGSolver obtained full convergence with a 5ms time step, while RELAP5-3D required a 1ms time step, due to the fully coupled time integration that BGSolver employed, compared to an operator splitting-based time integrator of RELAP5-3D. BGSolver’s time integrator demonstrated 3rd-order convergence in time, a very desirable property. A single nonlinear solve was used to obtain the steady state with BGSolver.

Generating Unstructured Nuclear Reactor Core Meshes in Parallel

Recent advances in supercomputers and parallel solver techniques have enabled users to run large simulations problems using millions of processors. Techniques for multiphysics nuclear reactor core simulations are under active development in several countries. Most of these techniques require large unstructured meshes that can be hard to generate in a standalone desktop computers because of high memory requirements, limited processing power, and other complexities. We have previously reported on a hierarchical lattice-based approach for generating reactor core meshes. Here, we describe efforts to exploit coarse-grained parallelism during reactor assembly and reactor core mesh generation processes. We highlight several reactor core examples including a very high temperature reactor, a full-core model of the Korean MONJU reactor, a ¼ pressurized water reactor core, the fast reactor Experimental Breeder Reactor-II core with a XX09 assembly, and an advanced breeder test reactor core. The times required to generate large mesh models, along with speedups obtained from running these problems in parallel, are reported. A graphical user interface to the tools described here has also been developed.

压水堆堆芯稳态单通道热工计算

本文通过对六控制体压水堆堆芯单通道热工计算及模拟，发现：1) 燃料棒包壳温度在第四控制体出现峰值；2) 燃料芯块外壁及中心温度最大值出现在第四控制体；3) 最小烧毁比在第四控制体。这些结果显示在压水堆运行安全监控中，对温度的监测重点应放在第四控制体。本文计算及模拟结果可为反应堆热工设计及堆芯温度校核提供一个参考。 The heat transfer in the pressurized water reactor (PWR) core, which is divided into six control volumes, is investigated by stable single channel calculation and simulation. It is concluded that: 1) Temperature peak of fuel cladding arises in the fourth control volume; 2) The maximum temperatures of the outer and center fuel pellets appear in the fourth control volume; 3) The minimum departure from nucleate boiling ratio (DNBR) also appears in the fourth control volume. These results suggest that the key of temperature monitoring should be in the fourth control volume in the PWR operation. This phenomenon may provide a reference for the thermal design of reactor and the check of core temperature.

Investigations of boron transport in a PWR core with COBAYA3/SUBCHANFLOW inside the NURESIM platform

Multi-scale, multi-physics problems reveal significant challenges while dealing with coupled neutronic/thermal-hydraulic solutions. Current generations of reactor dynamic codes applied to Light Water Reactors (LWRs), and in the context of this paper, pressurized water reactors (PWRs), are based on 3D neutronic nodal methods coupled with single or two phase flow thermal hydraulic system or sub-channel codes. This paper describes the extension of the coupling scheme between the 3D neutron diffusion codes COBAYA3 and DYN3D, and the sub-channel thermal-hydraulic code SUBCHANFLOW for the simulation of boron dilution transients. This includes the validation of the boron transport model of SUBCHANFLOW. The coupling of COBAYA3 and DYN3D with SUBCHANFLOW is performed inside the NURESIM platform making use of the novel automatic mesh superposition for code coupling. Boron transport models are needed for the simulation of boron dilution transients following a SBLOCA (after loop-seal clearing). In this case, the mixing is a key mechanism determining the positive reactivity insertion in the core. The results obtained with the coupled codes COBAYA3/SUBCHANFLOW, DYN3D/SUBCHANFLOW will be presented and discussed for two transient scenarios; a homogeneous and a heterogeneous boron dilution problem for a mini-core and for a PWR core defined in the NURISP boron dilution Benchmark.

Coarse mesh finite difference formulation for accelerated Monte Carlo eigenvalue calculation

An efficient Monte Carlo (MC) eigenvalue calculation method for source convergence acceleration and stabilization is developed by employing the Coarse Mesh Finite Difference (CMFD) formulation. The detailed methods for constructing the CMFD system using proper MC tallies are devised such that the coarse mesh homogenization parameters are dynamically produced. These involve the schemes for tally accumulation and periodic reset of the CMFD system. The method for feedback which is to adjust the MC fission source distribution (FSD) using the CMFD global solution is then introduced through a weight adjustment scheme. The CMFD accelerated MC (CMFD-MC) calculation is examined first for a simple one-dimensional multigroup problem to investigate the effectiveness of the accelerated fission source convergence process and also to analyze the sensitivity of the CMFD-MC solutions on the size of coarse meshes and on the number of CMFD energy groups. The performance of CMFD acceleration is then assessed for a set of two-dimensional and three-dimensional multigroup (3D) pressurized water reactor core problems. It is demonstrated that very rapid convergence of the MC FSD is possible with the CMFD formulation in that a sufficiently converged MC FSD can be obtained within 20 cycles even for large three-dimensional problems which would require more than 600 inactive cycles with the standard MC fission source iteration scheme. It is also shown that the optional application of the CMFD formulation in the active cycles can stabilize FSDs such that the real-to-apparent variance ratio of the local tallies can be reduced. However, due to the reduced importance of the variance bias in fine local tallies of 3D MC eigenvalue problems, the effectiveness of CMFD in tally stabilization turns out to be not so great.

On numerical simulation of fuel assembly bow in pressurized water reactors

Fuel assembly bow in pressurized water reactor cores is largely triggered by lateral hydraulic forces together with creep processes generated by neutron flux. A detailed understanding of the flow induced bow behaviour is, therefore, an important issue. The experimental feedbacks and laboratory tests on fuel assembly bow show that it is characterized to a high degree by fluid–structure interaction (FSI) effects, therefore, consideration of FSI is essential and indispensable in full comprehension of the bow mechanism.In the present study, coupled computational fluid dynamics (CFD) and finite element simulations are introduced, calculating fuel assembly deformation under different conditions as a quasi-stationary phenomenon. The aim has been, on the one hand, to develop such a simplified fuel assembly CFD model, which allows set up of fuel assembly rows without loosing its main hydraulic characteristic; on the other hand, to investigate the bow pattern of a given fuel assembly row under different boundary conditions. The former one has been achieved by comparing bow shapes obtained with different fuel assembly (spacer grid) modelling approaches and mesh resolutions with experimental data.In the second part of the paper a row model containing 7.5 fuel assemblies is introduced, investigating the effect of flow distribution at inlet and outlet boundary regions on fuel assembly bow behaviour. The post processing has been focused on the bow pattern, lateral hydraulic forces, and horizontal flow distribution. The results have revealed importance of consideration of FSI, and that an inhomogeneous inlet/outlet flow condition causes significant ‘C’ shaped deformation of fuel assemblies towards the core shroud. The important effect of the core shroud has been also shown.

Multimodel-based power-level control with state-feedback and observer for load-follow PWR core

The purpose of this investigation is that a nonlinear Pressurized Water Reactor (PWR) core load following control system is designed and the global stability of the system is analyzed theoretically. On the basis of modeling a nonlinear PWR core and proposing the equilibrium manifold and the nonlinearity measure of the core to calculate the distribution situation of the core nonlinearity measure in the entire range of power level, linearized models of the core at five power levels are chosen as local models of the core and the set of local models is used to substitute the nonlinear core model. The full-state feedback control with a full-order observer is utilized to design a controller with robustness of every local model, which is treated as a local controller of the nonlinear core. The Kalman filter is contrived as an observer with robustness and the state feedback design with robustness is implemented via the robust pole assignment method. With the local models and local controllers, the flexibility partitioning of model and control is presented to design a decent flexibility controller of the nonlinear core at a random power level. A nonlinear core model and a flexibility controller at a random power level compose a core load following control subsystem. The combination of core load following control subsystems at all power levels is the core load following control system. Two global stability theorems are deduced to define that the core load following control system is globally asymptotically stable within the whole range of power level. Finally, the core load following control system is simulated and simulation results show that the control system is effective.

Multistart Simulated Annealing applied to a Reduced Scale Thermo-Hydraulic Loop of a Pressurized Water Reactor core

In this paper we investigate the reduced scale design of a third generation Pressurized Water Reactor core, with single phase flow under natural circulation, based on the Loss-of-Fluid Test facility. Recent works approach this issue applying metaheuristics such as Genetic Algorithms and Particle Swarm Optimization. Both approaches have, as a drawback, the high computational time to obtain an acceptable solution. Here, we propose an alternative method when computational time is critical. We approach the problem applying a Multistart Simulated Annealing method in order to obtain an acceptable solution in a lower computational time. Our results indicate a 98.7% computational time improvement over the state-of-the-art Particle Swarm Optimization method. Moreover, the Multistart Simulated Annealing results are 1.36% better than state-of-the-art Particle Swarm Optimization method. Thus, Multistart SA shows promising results and is a suitable method when time is critical.

CONSTRUCTION OF AN ELEMENTARY MODEL FOR THE DYNAMIC ANALYIS OF A PRESSURIZED WATER REACTOR

A lumped-parameter numerical model was constructed based on the conservation laws of mass and energy and the point neutron kinetics with 6 groups of delayed neutron to represent the dynamics of a pressurized water reactor core. On the viewpoint of control theory, the coupled phenomenon of neutron kinetics and thermal-hydraulics can be recognized as a dynamic system with feedback loops by the Doppler effect and the coolant temperature. Scilab was implemented to construct the equivalent transfer functions and associated feedback loops of a PWR core. The dynamic responses were performed by the perturbations of positive reactivity insertion, coolant flow rate, and coolant inlet temperature. This elementary PWR core model has been qualitatively assessed against independent numerical data to ensure the models and codes have a certain level of confidence or validation.

Brownian bridge and statistical error estimation in Monte Carlo reactor calculation

Brownian bridge (BB) is an effective vehicle in processing an output series in Monte Carlo (MC) simulation. However, most estimators based on BB cost the capability of on-the-fly monitoring. Here, on-the-fly implies that statistical error can be computed at every generation except some initial generations. In this work, on-the-fly estimation of standard deviation by the way of BB, which maintains a fixed storage size of tallies, has been investigated within a framework of the iterated integration of simulation output (IISO). Numerical tests on the MC power distribution calculation of a pressurized water reactor core reveal that the IISO approach with a relatively few number of integrations performs fairly well on average. The bias of statistical error can be managed to be about 10% or less.

Preliminary study of parameter uncertainty influence on Pressurized Water Reactor core design

Sub-channel analysis can improve the accuracy of reactor core thermal design. However, the important initial parameters contain various uncertainties during reactor operation. In this work, the Sub-channel Analysis Code of Supercritical reactor (SACOS) code, which is also applicable for Pressurized Water Reactor (PWR), was used to study the coolant flow characteristic and fuel rod heat transfer characteristic of 1/8 assembly which has the maximum linear power density in 300 MWe PWR core firstly. Then the Wilks' method and Response Surface Method (RSM) were utilized to determine the influence of sub-channel input parameters uncertainties on the highest temperature of reactor core fuel rod and Minimum Departure from Nucleate Boiling Ratio (MDNBR). The results show that in the most conservative conditions, the maximum temperature of the fuel rod and MDNBR were 2167.4 °C and 1.08, respectively. Considering the uncertainties of assembly inlet flow rate, inlet coolant temperature and system pressure, the 95% probability values (with 95% confidence) of fuel rod maximum and MDNBR calculated using response surface methodology were 2144.0 °C and 1.6, while they were 2137 °C and 1.74 calculated by Wilks' approach. Results show that the uncertainty analysis methods can provide larger reactor design criteria margin to improve the economy of reactor. Furthermore, the code was developed to have the capacity to perform the uncertainty study of sub-channel calculation.

Load following control and global stability analysis for PWR core based on multi-model, LQG, IAGA and flexibility idea

The work is to design a nonlinear Pressurized Water Reactor (PWR) core load following control system and analyze the global stability of this system. On the basis of modeling a nonlinear PWR core, linearized models of the core at five power levels are chosen as local models of the core to substitute the nonlinear core model in the global range of power level. The combination control strategy of the Linear Quadratic Gaussian (LQG) control and the Proportional Integral Derivative (PID) control with an optimization process of Improved Adaptive Genetic Algorithm (IAGA) proposed is used to contrive a combined controller with the robustness of a core local model as a local controller of the nonlinear core. Based on the local models and local controllers, the flexibility idea of modeling and control is presented to design a decent controller of the nonlinear core at a random power level. A nonlinear core model and a flexibility controller at a random power level compose a core load following control subsystem. The combination of core load following control subsystems at all power levels is the core load following control system. The global stability theorem is deduced to define that the core load following control system is globally asymptotically stable within the whole range of power level. Finally, the core load following control system is simulated and the simulation results show that the control system is effective.

Flexibility control and simulation with multi-model and LQG/LTR design for PWR core load following operation

The objective of this investigation is to design a nonlinear Pressurized Water Reactor (PWR) core load following control system. On the basis of modeling a nonlinear PWR core, linearized models of the core at five power levels are chosen as local models of the core to substitute the nonlinear core model in the global range of power level. The Linear Quadratic Gaussian with Loop Transfer Recovery (LQG/LTR) robust optimal control is used to contrive a controller with the robustness of a core local model as a local controller of the nonlinear core. Meanwhile, LTR principles are analyzed and proved theoretically by adopting the matrix inversion lemma. Based on the local controllers, the principle of flexibility control is presented to design a flexibility controller of the nonlinear core at a random power level. A nonlinear core model and a flexibility controller at a random power level compose a core load following control subsystem. The combination of core load following control subsystems at all power levels is the core load following control system. Finally, the core load following control system is simulated and the simulation results show that the control system is effective.

Frequency Domain Comparison of Multi-lump and Distributed Parameter Models for Pressurized Water Reactor Cores

Multi-lump and distributed parameter models are used to analyze the frequency behavior of a pressurized water reactor (PWR). The distributed parameter model is built upon the partial differential equations describing heat transfer and fluid flow in the reactor core. For comparison, a lumped parameter reactor core model with multiple fuel and coolant lumps is employed. The features of the transfer functions for both models are evaluated. The distributed parameter model has the ability to offer an accurate transfer function at any location throughout the reactor core. In contrast, the multi-lump parameter model only provides an average value in a given region (lump). Comparisons show that the multi-lump model results are only most favorable for frequencies less than ~0.1 Hz.