Axial Power Distribution Research Articles

Improving the Neutronic Characteristics of a Boiling Water Reactor by Using Uranium Zirconium Hydride Fuel Instead of Uranium Dioxide Fuel

The present work discusses two different models of boiling water reactor (BWR) bundle to compare the neutronic characteristics of uranium dioxide (UO₂) and uranium zirconium hydride (UZrH 1.6 ) fuel. Each bundle consists of four assemblies. The BWR assembly fueled with UO₂ contains 8 × 8 fuel rods while that fueled with UZrH 1.6 contains 9 × 9 fuel rods. The Monte Carlo N-Particle Transport code, based on the Mont Carlo method, is used to design three dimensional models for BWR fuel bundles at typical operating temperatures and pressure conditions. These models are used to determine the multiplication factor, pin-by-pin power distribution, axial power distribution, thermal neutron flux distribution, and axial thermal neutron flux. The moderator and coolant (water) are permitted to boil within the BWR core forming steam bubbles, so it is important to calculate the reactivity effect of voiding at different values. It is found that the hydride fuel bundle design can be simplified by eliminating water rods and replacing the control blade with control rods. UZrH 1.6 fuel improves the performance of the BWR in different ways such as increasing the energy extracted per fuel assembly, reducing the uranium ore, and reducing the plutonium accumulated in the BWR through burnup.

Impacts of Burnup-Dependent Swelling of Metallic Fuel on the Performance of a Compact Breed-and-Burn Fast Reactor

The U-Zr or U-TRU-Zr cylindrical metallic fuel slug used in fast reactors is known to swell significantly and to grow during irradiation. In neutronics simulations of metallic-fueled fast reactors, it is assumed that the slug has swollen and contacted cladding, and the bonding sodium has been removed from the fuel region. In this research, a realistic burnup-dependent fuel-swelling simulation was performed using Monte Carlo code McCARD for a single-batch compact sodium-cooled breed-and-burn reactor by considering the fuel-swelling behavior reported from the irradiation test results in EBR-II. The impacts of the realistic burnup-dependent fuel swelling are identified in terms of the reactor neutronics performance, such as core lifetime, conversion ratio, axial power distribution, and local burnup distributions. It was found that axial fuel growth significantly deteriorated the neutron economy of a breed-and-burn reactor and consequently impaired its neutronics performance. The bonding sodium also impaired neutron economy, because it stayed longer in the blanket region until the fuel slug reached 2% burnup.

Conjugate heat transfer investigation of core damage propagation during total instantaneous blockage in SFR fuel subassembly

Total instantaneous blockage at the inlet of a fuel subassembly (SA) is considered as a beyond design basis event in sodium cooled fast reactors. It is the bounding case of various types of local blockages and to cater for this event, a core catcher is provided at the bottom of the core. The extent of core damage propagation, before reactor trips, forms an important input for thermal design of the core catcher. Neutronics of the core is influenced by various phenomena that take place within the blocked SA, viz., (i) sodium boiling and clad/fuel melting, (ii) location within the blocked SA where these phenomena initiate and (iii) their rate of propagation inside the SA. Reactor trip by core temperature monitoring system of the neighboring SA is affected by (i) heat transfer between the molten fuel pool and the neighboring SA, (ii) number of fuel pins in the SA, (iii) rate of melting of the hexcan and (iv) thermocouple time constant. Towards understanding the thermal hydraulics of damage propagation, a coupled 2-dimensional transient thermal hydraulic model has been proposed. The model considers explicit representation of all the rows of fuel pins within the blocked SA and axial power distribution in the pins. For a realistic estimate of heat flux on the neighboring SA hexcan, natural convection in the heat generating molten fuel pool is considered. The damage propagation to the hexcan is determined by an enthalpy based energy equation, to model moving interface with melting/solidification. The models for turbulent natural convection in the fuel pool, and thermocouple response of neighboring SA are validated against published data in open literature. By detailed parametric studies, it is established that the damage is restricted to seven SA, in the event of TIB for a medium size fast reactor. The proposed 2-D model predicts a faster damage propagation than the 1-D models. However, residual thickness of the hexcan at the time reactor trip is 51%, which is nearly same as that predicted by the 1-D model. Thermocouple time constant is found to be a sensitive parameter for early detection of the TIB. When the number of pins in a SA is reduced, the residual thickness of the neighboring SA hexcan increases.

Dosimetry Evaluation of In-Core and Above-Core Zirconium Alloy Samples in a PWR

A description of the neutron fluence analysis of activated zirconium alloys samples at a Westinghouse 3-loop reactor is presented. These samples were irradiated in the core and in the fuel plenum region, where dosimetry measurements are relatively rare compared with regions radially outward of the core. Dosimetry measurements performed by Batelle/PNNL are compared to the calculational models. Good agreement is shown with the in-core measurements when using analysis conditions expected to best represent this region, such as an assembly-specific axial power distribution. However, the use of these conditions to evaluate dosimetry in the fuel plenum region can lead to significant underestimation of the fluence. The use of a flat axial power distribution, however, does not underestimate the fluence in the fuel plenum region.

Axial Power and Coolant-Temperature Profiles for a Non-Re-Entrant Pressure-Tube Supercritical Water-Cooled Reactor Fuel Channel

The axial power and coolant-temperature distributions in a fuel channel of the Generation IV pressure-tube super-critical water-cooled reactor (PT-SCWR) are found using coupled neutronics-thermal-hydraulics calculations. The simulations are performed for a channel loaded with a fresh, 78-element Th-Pu fuel assembly. Neutronics calculations are performed using the DONJON diffusion code using two-group homogenized cross sections produced using the lattice code DRAGON. The axial coolant temperature profile corresponding to a certain axial linear heat generation rate is found using a code developed in-house at University of Ontario Institute of Technology (UOIT). The effect of coolant density, coolant temperature, and fuel temperature variation along the channel is accounted for by generating macroscopic cross sections at several axial positions. Fixed-point iterations are performed between neutronics and thermal-hydraulics calculations. Neutronics calculations include the generation of two-group macroscopic cross sections at several axial positions, taking into account local parameters such as coolant temperature and density and average fuel temperature. The coolant flow rate is adjusted so that the outlet temperature of the coolant corresponds to the SCWR technical specifications. The converged axial power distribution is found to be asymmetric, resembling a cosine shape skewed toward the inlet (reactor top).

RETRACTED: A new strategy to select axial power distribution for thermal hydraulic analysis

Abstract An appropriate method for selecting the axial power distribution that results in the most conservative thermal margins was developed in this study. Nuclear physics calculations provided axial power distributions with various shapes based on the core states and cycles. A total of 17 cycles were required to reach the equilibrium core from the initial core. The axial power distributions were sorted based on the power peaking and sum-to-peak (STP) values. In the present study, three different power peaking criteria were used to sort the axial power distributions: the upper 50%, upper 25%, and upper 10%. After the first sorting based on the power peaking, the axial power distributions were grouped based on the power peak location in the axial direction. In each group, the axial power distribution with the highest STP was chosen for thermal margin analyses. In addition, the axial power distributions in the hottest channel and fuel assembly from the initial to the equilibrium core were obtained. Since the axial power distributions in the hottest channel and fuel assembly were bounded by the axial power distribution with the upper 10% F Q , the thermal hydraulic analysis results gave the more conservative thermal margins using the selection method presented in this study. The Onset of Nucleate Boiling (ONB) temperature margin with the upper 10% F Q was 22.5 °C, but it was 25.0 °C for the hottest channel. Therefore, the axial power distribution used for thermal hydraulic and safety analyses should be selected using the appropriate method presented in this study.

PARCS code multi-group neutron diffusion constants generation using Monte Carlo method

PARCS code is a three-dimensional (3D) reactor core simulator which solves the steady-state and time-dependent multi-group neutron diffusion equations if the multi-group diffusion constants (MGDCs) are provided. The MGDCs are mostly prepared for reactor physics problems using deterministic lattice codes. Beside approximation in the geometry, a lattice code inherently applies estimates to the neutron transport model. On the other hand, the geometric flexibility and use of continuous energy cross sections data library associated with the Monte Carlo (MC) method makes it a good candidate for the generation of highly accurate multi-group cross sections. In this study, a new MC based methodology is applied to generate the MGDCs which can be utilized in the PARCS code input file directly or as PMAXS files for a reactor core simulation. To achieve this, a new tool in MATLAB software is developed to compute the MGDCs from the MCNPX 2.7 MC code outputs. Verification of the proposed method for two-group constants generation is carried out using Tehran research reactor (TRR) core simulation in different steady state conditions. The calculated values of axial and radial power distributions and multiplication factor using the PARCS code are verified against the MCNPX 2.7 code results. The results illustrate that the proposed method has high accuracy in MGDCs generation.

Nonlinear control for core power of pressurized water nuclear reactors using constant axial offset strategy

One of the most important operations in nuclear power plants is load following, in which an imbalance of axial power distribution induces xenon oscillations. These oscillations must be maintained within acceptable limits otherwise the nuclear power plant could become unstable. Therefore, bounded xenon oscillation is considered to be a constraint for the load following operation. In this paper, the design of a sliding mode control (SMC), which is a robust nonlinear controller, is presented. SMC is a means to control pressurized water nuclear reactor (PWR) power for the load following operation problem in a way that ensures xenon oscillations are kept bounded within acceptable limits. The proposed controller uses constant axial offset (AO) strategy to ensure xenon oscillations remain bounded. The constant AO is a robust state constraint for the load following problem. The reactor core is simulated based on the two-point nuclear reactor model with a three delayed neutron groups. The stability analysis is given by means of the Lyapunov approach, thus the control system is guaranteed to be stable within a large range. The employed method is easy to implement in practical applications and moreover, the SMC exhibits the desired dynamic properties during the entire output-tracking process independent of perturbations. Simulation results are presented to demonstrate the effectiveness of the proposed controller in terms of performance, robustness, and stability. Results show that the proposed controller for the load following operation is so effective that the xenon oscillations are kept bounded in the given region.

Control parameter optimization for AP1000 reactor using Particle Swarm Optimization

The advanced mechanical shim (MSHIM) core control strategy is implemented in the AP1000 reactor for core reactivity and axial power distribution control simultaneously. The MSHIM core control system can provide superior reactor control capabilities via automatic rod control only. This enables the AP1000 to perform power change operations automatically without the soluble boron concentration adjustments. In this paper, the Particle Swarm Optimization (PSO) algorithm has been applied for the parameter optimization of the MSHIM control system to acquire better reactor control performance for AP1000. System requirements such as power control performance, control bank movement and AO control constraints are reflected in the objective function. Dynamic simulations are performed based on an AP1000 reactor simulation platform in each iteration of the optimization process to calculate the fitness values of particles in the swarm. The simulation platform is developed in Matlab/Simulink environment with implementation of a nodal core model and the MSHIM control strategy. Based on the simulation platform, the typical 10% step load decrease transient from 100% to 90% full power is simulated and the objective function used for control parameter tuning is directly incorporated in the simulation results. With successful implementation of the PSO algorithm in the control parameter optimization of AP1000 reactor, four key parameters of the MSHIM control system are optimized. It has been demonstrated by the calculation results that the optimized MSHIM control system parameters can improve the reactor power control capability and reduce the control rod movement without compromising AO control. Therefore, the PSO based optimization method can be used to optimize MSHIM control system parameters to provide much better reactor control capabilities.

Estimation of relative power distribution and power peaking factor in a VVER-1000 reactor core using artificial neural networks

Designing a computational tool to predict in real-time neutronic parameters of a VVER-1000 reactor core such as axial and radial relative power distributions (RPDs) and power peaking factor (PPF) based on an artificial neural network (ANN) framework is presented in this paper. The method utilizes ex-core neutron detector signals, some core parameters data, and a neural network to setup a real-time monitoring system for RPD and PPF predictions. To detect the hottest fuel assemblies (FAs), the radial RPD in the core is first monitored and then the axial relative power of those FAs is screened to detect the PPF in the core. To achieve this, two hundred reactor operation states with different power density distributions are obtained by positioning the control rods in different configurations. Then a multilayer perceptron (MLP) neural network is trained by applying a set of experimental and calculated data for each core state. The experimental data are core parameters such as control rods position, coolant inlet temperature, power level and signal of ex-core neutron detectors taken from Bushehr nuclear power plant (BNPP) for each operation state. The RPD and PPF for each corresponding state are calculated using a validated model developed in MCNPX 2.7 code. The results of this study indicate that the RPD and PPF can be determined through a neural network having in input the position of control rods, the power level, the coolant inlet temperature, the boric acid concentration, the effective days of reactor operation, and the signal of ex-core neutron detectors, accurately. Also, the sensitivity study of the ANN response to different selection of input parameters illustrates that the signal of ex-core neutron detector plays an important role in the ANN prediction accuracy.

Drift-flux model for rod bundle geometry

In view of an important role of a one-dimensional drift-flux correlation in nuclear thermal-hydraulic system analysis codes, several drift-flux correlations such as Lellouche–Zolotar, Chexal–Lellouche, TRAC-BF1 and Ozaki correlations have been reevaluated by rod bundle test data taken in FRIGG and NUPEC test facilities. The mean absolute error of void fraction representing a correlation bias of the Lellouche–Zolotar, Chexal–Lellouche, TRAC-BF1 and Ozaki correlations are, respectively, −1.0, 0.5, −6.3 and −3.3% for the FRIGG test data and 2.0, 2.3, −0.4 and −0.7% for the NUPEC test data. The effects of unheated rods, axial and radial power distributions, large unheated center rod and geometry of a shroud or casing on void fraction are identified. The presence of unheated rods with similar size of other heated rods tends to increase a distribution parameter in a drift-flux correlation, whereas the presence of a large unheated center rod tends to decrease the distribution parameter. The axial and radial power distributions do not have significant effect on void fraction within the tested axial and radial power distribution range. The Ozaki correlation is recommended for predicting void fraction in a BWR core but it is suggested to reduce the distribution parameter in the Ozaki correlation if a large unheated center rod exists in the core. It is indicated that drift-flux correlations developed based on bounded rod bundle test facility data may overestimate the distribution parameter for a PWR core.

Safety assessment of U–Mo fuel mini plates irradiated in HANARO reactor

Neutronic and thermal hydraulic characteristics of U–Mo fuel mini plates irradiated in the HANARO reactor were analyzed for the safety assessment of these plates. A total of eight fuel plates were double-stacked; each stack contained three 8.0gU/cc U–7Mo fuel plates and one 6.5gU/cc U–7Mo fuel plate. The neutronic and thermal hydraulic analyses were carried out using the MCNP code and TMAP code, respectively. The core status used in the study was the equilibrium core, and four Control Absorber Rod (CAR) locations were considered: 350mm, 450mm, 550mm, and 650mm away from the bottom of the core. For the fuels in the lower stack, the maximum heat flux was found at the CAR located at 450mm. For the fuels in the upper stack, the maximum heat flux was found at the CAR located at 650mm. The axial power distributions for the upper and lower stacks were selected on the basis of thermal margin analyses. A mock-up irradiation target assembly was designed and tested at the out-of-pile test facility to measure the flow rate through the irradiation site, given that the maximum flow rate through the irradiation site at the HANARO reactor is limited to 12.7kg/s. For conservative analyses, measurement and correlation uncertainties and engineering hot channel factors were considered. During normal operation, the minimum ONB temperature margins for the lower and upper stacks are 41.6°C and 31.8°C, respectively. This means that boiling does not occur. However, boiling occurs during the limiting accidents. Nevertheless, the fuel integrity is maintained since the minimum DNBR are 1.96 for the Reactivity Insertion Accident (RIA) and 2.10 for the Locked Rotor Accident (LRA). From the neutronic and thermal hydraulic analyses of the U–Mo fuel mini plates irradiated in the HANARO reactor, it is concluded that boiling does not occur during normal operation and that the fuel integrity is maintained during limiting accidents.

Study on the Use of Hydride Fuel in High-Performance Light Water Reactor Concept

Hydride fuels have features which could make their use attractive in future advanced power reactors. The potential benefit of use of hydride fuel in HPLWR without introducing significant modification in the current core design concept of the high-performance light water reactor (HPLWR) has been evaluated. Neutronics and thermal hydraulic analyses were performed for a single assembly model of HPLWR with oxide and hydride fuels. The hydride assembly shows higher moderation with softer neutron spectrum and slightly more uniform axial power distribution. It achieves a cycle length of 18 months with sufficient excess reactivity. At Beginning of Cycle the fuel temperature coefficient of the hydride assembly is higher whereas the moderator and void coefficients are lower. The thermal hydraulic results show that the achievable fuel temperature in the hydride assembly is well below the design limits. The potential benefits of the use of hydride fuel in the current design of the HPLWR with the achieved improvements in the core neutronics characteristics are not sufficient to justify the replacement of the oxide fuel. Therefore for a final evaluation of the use of hydride fuels in HPLWR concepts additional studies which include modification of subassembly and core layout designs are required.

Sliding mode observer design for a PWR to estimate the xenon concentration & delayed neutrons precursor density based on the two point nuclear reactor model

One of the important operations in nuclear power plants is load-following in which imbalance of axial power distribution induces xenon oscillations. These oscillations must be maintained within acceptable limits otherwise the nuclear power plant could become unstable. Therefore, bounded xenon oscillation considered to be a constraint for the load-following operation. In other hands, precursors produce delayed neutrons which are most important in control of nuclear reactor, but xenon concentration & precursor density cannot be measured directly. In this paper, non-linear sliding mode observer which has the robust characteristics facing the parameters uncertainties and disturbances is proposed based on the two point nuclear reactor model to estimate the xenon concentration & delayed neutron precursor density of the Pressurized-Water Nuclear Reactor (PWR) using reactor power measurement. The stability analysis is given by means Lyapunov approach, thus the system is guaranteed to be stable within a large range. The employed method is easy to implement in practical applications. This estimation is done taking into account the effects of reactivity feedback due to temperature and xenon concentration. Simulation results clearly show that the sliding mode observer follows the actual system variables accurately and is satisfactory in the presence of the parameters uncertainties & disturbances.

Estimation of the xenon concentration and delayed neutrons precursors densities in the pressurized-water nuclear reactors (PWR) with sliding mode observer considering xenon oscillations

One of the important operations in nuclear power plants is load-following in which the imbalance in axial power distribution induces xenon oscillations. These oscillations must be maintained within acceptable limits otherwise the nuclear power plant could become unstable. Therefore, bounded xenon oscillation is considered to be a constraint for the load-following operation. On the other hands, precursors produce delayed neutrons which are important with respect to reactor period and control, but xenon concentration and precursors densities cannot be measured directly. In this paper, the non-linear sliding mode observer which has the robust characteristics facing the parameters uncertainties and disturbances is proposed based on the two point nuclear reactor model equations with three groups of the delayed neutrons to estimate the xenon concentration and delayed neutrons precursor densities of the pressurized-water nuclear reactor (PWR) using reactor power measurements. The stability analysis is provided by means of the Lyapunov approach, thus the system is guaranteed to be stable over a wide range. The employed method is easy to implement. This estimation is done taking into account the effects of reactivity feedback due to temperature and xenon concentration. Simulation results clearly show that the sliding mode observer follows the actual system variables accurately and is satisfactory in the presence of the parameter uncertainties and disturbances.

Sliding Mode Control for Pressurized-Water Nuclear Reactors in load following operations with bounded xenon oscillations

One of the important operations in nuclear power plants is load-following in which imbalance of axial power distribution induces xenon oscillations. These oscillations must be maintained within acceptable limits otherwise the nuclear power plant could become unstable. Therefore, bounded xenon oscillation considered to be a constraint for the load-following operation. In this paper, sliding mode control (SMC) which is a robust nonlinear controller is designed to control the Pressurized-Water Nuclear Reactor (PWR) power for the load-following operation problem that ensures xenon oscillations are kept bounded within acceptable limits. The proposed controller uses constant axial offset (AO) strategy to maintain xenon oscillations to be bounded. The constant AO is a robust state constraint for load-following problem. The reactor core is simulated based on the two-point nuclear reactor model and one delayed neutron group. The stability analysis is given by means Lyapunov approach, thus the control system is guaranteed to be stable within a large range. The employed method is easy to implement in practical applications and moreover, the sliding mode control exhibits the desired dynamic properties during the entire output-tracking process independent of perturbations. Simulation results are presented to demonstrate the effectiveness of the proposed controller in terms of performance, robustness and stability. Results show that the proposed controller for the load-following operation is sufficiently effective so that the xenon oscillations are kept bounded in the considered region.

Coupling of system thermal–hydraulics and Monte-Carlo code: Convergence criteria and quantification of correlation between statistical uncertainty and coupled error

Coupled multi-physics approach plays an important role in improving computational accuracy. Compared with deterministic neutronics codes, Monte Carlo codes have the advantage of a higher resolution level. In the present paper, a three-dimensional continuous-energy Monte Carlo reactor physics burnup calculation code, Serpent, is coupled with a thermal–hydraulics safety analysis code, RELAP5. The coupled Serpent/RELAP5 code capability is demonstrated by the improved axial power distribution of UO2 and MOX single assembly models, based on the OECD-NEA/NRC PWR MOX/UO2 Core Transient Benchmark.Comparisons of calculation results using the coupled code with those from the deterministic methods, specifically heterogeneous multi-group transport code DeCART, show that the coupling produces more precise results. A new convergence criterion for the coupled simulation is developed based on the statistical uncertainty in power distribution in the Monte Carlo code, rather than ad-hoc criteria used in previous research. The new convergence criterion is shown to be more rigorous, equally convenient to use but requiring a few more coupling steps to converge. Finally, the influence of Monte Carlo statistical uncertainty on the coupled error of power and thermal–hydraulics parameters is quantified. The results are presented such that they can be used to find the statistical uncertainty to use in Monte Carlo in order to achieve a desired precision in coupled simulation.

Application of an Improved Mechanical Shim Control Strategy for AP1000 Reactor

This paper presents the performance evaluation of an improved mechanical shim (MSHIM) control strategy that is implemented in the AP1000 reactor by a digital rod control system. The MSHIM control system automatically controls the core reactivity and axial power distribution using gray and black M control banks (M-banks) and an axial offset (AO) control bank (AO-bank). The M-banks and AO-bank are independently controlled by the power control subsystem and the AO control subsystem. In the original MSHIM strategy, the power control subsystem takes precedence, and the AO-bank is blocked from moving when a demand signal exists for the movement of the M-banks. This rod control logic can minimize the potential for interactions between the two rod control subsystems and guarantee the safety and stability of the MSHIM control system. However, the AO control capability is weakened at the same time. Thus, Westinghouse has improved this core control strategy, which gives preference to the AO-bank when both the AO-bank and the M-banks have a demand to move in the same direction.In this paper, first, the coupling characteristic of the MSHIM control strategy is analyzed to illustrate the coupling effect between the two rod control subsystems. Then, both the original and the improved MSHIM control strategies are applied to AP1000. It has been demonstrated by the MSHIM load-follow and load regulation simulation results that the improved strategy not only can provide much tighter AO control but also can reduce the total control rod movement without compromising the coolant average temperature control. Therefore, the improved MSHIM strategy can provide much better reactor control capabilities than the original strategy.

Study the neutronic analysis and burnup for BWR fueled with hydride fuel using MCNPX code

This work presents the neutronic characteristics of advanced boiling water reactor (BWR) which fueled with hydride fuel. MCNPX Computer code based on Mont Carlo Method, is used to design a three dimensional model for BWR fuel assembly in a typical operating temperature and pressure conditions. A test case was compared with a benchmark problem and good agreement was found. This model is used to determine attainable discharge burnup, pin-by-pin power distribution, axial power distribution and reactivity effect of voiding. It is found that hydride fuel bundle design can be simplified by reducing the volume of water in-between the fuel bundles. The increase in the number of fuel rods per given core volume enables an increase in the BWR power density relative to oxide fueled core design.

Reducing axial offset and improving stability in PWRs by using uranium–thorium fuel

The axial offset (AO) is a parameter used to monitor the core axial power distribution, and is important for safe reactor operation. Previous works have showed that a new type uranium–thorium (U–Th) based fuel assembly could be used to achieve a more homogenous radial power distribution, and thereby improve the thermal margins in the core. In this paper, it is shown that a core containing U–Th fuel assemblies also reduces the AO and improves the core stability. For an equilibrium U–Th core, the maximum AO could be reduced by 33%, and the minimum AO could be reduced by 8% compared with a standard uranium core. In the U–Th core, the maximum AO was influenced by the more negative moderator temperature coefficient of reactivity, while the minimum AO is mainly affected by the more homogenous radial power distribution. These findings conclude that the U–Th core displays a more homogenous power distribution both axially and radially, thus offering better thermal margins for power uprates and flexible power operation. Moreover, xenon oscillations in the core due to perturbations induced by the control rods are 30% more effectively damped for the U–Th core compared with the standard core, improving the stability in AO.