Axial Offset Research Articles

Numerical Investigations of Static and Dynamic Characteristics of a Novel Staggered Labyrinth Seal with Semi-Elliptical Structure

In order to optimize sealing performance, a novel labyrinth seal with semi-elliptical teeth (SET) structure is proposed in this paper, which includes semi-elliptical teeth and a series of cavities. The simulation results calculated by the numerical methods are compared with the experimental and theoretical results, and static and dynamic characteristics of the novel SET structure are further investigated. The numerical simulations of labyrinth seals with the SET structure demonstrate high accuracy and reliability, with a maximum relative error of less than 6% as compared to experimental results, underscoring the validity of the model. Notably, leakage rates are directly influenced by pressure drop and axial offset, with optimal sealing achieved at zero axial displacement. The direct damping coefficient increases as the pressure drop increases while the other dynamic coefficients decrease. Additionally, the stability results show that the novel SET structure exhibits higher stability for positive axial offsets. The novel model and corresponding results can provide a meaningful reference for the study of sealing structure and coupled vibration in the field of fluid machinery.

Effects of detection-beam focal offset on back-focal-plane displacement detection

High-resolution displacement detection can be achieved by analyzing the scattered light of the trapping beams from the particle in optical tweezers. In some applications where trapping and detecting beams must be separated, a detecting beam can be introduced for independent displacement measurement. However, the detecting beam focus possibly deviates from the center of the particle, which will affect the performance of displacement detection. Here, we detect the displacement of the particle by utilizing the forward scattered light of the detection beam from the particle. The effects of the lateral and axial offsets between the detection beam focus and the particle center on displacement detection are analyzed by the simulation and experiment. These results show that the lateral offsets will decrease the detection sensitivity and linear range. Moreover, it aggravates the crosstalk between the x-direction signal and the y-direction signal of the quadrant photodiode. Besides, the axial offsets also affect the detection sensitivity. More interestingly, an optimal axial offset can improve the sensitivity of displacement detection substantially. In addition, the influence of system parameters, such as particle radius a, numerical aperture of the condenser NAc, and numerical aperture of the objective NAo, on the optimal axial offset is also discussed. This work not only provides ideas for improving the performance of precision measurement by the method of forward scattered light detection but also expands the application of this method in fundamental physics.

A Knowledge-Based Analysis of Interlaminar Faults for Condition Monitoring of Magnetic Cores With Predominant Focus on Axial Offset Between the Fault Points

A Knowledge-Based Analysis of Interlaminar Faults for Condition Monitoring of Magnetic Cores With Predominant Focus on Axial Offset Between the Fault Points

Effects of axial offset and deflection on load-bearing characteristics of the permanent magnet bearing

The permanent magnet bearing (PMB) has the advantage of non-contact support, which is used to reduce mechanical friction and wear of journal bearings. The effect of translation or deflection between the magnets on the load-bearing characteristics has been studied separately rather than simultaneously, causing the load-bearing characteristics of the device in use to deviate significantly from those intended. In this study, the magnetic force, magnetic moment and stiffness are used to evaluate the load-bearing characteristics of the PMB. The load-bearing characteristics in service are investigated using numerical simulation, taking into account the coupling of axial offset and deflection. The results showed that the alignment-capable magnetic moment appears only in single-sided axial offsets, and its threshold changed by 0.14 times the deflection angle, both were positively correlated with each other. Under the coupling of axial offset and deflection, there is a significant error of up to 200 % between the actual and design values. In addition, the axial force and axial stiffness were affected significantly by axial offset but were insensitive to the deflection angle. Translation and deflection are critical factors affecting load-bearing characteristics. This study helps to narrow the gap between the design performance and service performance of the PMB, avoid magnets collisions, and reduce the possibility of device failure.

Control rod driven long-term load-follow operation in small modular reactor

The need for extensive load following with Small Modular Reactor (SMR) is increasing as its potential coupling with intermittent renewable energy sources increases. SMR is generally considered suitable for load following, though, its load maneuvering capability depends on the system design features and reactor control algorithm. In this study, it is shown that a control rod driving algorithm based on the core outlet temperature of a typical IPWR type of SMR, SMART100 facilitates the extensive load following operations (IAEA, 2018, Song et al., 2010, Lee et al., 2012). Addition of control parameter such as Axial Offset (AO) and Boron concentration change into the control algorithm makes a reactor control possible when the AO is close to the limit or control rod position is close to Power Dependent Insertion Limit(PDIL). Simulations for various scenarios were performed to verify the above algorithm Short-term simulations less than 2 days and Long-term simulations longer than 7 days were performed. For each simulation, random demand or scheduled demand considering demand changes incurred by renewable energy was used. In all simulations, it is confirmed that the reactor facilitates control rod driven load-following operation within the operation limit. Further, it is shown that more efficient load-following operation is achieved by additional adjustment of control band of outlet temperature.

Axial-offset analysis in iPWR by developing the neutronic/thermal-hydraulic core simulator based on coarse-mesh methods

Axial-Offset (AO), as an important operational parameter, should be monitored in the load-following procedure due to the safety limits related to xenon oscillation and axial peaking factor in a nuclear power plant. In this study, to calculate AO for a Small Modular Reactor, a neutronic/thermal–hydraulic simulator has been developed based on coarse mesh methods. In this simulator, the average current nodal expansion method and the single heated channel approach have been used for neutronic and thermal–hydraulic analysis, respectively. The developed simulator is verified by the IAEA-3D model and thermal–hydraulic benchmark model. As the iPWR small modular reactor case study, SMART reactor has been simulated, and the neutronic and thermal–hydraulic parameters have been calculated. For investigation of AO behavior during power changes, the regulating bank repositioning approach is employed, and the reactor core characteristics are estimated by a developed simulator. The results demonstrate that the AO variation remains in a safe and standard operating region for SMART reactor.

파울링된 피복관 표면의 가압 경수로 운전환경에서의 미포화 비등 열전달 성능평가를 위한 실험장치 구축 연구

The CRUD (Chalk River Unidentified Deposit or Corrosion Related Unidentified Deposit) is a fouling deposit of metal or metal oxide on the nuclear fuel cladding under PWR (Pressurized Water Reactor) operating conditions and causing the several operational and safety-related problems. The major concerns related to the CRUD are AOA (Axial Offset Anomaly) caused by the accumulation of the boron species inside the porous CRUD from the primary reactor coolant and CILC (CRUD Induced Localized Corrosion) caused by locally increased cladding surface temperature due to the additional thermal resistance of the CRUD layer. The growth of CRUD and the CRUD-related problems are known to be governed by the sub-cooled nucleate boiling phenomena inside the upper part of the reactor core, especially on the hot fuel assembly and hot fuel pin. In the current study, the experimental facility called DISNY (crud DeposItion Simulator for Nuclear energY) was proposed as a testbed to simulate the CRUD growth and to investigate the sub-cooled nucleate boiling heat transfer performance of the CRUD deposited cladding surface under prototypical PWR operating conditions.

Extending a low-order inhomogeneous adjoint equations model to a higher-order model with verification on integral applications

A higher-order nodal mathematical inhomogeneous adjoint model conjugate to the NEM-M2B2 nodal diffusion forward model is developed and introduced in this research. Verification of the developed model is presented through applications in perturbation analysis and the IAEA-3D benchmark including adjusted forms of it. This paper’s objective is to explore ways of extending and optimizing a mathematical adjoint capability suitable for use in an industrial reactor code, such that it becomes not merely an approximate but rather the exact adjoint counterpart to the typically used higher-order nodal forward solvers used in mature industrial reactor codes. Specifically, it is investigated how to upgrade an already available lower-order nodal mathematical adjoint solver towards higher-order accuracy. An example of the latter is the lower-order nodal adjoint solver used in the ARTEMIS reactor code, in the technical context of stabilization and acceleration of embedded control rod search mechanisms. Though the latter adjoint solver proved suitable for the needed preconditioning purposes, while also enabling the benefit of computationally very lean adjoint iterations, several future developments could benefit from having a higher-order adjoint nodal solver available as well. By using a preconditioned form of the base NEM-M2B2 nodal diffusion forward model and by using variational analysis, we have obtained a higher-order nodal mathematical adjoint that can have a physical interpretation associated with it as a Lagrangian multiplier. The nodal mathematical adjoint is then developed for the Axial Offset (AO) as a Response of Interest (RoI) which leads to an inhomogeneous adjoint system of equations. A solution verification of the adjoint developed is done through analyzing the effects coming from perturbations in the absorption and the scattering cross-sections. The applications investigated include axially and radially traveling perturbations along the reactor’s core. Several locations for the traveling perturbations are chosen to represent important locations in the core. Comparison between the low-order and the higher-order adjoint models is conducted. The forward model is set to the NEM-M2B2 nodal diffusion equation for both adjoints during the comparison. The higher-order adjoint model developed show consistent results in comparison to its lower-order sibling, suggesting the preference of using the developed higher-order model for adjoint computations.

A boron-adjustment-free control strategy for large pressurized water reactors

This paper proposes an advanced boron-adjustment-free (BAF) control strategy for large pressurized water reactors (PWRs). The strategy combines the advantages of fast power compensation of the boron-adjustment Mode-G control strategy with the closed-loop axial offset (AO) control through control rods in the Mechanical Shim (MSHIM) control strategy. It can achieve fast power compensation, exact coolant average temperature control, and automatic AO control through three independently-moving control banks, respectively. Also, to avoid mutual interference between the core power and AO control, a novel blocking logic for the three control banks was developed. Simulation results of a large PWR implementing the BAF control strategy indicate satisfactory load-follow capabilities of the reactor without the need to adjust boron concentration. Moreover, the proposed blocking logic can provide better AO control without compromising reactor power control than that referring the blocking logic of reactor power and AO control banks in the MSHIM control strategy.

Load-following control of a nuclear reactor using optimized FOPID controller based on the two-point fractional neutron kinetics model considering reactivity feedback effects

Load-following control of a nuclear reactor core is very crucial. The main challenge in examining power distribution control of the reactor core is to perform axial power distribution control rather than handling radial power distribution.In this work, a new model consisting of fractional order derivatives and two nodes of the reactor core with reactivity feedbacks is presented named as the two-point fractional neutron point kinetics (TPFNPK) model. According to neutron diffusion phenomena, this modeling method has a better physical interpretation for a quick change of neutron flux in load-following operation mode.For load-following control, a fractional order PID controller is implemented. Optimization of the parameters of this controller (KP, KI, λ, KD, and μ) is carried out utilizing a genetic algorithm (GA) which is an evolutionary algorithm.The objective is the minimization of the weighted sum of the integral of time-weighted absolute error (ITAE), and the overshoot or the undershoot (MP).The new reactor core model is simulated in a MATLAB/SIMULINK environment coupled with a genetic algorithm.Different load patterns (the assumed tracking signal) considering different values of the model parameter (α) are introduced to address the effectiveness of the implemented control method.The simulation result demonstrates that the optimized control methods (GA-PID and GA-FOPID) have satisfactory and suitable functionality during load pattern tracking for all selected values of the model parameter. However, the GA-FOPID controller has a relatively better performance compared to the GA-PID controller. In all cases, it has lower costs and faster convergence. In addition, core normalized axial offset (AO) is always maintained within a certain limit during load-following operation for all the cases. Furthermore, in all the cases, the normalized axial xenon oscillation index (AXOI) remains bounded during the power transient.

ANALYSIS OF THE BEAVRS BENCHMARK USING CASMO5/SIMULATE5 WITH JENDL-4.0 AND ENDF/B-VII.1

The BEAVRS benchmark was analyzed using the CASMO5/SIMULATE5 in order to compare the measurement data and the calculation results based on the JENDL-4.0 and ENDF/B-VII.1 and investigate the difference between those calculation results. For the hot zero power (HZP) physics test, the calculation results showed good agreement with the measurement data for both of cycles 1 and 2. For cycle 1, the calculation results of the isothermal temperature coefficient (ITC) differed from the measurement data by approximately 1 pcm/℉, and the same tendency has been reported in previous studies. For the cycle operation, the calculation results of the boron letdown agreed well with the measurement data. On the other hand, some calculation results of the axial detector signals had a large difference from the measurement data, which is supposedly attributed to the discrepancy of the axial offset (AO) caused by the authors’ approximation for the control rod and shutdown bank positions. In terms of the comparison between the JENDL-4.0 and ENDF/B-VII.1, although approximately 15 ppm difference of the boron letdown in the cycle operation was observed, no significant difference was seen for other core parameters, thus, the influence of the two nuclear data library was small on the present results.

Water exchange amount reduction algorithm for power control of VVER-1200 reactor operating in load-following mode

In order to solve the problem of water exchange minimization in the primary loop of VVER-1200 reactor operating in load-following mode, we chose the dynamic programming method (DPM). However, this method is very expensive in terms of RAM and computing time. A heuristic is introduced for the DPM to decrease the computational costs. The introduction of the heuristics makes it possible to cut the inefficient branches of the DPM algorithm and to increase its speed without loss of precision. In the proposed algorithm, the use of temperature regulation control reduces the amount of coolant removed from the reactor primary loop, the movement of control rods is limited, which keeps the current axial offset (AO) in the recommended area, makes it possible to equalize the energy release in the reactor core volume. The simulation results obtained confirm the improvement of reactor power control in terms of load following: deviation of core power from the load schedule is reduced, water exchange is decreased by more than 50%, which is useful from the point of view of liquid waste management and treatment.

Core size and axial offset dependent extinction characteristics for silver nanotube and its application to directional sensing

We report the results of a study using the classical Mie theory and available experimental data of Johnson and Christy [Phys. Rev. B6, 4370 (1972)] on the extinction spectra resulting from a transverse electric (TE) polarized wave incident upon a silver nanotube with a dielectric core. It is shown that the spectral changes separately induced by varied core radius (R in ) and the axial offset (d) are consistent with those reported for a gold spherical nanoshell calculated by the celebrated plasmon hybridization model, including the core offset induced symmetry breaking effect. This is followed by an analysis of the combined influences of R in and d on the extinction efficiency Q ext , which results in the optimal geometrical parameters of R in =31.5 nm, d=16 nm, and Ag minimum shell thickness Δ=2.5 nm for the maximum Q ext at the resonance wavelength of λ=756 nm. The different axial offsets are further shown to exhibit interesting variations of the angular distribution of the corresponding scattered wave intensity, which reveals significantly sensitive variations to different incident wave directions. The result has thus led to the following study for the exploration and demonstration of its potential development for sensing the direction of incoming TE polarized waves.

Control of a PWR nuclear reactor core power using scheduled PID controller with GA, based on two-point kinetics model and adaptive disturbance rejection system

Nuclear reactor dynamics has a non-linear nature, and some parameters depend on the output power level. Accordingly, a load-following issue is important. To this end, it is important to use the proper controller with a simple implementation such as a proportional-integral-derivative (PID). In this work, the load-following of a typical pressurized water reactor (PWR) is considered based on the two-point kinetic model and constant axial offset (AO) power-distribution strategy. Subsequently, the power level is controlled by the PIDs, which are tuned by a real-coded genetic algorithm (GA) with decision variables include the integral of time-weighted absolute error (ITAE) and a stability condition. The oscillations of the power distribution occur due to axial xenon oscillations in long-time operation conditions. Therefore, AO, normalized axial offset (ΔI), and axial xenon oscillation index (AXOI) must be considered. As well as, the Lyapunov approach is used to guarantee controlling system stability, and design an adaptive system to reject unwanted disturbance to the input of the plant. The simulation results show the high performance of the closed-loop real-coded GA-PID (RGA-PID) controller with the least errors. Also, the system outputs, ΔI, and AXOI are in the acceptable range based on constant AO power-distribution strategy, and these indexes are robust to parametric uncertainties of the dynamics model.

Validation of New Procedure of Axial Xenon Oscillation Dampening in Pressurized Water Reactors (PWRs) – Case Study

Xenon oscillation is a serious issue in nuclear power plants that affects the efficiency of such power plants. Xenon oscillations result from the imbalance between three key parameters, flux distribution in the core, Xenon distribution, and lastly iodine distribution. An improved procedure to simulate and dampen Xenon oscillations by determining only two parameters is previously proposed by the authors (Shimazu, 2009; Al Nuaimi et al., 2019). These two parameters can be calculated from actual nuclear reactor data obtained from nuclear power plants during their operation. The previously mentioned improved procedure assists the nuclear operators in determining when to insert and withdraw the control rods and the number of control rods’ steps involved in order to eliminate Xenon oscillations. In this paper, the approach described earlier (Al Nuaimi et al., 2019) will be validated by solving for the two reactor parameters, namely, σaϕ and the proportional constant for Xenon concentration difference on axial offset K, through determination of the stability index, γ and angular velocity, ω. This can be done by using fitting algorithm on PWRs’ real data in order to characterize the expected Xenon oscillations behavior. The Axial Offset is plotted utilizing plant data obtained from a Generic PWR simulator. Using linear fitting, the values of γ and ω are then obtained to determine σaϕ and K which can be inserted in a twopoint model to plot the resultant Axial Offset. Both Axial Offset plots from the Generic PWR Simulator and the two-point model are quantitatively compared and evaluated in this present study.

Robust tuned PID controller with PSO based on two-point kinetic model and adaptive disturbance rejection for a PWR-type reactor

Nonlinear systems such as nuclear reactor dynamics are associated with parametric uncertainties and stability conditions. These properties must be taken into account in controller design. In this paper, an effective and robust Proportional–Integral–Derivative (PID) controller is designed and tuned. Particle Swarm Optimization (PSO) is used as a metaheuristic algorithm to optimize PID gains. The PSO–PID controller is scheduled based on the power level control of a PWR-type reactor. According to Axial Offset (AO) power-distribution characteristics in the PWRs, the two-point kinetic model is used with a constant AO strategy. Lyapunov stability synthesis is intended to guarantee the stability condition of the system at various time intervals. Disturbance Rejection System (DRS) is designed based on a Lyapunov approach to avoid output disturbance. The control signal disturbance is properly removed by the designed DRS. Simulation results show output performance and robustness of the tuned PSO–PID controller against parametric uncertainties.

A decoupled Mechanical Shim core control strategy for a pressurized water reactor using feedforward compensation and a multimodel approach

The advanced Mechanical Shim (MSHIM) core control strategy employs two separate and independent control rod banks, namely the MSHIM control banks (M-banks) and axial offset (AO) control bank (AO-bank), for automatic reactivity/temperature and axial power distribution control respectively. The M-banks and AO-bank are controlled by two closed-loop controllers, independently, called the coolant average temperature (Tavg) controller and the AO controller. Since the motion of the M-banks and AO-bank can both affect the Tavg and AO, an interlocking design between the Tavg controller and the AO controller is adopted in the MSHIM control strategy to avoid the interference between the two controllers during power maneuvers. This design can enhance the stability of the MSHIM control system by avoiding the simultaneous movement of the M-banks and AO-bank and keeping the priority of the M-bank movement. However, the AO control performance is degraded at the same time. In the present study, a feedforward compensation decoupling method and a multimodel approach have been used to eliminate the coupling effect between the two controllers in the MSHIM control system during a wide range of power maneuvers. A multiple feedforward compensation system has been designed with integration of the feedforward compensators for the Tavg and AO controllers at five equilibrium conditions using the multimodel approach. By implementing it in the MSHIM control system, the interlocking between the M-banks and the AO-bank can be released to realize the independent and decoupling control between the Tavg and AO. The effectiveness of the decoupled MSHIM control strategy has been verified by comparing its control performance with that of the original MSHIM control strategy during typical load change transients of the AP1000 reactor. The obtained results show that superior and decoupling control of the Tavg and AO can be achieved using the proposed decoupled MSHIM control strategy.

An alternative to standard nuclear core control using a multi-objective approach

This paper proposes an alternative to standard nuclear core control. The control objectives are standard and concern the Average Coolant Temperature, the Axial Offset and the rod bank position (Pbank in this study). They were carefully formalized before proceeding to LTI structured controllers synthesis at various operating points, using a multi-objective approach. This study relies on a point kinetic core model, embedding an AO estimator. A Non-smooth optimization technique is used to solve the control problems at each operating point. Then gain scheduling is performed, taking advantage of the parsimonious parameterization of the considered multivariable controller. Finally, simulations are carried out on a highly realistic reactor model including a Xenon model and show the benefits of the new control

Smart sensing of the axial power and offset in NPPs using GMDH method

The status of nuclear power plants’ conditions must be checked to avoid initial events which may eventually lead to accidents. Axial power and axial offset (AO) are key parameters which are usually used to state 3-dimensional core power peaking, in the form of a practical parameter. Group method of data handling (GMDH) has a wide range of applications. Here, a GMDH is used and modified as an efficient method to predict the axial power and AO of the reactor core as well as fuel assemblies. In this paper, axial power offset of the whole reactor core is reconstructed by using in-core detectors. By using the developed GMDH algorithm, the optimum relationship between the independent in-core detector signals and the dependent variables, the core axial power and AO, is determined. Two separate sets of big data are prepared and analyzed. The first set includes power at each of 24 axial nodes at different core states. The second set is similar to the first set except as it also contains fuel assembly data.

Robust feedback-linearization control for axial power distribution in pressurized water reactors during load-following operation

Abstract Improved load-following capability is one of the most important technical tasks of a pressurized water reactor. Controlling the nuclear reactor core during load-following operation leads to some difficulties. These difficulties mainly arise from nuclear reactor core limitations in local power peaking: the core is subjected to sharp and large variation of local power density during transients. Axial offset (AO) is the parameter usually used to represent the core power peaking. One of the important local power peaking components in nuclear reactors is axial power peaking, which continuously changes. The main challenge of nuclear reactor control during load-following operation is to maintain the AO within acceptable limits, at a certain reference target value. This article proposes a new robust approach to AO control of pressurized water reactors during load-following operation. This method uses robust feedback-linearization control based on the multipoint kinetics reactor model (neutronic and thermal-hydraulic). In this model, the reactor core is divided into four nodes along the reactor axis. Simulation results show that this method improves the reactor load-following capability in the presence of parameter uncertainty and disturbances and can use optimum control rod groups to maneuver with variable overlapping.