Ex-core Detectors Research Articles

Core axial power shape reconstruction based on radial basis function neural network

The core axial power shape reconstruction method based on radial basis function neural network (RBFNN) is proposed, and 18-node axial core power shape can be reconstructed from 6-segment in-core detector signals or 6-segment ex-core detector signals. Alternating conditional expectation algorithm is also used to validate the effectiveness of RBFNN algorithm. The results show that no matter what kind of detector is used, the RBFNN algorithm performs better than the ACE algorithm. The RBFNN algorithm has a good anti-noise ability when the in-core detector signals with noise are used, while the correct axial power shape can’t be reconstructed from the ex-core detector signals with noise. By analyzing the ex-core axial spatial weighting function’s condition number, the determination of the axial power shape from ex-core detector signals is found to be a typical ill-posed inverse problem. A regularized RBFNN algorithm is used to eliminate this ill-posedness and get the physically meaningful axial power shape.

EVALUATION OF THE APPLICABLE REACTIVITY RANGE OF A REACTIVITY COMPUTER FOR A CANDU-6 REACTOR

Recently, a CANDU digital reactivity computer system (CDRCS) to measure the worth of the liquid zone controller in a CANDU-6 was developed and successfully applied to a physics test of refurbished Wolsong Unit 1. In advance of using the CDRCS, its measureable reactivity range should be investigated and confirmed. There are two reasons for this investigation. First, the CANDU-6 has a larger reactor and smaller excore detectors than a general PWR and consequently the measured reactivity is likely to reflect the peripheral power variation only, not the whole core. The second reason is photo neutrons generated from the interaction of the moderator and gamma-rays, which are never considered in a PWR. To evaluate the limitations of the CDRCS, several tens of three-dimensional steady and transient simulations were performed. The simulated detector signals were used to obtain the dynamic reactivity. The difference between the dynamic reactivity and the static worth increases in line with the water level changes. The maximum allowable reactivity was determined to be 1.4 mk in the case of CANDU-6 by confining the difference to less than 1%.

Calculation of VVER-1000 reactor scaling factor for inference of core barrel motion

To quantify the core barrel motion (CBM) in a pressurized water reactor, a scaling factor can be calculated to convert the Root Mean Square (RMS) value of the ex-core signals (%) to the core barrel motion amplitude (mil) (Thompson et al., 1980). In the current paper, a scaling factor is calculated using the direct and adjoint methods for a typical VVER-1000 reactor. The scaling factor is calculated using the perturbed parameters that result from CBM. The results show that the calculated scaling factors are not the same in one and two-dimensional modeling, and strongly depend on the ex-core detector location. The linearity assumption of relative detector response versus the small displacement of core barrel is investigated as well.

A preliminary simulation study of dynamic rod worth for the SMART (System-integrated Modular Advanced ReacTor) reactor

This paper describes a preliminary simulation of the dynamic rod worth for the SMART (System-integrated Modular Advanced ReacTor) reactor core which has been developed by KAERI (Korea Atomic Energy Research Institute). This work was done by comparing the dynamic rod worth calculated using a simple inverse kinetic model with simulated pseudo ex-core detector signals and the static rod worth calculated with 3D static core diffusion nodal calculations. The kinetic parameters for the simple inverse kinetic model are estimated by using 3D static core diffusion nodal calculations as functions of the rod positions while the pseudo ex-core detector signals as the control rod positions change are simulated by using 3D transient core diffusion calculations with the MASTER (Multi-purpose Analyzer for Static and Transient Effects of Reactors) code and the ex-core detector response function calculated with the DORT code. Then, the pseudo ex-core detector signals are converted into the core neutron flux using the pre-estimated ex-core detector response conversion factor (DRCF). The simulation results show that the dynamic rod worth with the simulated pseudo ex-core detector signals have good agreement with the static rod worth for the SMART reactor and that the deviations of the static and dynamic rod worth from uncertainties of control rod group constants show good agreements with each other. So, it is considered that this work can provide baseline data for the actual simulation using real ex-core detector signals for the SMART reactor in the future.

Computation of ex-core detector weighting functions for VVER-440 using MCNP5

The paper deals with the problem of weighting factor calculation and the determination of spatial weighting functions of ex-core detectors for VVER-440 using the Monte Carlo method. The computational results were obtained by the well-known code MCNP5 allowing high performance three-dimensional modeling of complex geometry of the in-vessel and ex-vessel reactor parts. Despite the fact that adjoint methods dominate in practice, forward mode of code running was chosen and applied to provide more accurate results contrary to the adjoint one. The calculation was performed for a boron lined proportional counter CPNB44 installed at the 3rd unit of NPP Jaslovské Bohunice. The base is the calculation of ex-core detector reaction rate induced by a neutron generated in a given volume element of a fuel pin. All the geometrical details and arising space heterogeneities were taken into account with the highest accuracy in the complex reactor model. Having obtained computational results, the weighted least square method was used to fit axial weighting functions. With respect to horizontal direction, the polyhedral approximation of closed Jordan surfaces was used to find the proper shape of horizontal weighting factor distribution. Sensitivity and parametric analysis was performed to evaluate the influence of various reactor operational parameters as well as the ex-core detector positioning on the weighting function values.

Calibration method of liquid zone controller using the ex-core detector signal of CANDU 6 reactor

The Phase-B test (low-power reactor physics test) is one of the commissioning tests for Canada Deuterium Uranium (CANDU) reactors that ensures the safe and reliable operation of the core during the design lifetime. The Phase-B test, which includes the approach to the first criticality at low reactor powers, is performed to verify the feasibility of the reactor’s physics design and to ensure the integrity of the control and protection facilities. The commissioning testing of pressurized heavy water moderated reactors (PHWRs) is usually performed only once (at the initial commissioning after construction). The large-scale facilities of the Wolsong nuclear power plant (NPP) Unit 1 have been gradually improved since May 2009 to extend its lifetime. The refurbishment was completed in April 2011 – then this NPP has been in operation again. We discusses the new methodology and measurement system that uses an ex-core detector signal for liquid zone controller (LZC) calibration of the Phase-B test instead of conventional methods. The inverse kinetic equation in the reactivity calculator is modified to treat the 17 delayed neutron groups including 11 photo-neutron fractions. The signal acquisition resolution of the reactivity calculator was enhanced and installed reactivity calculating module by each channel. The ex-core detector was confirmed to be applicable to a large reactor core, such as the CANDU 6 by comparison with the in-core flux detector signal. A preliminary test was performed in Wolsong NPP Unit 2 to verify the robustness of the reactivity calculator. This test convincingly demonstrated that the reactivity calculator works well. Commissioning testing of Wolsong NPP Unit 1was performed after successful refurbishment in June 2011. The LZC calibration test was completed successfully, and the requirement of the test was satisfied. The test difference was biased by approximately −6% between 20% and 70% of the liquid zone level. Moreover, the test was completed within 4h compared with about 48h required for Wolsong NPP Units 2, 3, and 4.

Comparison of Three-Dimensional Flux Synthesis and Full Three-Dimensional Discrete Ordinates Methods for the Calculation of Reactor Cavity Bioshield Heat Generation Rates

In the computational fluid dynamics analysis to determine the necessary cooling airflow rates in the reactor cavity of a nuclear power plant during operation, the heat generated in the sacrificial bioshield and adjacent components is a significant source term. Traditionally, a three-dimensional (3-D) flux synthesis method is used to calculate the heat generation rate in the bioshield for reactors with a cylindrical reactor cavity because there is minimal azimuthal variation. However, the AP1000™ reactor incorporates an octagonal reactor cavity design with 12 ex-core detectors, leading to potentially significant impacts on the azimuthal heat generation rate distribution. Therefore, it was of interest to benchmark the traditional flux synthesis method with full 3-D discrete ordinates methods. Because of an uncertainty in the amount of mesh refinement necessary to have confidence in the results, a sensitivity study on the mesh refinement was performed with a parallel 3-D discrete ordinates code. This allowed a comparison with an industry-standard serial 3-D discrete ordinates code in terms of both execution speed and calculated results.The results suggest that for angular positions where the flux synthesis method incorporates an axial model, there is relatively good agreement with 3-D methods (within ±20%). In areas remote from axial models, there are differences of up to a factor of 2 in a nonconservative direction. Furthermore, a recently developed parallel 3-D discrete ordinates radiation transport code was shown to produce results generally consistent with the industry-standard 3-D code used (within 2.5%). Finally, the parallel code completed its calculations in 10% of the time required by the serial code for an identically sized problem.

Simulation of start-up measurements with the KIKO3D code and its application for determining the scram rod worth uncertainty in the VVER-440 reactor

The reasons for large discrepancies between the computed and measured values of the efficiency of control rods observed during start-up experiments on the Russian pressurized water type VVER reactors are discussed. The numerical simulation of the measurements including the prediction of the ex-core detector signals was used to resolve the discrepancies. The time and space dependent neutron flux in the core during these measurements have been calculated by the KIKO3D nodal kinetic code. For calculating the ionization chamber signals the Green function technique has been applied. The Green functions of ionization chambers have been evaluated via solving the neutron transport equation in the reflector regions with the MCNP Monte Carlo code. The detector signals have been calculated and compared with measured ones using the inverse point kinetics transformation. Large number of asymmetric rod drop measurements (with one rod stuck) and some differential rod worth measurements from the Zero Power Physics Tests were provided by the Paks NPP for validation. The experiments cover different fuels (without and with enrichment zoning) and loading patterns. The intermediate range ionization chambers have been used during the scram measurements. The newly developed method provides fairly sufficient match of measured and calculated results. The time behavior of the detector readings observed in the measurements are described by the code in a consistent manner. As a further application the uncertainty of scram rod worth of the KARATE-440 code system was determined by static calculations and subsequent simulation of rod drop with the KIKO3D code. The calculated results were compared to measurements carried out by the Paks NPP. The uncertainty of scram rod worth is established by statistical analysis.

Renormalization of power and burnup independent shape annealing function for excore detectors

This paper describes a predictive mathematical modeling of the excore neutron detectors using a renormalization of power and burnup independent shape annealing function for Korean Optimized Power Reactor (OPR-1000) and demonstrates its validity via comparison with the measurement data. The mathematical model is based on the assembly-wise spatial weighting functions and the core axial spatial weighting functions. Detector responses are estimated through two-step calculations, first the core peripheral power distributions (power distribution of outermost assemblies) are obtained from the three-dimensional power distribution by using the assembly-wise spatial weighting functions and then the relative responses of the axial detector segments are evaluated by applying the core axial spatial weighting functions. To overcome the uncertainty from mathematical modeling, a renormalization scheme is introduced, where the spatial weighting functions are renormalized with respect to the reference measurement data and then used throughout the remaining fuel cycle. Validity tests for the renormalization method show that the detector responses can be estimated very accurately, within 1% error, with the variation of power levels and distributions. The successful application of the renormalization scheme has very important implication that the excore detector system can be accurately modeled in a priori , provided a single measurement is available.

Locally optimal solution of robust ex-core detector response using constrained simulated annealing

This note describes the determination of the parameter vector used to estimate the axially 3-level average core power with ex-core detectors. The theoretical result of the previous work is performed by the well-known constrained quadratic programming method with active set method. Sometimes the previous method gives the solutions on the constraint boundaries not far from the inequality constraints although the solutions are feasible and acceptable. In this note, a constrained simulated annealing method is proposed to find the locally optimal but robust solutions. The method is applied to plant measurement data and its performance is demonstrated by core follow calculation for a core depletion cycle. The test results show the improvement in finding solutions not stuck on constraint boundary and its robustness by reconstruction accuracy for saddle type power distributions using the noisy measurement data.

Ex-Core Detector Response Evaluation of the SMART Reactor by Using the DORT Code

The development of a 660 MWt integral reactor SMART (System integrated Modular Advanced ReacTor), called SMART-660, has been initiated in Korea. A preliminary evaluation of the detector response functions was performed for the ex-core detector of the SMART-660. First, a candidate position to install the ex-core detector was selected by considering the reactor configuration, the detector performance, and the thermal neutron flux distribution in the reactor assembly. Second, the detector response functions such as the shape annealing function (SAF) and assembly weighting factor (AWF) for the candidate ex-core detector were calculated by using an adjoint transport calculation with the DORT code and the BUGLE-96 cross-section library. The GEOSHIELD program was used to generate the DORT input file and to process the DORT output file with a graphic visualization. This study has shown that the response functions of the ex-core detector are only sensitive to some parts of the reactor and additional efforts are required to reduce the locality of the ex-core detector response.

Calculation of the Neutron Noise Induced by Shell-Mode Core-Barrel Vibrations in a 1-D, Two-Group, Two-Region Slab Reactor Model

The subject of this paper is the calculation of the in-core neutron noise induced by the shell-mode vibrations of the core barrel. The original motivation was to investigate whether an out-of-phase behavior can exist between the in-core and ex-core (ex-vessel) detectors lying at the same azimuthal position. To this end, a two-region two-group diffusion model was used in one dimension. The noise was calculated by representing the vibrations of the core barrel by a model developed earlier to describe control rod vibrations. It was found that such an out-of-phase behavior indeed exists, although only for in-core detector positions close to the core boundary. This behavior is due to the local component of the noise, which is accounted for in a two-group treatment. The finding is in accordance with the experiment whose result prompted the present work. In addition to its effect on the phase, the local component also manifests itself by a large amplitude of the noise around the vibrating core boundary, i.e., in both the core and the reflector. The appearance and the properties of the local component of the neutron noise for core-barrel vibrations is the main finding of this paper. The results suggest that the efficiency of core-barrel vibrations can be enhanced if in addition to the ex-core detectors, the in-core detectors in the outermost fuel assemblies are used.

Neural network correlation for power peak factor estimation

This paper proposes a method, based on the artificial neural network technique, to predict accurately and in real time the power peak factor in a form that can be implemented in reactor protection systems. The neural network inputs are the position of control rods and signals of ex-core detectors. The data used to train the networks were obtained in the IPEN/MB-01 zero-power reactor from especially designed experiments. The relative error for the power peak factor estimation ranged from 0.19% to 0.67%, an accuracy better than what is obtained performing a power density distribution map with in-core detectors. The networks were able to identify classes and interpolate the power peak factor values. It was observed that the positions of control rods bear the detailed and localised information about the power density distribution, and that the axial and the quadrant power differences, obtained from signals of ex-core detectors, describe its global variations in the axial and radial directions. In the power reactor environment, the neural networks would require in the input vector the position of control rods, and axial and quadrant power differences. The results showed that the RBF networks produced slightly better results than the MLP networks, but, for practical purposes, both can be considered of similar accuracy. The results indicate that they may allow decreasing the power peak factor safety margin by as much as 5%.

Power peak factor for protection systems – Experimental data for developing a correlation

This paper aims to construct a data set that can be used to train neural networks to furnish the power density peak factor during reactor operation. The inputs considered were those available in the reactor protection systems, namely, the axial and quadrant power differences obtained from measured ex-core detector signals, and the position of control rods. The response of ex-core detector signals was measured in experiments performed in the IPEN/MB-01 zero-power reactor. Several reactor states with different power density distribution were obtained by positioning the control rods in different configurations. The power distribution and its peak factor were calculated for each of these reactor states. The obtained results show that the power peak factor correlates well with the control rod position and the quadrant power difference, and with a lesser degree with the axial power differences. The data presented an inherent organisation and could be classified into different classes of power peak factor behaviour as a function of position of control rods, axial power difference and quadrant power difference. The analysis of the data set indicates that the power peak factor can be determined through a neural network having as input the position of control rods. Regarding only signals of ex-core detectors, the data indicate that a neural network may estimate better the power peak factor if the input vector comprises both the axial and the quadrant power differences.

New dynamic method to measure rod worths in zero power physics test at PWR startup

To measure and validate the worth of control (or shutdown) bank in zero power physics test at PWRs, a dynamic control rod reactivity measurement (DCRM) technique has been developed and applied to six startups of Westinghouse plants as well as Korea Standard Nuclear power Plants based on the Combustion Engineering System 80 NSSS. With this technique, just one test bank is inserted into the bottom of the core at maximum stepping rate and withdrawn immediately to the all rod-out position. Specially designed inverse point kinetics equations are used to determine the test bank worth from the measured ex-core detector signals, which are controlled by the neutron-to-response conversion factor and the dynamic-to-static conversion factor. These two parameters are predetermined by the three-dimensional neutron adjoint flux distribution for both the top and bottom ex-core detector and the three-dimensional steady and transient core power distribution for test bank movement. To eliminate the gamma-ray effect on ex-core detector signals, a simple method, using reactivity curve characteristics, was also developed. To verify the DCRM method, a total of 28 bank worths of six different PWRs was measured by the DCRM and compared with those of conventional method. Results show that the DCRM method has a similar accuracy as the conventional technique. However, with the DCRM method, it only takes ∼15 min per bank from the beginning of rod insertion to the determination of measured static worth. From its performance, one can conclude that the DCRM method is an effective replacement for the conventional rod worth measurement method.

A Case Study in Manual and Automated Monte Carlo Variance Reduction with a Deep Penetration Reactor Shielding Problem

Certain reactor transients cause a reduction in moderator temperature and, hence, increased attenuation of neutrons and decreased response of excore detectors. This decreased detector response is of concern because of the credit assumed for detector-initiated reactor trip to terminate the transient. Explicit modeling of this phenomenon presents the analyst with a difficult problem because of the dense and optically thick neutron absorption media, given the constraint that precise response characteristics must be known in order to account for this phenomenon. The solution in this study was judged to be the use of Monte Carlo techniques coupled with robust variance reduction to accelerate problem convergence. A fresh discussion on the motivation for variance reduction is included, followed by separate accounts of manual and automated applications of variance reduction techniques. Finally, the results of both manual and automated variance reduction techniques are presented and compared.

Minimum-norm solution of ill-posed neutron detector response using constrained quadratic programming

Least squares problems occur frequently in nuclear science including the parameter identification of linear/nonlinear dynamic models, modeling the responses of the spatially distributed detectors, nuclear data treatment, response surface modeling of the thermal margin estimation, etc. Considering the inevitable measurement noise and transport kernel simplification, the ill-posedness of the least squares method can arise and limit the applicability of the assumed model structures. In this paper, a constructive method is proposed with the constrained quadratic programming approach to get the physically meaningful solution. The method is applied to the determination of the parameter vector used to estimate the axially 3-level average core power with ex-core detectors. The test results show the remarkable improvement in accuracy and robustness for the noisy measurement data.

Diagnostics of core barrel vibrations by in-core and ex-core neutron noise

Diagnostics of core-barrel vibrations has traditionally been made by use of ex-vessel neutron detector signals. We suggest that in addition to the ex-core noise, also the in-core noise, induced by core barrel vibrations, be also used. This would enhance the possibilities of diagnostics where the number of the ex-core detectors is not sufficient or their positions are disadvantageous for effective diagnostics, especially for shell-mode vibrations.To this order, the theory of in-core noise induced by a fluctuating core boundary has been elaborated and applied to the diagnostics of beam and shell mode vibrations. The formulas were tested on some measurements taken in the Ringhals PWRs. The results confirm the validity of the model itself, and the possibilities for enhanced diagnostics were demonstrated. A more effective use of these novel possibilities requires more in-core detectors and/or better detector positioning.

Improved methodology for generation of axial flux shapes in digital core protection systems

An improved method of axial flux shape (AFS) generation for digital core protection systems of pressurized water reactors is presented in this paper using an artificial neural network (ANN) technique—a feedforward network trained by backpropagation. It generates 20-node axial power shapes based on the information from three ex-core detectors. In developing the method, a total of 7173 axial flux shapes are generated from ROCS code simulation for training and testing of the ANN. The ANN trained 200 data predicts the remaining data with the average root mean square error of about 3%. The developed method is also tested with the real plant data measured during normal operation of Yonggwang Unit 4. The RMS errors in the range of 0.9∼2.1% are about twice as accurate as the cubic spline approximation method currently used in the plant. The developed method would contribute to solve the drawback of the current method as it shows reasonable accuracy over wide range of core conditions.

Burg spectrum estimation of neutron noise for the monitoring of reactor internal vibration with a hypothesis test

Traditionally, non-parameter spectrum estimation has been widely used in the analysis of neutron noise obtained from ex-core detectors for reactor structure monitoring. Because a limited data results in a severe bias, the resolution is not adequate for a monitoring application. The Burg spectrum estimation of the parameter method distinctively traces the modes of the reactor's internal structures with the order of 160 tested by χ 2 (chi) distribution and F distribution. Fuel 1st mode, 2nd mode, beam mode and shell mode in association with a reactor's internal vibration are more discernable than the spectrum estimator method proposed in ASME-OM/SG part 5 with the neutron noise signals of Ulchin 1. The result gives us the early information of the joint condition between thermal shield and core support barrel.