Assessment of linear and non-linear autoregressive methods for BWR stability monitoring

A benchmark has been performed to compare the performances of exponential autoregressive (ExpAR) models against linear autoregressive (AR) models with respect to boiling water reactor stability monitoring. The well-known March-Leuba reduced-order model is used to generate the time-series to be analysed, since this model is able to reproduce the most significant non-linear behaviour of boiling water reactors (i.e. converging, diverging and limit-cycle oscillations). In this way the stability characteristics of the signals to be analysed are known a priori. An application to experimental time-traces measured on a thermalhydraulic natural circulation loop is reported as well. All methods perform equally well in determining the stability characteristics of the analysed signals.     

Time dependence of linear stability parameters of a BWR

In this work we present several tools to study the time dependence of the linear stability parameters of a BWR using neutron noise analysis. Particularly, we have studied the variation in time of the fundamental frequency of a signal using the short-time Fourier transform and we have compared this method with the calculation of a time dependent Power Spectral Density (PSD) function. The temporal variation of the decay ratio is analysed using a method based on an autoregressive model to fit the different blocks of the signal. The performance of the tools presented is compared analysing analytic signals and a real signal of Forsmark 1&2 Stability Benchmark.     

The study of aeroball system for measuring 3D neutron flux distribution in reactor core

Aeroball system is attractive in several aspects because it can easily transport the map of neutron flux distribution to be measured from incore to outside of a reactor vessel.However,before the aeroball system is put to practical use in the heating reactor.there are four topics that have to be further studied.They are the stability of the activated positions,enhancement of signal/noise(S/N)ratio,distributed control and data-acquisition system and on-lin nbeutron flux distribution reconstruction.Besides describing the rasons for them,this paper gives out the theory,concept and solution about the first two topics and it is helptul to give the possibility to enhance the reactor-power.     

Flow measurements by noise analysis of thermocouple signals from the BOCA experiment at the Studsvik R2 reactor

At the Studsvik research reactor R2, a Boiling Capsule (BOCA) is used for long-term irradiation of BWR and PWR fuel rods. The BOCA experiment consists of a pressurised container that can hold a number of fuel rods in a bundle type configuration. The water flow inside the tube is driven by natural circulation. The coolant flow rate is not normally measured in the BOCA rig. Only thermocouples, measuring the water temperature at pertinent locations, are located inside the pressure tube. To confirm calculated values of the flow rate, transit time determination through the cross-correlation technique has been implemented.

Campaigns of noise measurements have been performed at five different occasions. The measurement campaigns have included 10 thermocouples at 3–4 different power levels. The results for the flow rate range between 0.15 and 0.35 m/s depending on reactor power level. The statistical accuracy of the results has also been evaluated. This paper shows that signal processing of thermocouple signals can be used to obtain rather accurate values of the flow rate in BOCA.     

Dynamics modeling and stability analysis of a fluidized bed nuclear reactor

A theoretical model describing the coupling of neutronics, thermohydraulics and fluidization in a fluidized bed nuclear reactor is presented. The stability of the system is investigated by linearizing and perturbing the system around its equilibrium points and identifying the root loci of the sytem. It is found that within the operational range, the eigenvalues are located in the negative part of the phase plane, implying linear stability. Simulations of transient conditions are performed, viz. a hypothetical startup transient and a quasistatic transient related to noise resulting from stochastic movements of the fuel particles. These simulations show that although the total power of the reactor may reach high values, the fuel temperature is well below safety limits at all times.     

Investigation of the space-dependent noise induced by propagating perturbations

The space-dependent behaviour of the neutron noise, induced by perturbations represented by the fluctuations of the absorption cross sections, propagating with the coolant of a PWR, is investigated in a one-dimensional one-group approach. The general space–frequency dependent problem is solved for this specific noise source with the help of the Green’s function technique. All calculations are made in the frame of first-order perturbation theory. The solution is investigated for different frequencies and system sizes. The limits of point kinetic and space-dependent behaviour were investigated. An interesting interference phenomenon was found between the point kinetic and the pure space dependent components of the noise for certain domains of the frequency and system size. The results bear some significance for the dynamics of Molten Salt Reactors (MSR), which is reported on in a companion paper.     

Calculation of the ex-core neutron noise induced by individual fuel assembly vibrations in two PWR cores

Calculation of the neutron noise induced by fuel assembly vibrations in two pressurized water reactor(PWR) cores has been conducted to investigate the effect of cycle burnup on the properties of the ex-core detector noise. An extension of the method and the computational models of a previous work have been applied to two different PWR cores to examine a hypothesis that fuel assembly vibrations cause the corresponding peak in the auto power spectral density(APSD) increase during the cycle. Stochastic vibrations along a random two-dimensional trajectory of individual fuel assemblies were assumed to occur at different locations in the cores. Two models regarding the displacement amplitude of the vibrating assembly have been considered to determine the noise source. Then, the APSD of the ex-core detector noise was evaluated at three burnup steps. The results show that there is no monotonic tendency of the change in the APSD of ex-core detector; however, the increase in APSD occurs predominantly for peripheral assemblies. When assuming simultaneous vibrations of a number of fuel assemblies uniformly distributed over the core, the effect of the peripheral assemblies dominates the ex-core neutron noise.This behaviour was found similar in both cores.     

Nonlinear stability analysis of a reduced order model of nuclear reactors: A parametric study relevant to the advanced heavy water reactor

In this paper, we perform a parametric study of the nonlinear dynamics of a reduced order model for boiling water reactors (BWR) near the Hopf bifurcation point using the method of multiple scales (MMS). Analysis has been performed for general values of the parameters, but the results are demonstrated for parameter values of the model corresponding to the advanced heavy water reactor (AHWR). The neutronics of the AHWR is modeled using point reactor kinetic equations while a one-node lumped parameter model is assumed both for the fuel and the coolant for modeling the thermal-hydraulics. Nonlinearities in the heat transfer process are ignored and attention is focused on the nonlinearity introduced by the reactivity feedback. It is found that the steady-state operation of the AHWR mathematical model looses stability via. a Hopf bifurcation resulting in power oscillations as some typical bifurcation parameter like the void coefficient of reactivity is varied. The bifurcation is found to be subcritical for the parameter values corresponding to the AHWR. However, with a decrease in the fuel temperature coefficient of reactivity the bifurcation turns to supercritical implying global stability of the steady state operation in the linear stability regime. Moreover slight intrusion into the instability regime results in small-amplitude limit cycles leaving the possibility of retracting back to stable operation.     

Application of reactor noise analysis in the candu reactors of Ontario hydro

Reactor noise analysis techniques are being applied in Ontario Hydro's CANDU nuclear generating stations to monitor the dynamic characteristics of critical plant components and processes. A comprehensive analysis of stationary signal fluctuations (noise) of the standard instrumentation of Pickering-B, Bruce-B and Darlington units has been carried out in the past two years. In these measurements the feasibility of applying noise analysis techniques to actual operating data has been demonstrated. The results indicated that the detection and characterization of instrument and process failures, and validation of process signals and instrument functionality can be based on the existence of certain statistical signatures derived from the measured reactor noise signals.     

Calcium Sulfate Activated by Lead and Manganese for Thermoluminescence Dosimetry

CaSO₄: Pb, Mn has been found to be free from the serious disadvantage of rapid fading possessed by CaSO₄: Mn, the most sensitive thermoluminescence phosphor available so far. A study has been made on the effect of lead and manganese content on CaSO₄, and it is concluded that lead in CaSO₄ produces new traps for radiation energy, resulting in improvement of the properties of the phosphors for dosimetry. The optimum content of such activator additives was found to be 0.2 mol/₀ of lead and 3 mol/₀ of manganese.

The improved phosphor thus obtained produces glow peaks at 160° and 190°C, and the energy yield of the thermoluminescence is about which is twice that of CaSO₄: Mn. The more significant properties of this phosphor from the viewpoint of application to radiation dosimetry include:

(1) Linear responce from 50μR to 10⁴R

(2) Minimum detectable dose of 50μR±25% by experimental reader

(3) Fading rate of 5% in a week     

New proposal of reactivity coefficient estimation method using a gray-box model in nuclear power plants

A new method for estimating reactivity parameters, such as moderator temperature coefficient (MTC) and void reactivity coefficient (VRC), is proposed using steady-state noise data. In order to solve the ill-posed problem of reactivity parameter estimation, a concept of a gray box model is newly introduced. The gray box model includes a first principle based model and a black-box fitting model. The former model acts as a priori knowledge based constraints in a parameter estimation problem. After establishing the gray box and noise source models, the maximum likelihood estimation method based on Kalman filter is applied. Furthermore, it is shown that the frequency domain approach of the gray box model is useful in the case of VRC estimation. The effectiveness of the proposed algorithms is shown through numerical simulation and actual plant data analysis.     

Determination of Microamount of Aluminum,Chromium, Copper,Iron, Manganese,Molybdenum and Nickel in Pure Water by Extraction Photometry

Aluminum, iron (III), copper, and molybdenum 8-quinolinol complexes, chromium (III) and manganese 8-hydroxyquinaldine complexes and nickel dimethylglyoxime complex can be quantitatively extracted into chloroform from large volumes of aqueous phases adjusted to an approriate pH for each metal. These metals can be determined by measuring the absorbance of the organic phases containing their complexes at an appropriate wavelength for each metal. By the proposed method, quantities exceeding 3 p.p.b. of aluminum, chromium, and manganese, and 5 p.p.b. of copper, iron, molybdenum and nickel can be determined when a 500 ml sample of water is available.     

Study of the MTC estimation by noise analysis in 2-D heterogeneous systems

The effect of a heterogeneous distribution of the temperature noise on the MTC estimation by noise analysis is investigated. This investigation relies on 2-group diffusion theory, and all the calculations are performed in a 2-D realistic heterogeneous core. It is shown, similarly to the 1-D case, that the main reason of the MTC underestimation by noise analysis compared to its design-predicted value lies with the fact that the temperature noise might not be homogeneous in the core, and therefore using the local temperature noise in the MTC noise estimation gives erroneous results. A new MTC estimator, which was previously proposed for 1-D 1-group homogeneous cases and which is able to take this heterogeneity into account, was extended to 2-D 2-group heterogeneous cases. It was proven that this new estimator is always able to give a correct MTC estimation with an accuracy of 3%. This small discrepancy comes from the fact that the reactor does not behave in a point-kinetic way, contrary to the assumptions used in the noise estimators. This discrepancy is however quite small.     

Application of advanced core process monitoring procedures in German power reactors

The nuclear reactor core design and the nuclear fuel management have been changed remarkable during the last few years. This development was initiated by increasing costs for the fuel recycling and nuclear waste storage. The fuel material, the fuel pellet fabrication, the fuel assembly structure and the core composition have been varied to get an effective fuel exploitation. Based on advanced core process conditions the reactor power and the fuel burn-up have been increased at German plants in recent years. Improved dynamic process monitoring procedures are required to get more information about the varied core process behaviour during the reactor operation. Since several years ISTec has been performed investigations to the process monitoring based on process signal measurements in German nuclear power plants. Using the standard instrumentation of the plants process signals have been measured and analysed by means of the digital data acquisition system SIGMA. The measured time signals are influenced by core process transients, global and local process fluctuations and by signal line transfer functions. Advanced time series analysis methods have been applied to separate different process effects in the multiple signal matrix. The separation of different process influences can improve significantly the information about the process condition in the reactor core.     

Thermal power calibrations of the IPR-R1 TRIGA reactor by the calorimetric and the heat balance methods

Since the first nuclear reactor was built, a number of methodological variations have been evolved for the calibration of the reactor thermal power. Power monitoring of reactors is done by means of neutronic instruments, but its calibration is always done by thermal procedures. The purpose of this paper is to present the results of the thermal power calibration carried out on March 5th, 2009 in the IPR-R TRIGA reactor. It was used two procedures: the calorimetric and heat balance methods. The calorimetric procedure was done with the reactor operating at a constant power, with primary cooling system switched off. The rate of temperature rise of the water was recorded. The reactor power is calculated as a function of the temperature-rise rate and the system heat capacity constant. The heat balance procedure consists in the steady-state energy balance of the primary cooling loop of the reactor. For this balance, the inlet and outlet temperatures and the water flow in the primary cooling loop were measured. The heat transferred through the primary loop was added to the heat leakage from the reactor pool. The calorimetric method calibration presented a large uncertainty. The main source of error was the determination of the heat content of the system, due to a large uncertainty in the volume of the water in the system and a lack of homogenization of the water temperature. The heat balance calibration in the primary loop is the standard procedure for calibrating the power of the IPR-R1 TRIGA nuclear reactor.     

Identification of reactor internals'' vibration modes of a Korean standard PWR using structural modeling and neutron noise analysis

The vibration characteristics of a Korean standard PWR reactor internals have been estimated through a three-dimensional finite element analyses and verified by using the mode separated power spectral density functions obtained from the ex-core neutron noise signals. Also the natural vibration modes of the fuel assembly have been identified measuring both the ex-core and the in-core neutron noise signals which are close to each other. As a result, the fundamental bending mode frequency of the reactor internal structure is found to be around 8 Hz and the fundamental shell mode frequency 14.5 Hz, respectively. It is also shown that the fundamental bending mode frequency of the fuel assembly is 2.3 Hz and the 2^nd bending mode frequency 5.8 Hz, respectively. These results can be used for the supplements of the Korean standard PWR's CVAP (Comprehensive Vibration Assessment Program) data.     

Investigation on the stability of water-soluble ZnO quantum dots in KB cells by X-ray fluorescence and absorption methods

The structural stability of water-soluble ZnO quantum dots (QDs) in oral epidermoid carcinoma (KB) cells was studied by the External Micro Proton Induced X-ray Emission (External Micro-PIXE) technique and the X-ray absorption fine structure (XAFS) measurement. The External Micro-PIXE and XAFS experiments were respectively performed at the JAEA and the Shanghai Synchrotron Radiation Facility. The elements’ distributions were detected by the External Micro-PIXE technique. The XAFS method was applied to obtain information about zinc (Zn) K-edge spectra. The fits of the XAFS data showed that the Zn-O bond structure of water-soluble ZnO QDs was stable after being absorbed by KB cells. Its local structural parameters were almost identical with those of the standard wurtzite structure. Water-soluble ZnO QDs had good structural stability in KB cells.