Analysis of an MTC noise measurement performed in ringhals-2 using gamma-thermometers and in-core neutron detectors

A noise measurement in the Swedish Ringhals-2 PWR was performed in January 2002 by using twelve gamma-thermometers and two in-core neutron detectors, all located on the same axial level in the reactor. The gamma-thermometers are very versatile tools since they allow estimating the core-averaged moderator temperature noise throughout the core. This core-averaged temperature noise was then used to estimate the MTC by noise analysis, via a new MTC noise estimator. It was shown that whatever the location of the neutron detector might be, the MTC is always correctly estimated by this new MTC noise estimator, without any calibration to a known value of the MTC prior to the noise measurement. For the purpose of comparisons, the MTC was also estimated by using a single gamma-thermomemeter and a single core-exit thermocouple, together with an in-core neutron detector. In such cases, the MTC was systematically underestimated, with a stronger bias for the core-exit thermocouple than for the gamma-thermometer. This shows that the main reason of the MTC underestimation by noise analysis in all the experimental work until now was due to the radially non-homogeneous temperature noise throughout the core. The resulting deviation from point-kinetics of the reactor response has a negligible effect.     

MTC estimation based on neutron noise and propagating temperature perturbation in VVER-440 reactors

Moderator Temperature Coefficient (MTC) is an important parameter characterizing inherent safety in PWRs. Noise diagnostics provides a theoretically well established method to estimate its value without changing the reactor state with using fluctuation of the temperature and neutron flux measurements in frequency domain. However, several difficulties arise when determining the core average neutron and temperature fluctuation from the real measured signals, due to the specific instrumentation of each reactor type. Coolant temperature fluctuations originate from inhomogeneities traveling with the coolant flow and the treatment of this phenomenon requires an approach using the theory of propagating perturbations. Traditional MTC estimation methods do not consider these effects and they result in substantial under- and overestimations.     

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.     

Guidelines to determine the optimal variables for the MTC measurement by noise analysis

In this paper guidelines will be given in order to determine the required measurement time for a specified precision of the Moderator Temperature Coefficient (MTC) estimate by noise analysis. Until now the discussion of the precision of the MTC estimate was neglected. We will study the relation between the precision, the coherence, the amount of temperature sensors and the measurement time. Based on this relation guidelines to determine the optimal measurement time will be given. Simulations in MATLAB will be used to verify the theoretical analysis. Realistic values for the different influencing variables for a specific measurement setup will be given by use of the analysis of a measurement at a Nuclear Power Plant in Belgium.     

Estimation of the moderator temperature coefficient of reactivity via noise analysis using closed-loop transfer functions

The accuracy of the estimation, via noise analysis, of the moderator temperature coefficient (MTC) of reactivity is investigated, assuming that closed-loop data are used in the estimators. The noise field is generated through numerical simulations. The focus is on the approach using the proportionality between estimated and actual MTC values during the fuel cycle. The results show that the bias induced on the proportionality constant (calibration factor) depends, as expected, on the strength of the feedback. However, it remains within tolerable limits, considering that the introduced uncertainty is ⩽30%, which is comparable with the measurement uncertainty of the standard boron dilution method.     

Evaluation of nuclear heating of small samples in a research reactor core

A simple analytical model is presented which indicates that the ratio of heating power densities of two different materials, irradiated under the same conditions inside a reactor core, can be estimated from material properties only. The developed approximate method allows simplifying the measurement technique of a number of samples from different materials by performing measurement of only one sample. The latter is a primary result of the proportionality between the heating and the thermal neutron flux for samples irradiated under the same conditions. This is confirmed by measurements in the Greek Research Reactor (GRR1) showing that the temperature of materials irradiated at various positions of a vertical core channel due to all heating mechanisms follows the spatial variation of thermal neutron flux. Validation by the numerical 3D gamma heating code GHRRC developed in NCSR Demokritos shows that the conclusions of the simple analytical method apply also for the total heating by all gammas in the core. A model is also presented for the estimation of heating by elastic neutron scattering. Furthermore, a methodology is suggested for the estimation of the temperature and the heat power deposited on materials irradiated during normal reactor operation, based on in-pile temperature measurements performed at low reactor power levels.     

On the calculation of flux in slightly subcritical reactors with external neutron sources

The behaviour of the flux inside a subcritical reactor in the presence of external neutron sources is examined. It is shown, in particular, that the flux can be approximated by the flux resulting from eigenvalue calculation as the reactor approaches its critical state. A method based on the perturbation technique is described, allowing an estimation of spatial effects on the flux by the local sources.     

Estimation of time-dependent neutron transport from point source based on Monte Carlo power iteration

This study proposes a method for calculating time-dependent neutron transport from a point source with a continuous-energy Monte Carlo code. To deal with neutron multiplication and attenuation in orders of magnitude, the power iteration method conventionally used to estimate the effective multiplication factor k_eff was utilized. The time of a neutron flying in a cycle from emission of its ancestor at the point source was estimated. In the estimation, the decay time of the delayed neutron precursor was considered. The neutron flux was tallied in time bins in each cycle. The source strength in the cycle was considered as the product of k_eff estimators from the first to the previous cycle. By summing up the tallied flux multiplied by the strength, the neutron flux variation with time was obtained. This method was verified against a UO₂ fuel lattice moderated and reflected by light water.     

用MCNP程序计算核燃料废包壳缓发裂变中子形成的热中子通量密度

用Monte Carlo方法计算核燃料废包壳缓发裂变中子形成的热中子通量密度分两步进行:第一步,计算出外中子源在包壳中生成的缓发裂变中子;第二步,计算这个缓发裂变中子源在探测器中所形成的热中子通量密度。为利用现有的MCNP程序进行计算,编制了有关的缓发裂变中子源生成及抽样子程序和体通量统计估计方法的记数子程序。计算表明:针对解决所遇到的深穿透问题,体通量统计估计法比径迹长度法要好些。     

Comparison of the least squares and the maximum likelihood estimators for gamma-spectrometry

A comparison of the characteristics of the maximum likelihood (ML) and the least squares (LS) estimators of nuclides activities for low-intensity scintillation γ-spectra has been carried out by the computer simulation. It has been found that the part of the LS estimators gives biased activity estimates and the bias grows with increase of the multichannel analyzer resolution (the number of the spectrum channels). Such bias in estimates leads to the significant deterioration of the estimation accuracy for low-intensity spectra. Consequently, the threshold of nuclides detection rises up to 2–10 times in comparison with the ML estimator. It has been shown that the ML estimator and the special LS estimator provide non biased estimates of nuclides activities. Thus, these estimators are optimal for practical application to low-intensity spectrometry.     

Monitoring MTC using cold leg thermocouple and background neutron detector noise signals in a VVER-440 reactor during a whole fuel cycle

Monitoring of the Moderator Temperature Coefficient (MTC) was performed from the noise signals of cold leg thermocouples and background neutron detectors in a VVER-440 type reactor during a whole fuel cycle. A modified traditional noise based estimator was applied: the estimator was extended in order to take into account the effects of measurement geometry, coolant velocity and the relatively long time constant of the thermocouples. A systematic evaluation of measurement settings and evaluation parameters was carried out in order to determine optimal parameters. Optimal evaluation parameters were determined by considering the frequency dependence of the estimator, and by minimizing the statistical and systematic errors of the results. It can be concluded that the modified estimator provides adequate results which are close to the MTC given by the core design code calculations. It was found that relatively long FFT window sizes are needed to obtain correct results. The method needs long but industrially acceptable measurements for robust operation.     

Constitutive laws for the neutron density current

In this technical note, a fractional wave equation for the average neutron motion in nuclear reactor is considered. This representation covers the full spectrum of the average neutron transport behavior, i.e., Fickian and non-Fickian effects. The fractional diffusion model retains the main dynamic characteristics of the neutron motion in which the relaxation time associated with a rapid variation in the neutron flux contains a fractional exponent that can be manipulated to obtain the best representation of the neutron transport phenomena. The detrended fluctuation analysis (DFA) method is presented in this paper to estimate the fractional exponent.     

Influence of the external neutron sources in the criticality prediction using 1/M curve

The influence of external neutron sources in the process to obtain the criticality condition is estimated. To reach this objective, the three-dimensional neutron diffusion equation in two groups of energy is solved, for a subcritical PWR reactor core with external neutron sources. The results are compared with the solution of the corresponding problem without external neutron sources, that is an eigenvalue problem. The method developed for this purposes it makes use of both the nodal method (for calculation of the neutron flux) and the finite differences method (for calculation of the adjoint flux). A coarse mesh finite difference method was developed for the adjoint flux calculation, which uses the output of the nodal expansion method. The results regarding the influence of the external neutron source presence for attaining criticality have shown that far from criticality it is necessary to calculate the reactivity values of the system.     

Biased Selection of Particle Flight Directions as a Variance Reduction Technique in Monte Carlo Calculations

As a practical variance reduction technique applicable to Monte Carlo shielding calculations, the present article shows a new simple biased sampling technique on particle flight directions. Scattered particles not directed towards the detector positions are killed if they are not so important, that is, if the particle weights are sufficiently small compared to the source weight. In this way, we can reduce the sample size required for obtaining an accurate estimate for the detector response.

The present technique was incorporated into the multigroup neutron and γ-ray transport code MORSE, and sample calculations were performed on spherical fast neutron systems. The results have shown that this biased technique is effective for dealing with neutron multiplication as well as neutron transmission problems. The neutron flux or the effective multiplication factor of a nuclear reactor is estimated more accurately than from the method of path-length stretching with about the same computation time. In addition, it is shown that the flight-direction biasing can further effectively be used by combining it with other variance reduction techniques.     

Ratio estimation in SIMS analysis

The determination of an isotope ratio by secondary ion mass spectrometry (SIMS) traditionally involves averaging a number of ratios collected over the course of a measurement. We show that this method leads to an additive positive bias in the expectation value of the estimated ratio that is approximately equal to the true ratio divided by the counts of the denominator isotope of an individual ratio. This bias does not decrease as the number of ratios used in the average increases. By summing all counts in the numerator isotope, then dividing by the sum of counts in the denominator isotope, the estimated ratio is less biased: the bias is approximately equal to the ratio divided by the summed counts of the denominator isotope over the entire measurement. We propose a third ratio estimator (Beale’s estimator) that can be used when the bias from the summed counts is unacceptably large for the hypothesis being tested. We derive expressions for the variance of these ratio estimators as well as the conditions under which they are normally distributed. Finally, we investigate a SIMS dataset showing the effects of ratio bias, and discuss proper ratio estimation for SIMS analysis.     

HFETR堆芯不锈钢反射层的研究

用快中子分出截面法估算了不锈钢棒对压力容器处快中子注量率的减弱程度,用二维多群粒子输运程序ＤＯＴ３．５计算了不锈钢棒的γ释热,计算了高通量工程试验堆（ＨＦＥＴＲ）设计工况和目前运行工况下不锈钢壁面温度和中心温度,对承重栅板的安全性进行了讨论,分析了不锈钢棒对堆芯的性能影响。结果表明,用不锈钢代替铝棒作最外层反射层,堆芯安全性能不变,压力容器处快中子注量率被大幅度降低。     

Irradiation temperature, flux and spectrum effects

Although great progress has been made in understanding the irradiation behaviour of reactor pressure vessel (RPV) steels, many aspects are still not fully understood. A large amount of data has been generated for understanding the effects of different irradiation conditions on material properties. The data needed for the long term operation of RPVs is almost always created by accelerated irradiations in test reactors, and due to insufficient knowledge on the damage interaction between the material and the high energy neutrons the potential bias of the conclusions on material properties in non-accelerated irradiation conditions can not be excluded. Important parameters for the extrapolation of results from accelerated irradiations to typical power irradiation conditions are the irradiation temperature, the neutron flux and the neutron spectrum. In particular, the effect of neutron flux on embrittlement behaviour is considered a complex phenomenon, and it seems to be dependent on the alloy composition, the neutron fluence range and the irradiation temperature. This paper will present the current knowledge on temperature, flux and spectrum effects, based on a recent literature survey and other relevant publications on the subject. It will explore the implications these effects may have for the safety evaluation of aged RPVs, especially for those exposed to long irradiation periods.     

Estimating Temperature Reactivity Coefficients by Experimental Procedures Combined with Isothermal Temperature Coefficient Measurements and Dynamic Identification

A method to evaluate the moderator temperature coefficient (MTC) and the Doppler coefficient through experimental procedures performed during reactor physics tests of PWR power plants is proposed. This method combines isothermal temperature coefficient (ITC) measurement experiments and reactor power transient experiments at low power conditions for dynamic identification. In the dynamic identification, either one of temperature coefficients can be determined in such a way that frequency response characteristics of the reactivity change observed by a digital reactivity meter is reproduced from measured data of neutron count rate and the average coolant temperature. The other unknown coefficient can also be determined by subtracting the coefficient obtained from the dynamic identification from ITC. As the proposed method can directly estimate the Doppler coefficient, the applicability of the conventional core design codes to predict the Doppler coefficient can be verified for new types of fuels such as mixed oxide fuels.

The digital simulation study was carried out to show the feasibility of the proposed method. The numerical analysis showed that the MTC and the Doppler coefficient can be estimated accurately and even if there are uncertainties in the parameters of the reactor kinetics model, the accuracies of the estimated values are not seriously impaired.     

Reference model parameter identification of space–time dependent reactivity in a CANDU-PHWR

The problem of estimating reactivity transients from an observed neutron flux transient is considered. This is relevant, for example, to analyzing a power rundown test or to estimating reactivity variations associated with some computer codes that do not specifically compute individual reactivity components. A method is presented which utilizes inverse space–time kinetics and optimal state estimators to extract the components of the reactivity transient from observed neutron flux measurements. The approach takes into account geometric characteristics and composition of the reactor core, as well as reactor operating conditions. Measurements from a limited number of in-core neutron flux detectors are the inputs used to extract reactivity components that fit a modal model of the reactor, referred to as the “reference model”. An improved solution for the reactivity components is then generated using the modal approximation solution for the neutron transport equation in conjunction with optimal estimation techniques. The method has been applied to a reactivity initiated accident in which a transient is initiated by a non-uniform loss-of-coolant. This results in a spatially varying neutron overpower transient that is terminated by the asymmetric insertion of shutoff rods. In this paper the Joint Extended Kalman Filter and Rauch–Tung–Striebel smoother is employed to estimate the neutron flux distribution in the core and identify the reactivity components of the reference model. The reference model in the state space and the Kalman filter algorithm are shown. Results of numerical simulations of the reactor transient and the optimal estimation of the reactivity components are presented to demonstrate the capabilities of the method.     

5MW低功率堆主屏蔽设计与安全分析

本文介绍了5MW 低功率堆(5MW LPR)主屏蔽辐射场和温场的计算模型、方法和程序,给出了修改设计的主要计算结果。混凝土屏蔽层内表面的入射中子通量和γ通量均满足设计标准规定。最高温度、最大温升及最大温度梯度亦均符合规定要求。为证明温场程序的可靠性,将HFETR 混凝土屏蔽层内温度计算值与实测值作了比较,结果符合得很好。