On-line reconstruction of in-core power distribution by harmonics expansion method

Fixed in-core detectors are most suitable in real-time response to in-core power distributions in pressurized water reactors (PWRs). In this paper, a harmonics expansion method is used to reconstruct the in-core power distribution of a PWR on-line. In this method, the in-core power distribution is expanded by the harmonics of one reference case. The expansion coefficients are calculated using signals provided by fixed in-core detectors. To conserve computing time and improve reconstruction precision, a harmonics data library containing the harmonics of different reference cases is constructed. Upon reconstruction of the in-core power distribution on-line, the two closest reference cases are searched from the harmonics data library to produce expanded harmonics by interpolation. The Unit 1 reactor of DayaBay Nuclear Power Plant (DayaBay NPP) in China is considered for verification. The maximum relative error between the measurement and reconstruction results is less than 5.5%, and the computing time is about 0.53 s for a single reconstruction, indicating that this method is suitable for the on-line monitoring of PWRs.     

On-line monitoring the incore power distribution by using excore ion-chambers

For most of nowaday pressurized water reactors (PWR), excore ion-chambers (EIC) are the sole real-time sensors responding to the incore power distribution (IPD). Conventionally, it is supposed that the EIC could not carry out information of the IPD in radial direction. As a result, there is an excess conservatism when they are being used for the core monitoring so far, and some flexibilities of the reactor operation are sacrificed. Though progresses have been made, there are still some inevitable obstacles about newly developed monitoring methods: mounting and maintaining a large amount of fixed incore detectors are costly; and the IPD calculated by on-line simulators is not the “measured” one. Fortunately variations in the IPD must be driven by reasonable physical causes, and the corresponding variations in the readings of the EIC are notable enough to be identified. So with a specific referenced IPD measured from periodical flux mappings, it is possible to on-line monitor such variations by using the EIC. Aimed at this, a harmonics grouping method and an algorithm of higher order perturbation variables are developed, and an influence equation for control rods is also proposed. Then a precise restriction equation describing the reasonable variations in the IPD is deduced for example of the Heating Reactor. Combined with a proper-configured EIC, a systematic “excore-to-incore” method is realized finally.     

The three-dimensional power distribution control in load following of the heating reactor

A new optimizing objective (three-dimensional power distribution control) for the load-following problem in nuclear reactor is presented. To realize such an objective, a combination of Harmonic Synthesis Method and Nodal Method has been practiced on the numeric calculation for optimizing problem on the 200 MW Heating Reactor, in which the control rods serve as the only control variables. In contrast, most of the load-following problems have been solved under a one-dimensional neutron model. And it seems that such a model is not suitable for the reactor core whose power was controlled only by control rods. In this case, the control rod causes a strong absorption of neutron in a local area thus makes the radial power distribution play a much more important role in the load-following process. As the 3-dimensional model is used and the corresponding method is performed, both of the total power level and power distribution are controlled well. For example, the power peak-factor is lower about 4% than that with one-dimensional method.     

基于离散纵标法的三维耦合燃耗与活化计算方法的发展

燃耗与活化分析在反应堆的燃耗管理与辐射屏蔽设计分析中起关键性的作用.基于一维、二维的输运程序的燃耗与活化分析方法难以解决复杂几何和强烈各向异性散射问题.本文通过耦合三维离散纵标(SN)方法粒子输运程序以及指数欧拉法活化计算程序,发展了快速精确的三维耦合燃耗与活化计算方法.该方法考虑了共振自屏效应动态修正,并采用重要核素...     

Effective one-group coarse-mesh method for calculating three-dimensional power distribution in fast reactors

An effective one-group coarse-mesh method for calculating three-dimensional power distribution in fast reactors has been developed. This method uses direction dependent one-group diffusion coefficients in each region so as to preserve neutron leakage rates before and after energy condensation. Furthermore, to correct coarse meshes of one point per hexagonal assembly used in the three-dimensional diffusion calculation, one-group cross-sections are modified by applying Askew's method. Based upon this method an effective three-dimensional diffusion code has been made. Results obtained in test cases on a prototype fast reactor indicate that this method is as accurate as six-group fine-mesh diffusion calculations using six mesh points per assembly in each radial plane and the solution of this method is a factor of 40 faster than the six-group fine-mesh calculations.     

Vibration measurements in PWR obrigheim by use of in-core accelerometers

Two accelerometers were inserted into the reactor of the NPP Obrigheim (Germany), one into the core and the other above the core. The amplitude of different components vibrations (fuel element (FE), reactor pressure vessel-core barrel (RPV/CB) and the instrument string-instrument tube (IS/IT) system) were measured. Neutron-mechanical scale factors (SFs) were calculated for the in-core detectors.     

Change of fuel-to-cladding gap width with the burn-up in FBR MOX fuel irradiated to high burn-up

In order to study the dependence of the gap width change on the burn-up, the fuel-to-cladding gap widths were investigated by ceramography in a large number of FBR MOX fuel pins irradiated to high burn-up. The dependence of gap widths on the burn-up was closely connected with the formations of JOG (joint oxyde-gaine) and rim structure. The gap widths decreased gradually due to the fuel swelling until ∼30 GWd/t, but beyond this burn-up the dependence showed two different tendencies. With the increase of burn-up, the gap widths decreased due to the increase of fuel swelling in the low fuel temperature region where the rim structure was observed, but they increased in the high fuel temperature region where the JOG rich in Cs and Mo formed in the gap.     

含有可燃毒物的压水堆核电站堆芯装料设计优化研究

含可燃毒物的压水堆装料优化是燃料管理优化研究中的难点,应用通常的脱耦方法和优化算法效率低、全局性差。研究提出局部脱耦方法用以简化问题规模、缩小搜索空间,选择特征统计算法进行优化方案的搜索。利用局部脱耦方法结合特征统计算法研制出压水堆核电站堆芯LP和BP耦合装料优化程序CSALPBP。使用该程序对大亚湾第10循环和第12循环进行了装料优化计算。结果表明CSALPBP程序在求解含可燃毒物的压水堆装料优化问题方面具有很高的搜索效率和很好的全局性,能够较好地解决含可燃毒物的压水堆堆芯装料优化难题。     

The variance of the temperature distribution in a reactor cell

Local variations in fuel packing density, fuel enrichment, bond-gap thickness, surface asperities, etc. give rise to potentially significant deviations in the temperature distribution in a reactor cell. Treating the second moments of the statistical variations of the fuel thermal conductivity, gap conductance, heat transfer coefficient from can to bulk coolant, etc. by means of specific variances the standard deviation of the temperature distribution is calculated. To account for the temperature dependence of the fuel thermal conductivity and to remover non-linearities in the equations describing the temperature deviations, a linearization approximation is adopted and the resulting equations are solved by means of an expansion over azimuthal harmonics utilizing radially dependent coefficients. In the main text, axial conduction effects are neglected in order to simplify algebraic expressions; however, in Appendix I it is shown how an expansion over axial harmonics enables the inclusion of axial conduction which is important in describing strong localized deviations. It is demonstrated that the standard deviation of a quantity that is a linear combination of the harmonics of the temperature has a variance that contains no cross-correlation between different harmonics.     

On-line monitoring applications in nuclear power plants

The nuclear power industry is working to reduce generation costs by adopting condition-based maintenance strategies and automating testing activities. These developments have stimulated great interest in on-line monitoring (OLM) technologies and new diagnostic and prognostic methods to anticipate, identify, and resolve equipment and process problems and ensure plant safety, efficiency, and immunity to accidents. This paper provides examples of these technologies with particular emphasis on eight key OLM applications: detecting sensing-line blockages, testing the response time of pressure transmitters, monitoring the calibration of pressure transmitters on-line, cross-calibrating temperature sensors in situ, assessing equipment condition, performing predictive maintenance of reactor internals, monitoring fluid flow, and extending the life of neutron detectors. These applications are discussed in the following sections. Emphasis is placed on the principles of a core OLM method - noise analysis - and the technical requirements for an integrated OLM system are summarized.     

Extension of the TRANSURANUS burn-up model

The validation range of the model in the TRANSURANUS fuel performance code for calculating the radial power density and burn-up in UO₂ fuel has been extended from 64 MWd/kgHM up to 102 MWd/kgHM, thereby improving also its precision. In addition, the first verification of calculations with post-irradiation examination data is reported for LWR-MOX fuel with a rod average burn-up up to 45 MWd/kgHM. The extension covers the inclusion of new isotopes in order to account for the production of ²³⁸Pu. The corresponding one-group cross-sections used in the equations rely on results obtained with ALEPH, a new Monte Carlo burn-up code. The experimental verification is based on electron probe microanalysis (EPMA) and on secondary ion mass spectrometry (SIMS) as well as radiochemical data of fuel irradiated in commercial power plants. The deviations are quantified in terms of frequency distributions of the relative errors. The relative errors on the burn-up distributions in both fuel types remain below 12%, corresponding to the experimental scatter.     

On the rate determining step in fission gas release from high burn-up water reactor fuel during power transients

The radial distribution of grain boundary gas in a PWR and a BWR fuel is reported. The measurements were made using a new approach involving X-ray fluorescence analysis and electron probe microanalysis. In both fuels the concentration of grain boundary gas was much higher than hitherto suspected. The gas was mainly contained in the bubble/pore structure. The factors that determined the fraction of gas released from the grains and the level of gas retention on the grain boundaries are identified and discussed. The variables involved are the local fuel stoichiometry, the amount of open porosity, the magnitude of the local compressive hydrostatic stress and the interaction of metallic precipitates with gas bubbles on the grain faces. It is concluded that under transient conditions the interlinkage of gas bubbles on the grain faces and the subsequent formation of grain edge tunnels is the rate determining step for gas release; at least when high burn-up fuel is involved.     

Analysis of mechanical load on cladding induced by fuel swelling during power ramp in high burn-up rod by fuel performance code FEMAXI-6

Mechanical load on cladding induced by fuel swelling in a high burn-up BWR type rod was analyzed by a fuel performance code FEMAXI-6. The code was developed for the analysis of LWR fuel rod behaviors in normal operation and transient conditions using finite element method (FEM).During a power ramp for the high burn-up rod, instantaneous pellet swelling can significantly exceed the level that is predicted by a “steady-rate” swelling model, causing a large circumferential strain in cladding. This phenomenon was simulated by a new swelling model to take into account the fission gas bubble growth. As a result it was found that the new model can give reasonable predictions on cladding diameter expansion in comparison with PIE data. The bubble growth model assumes that the equilibrium state equation holds for a bubble under external pressure, and simultaneous solution is obtained with both bubble size determination equation and diffusion equation of fission gas atoms. In addition, a pellet-clad bonding model which has been incorporated in the code to assume solid mechanical coupling between pellet outer surface and cladding inner surface predicted the generation of bi-axial stress state in the cladding during ramp.     

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.     

Optimization layer by layer networks for in-core fuel management optimization computations in PWRs

The optimization layer by layer (OLL) learning algorithm is applied to prediction of assembly-wise power and burnup distribution, the critical soluble boron concentration, and the pin power peaking factor (PPPF) with core burnup in the pressurized water reactor (PWR) of the Korean Nuclear Unit (KNU) 11. It is shown that the OLL trained neural networks can predict core depletion characteristics as accurately as the high-precision modern nodal method codes and that the OLL trained neural networks can compute core depletion characteristics about 40 times faster than the modern nodal method code. The OLL networks are then utilized for determining the optimum fuel assembly (FA) loading pattern (LP) of the equilibrium cycle KNU 11 PWR core by a simulated annealing (SA) scheme. By demonstrating that the FA LP optimization by the SA scheme can be carried out within 10 to 15 min thanks to the speedy neutronics evaluation of the OLL networks, it is proposed that the OLL networks can make a satisfactory substitute for core evaluation codes based on modern nodal methods in in-core fuel management optimization computations where neutronics analysis for a large number of trial loading patterns has to be carried out.