Calculation of the void reactivity of CANDU lattices using the code system

The reactivity effect of coolant voiding in CANDU-type fuel lattices has been calculated with different methods using the code system. The known positive void reactivity coefficient of the original lattice was correctly obtained. A modified fuel bundle containing dysprosium and slightly enriched uranium to eliminate the positive reactivity effect was also calculated. Owing to the increased heterogeneity of this modified fuel the one-dimensional cylindrical calculation with XSDRN proved to be inadequate. Code options allowing bundle geometry were successfully used for the calculation of the strongly space dependent flux and spectrum changes which determine the void reactivity.     

Three-dimensional dynamic response modeling of floating nuclear plants using finite element methods

A modelling technique which can be used to obtain the dynamic response of a floating nuclear plant (FNP) moored in an artificial basin is presented. Hydrodynamic effects of the seawater in the basin have a significant impact on the response of the FNP and must be included. A three-dimensional model of the platform and mooring system (using beam elements) is used, with the hydrodynamic effects represented by added mass and damping. For an essentially square plant in close proximity to the site structures, the three-dimensional nature of the basin must be considered in evaluating the added mass and damping. However, direct solutions for hydrodynamic effects with complex basin geometry are not, as yet, available. A method for estimating these effects from planar finite element analysis is developed.First, added mass and damping values are obtained from plane-strain finite element models of vertical cross sections through the platform. Fluid finite elements are used to model the seawater. For added mass calculations, the planar models include the platform cross section, the basin profile and the seawater in the basin. For hydrodynamic damping calculations, the planar model includes the platform cross section, the seabed and seawater, infinite in horizontal extent. Added mass and damping values are obtained for each significant mode of platform response. Estimates of three-dimensional added mass and damping are then obtained through combinations of the planar values. The release of the planar contraints of seawater motion and the reflection of gravity waves back to the platform are considered. Effective damping values applicable, on an average, for the entire response time are calculated for each plant mode of response. Since added mass and damping are frequency dependent, the selection of values to be used for a specific loading condition is usually an iterative process.The accuracy of the planar finite element model in obtaining two-dimensional added mass and damping is shown through comparison with existing and documented results. In addition, a comparison is shown for open ocean added mass and damping with a three-dimensional solution using velocity potential functions. It is concluded that the overall technique results in a reasonable and conservative calculation of the dynamic response of the floating nuclear plant.     

Seismic response analysis of full-scale boiling water reactor using three-dimensional finite element method

This paper presents the three-dimensional finite element seismic response analysis of full-scale boiling water reactor BWR5 at Kashiwazaki-Kariwa Nuclear Power Station subjected to the Niigata-ken Chuetsu-Oki earthquake that occurred on 16 July 2007. During the earthquake, the automatic shutdown system of the reactors was activated successfully. Although the monitored seismic acceleration significantly exceeded the design level, it was found that there were no significant damages of the reactor cores or other important systems, structures and components through in-depth investigation. In the seismic design commonly used in Japan, a lumped mass model is employed to evaluate the seismic response of structures and components. Although the lumped mass model has worked well so far for a seismic proof design, it is still needed to develop more precise methods for the visual understanding of response behaviors. In the present study, we propose the three-dimensional finite element seismic response analysis of the full-scale and precise BWR model in order to directly visualize its dynamic behaviors. Through the comparison between both analysis results, we discuss the characteristics of both models. The stress values were also found to be generally under the design value.     

Signal modeling and impulse response shaping for semiconductor detectors

The output-signal models and impulse response shaping(IRS) functions of semiconductor detectors are important for establishing high-precision measurement systems. In this paper, an output-signal model for semiconductor detector systems is proposed. According to the proposed model, a multistage cascade deconvolution IRS algorithm was developed using the C-R inverse system,R-C inverse system, and differentiator system. The silicon drift detector signals acquired from the analog-to-digital converte...     

Calculation of temperature coefficients of reactivity for EBR-II kinetic analyses

Component and regional temperature coefficients of reactivity for four loading configurations of the Experimental Breeder Reactor-II (EBR-II) are compared. The coefficients are calculated by summations of microcoefficients obtained by fine axial delineations of every subassembly. A special-sum method for obtaining effective coefficients for use in kinetics code channels representing subassembly groupings is described. Evaluations of rod-bank suspension coefficients and of grid-plate radial-expansion coefficients are also presented.     

Generic impulse response function for MOS systems and itsapplication to linear response analysis

A generalized response function is presented that can describe several of the practically important transient-response features of MOS systems. It allows for deviations from strict logarithmic time dependencies yet is mathematically tractable in performing linear response analysis. Fits of the generic response function to experimental data are discussed, including the short-term recovery due to hole transport, the long-term recovery due to trapped hole annealing, and the long-term, time-dependent buildup of interface traps. Analytic results for the convolution integral of linear response theory are derived for a square irradiation pulse, and some simple applications are discussed     

On the response of a critical point reactor to inherent reactivity noise input

It is shown that the use of linearization and/or quasistatic approximation leads to general methods for assessing the influence of reactivity noise on a power reactor. Exact time dependent expressions have been found for the moments of state variables for the case of an uncontrolled critical point reactor. For the special case of an initial equilibrium between neutrons and precursors, it is found that the normalized centred covariances of neutrons and precursors increase linearly with time exactly at the same rate.     

Calculation of the moderator temperature coefficient of reactivity for water moderated reactors

An American nuclear standard has been recently issued, providing guidance and qualitative recommendations on how the moderator temperature coefficient (MTC) of reactivity should be determined through reactor calculations in water moderated (and cooled) reactor cores (ANS, 1997. Calculation and measurement of the moderator temperature coefficient of reactivity for water moderated power reactors. American Nuclear Society, American National Standard ANSI/ANS-19.11-1997). The present work provides quantitative information on areas of concern and effects addressed in this standard, namely, the effect of the core reflector region and the effect of the magnitude of the moderator temperature change. The calculations consist of a sequence of static criticality analyses, and are performed with a purposely developed two-dimensional reactor model based on two neutron energy groups. The numerical results indicate that the thickness of the reflector has a measurable effect on the accuracy of the MTC value only for a small core, introducing uncertainties of the order of 10%. Instead, the effect of temperature change is found to be negligible within the recommended range of 3 to 5°C.     

Calculation of reactivity and power factors depending on the external source location

We used the neutron diffusion equation with external neutron sources, in cartesian geometry and the two groups of energy, to verify the influence of external neutron source locations in the calculation of reactivity and power factors. To this end, the Coarse Mesh Finite Difference (CMFD) method was applied to the adjoint flux calculation and to simplify reactivity calculation in PWR type reactor, using the output of the Nodal Expansion Method (NEM). Different locations on the two-dimensional plane, as well as different types of fuel elements in the reactor core were used in the present study.     

Accuracy of dynamic calculations using shell models under local impulse loading

Depending on soil conditions and load cases in dynamic calculations of nuclear power plants today more exact mathematical models may be used. For axisymmetric structures like reactor buildings, steel containments, circular tanks or coolant towers mathematical idealisations are used which especially deal with axisymmetric shell models. The calculations for these structures mentioned above, in the last 10 years, were generally carried out by applying specialised and qualified FE-programs.In order to qualify the results obtained using axisymmetric shell models as well the approved computer program MESY (Schrader 1976, 1978) several comparisons between computation and measurements were performed. As an example for these comparisons, impulse loadings, such as aircraft impact, applied by means of a pendulum on the HDR reactor will be shown.The analytical results were obtained prior to the general tests based on a loading function measured in a preliminary test step. In these calculations 11 harmonics were considered in the frequency range up to 80 Hz.Typical results will be shown and discussed, particularly the distribution of the maximum acceleration in the meridional and circumferential direction of the building.The analytical results for the structural response obtained using axisymmetric shell models conform satisfactorily to test results, especially in the area of load introduction in both (meridian and circumferential) directions.     

Study of ultimate seismic response and fragility evaluation of nuclear power building using nonlinear three-dimensional finite element model

The probabilistic safety assessment (PSA) is important for nuclear power buildings in Japan because the risk of the occurrence of seismic ground motions beyond the design assumption cannot be denied. In this paper, the building fragility of the seismic PSA was evaluated using a high accuracy analysis model (three-dimensional nonlinear FEM building model considering soil-structure interaction and basemat uplift behavior). First, the response analyses were conducted increasing the input acceleration up to 3500 Gal, until the damage of the building reached the ultimate condition. The damage of the building was estimated from the shear strain, the axial stress, and the consumed strain energy of the shear walls. Then, the influence on the response given by the vertical ground motion and the basemat uplift was evaluated. In addition, considering the shear destruction of the web wall and compressive crash of the flange wall as the fracture modes, the building fragility was evaluated. As a result, it was shown that the investigated method is efficient for more accurate seismic PSA estimation.     

Elastic-plastic finite element analysis using superposition

This paper concerns the method of calculation and solution using the superposition technique of analytic and finite element solutions, which is applied to elastic-plastic plane problems. The incremental form of the principle of virtual work is employed to derive the equations, from which the nodal displacements of the finite elements together with the generalized displacements of the analytic solution are calculated simultaneously. Several example problems are solved for elastic-plastic material with the use of the von Mises yield criteria and the associated flow rule. It is concluded that the present method is so effective as to give enough accuracy in strain concentration problems with small numbers of elements.     

钒自给能探测器中子响应计算方法

钒自给能探测器被广泛用作核动力反应堆的堆内固定式探测器,为堆芯中子注量率分布测量连续不断地提供信息。研究钒自给能探测器的响应电流计算方法,为堆芯在线功率分布监测与探测器设计优化提供理论依据。首先描述钒自给能探测器的响应机理与特性,然后基于Warren提出的理论模型,详细介绍中子响应电流控制方程及电子逃脱概率的计算方法,最后根据公开报道的典型钒探测器规格与实验数据进行数值模拟分析。结果显示,单位长度热中子灵敏度计算值与测量值相对偏差在±5%以内,论证了该方法的有效性与计算精度。     

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.     

Stress analysis of heated concrete using finite elements

Described is a finite element analysis of concrete, which is subjected to rapid heating. Using thermal mass transport calculation, the moisture content, temperature and pore pressure distribution over space and time is obtained first. From these effects, stress at various points of the concrete are computed using the finite element method. Contribution to the stress formulation comes from three components, namely the thermal expansion, pore pressure, and the shrinkage of concrete due to moisture loss (from dehydration). The material properties of concrete are assumed to be homogenous, elastic, and cracking is not taken into consideration.