A dynamic model for element reliability

A dynamic model is developed for a system element reliability distribution over a generalized strength space. A differential equation is obtained describing the time-dependence of the reliability distribution function (RDF). The equation covers a wide class of power reactor system components which perform under intense stress conditions where a standard subdivision into a “burn-in” period, a “chance failures” range and a “wear-our” period is inapplicable.The hazard distribution function (HDF) over strength is introduced within the model and it is shown that a standard hazard rate is a strength-averaged failure intensity parameter with the RDF as a weighting function.It is shown that a well-known “bathtub” form of the hazard rate function corresponds to an analytical solution of the principal RDF transfer equation under some simplifying assumptions.     

The frequency-dependent elements in the code SASSI: A bridge between civil engineers and the soil–structure interaction specialists

After four decades of the intensive studies of the soil-structure interaction (SSI) effects in the field of the NPP seismic analysis there is a certain gap between the SSI specialists and civil engineers. The results obtained using the advanced SSI codes like SASSI are often rather far from the results obtained using general codes (though match the experimental and field data). The reasons for the discrepancies are not clear because none of the parties can recall the results of the “other party” and investigate the influence of various factors causing the difference step by step. As a result, civil engineers neither feel the SSI effects, nor control them. The author believes that the SSI specialists should do the first step forward (a) recalling “viscous” damping in the structures versus the “material” one and (b) convoluting all the SSI wave effects into the format of “soil springs and dashpots”, more or less clear for civil engineers. The tool for both tasks could be a special finite element with frequency-dependent stiffness developed by the author for the code SASSI. This element can represent both soil and structure in the SSI model and help to split various factors influencing seismic response. In the paper the theory and some practical issues concerning the new element are presented.     

Elementary catastrophe theory modelling of duffing's equation for seismic excitation of nuclear power facilities

Elementary catastrophe theory can provide conceptual insight into some aspects of a variety of problems in dynamics. It is a qualitative tool with some quantitative results. In this paper, it is applied to forced nonlinear vibrations of seismic disturbances, which may be approximated by Duffing's equation. The behavior of such a system fits naturally into ECT modelling, where changes in parameters of the system lead to “jump” type behavior. The important conclusion is that nonlinear oscillators can exhibit elementary catastrophes, but the design engineer may be able to manipulate characteristics of the system in order to avoid the “jump” behavior of the response.     

The development of a diagnostic and monitoring system for vibrating pipe branches

This paper deals with a diagnostic and monitoring system for assessing the integrity of pipe branches, during the operation of the nuclear power plant. This system have been developed under the concept of “easy to use without any sophisticated analysis” and “portable”. The accuracy of the diagnosis is based on the model optimization subsystem, which automatically modifies the numerical vibration model so as to fit its natural frequency to the actual natural frequency. The information obtained by this system may be reflected to a maintenance program of the plant to assure more reliable operation of the plant.     

A new computational approach to nuclear aerosol problems

The nonlinear kinetic aerosol equation, describing the time evolution of an aerosol distribution within a well-stirred container, is formulated in a mathematically “conservative” form. A numerical method is then developed for which conservation of mass is automatically satisfied. This procedure simplifies the derivation of conservative numerical schemes by reducing the number of approximations that must be made. Comparisons between an exact solution of the kinetic aerosol equation and numerical approximations show the following: numerical solutions based on the conservative form of the kinetic equation are more accurate and are obtained more efficiently than numerical solutions based on the standard “nonconservative” form of the kinetic equation.     

On-line monitoring of instrument channel performance in nuclear power plant using PEANO

On-Line monitoring evaluates instrument channel performance by assessing its consistency with other plant indications. Industry and EPRI experience at several plants has shown this overall approach to be very effective in identifying instrument channels that are exhibiting degrading or inconsistent performance characteristics “On-Line Monitoring of Instrument Channel Performance by EPRI (2000)”.

On-Line monitoring of instrument channels provides information about the condition of the monitored channels through accurate, more frequent monitoring of each channel's performance over time. This type of performance monitoring is a methodology that offers an alternate approach to traditional time-directed calibration. On-line monitoring of these channels can provide an assessment of instrument performance and provide a basis for determining when adjustments are necessary. Elimination or reduction of unnecessary field calibrations can reduce associated labor costs, reduce personnel radiation exposure and reduce the potential for miss-calibration.

PEANO “A Neuro-Fuzzy Model Applied to Full Range Signal Validation of PWR Nuclear Power Plant Data by Fantoni (2000)” is a system for on-line calibration monitoring developed in the years 1995–2000 at the Institutt for energiteknikk (IFE), Norway, which makes use of Artificial Intelligence techniques for its purpose. The system has been tested successfully in Europe in off-line tests with EDF (France), Tecnatom (Spain) and ENEA (Italy). PEANO is currently installed and used for on-line monitoring at the HBWR reactor in Halden. This paper describes the results of performance tests on PEANO with real data from a US PWR plant, in the framework of a co-operation among IFE, EPRI and Edan Engineering, to evaluate the potentials of PEANO for future installations in US nuclear plants.     

The use of energy absorbers to protect structures against impact loading

When a flying missible impacts a fixed structure, the interface loading is dependent on the deformation characteristics of both impacting and impacted bodies. If both are too rigid to accommodate the amount of gross deformation required to neutralize the incoming kinetic energy, or if such energy absorption has a chance to proceed in uncontrolled and unreliable ways, then there is a need to interpose a specifically designed “energy absorber” between missile and structure, from which a well-defined load time history can be derived during the course of impact.

The required characteristics of such an energy absorption material are:

• the capability to accommodate large permanent deformation without structural failure; and

• the reliable and controlled “load-deformation” (or “stress-strain”) behaviour under dynamic conditions, with an aim at an optimal square shape curve.

Consideration must also be given to environmental or other disturbing effects, like temperature, humidity, and “out of plane” loading. A short survey is presented of the wide range of energy absorbers already described in technical papers or used in a number of practical safety applications within varied engineering fields (from vehicle crash barriers to high energy pipe whipping restraints). However, with such open a literature, information is usually lacking in the specific data required for design analysis.

The following “energy absorption” materials and processes have thus been further experimentally investigated, with an a aim at pipe whipping restraint application for nuclear power plants:

1. (1) plastic extension of austenitic stainless steel rods;

2. (2) plastic compression of copper bumpers; and

3. (3) punching of lightweight concrete structures.

Dynamic “stress-strain” characteristics have been established for stainless steel bars at several temperatures under representative loading conditions. For this purpose, a test rig has been specifically designed to incorporate a number of adjustable parameters and to behave as a representative “slice” of an actual pipe whipping restraint; typical strain rates are in the 10 sec⁻¹ range. The behaviour of copper bumpers has been compared under static and dynamic conditions (using a conventional drop weight test (DWT) machine); as no significant strain rate effects were emphasized, only static tests have been further developed. The DWT rig was used again to investigate crushing or punching of cellular concrete under varying geometries and loading conditions. To remedy certain deficiencies of the regular commercial grades of cellular concrete, special lightweight mixtures have been studied to optimize material toughness and provide a wider range of specific resistance.Results of this experimental program are presented and discussed. The use of energy absorbers is then illustrated for a few typical pipe whipping restraints. The design of restraints is based on real dynamic characteristics of “energy absorption” material as produced by the test program. To derive design loads of restraints, a number of methods can be used ranging from a simplified “energy balance” graph to sophisticated plastodynamic computer analysis. Typical results are presented and discussed to compare the efficiency of these alternative methods.     

SCALE calculation for evaluation of spent fuel condition during long-term storage

Experiences with an advanced spent nuclear fuel management in Slovakia are presented in this paper. The evaluation and monitoring procedures are based on practices at the Slovak wet interim spent fuel storage facility in NPP Jaslovské Bohunice. Since 1999, leak testing of WWER-440 fuel assemblies were completed using a special leak tightness detection system developed by Framatome-anp, “Sipping in Pool”. This system utilized external heating for the precise defects determination.Optimal methods for spent fuel disposal and monitoring were designed. A new conservative factor for specifying of spent fuel leak tightness is introduced in the paper. Limit values of leak tightness were established from the combination of SCALE4.4a (ORIGEN-ARP) calculations and measurements from the “Sipping in Pool” system. These limit values are: limiting fuel cladding leak tightness coefficient for tight fuel assembly – k_FCT(T) = 3 × 10⁻¹⁰, limiting fuel cladding leak tightness coefficient for fuel assembly with leakage – k_FCT(L) = 8 × 10⁻⁷.     

A bubble number density constitutive equation

A statistical formulation is used to describe gas-liquid two-phase flows. It is shown that this kind of flow cannot be considered a dilute system as is currently done. A correction factor, the pair correlation function, is introduced to account for “dense effects”. Integrating the transport equation of the bubble volume distribution function over all possible volumes, a number density transport equation is obtained, which explicitly accounts for bubble breakup and coalescence phenomena. A complete model is constructed in conjuction with the mass and momentum conservation equations. Its predictions were compared with experimental results on bubble columns. Excellent agreement was found. The theoretical model was able to predict the void fraction axial distributions, which showed strong variations.     

Development of elevated temperature structural design guide for Japanese demonstration breeder reactor

Programs to develop the “elevated temperature structural design guide for the demonstration fast breeder reactor” (DDS) in Japan have been conducted since 1987. The DDS is to be developed on the basis of the “elevated temperature structural design guide for class 1 components of prototype fast breeder reactors” (ETSDG), by considering structural and material features of the demonstration fast breeder reactor (DFBR) and incorporating results of the latest R&D. This paper describes the progress of the R& D concept of the DDS, and discusses some typical results of current studies on the DDS.     

Methods and requirements for seismic design in the United Kingdom

The United Kingdom is in an area of low but significant seismicity compared with the more active areas of the world where there are major active faults or tectonic plate boundaries. This paper presents the methods and requirements that are adopted to consider the extreme load in the design of nuclear facilities. In the United Kingdom, detailed procedures for demonstrating seismic adequacy are not specified by the nuclear licensing authority and as such the methods described in this paper are based on precedents arising from recent licensing applications. In presenting the method and requirements, the paper discusses the applicability of simplified methods for seismic qualification for both “new” and “existing” facilities. The paper concludes that simplified methods are applied to a significant extent for demonstrating the adequacy of existing plant. However, for new plant these methods have been limited in some cases to the evaluation of design loads and to the qualification of items where the required degree of assurance is less than that associated with formal qualification and for supporting studies which do not directly affect design. It is expected that as the body of experience in earthquake engineering develops in the United Kingdom, there will be a greater tendency to adopt more simplified procedures with a greater degree of confidence.     

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.     

Discretizing the diffusion equation on unstructured polygonal meshes in two dimensions

We derive a discretization of the two-dimensional diffusion equation for use with unstructured meshes of polygons. The scheme is presented in r–z geometry, but can easily be applied to x–y geometry. The method is “node”- or “point”-based and is constructed using a finite volume approach. The scheme is designed to have several important properties, including second-order accuracy, convergence to the exact result as the mesh is refined (regardless of the smoothness of the grid), and preservation of the homogeneous linear solution. Its principle disadvantage is that, in general, it generates an asymmetric coefficient matrix, and therefore requires more storage and the use of non-traditional, and sometimes slowly-converging, iterative linear solvers. On an unstructured triangular grid in x–y geometry, the scheme is equivalent to the linear continuous finite element method with “mass-matrix lumping”. We give computational examples that demonstrate the accuracy and convergence properties of the new scheme relative to other schemes.     

Main R&D issues for fast reactor structural design standard

For realization of economical and reliable fast reactor (FR) plants, the Japan Atomic Energy Agency (JAEA) and the Japan Atomic Power Company (JAPC) are cooperating on the “Feasibility Study on Commercialized FR Cycle Systems”. To certify the design concepts through evaluation of the structural integrity of FR plants, the research and development of the “Elevated Temperature Structural Design Guide for Commercialized Fast Reactor (FDS)” is recognized as an essential theme. The FDS focuses on particular failure modes of FRs such as ratchet deformation and creep-fatigue damage due to cyclic thermal loads. For precise evaluation of these modes, the research and development for three main issues is in progress. First, the “Refinement of Failure Criteria” needs to be addressed for particular failure modes of FRs. Secondly, the development of “Guidelines for Inelastic Design Analysis” is conducted to predict elastic plastic and creep deformation under elevated temperature conditions. Lastly, efforts are being made toward preparing “Guidelines for Thermal Load Modeling” for the design of FR components where thermal loads are dominant.     

A two-dimensional model for fluid-structure interaction in curved pipes

A “channel” model was developed for the purpose of simulating the interactive fluid-structural response of curved pipes to pressure pulses. Simulation is shown to have been achieved analytically in both the axisymmetric (“breathing”) and transverse (“bending”) modes of interactive behavior.An experimental program which was aimed at the validation of the model is also described. Tests were run in both straight and curved pipe configurations. Comparisons between measurements and model calculations demonstrate the validity of the model within the range of parameters under consideration.The model was implemented into the DISCO code for nonlinear fluid-shell interaction.     

BEACON堆芯在线监测系统概述

历经20多年的发展,堆芯在线监测系统的核心技术在国际上的发展已趋于成熟,但国内仍无可与之相比的综合系统。通过对全球应用最广泛的堆芯监测系统--BEACON进行调研分析,为自主研发此类系统提供技术指引。BEACON利用堆外中子探测器、堆芯出口热电偶、堆内可移动探测器的测量数据,进行堆芯监视、测量数据分析以及预测。在节点均匀的假设下,以有效快中子群（EFG）模型简化扩散方程求解,再用格林函数对全堆芯插值,最后利用样条函数拟合探测器数据,给出较为准确的堆芯功率分布。BEACON的显著技术特点包括能进行非稳态下的堆芯监测,引用节点展开法（NEM）增加堆芯功率重构的准确性,以及使用单点校准技术增加两次全堆校准间的间隔。     

On the zero-energy moments of the distribution of fast atoms and cascades

The slowing down of neutrons in capture-free hydrogen is not only a classic problem in transport theory but is a paradigm for several problems in the interaction of energetic ions with matter. Here we are concerned primarily with the distribution of stopped particles. We describe a novel expansion for the transport equation which which gives extremely accurate results for the moments of the distribution and which proves an earlier conjecture made by E.M. Baroody. We discuss additional applications of the expansion, which appears to be an improved “straight-ahead” approximation.     

A bounding technique for dynamic plastic deformations of damped structures

A bounding principle for elastic-perfectly plastic creeping and noncreeping structures subjected to mechanical and/or thermal loads varying below or above the shakedown limit is presented. This principle contains some free “perturbation functions” which, suitably chosen, enable it to specialize, so generating bounds on a variety of deformation measures (such as inelastic work dissipated within any portion of the body, inelastic strains and displacements), some of which are new results, others recover or generalize known results. The resulting bounding technique possesses a quite unified character which is useful for computational purposes. The concept of “pseudo-plastic” strain is shown to be crucial for the derivation of bounds applicable above the shakedown limit.     

Unavailability and failure intensity of components

A comprehensive and standarized set of equations to calculate component unavailability and component failure intensity has been obtained in the case of the repair and inspection policies which are usually not in practice. It has been found that some of the processes describing the component behaviour can be classified under the heading of so-called “closed chain renewal processes” which have been described in the paper. In addition a general theory for the inspected components has been developed.