Probabilistic analysis of core shroud cracks

Traditional limit load analysis and fracture mechanics analysis have been applied to evaluate the integrity of the degraded nuclear power plant components. Although these methodologies are generally accepted by the regulatory authorities in the nuclear industry, conservatism introduced by the uncertainties of inspection, material property, crack geometry, applied loading, neutron environment, etc. is recognized to have great impact on the evaluation accuracy. A probabilistic analysis may overcome this shortcoming and reveal some additional insight to the problem. The purpose of the present study is to apply probabilistic methods to analyze the degraded core shroud, and to predict the quantitative risk of the cracked shroud. In the analysis, the loading condition, crack growth rate, material properties and existing defects are all considered random. A sample analytical result shows that, based on some previously observed data and under certain assumptions, the crack-through probability of the studied core shroud is in the order of 10⁻⁷ after 13 cycles of operation. The probability will increase considerably through operation cycles or operation years if no repair action is taken.     

Modeling of weld residual stresses in core shroud structures

This paper presents a computational model to predict residual stresses in a girth weld (H4) of a BWR core shroud. The H4 weld is a multi-pass submerged-arc weld that joins two type 304 austenitic stainless steel cylinders. An axisymmetric solid element model was used to characterize the detailed evolution of residual stresses in the H4 weld. In the analysis, a series of advanced weld modeling techniques were used to address some specific welding-related issues, such as material melting/re-melting and history annihilation. In addition, a 3-D shell element analysis was performed to quantify specimen removal effects on residual stress measurements based on a sub-structural specimen from a core shroud. The predicted residual stresses in the H4 weld were used as the crack driving force for the subsequent analysis of stress corrosion cracking in the H4 weld. The crack growth behavior was investigated using an advanced finite element alternating method (FEAM). Stress intensity factors were calculated for both axisymmetric circumferential (360°) and circumferential surface cracks. The analysis results obtained from these studies shed light on the residual stress characteristics in core shroud weldments and the effects of residual stresses on stress corrosion cracking behavior.     

Seismic model test of the GCFR core and core support structure

A 15% scale model was constructed to study the dynamic structural behavior of the GCFR (gas cooled fast breeder reactor) core support structure during seismic excitation. The model contains a perforated aluminum plate with a diameter of 20 in. and 265 model core elements constructed from 7/8 in.-diameter aluminum tubes. The proper frequency and mass ratios of the core elements and the perforated plate was ensured by placing steel inserts in the tubes. The natural frequencies, mode shapes and damping factors were individually measured for each of the components and for the complete system. Harmonic and simplified seismic forcing functions were applied to study the dynamic behavior of the core and its support structure. The test results were compared with both analytical and computer code results. Applying thick plate theory, the effective elastic modulus is 27% lower than that given in the ASME code. The resonant frequencies and the mode shapes of the “combined” core and grid plate assembly were also calculated. Applying thick plate theory to the analytical method, the two lowest frequencies were determined and the comparison with the test results shows differences od 3 and 6%.     

Effects of thermal load and cooling condition on weld residual stress in a core shroud with numerical simulation

Stress corrosion cracking (SCC) in the heat affected zone is the primary damage form due to weld residual stress, corrosion and neutron irradiation environment in the core shroud of a boiling water reactor. The distribution of weld residual stress around a weld is necessary to be clarified to evaluate the structural integrity of core shroud for SCC. Moreover, studying the effects of welding parameters on residual stress on reducing the residual stress is very important to suppress the initiation and propagation of SCC.In this paper, we used a finite element method (FEM) to clarify the distribution of weld residual stress around the sixth horizontal weld (H6a) between the lower ring and the cylinder in the core shroud. The simulation results of axial stress were consistent with the experimental results at the inside and outside surfaces of the core shroud, respectively. The effects of thermal loads and cooling conditions were also investigated with the same model. We simulated the welding progress with water cooling on the inside and outside surfaces of the core shroud in order to study the influence of cooling conditions on the residual axial stress around the weld. The simulation results indicated that water cooling decreased the residual axial stress at the same side due to changing the temperature-affected fields. Moreover, with fixing the peak temperatures of weld passes, the simulation results of the distribution of residual axial stress by the thermal loads with different heating time were compared. The simulation results suggested that the heating time was expected to be longer and the heat flux to be smaller for reaching the small tension residual axial stress or even compression stress around the H6a weld.     

Seismic response of the advanced gas cooled reactor core

The seismic response of the Advanced Gas Cooled Reactor (AGR) core has been calculated using an idealisation having several hundred thousand degrees of freedom. The graphite bricks which make-up the core are idealised as rigid masses, whilst contact spring elements are used to represent the load transmissions or impacts that can take place between the bricks. The necessary input information for the contact spring elements (i.e. stiffness, damping and friction) has been obtained by test work. Whilst the dynamic analysis of the core itself is highly non-linear, the supporting steel structures are linearly elastic. Consequently, the dynamic characteristics of the supporting structures are evaluated with the non-linear core structure uncoupled and are then used with the non-linear core data in a step-by-step explicit time-history. This paper discusses the development of the analytical model, the theory and the computer codes used. Results from some of the parameter studies, sensitivity studies and predictions of core response to earthquakes are presented.     

Spatial and model-order based reactor signal analysis methodology for BWR core stability evaluation

A new methodology for the boiling water reactor core stability evaluation from measured noise signals has been recently developed and adopted at the Paul Scherrer Institut (PSI). This methodology consists in a general reactor noise analysis where as much as possible information recorded during the tests is investigated prior to determining core representative stability parameters, i.e. the decay ratio (DR) and the resonance frequency, along with an associated estimate of the uncertainty range. A central part in this approach is that the evaluation of the core stability parameters is performed not only for a few but for ALL recorded neutron flux signals, allowing thereby the assessment of signal-related uncertainties. In addition, for each signal, three different model-order optimization methods are systematically employed to take into account the sensitivity upon the model-order.     

Remaining life prediction of the core shroud due to stress corrosion cracking failure in BWRs using numerical simulations

Stress corrosion cracking (SCC) of the welded joints in a reactor core shroud is the primary result of the residual stresses caused by welding, corrosion and neutron irradiation in a boiling water reactor (BWR). Therefore, the evaluation of SCC propagation is important for the safe maintenance of the core shroud. This paper attempts to predict the remaining life of the core shroud due to SCC failures in BWR conditions via SCC propagation time calculations. First, a two-dimensional finite element method model containing H6a girth weld in the core shroud was constructed, and the weld processing was simulated to determine the weld's residual stress distribution. Second, using a basic weld residual stress field, the SCC propagation was simulated using a node release option and the stress redistribution was calculated. Combined with the J-integral method, the stress intensity factors were calculated at depths of 2, 3, 4, 8, 12, 16, 19, 22, 25 and 30 mm in the crack setting inside the core shroud; then, the SCC propagation rates were determined using the relation between the SCC propagation rate and the stress intensity factor. The calculations show that the core shroud could safely remain in service after 9.29 years even when a 1-mm-deep SCC has been detected.     

Seismic test on a one-fifth scale HTGR core model

This paper describes a seismic test on a one-fifth scale HTGR graphite core model. The test program included: (a) a horizontal uniaxial excitation in two orthogonal directions at accelerations up to approximately 1.5 g; (b) sinusoidal, time history (El Centro, Taft, synthesized), excitations imposed on the model; (c) damping and resonance tests; and (d) variation in lateral restraint structure, soft and hard springs.The test program also included pendulum collision test of one-fifth scale and full-scale blocks, two-dimensional array tests, and instrumentation development in support of the final test. The purpose of the test was to: (a) study collision dynamics between graphite blocks; (b) employ data to aid in verifying model scaling laws; (c) investigate model dynamic behavior and response characteristics; (d) provide specific data on block relative displacement, acceleration and strain; and measure boundary support forces; (e) provide data for correlation with analytical models; and (f) provide preliminary design data.     

Seismic behavior of a free-standing core in a large LMFBR

This paper describes a study on the seismic analysis and qualification of an LMFBR core. A non-linear response analysis method with FINAS is validated by comparing its results to a set of existing experimental data. The method is then applied to assess the seismic response and safety capacity of some typical configurations of a large free-standing core, under various seismic inputs including a case of base isolation. Some discussions are made on the possibility of the free-standing core.     

Pressure wave propagation in an LWR downcomer and resultant load on the core shroud due to rupture of a primary coolant loop

Pressure differences and the resultant dynamic load act on the core shroud when pressure waves propagate in the downcomer of a light water reactor (LWR) pressure vessel after rupture of the primary pipe has occurred. An equivalent geometry, i.e. a diverging duct is used to solve by Euler and wave equation for acceleration and velocity of the fluid behind the wave front, that the two-dimensional, time-dependent pressure distribution, induced by the wave propagation, can be calculated. The assumptions lead to an approximate but conservative value of the resultant core shroud load.     

Core shroud replacement of Fukushima-Daiichi Unit #3

The core shroud replacement of a boiling water reactor (BWR) was successfully completed at Fukushima-Daiichi Unit #3 (1F3) of the Tokyo Electric Power Company (TEPCO) in Japan. The core shroud and other core internal components made of type 304 stainless steel (SS) were replaced with the ones made of low carbon type 316L SS to improve Intergranular Stress Corrosion Cracking (IGSCC) resistance. This project was the first application of the replacement procedure developed for the welded core shroud, and employed various advanced technologies. The outline of the core shroud replacement project and applied technologies are discussed in this paper.     

Seismic model of the gas cooled fast breeder reactor core support structure

The modelling technique for the seismic analysis of the core support structure of a gas-cooled fast breeder reactor is developed. The core support structure consists of the support cylinder and a perforated grid plate to which 265 fuel and blanket elements are clamped as cantilevered beams. The analysis of the core support structure consists of three steps: (1) analysis of the grid plate, (2) analysis of the core elements, and (3) modal synthesis.The first step in developing a solution to the problem is to assume that the core elements (fuel and blanket) are attached to the grid plate as rigid rods. In this case the influence of the rigid rods can be represented by their masses and rotary inertias. The solution of this problem was developed by applying the dynamic theory of grid plates. This was accomplished by generalizing the Reissner-Mindlin thick-plate theory with orthotropic constants and then modifying the formulations of the rotary inertia expressions to include the rotary inertia effects of the core elements. The numerical results showed that the grid plate's fundamental frequency is in the range of the fundamental frequencies of the core elements so that a dynamic coupling effect exists. Because of this dynamic coupling effect the elastic properties of the grid plate must be included in the seismic analysis of the GCFR'The second step was to develop a mathematical model of the grid-plate core-element system using the method of Rayleigh-Ritz. In this model the elastic coupling effect of the core elements was included.For the final application of the theory, the exact solution of the elastic plate with rigid rods was simulated on the computer by applying the elastic rotary inertias of the core elements to the model of the grid plate. With this technique it is possible to model the grid plate with a reasonable number of fuel and blanket elements and to replace the missing core elements with their equivalent effective rotary inertias. The method includes the capability of modeling the different mass, damping and elastic properties of the fuel and blanket elements.Comparing the results of the present analysis with the preliminary simple spring-mass core model, the amplitudes of vibration obtained, in some cases in the present analysis, are a factor of ten smaller than was previously computed. Applying this more elaborate analysis will lead to a simpler and less expensive design.     

Seismic failure probability evaluation of redundant fast breeder reactor piping system by probabilistic structural response analysis

The seismic failure probability and the correlation coefficient of the multiple failure mode of the heat transport system of a three-loop fast breeder reactor have been evaluated based on a probabilistic structural response analysis. It has been found that the most probable failure mode of the heat transport system has less impact on the core cooling capability than other modes. The correlation coefficient of the heat transport system loops is approximately 0.9. It is found that the correlation comes from the common structural properties rather than the common seismic input. The present approach is useful for quantifying the correlation coefficient and the seismic fragility of the redundant component failure that is used in the systems analysis.     

Seismic analysis of PWR-RCC fuel assemblies

The present paper investigates the dynamic behaviour of PWR-RCC fuel assemblies under seismic excitation. A simple vibrational model of the fuel assembly is proposed, which leads to natural frequencies whose spacing agree with experimental data. Available experimental results are reviewed. Impact characteristics of Zircaloy spacer grids are also discussed. It is proposed that their soundness criteria be expressed in terms of impact energy rather than in terms of impact force. The computer code CLASH is briefly described; it is utilized to perform a sensitivity analysis. An example of application is also given.     

Seismic analysis and design of hyperbolic cooling towers

The safety of hyperbolic cooling towers is important to the continuous operation of a power plant. Depending upon the site, earthquake may govern the design of the tower. Methods of seismic analysis have been presented. It is concluded that the response spectrum method of analysis is of maximum practical use. A method to construct the design response spectra for various earthquake zones is presented. An earthquake motion consists of three components; however, it is shown that designing for one horizontal component only is adequate. The use of boundary conditions and the effects of inelastic action on analysis and design are discussed.     

Seismic analysis of thin shell structures

We consider in this paper a vertically erected, axisymmetric shell, resting on a horizontal foundation. The foundation is subjected to a time-dependent motion in both the vertical and horizontal directions. The motion may be produced by an event such as an earthquake or explosion. An estimate of the response of the shell to such excitation can be obtained from the solution for time-dependent boundary conditions. This solution is adapted here for an analysis with the response spectrum of earthquakes, which has been pioneered by Biot and Housner. The modes of free vibration are calculated by the multisegment, direct numerical integration method using classical shell theory. An actual design case of a containment vessel of a nuclear power plant built in the US is presented. An estimate of the dynamic response of the shell to an earthquake is obtained for all the relevant variables, such as stresses and displacements. As an example, an estimate for the axial stress of the response is given at various stations of the shell.     

Seismic analysis of cracked reactor vessels

This paper deals with the dynamic response of a thin finite, elastic circular cylindrical shell representing a reactor vessel to time-dependent loadings symmetrical with respect to the axis of the cylinder. The shell contains an axial through-crack of length 2c. The dynamic counterpart of Donnell's shell equations are used in this investigation. Extensive numerical results are presented for stress intensity factors in aluminum and steel vessels and results are discussed.