Analytical study on dynamic buckling of reactor containment vessel

The dynamic buckling of a reactor containment vessel under earthquake conditions is evaluated using a nonlinear finite element method. It is based on the four-node MITC (mixed interpolated tensorial components) shell element originally proposed by K.J. Bathe, which has been modified by the authors to include the effect of large rotational increments. At first, the buckling modes for a thin cylindrical shell under a simplified base excitation were classified, then the dynamic buckling analysis of a typical PWR steel containment vessel was carried out, considering both geometrical and material nonlinearities, to compare the results with those of a conventional static analysis. It was found that the global shear buckling of a steel containment vessel occurred under a load level several times greater than the design earthquake, and the buckling load estimated by the conventional analysis was smaller than the buckling load estimated by the dynamic analysis.     

Analytical study on dynamic buckling of reactor containment vessel

The dynamic buckling of a reactor containment vessel under earthquake conditions is evaluated using a nonlinear finite element method. It is based on the four-node MITC (mixed interpolated tensorial components) shell element originally proposed by K.J. Bathe, which has been modified by the authors to include the effect of large rotational increments. At first, the buckling modes for a thin cylindrical shell under a simplified base excitation were classified, then the dynamic buckling analysis of a typical PWR steel containment vessel was carried out, considering both geometrical and material nonlinearities, to compare the results with those of a conventional static analysis. It was found that the global shear buckling of a steel containment vessel occurred under a load level several times greater than the design earthquake, and the buckling load estimated by the conventional analysis was smaller than the buckling load estimated by the dynamic analysis.     

Experimental investigation of the buckling of nuclear containment-like cylindrical geometries under combined shear and bending

This paper describes the method for and results of, determining the static buckling interaction curves for both ring-stiffened and unstiffened cylindrical geometries that have radius-to-thickness (R/t) ratios and other parameters characteristic of nuclear steel containments. The purpose of developing these test methods and interaction curves is to have this information available for a dynamic buckling study on the same or similar shells that will be directed at answering questions regarding the freezing-in-time analysis method.     

Leak-tightness characteristics concerning the containment structures of the HTTR

The containment structures of the HTTR consist of the reactor containment vessel, the service area, and the emergency air purification system, which minimise the release of fission products in postulated accidents, which lead to fission product release from the reactor facilities. The reactor containment vessel is designed to withstand the temperature and pressure transients and to be leak-tight in the case of a rupture of the primary concentric hot-gas duct, etc. The pressure inside the service area is maintained at a negative pressure by the emergency air purification system. The emergency air purification system will also remove airborne radioactivity and will maintain a correct pressure in the service area.The leak-tightness characteristics of the containment structures are described in this paper. The measured leakage rates of the reactor containment vessel were enough less than the specified leakage limit of 0.1%/d confirmed during the commissioning tests and annual inspections. The service area was kept in a way that the design pressure becomes well below its allowable limitation by the emergency air purification system, which filters efficiency of particle removal and iodine removal well over the limited values.The obtained data demonstrate that the reactor containment structures were fabricated to minimise the release of fission products in the postulated accidents with fission product release from the reactor facilities.     

Simplified method for evaluating the seismic buckling capacity of unstiffened steel containment structures

A simplified method is presented for evaluating the seismic buckling capacity of unstiffened, free-standing steel containment structures. The method is consistent with current US Nuclear Regulatory Commission seismic design standards and with containment buckling interaction equations given in the American Society of Mechanical Engineers Boiler and Pressure Vessel Code which includes the influence of geometrical imperfections of the shell on buckling. Stresses to be considered in the interaction equations are determined from beam theory using standard response spectrum analysis. An empirical correction factor is developed to account for hoop stresses that are not explicitly represented in the beam theory. As the results of these analyses are very sensitive to the damping that is assumed, the extensive three-dimensional finite element analyses that were performed to develop the hoop stress reduction factor were also used to study the sensitivity of containment buckling to the assumed damping. Experiments on model containment structures were then performed to further investigate the damping properties exhibited by these structures. The study in concluded by showing that the simplified method reasonably predicts seismic buckling capacities when compared with independently determined predictions from detailed finite element analyses.     

Thermal stress analysis of containment building in case of a Main Steam Line Break (MSLB)

In Indian PHWR, containment building is one of the primary barriers for mitigating the consequences of a Loss of Coolant Accident (LOCA), and Main Steam Line Break (MSLB) accident. It is desired to know the temperature transients as well as the resulting thermal stresses in the containment structures of 220MW(e) PHWR, Kaiga Nuclear Power plant under postulated MSLB event. The high enthalpy steam discharged into the containment space comes in contact with the Structural Wall (SW) of containment, Inner Containment Wall (ICW) and Raft. The containment wall temperature rises due to heat transfer from steam-air mixture. To calculate the transient temperature distribution across the containment walls, it is necessary to determine containment ambient temperature and heat transfer coefficient for the condensing steam on the internal structures. Hence, at the outset, a thermal hydraulic code was developed to predict the pressure-temperature transients and condensation heat transfer coefficient transients (using various condensation models) based on the mass and energy of high enthalpy steam released into containment. The effect of various condensation models on containment pressure-temperature was evaluated. The thermal boundary conditions such as containment temperature and heat transfer coefficient, evaluated from the thermal hydraulic code using Uchida condensation model, were subsequently applied as boundary conditions to a two-dimensional axi-symmetric containment model developed using a FEM code for estimating two-dimensional temperature profiles and the resulting thermal stresses.     

Spherical steel containments of pressurized water reactors under accident conditions: Investigation program and first results

The investigations will deal with the mechanical behavior of a free standing spherical containment shell built for the latest type of a German pressurized water reactor. The diameter of the containment shell is 56 m. The wall thickness is 38 mm. The material used is the ferritic steel 15MnNi63.The investigation program includes theoretical as well as experimental activities and concerns four different accidents which are beyond the scope of the common design and licensing practice: containment behavior under quasi-static pressure increase up to containment failure; containment behavior under high transient pressures; containment vibrations due to earthquake loadings (consideration of shell imperfections); containment buckling due to earthquake loadings. First results concerning the containment behavior under quasi-static pressure increase are presented. It turns out that the mechanical failure of the containment shell is controlled by plastic instability. A computer program to describe this problem has been developed and membrane tests to check the computational methods have been carried out.     

Containment pressure and temperature envelopes for a CANDU reactor equipment environmental qualification

An equipment environmental qualification is required to guarantee the safety function of safety related systems, structures and components during the harsh conditions which occur as a consequence of an accident. The first step of an environmental qualification program is to identify the events causing the harsh environmental conditions and to determine the environmental conditions. This paper shows a systematic approach to generate the containment pressure and temperature envelopes which will be used for an equipment environmental qualification. These envelopes are generated by two steps, the generation of mass and energy release data and an analysis of the containment pressure and temperature. Finally, the containment pressure and temperature envelopes which cover all the transients with a margin are determined for the large break loss of coolant accident and the main steam line break.     

Containment vessel stability analysis

The buckling characteristics of a typical free-standing welded steel containment vessel are considered. The results of analyses utilizing computer codes are compared for a variety of load combinations. Practical conclusions of the vulnerability of such a containment vessel to buckling for a variety of load inputs and combinations are drawn.     

小型堆安全壳在地震激励下的动力响应分析

小型核反应堆(小型堆)因具有模块化、高灵敏性及安全性等优良特性备受关注,其安全壳结构在地震作用时的动力特性对小型堆的安全性评定有着重大影响作用。将小型堆安全壳用ABAQUS软件建立三维有限元模型并模拟非线性抗震分析,模拟在地震作用下小型堆安全壳模型的频率、振型和加速度及位移等动力特性,对比前16阶振型和频率,表明安全壳的1和2阶、3和4阶等阶次的振动频率分别接近且主要振动方向为水平方向。同时以峰值分别为02g、03g与04g的地震动作为荷载输入,得到3种加速度峰值作用时预应力钢束和混凝土安全壳结构的最大主应力云图,对比发现3种地震峰值作用下混凝土安全壳的最大主应力均小于抗拉强度标准值265 MPa,且最大主应力主要集中分布在安全壳结构的闸门孔周边及基础相连的底部附近。最后对比安全壳结构的加速度与位移响应,评定结果表明在极限地震动作用下小型堆安全壳结构具有良好的安全性。     

Steel containment buckling

Two aspects of buckling of a free-standing nuclear steel containment building were investigated in a combined experimental and analytical program. In the first part of the study, the response of a scale model of a containment building to dynamic base excitation is investigated. A simple harmonic signal was used for preliminary studies followed by experiments with scaled earthquake signals as the excitation source. The experiments and accompanying analyses indicate that the scale model response to earthquake-type excitations is very complex and that current analytical methods may require that a dynamic capacity reduction factor be incorporated. The second part of the study quantified the effects of framing at large penetrations on the static buckling capacity of scale model containments. Results show little effect from the framing for the scale models constructed from the polycarbonate, Lexan. However, additional studies with a model constructed of the prototypic steel material are recommended.     

Buckling induced stresses in martensitic stainless steels for magnetic fusion reactors

Samples of martensitic stainless steel, (Sandvik HT-9) in the form of beams and plates, exhibited a buckling type of structural instability when placed in a uniform magnetic field. Post buckling stresses of up to 497 MPa (72000 psi) were observed for a cantilevered plate placed in a one tesla magnetic field normal to the plate surface. Buckling phenomena were observed for both cantilevered circular rods and flat plates of magnetic stainless steel. The buckling magnetic field was geometry dependent with values as low as 0.25 T for a plate with length to thickness ratio of 90. Above the buckling field the cantilevered structure exhibited two stable equilibrium positions with a tip displacement of as much as 8–10 times the plate thickness.These results suggest that further study be given to the structural design implications of using magnetic steels in magnetic fusion reactors.     

Research related to buckling design of nuclear containment

This paper discusses the recent experimental and analytical studies related to buckling design of fabricated steel shells. The effects of initial imperfections and residual stresses on buckling are under investigation. The test programs include ring and stringer stiffened as well as ring stiffened cylinders subject to combinations of axial compression and external pressure. Proposed modifications to ASME Code Case N-284, “Metal Containment Shell Buckling Design Methods,” as well as the need for additional research, are discussed.     

高温翅片管的长时蠕变屈曲分析及评定方法研究

由于翅片管处于高温环境和外压载荷下,需要考虑其发生蠕变屈曲失效的风险。本文对翅片管在高温环境下的蠕变屈曲分析及评定方法进行了研究,提出了一种基于塑性本构和蠕变本构的有限元长时蠕变屈曲分析方法,并通过数值拟合,获得了高温屈曲的失效评定图以及失效评定公式,提出了一种方便应用于工程的快速评定方法。针对翅片管结构,将该方法的评定结果与规范中的屈曲分析评定结果进行对比,验证了该方法的可行性。同时研究了在有压力波动的情况下,结构的临界屈曲时间与载荷历程的关系,为复杂结构和复杂载荷工况的蠕变屈曲分析奠定了基础。     

Experimental simulation of corium dispersion phenomena in direct containment heating

In a direct containment heating (DCH) accident scenario, the degree of corium dispersion is one of the most significant factors responsible for the reactor containment heating and pressurization. To study the mechanisms of the corium dispersion phenomenon, a DCH separate effect test facility of 1:10 linear scale for Zion PWR geometry is constructed. Experiments are carried out with air-water and air-woods metal simulating steam and molten core materials. The physical process of corium dispersion is studied in detail through various instruments, as well as with flow visualization at several locations. The accident transient begins with the liquid jet discharge at the bottom of the reactor pressure vessel. Once the jet impinges on the cavity bottom floor, it immediately spreads out and moves rapidly to the cavity exit as a film flow. Part of the discharged liquid flows out of the cavity before gas blowdown, and the rest is subjected to the entrainment process due to the high speed gas stream. The liquid film and droplet flows from the reactor cavity will then experience subcompartment trapping and re-entrainment. Consequently, the dispersed liquid droplets that follow the gas stream are transported into the containment atmosphere, resulting in containment heating and pressurization in the prototypic condition. Comprehensive measurements are obtained in this study, including the liquid jet velocity, liquid film thickness and velocity transients in the test cavity, gas velocity and velocity profile in the cavity, droplet size distribution and entrainment rate, and the fraction of dispersed liquid in the containment building. These data are of great importance for better understanding of the corium dispersion mechanisms.     

Deterministic and stochastic earthquake response analysis of the containment shell of a nuclear power plant

Response of the containment shell of a nuclear plant to earthquake ground motion is considered. A finite element model of the structure is developed and SAP IV structural analysis program is employed for the determination of the frequencies and the corresponding mode shapes of the structure. The response of the containment shell to several past earthquakes are analyzed and the results are discussed. Stochastic models of earthquake ground acceleration are then considered and the general expressions for the power spectra, cross correlations and the mean-square responses are derived. The root mean-square of the relative displacement responses of various nodal points of the containment shell structure subjected to stationary as well as nonstationary random support motion are evaluated. The stochastically estimated maximum displacement responses are compared with those obtained from a deterministic analysis and reasonable agreements are observed.     

The design and evaluation of a passively cooled containment for a high-rating pressurized water reactor

An integrated pressurized water reactor (PWR) containment was conceptualized that allows heat to be rejected passively to the environment. The proposed containment is based on the demonstrated Ebasco Waterford 3 design. The secondary concrete shell was equipped with inlet and outlet vents that create an air-convection annulus. These vents also permit the submersion of the lower part of the primary containment into an external water pool. An internal water pool located at the bottom of the lower containment was added to increase in-containment heat storage. The performance of the proposed passively cooled containment was evaluated using a subdivided volume code, version 3.4e; the relative novelty of subdivided volume analyses for containment performance evaluation requires experimental verification of principal code predictions. Two experiments were carried out; one to test the performance of the external moat, and one to verify the code’s ability to predict thermal-stratification inside the containment. To improve the subdivided-volume simulation of convection-related parameters, a modeling technique (boundary layer flow approximation) was devised. Finally, the behavior of the proposed containment was evaluated for the worst-case large break loss of coolant accident and the worst-case main steam line break accident. Peak pressures remained below 0.45 MPa during both transients; internal wall pressure differences, equipment qualification temperatures, pressure restoration time also remained below design limits. The mitigation capability of hydrogen recombiners was also evaluated.     

An evaluation method for elastic-plastic buckling of cylindrical shells under shear forces

Since vessels of fast breeder reactors are relatively thin-walled, the prevention of buckling against seismic loading is one of the key issues in their structural design. Buckling of cylindrical vessels under shear forces occurs with a shear and/or bending mode and in the elastic-plastic region. In this paper, we propose a buckling strength equation for cylindrical vessels under static shear loads, which is developed on the basis of theoretical considerations for plasticity and shape imperfections. The effects caused by nonlinear distribution of stresses along the circumference in the elastic-plastic region are also considered as correction factors. The equation is validated by the existing and the present buckling test data, as well as FEM analyses. The safety factors to be employed in the design are proposed by evaluating the reliability of the proposed equation in the light of available test data.     

The plastic buckling of a steel liner encased in a concrete cylinder

The inelastic buckling and postbuckling performances of a steel liner encased in a rigid concrete containment vessel are studied by taking a strip of unit width from a pattern — either rectangular or diamond — along the circumferential direction in such a way that the strip will have the maximum deflection of a buckled panel. The complete load-deflection curves are obtained and the effect of initial imperfections is also included in the curves. From the discussion of failure modes, a design criteria can be obtained for the liner to maintain its integrity under accident conditions. A simplified spring model is used to calculate the maximum shear displacement and the corresponding shear force of studs at buckling. A design analysis procedure is developed from the limit and the ultimate design conditions and can be used to determine the liner thickness, studsizes and stud spacings in both the axial and circumferential directions.     

Steel containment resistance under dynamic pressure

Loadings to cause severe accidents on containment buildings can include combinations of uniform internal pressure, dynamic pressure, and seismic. Most studies that have been conducted to predict containment building capacity have focused on the effect of overpressurization on containment performance. A simple methodology that permits rapid and reasonably accurate analysis for assessing the capacity of steel containment buildings due to global or local uniform or spatially varying dynamic loading was developed. An axisymmetric model was used and the circumferential variation of the pressure, displacements, and stress resultants were represented by Fourier series. Shell vibration and buckling analysis were performed using modified versions of BOSOR4 and BOSOR5 finite difference codes. The modified version of BOSOR5 allows the input of pressures that vary along the meridianal direction. These pressures were increased until failure of the containment occurred. Failure was defined to occur when membrane strains reached twice the yield strain or the bifurcation point was introduced. The applicability of this analysis method was verified by analyzing several problems as well as a simplified containment building. The axisymmetric analysis demonstrated a powerful tool to access the capacity of steel containment buildings.