Homogenisation method for the modal analysis of a nuclear reactor with internal structures modelling and fluid–structure-interaction coupling

A homogenisation method is presented and validated in order to perform the dynamic analysis of a nuclear pressure vessel with a “reduced” numerical model accounting for inertial fluid–structure coupling and describing the geometrical details of the internal structures, periodically embedded within the nuclear reactor. Homogenisation techniques have been widely used in nuclear engineering to model confinement effects in reactor cores or tubes bundles. Application of such techniques to rector internals is investigated in the present paper. The theory bases of the method are first recalled. Adaptation of the homogenisation approach to the case of rector internals is then exposed: it is shown that in such case, confinement effects can de modelled by a suitable modification of classical fluid–structure symmetric formulation. The method is then validated by comparison of 3D and 2D calculations. In the latter, a “reduced” model with homogenised fluid is used, whereas in the former, a full finite element model of the nuclear pressure vessel with internal structures is elaborated. The homogenisation approach is proved to be efficient from the numerical point of view and accurate from the physical point of view. Confinement effects in the industrial case can then be highlighted.     

Conceptual evaluation of fluid–structure interaction effects coupled to a seismic event in an innovative liquid metal nuclear reactor

The seismic response analysis of such liquid storage systems, especially liquid metal reactors, as for example the eXperimental Accelerator Driven System (XADS), was examined taking into account mainly the coupling effects of the fluid–structure interaction and their influence on its relevant internal systems and components.Therefore this paper deals with the structural analyses of the seismically induced hydrodynamic responses, in the event of a safe shutdown earthquake (SSE), and the free oscillation (known as sloshing waves) of a metal liquid coolant as well as the dynamic buckling effects on involved structures.To the mentioned purpose the interaction and coupling effects among the main reactor vessel structures and the primary coolant response were investigated by means of a numerical evaluation (with a qualified finite element code) because of the lack of analytical linear theories that in any case are not adequate to describe all the complex phenomena related to the seismic loading.For the numerical modelling procedure, 3D finite element models were set up to analyse the propagation of seismic waves as well as its derived structural effects, such as the fluid steep waves motion, the local buckling bulges, etc., taking into account the geometrical and material nonlinearities of the RPV and the considered simplified internals.The obtained numerical results in terms of stress intensity and of the capability of the structures to resist relevant seismic loads are, thus, presented and discussed. Moreover the performed analyses allowed to highlight the structures mostly affected by the assumed loading conditions in order to achieve data useful for an upgrading of the design geometry, if any, for the considered reactor.     

Seismic isolation of pool-type tanks for the storage of nuclear spent fuel assemblies

Seismic isolation of pool-type nuclear spent fuel storage tanks requires careful investigation of dynamic behavior of the fluid–structure–isolator interaction system to satisfy the requirements of safety functions and the prevention of nuclear criticality. This paper presents the investigation, results and discussions on the seismic design considerations of isolated pool-type tanks for the storage of nuclear spent fuel assemblies. A three-dimensional boundary element-finite element method is presented for the analysis of the fluid–structure–isolator systems in time domain. Scaled model tests were performed to verify the numerical method and to study the dynamic behavior of isolated pool-type storage tanks. Important factors affecting the dynamic behavior of tanks with a fixed base are further investigated as is the case for isolated tanks using base isolators with different mechanical properties. The base isolators are the high damping rubber-bearing type and are modeled using a bilinear analysis model. Based on the numerical analysis and experimental results, some conclusions and discussions on the design considerations for isolated storage tanks are presented. In general, it is shown that careful selection of mechanical properties of the isolators with a certain lower limit on the effective frequency can guarantee the reduction of the dynamic responses of the storage tanks and the enhancement of the stability of stored spent fuel assemblies against earthquake excitations.     

Dynamic analysis of a nuclear reactor with fluid–structure interaction: Part II: Shock loading, influence of fluid compressibility

The present paper is related to the dynamic (shock) analysis of a naval propulsion (on-board) reactor with fluid–structure interaction modelling. In a previous study, low frequency analysis has been performed; the present study deals with high frequency analysis, i.e. taking into account compressibility effects in the fluid medium. Elasto-acoustic coupling effects are studied and described in the industrial case. The coupled problem is formulated using the so-called (u, p, φ) formulation which yields symmetric matrices. A modal analysis is first performed on the fluid problem alone, then for the coupled fluid–structure problem in the following cases: (i) with incompressible fluid; (ii) with compressible fluid at standard pressure and temperature conditions; (iii) with compressible fluid at the operating pressure and temperature conditions. Elasto-coupling effects are then highlighted, in particular through the calculation of an elastic energy ratio. As a general conclusion, compressibility effects are proved significant in the dynamic response of the reactor in the high frequency range.     

Construction materials for reactor buildings for decommissioning and recycling

A conceptual fluid–steel structure was studied to investigate the seismic characteristics of its use in the reactor building of nuclear power plants. The results of the earthquake response analysis of the conceptual fluid–steel structure showed that the structure had the same seismic safety ability as conventional reactor buildings. Applying the fluid–steel structure to a rector building, results in the following advantages: more elastic and light weight building materials, reducing the decommissioning wastes; the ability to recycle the structure materials because the fluid in the steel structure can be discharged the steel can be reused easily; the fluid in the steel structure has the possibility of reducing the seismic response of the structure by the sloshing damper effect. Further study is encouraged by this results.     

Effects of nuclear island connected buildings on seismic behaviour of reactor internals in a pool type fast breeder reactor

The seismic analysis of reactor assembly housing the primary circuit of a typical 500 MWe capacity pool type fast breeder reactor (PFBR) is reported. The reactor assembly is supported on the reactor vault within the nuclear island connected buildings (NICB). The seismic responses, viz. critical displacements, sloshing heights, stresses and strain energy values in the vessels are determined for the reactor assembly by detailed finite element analysis including the fluid–structure interaction and sloshing effects. Analysis is carried out to quantify the effects of inter-connection of the reactor vault with the adjacent buildings under the assumptions that the reactor vault along with reactor assembly is: (1) an isolated structural system from the adjacent buildings within reactor containment building (RCB) and (2) connected with the adjacent civil structures through floor slabs. Analysis indicates that, by inter-connecting the vault with the NICB, there are overall increases of all the governing parameters which decide the seismic design criteria. The significant effects are increases of: (1) radial and axial displacements of core top and absorber rods and vertical accelerations of core subassemblies which are of concern to reactor safety, (2) primary membrane stress intensities for the inner vessel and (3) strain energies developed at the critical portions which can enhance the buckling risks of main vessel, inner vessel and thermal baffles. Hence, it is preferable to isolate the reactor vault, directly constructing from the base raft without inter-connecting it with the NICB, from the seismic loading considerations.     

Preliminary structural evaluations of the STAR-LM reactor vessel and the support design

In this paper, preliminary structural evaluations of the reactor vessel and support design of the STAR-LM (The Secure, Transportable, Autonomous Reactor – Liquid Metal variant), which is a lead-cooled reactor, are carried out with respect to an elevated temperature design and seismic design. For an elevated temperature design, the structural integrity of a direct coolant contact to the reactor vessel is investigated by using a detail structural analysis and the ASME-NH code rules. From the results of the structural analyses and the integrity evaluations, it was found that the design concept of a direct coolant contact to the reactor vessel cannot satisfy the ASME-NH rules for a given design condition. Therefore, a design modification with regards to the thermal barrier is introduced in the STAR-LM design. For a seismic design, detailed seismic time history response analyses for a reactor vessel with a consideration of a fluid–structure interaction are carried out for both a top support type and a bottom support type. And from the results of the hydrodynamic pressure responses, an investigation of the minimum thickness design of the reactor vessel is tentatively carried out by using the ASME design rules.     

DEMT experimental and analytical studies on seismic isolation

This paper reviews the experimental and theoretical studies performed at CEA/DEMT related to the overall behavior of isolated structures. The experimental work consists of the seismic shaking-table tests of a concrete cylinder isolated by neoprene sliding pads, and the vibrational tests on the reaction mass of the TAMARIS seismic facility. The analytical work consists of the development of procedures for dynamic calculation methods: for soil—structure interaction where pads are placed between an upper raft and pedestals, for time-history calculations where sliding plates are used, and for fluid—structure interaction where coupled fluid and structure motions and sloshing modes are important.Finally, this paper comments on the consequences of seismic isolation for the analysis of fast-breeder reactor (FBR) vessels. The modes can no longer be considered independent (SRSS Method leads to important errors), and the sloshing increases.     

Seismic analysis of liquid storage container in nuclear reactors

Seismic analysis of liquid storage containers is always difficult in the seismic design of nuclear reactor equipment. The main reason is that the liquid will generate significant seismic loads under earthquake. These dynamic liquid loads usually form the main source of the stresses in the container. For this kind of structure–fluid coupling problem, some simplified theoretical methods were usually used previously. But this cannot satisfy the requirements of engineering design. The Finite Element Method, which is now full developed and very useful for the structural analysis, is still not mature for the structure–fluid coupling problem. This paper introduces a method suitable for engineering mechanical analysis. Combining theoretical analysis of the dynamic liquid loads and finite element analysis of the structure together, this method can give practical solutions in the seismic design of liquid storage containers.     

Cost-effectiveness analysis of seismically isolated pool structures for the storage of nuclear spent-fuel assemblies

This study introduces a method for evaluating cost-effectiveness of seismically isolated pool structures, taking account of fluid–structure interaction effects. As a measure of cost-effectiveness, the procedure estimates minimum life-cycle cost, sum of initial construction cost and excepted damage cist over life-cycle of the structure. The expected damage cost is the function of failure probabilities, which are computed by frequency domain analysis for convenience. Input ground motions are represented by a power spectral density function compatible with site-dependent response spectrums. The interaction effects between flexible walls and contained fluid are considered in the form of the added mass matrix. The thickness of wall and the stiffness of isolator are considered two key design variables in achieving a design with minimum life-cycle cost. The numerical examples show that seismically isolated pool tanks are highly cost-effective in low-to-moderate seismic regions.     

Nonlinear seismic response analysis of an embedded reactor building based on the substructure approach

A practical method to calculate the elasto-plastic seismic response of structures considering the dynamic soil-structure interaction is presented. The substructure technique in the time domain is utilized in the proposed method. A simple soil spring system with the coupling effects which are usually evaluated by the impedance matrix is introduced to consider the soil-structure interaction for embedded structures. As a numerical example, the response of a BWR-MARK II type reactor building embedded in the layered soil is calculated. The accuracy of the present method is verified by comparing its numerical results with exact solutions. The nonlinear behavior and the soil-structure interaction effects on the response of the reactor building are also discussed in detail. It is concluded that the present method is effective for the seismic design considering both the material nonlinearity of the nuclear reactor building and the dynamic soil-structure interaction.     

Homogenisation method for the dynamic analysis of a complete nuclear steam generator with fluid-structure interaction

The present paper deals with the dynamic analysis of a steam generator tube bundle with fluid-structure interaction modelling. As the coupled fluid-structure problem involves a huge number of degrees of freedom to account for the tube displacements and the fluid pressure evolutions, classical coupled method cannot be applied for industrial studies. In the present case, the three-dimensional fluid-structure problem is solved with an homogenisation method, which has been previously exposed and successfully validated for FSI modelling in a nuclear reactor [Sigrist, J.F., Broc, D., 2007a. Homogenisation method for the modal analysis of a nuclear reactor with internal structures modelling and fluid-structure interaction coupling. Nuclear Engineering and Design 237, 431-440]. Formulation of the homogenisation method for general two- and three-dimensional cases is exposed in the paper. Application to a simplified, however representative, model of an actual industrial nuclear component (steam generator) is proposed. The problem modelling, which includes tube bundle, primary and secondary fluids and pressure vessel, is performed with an engineering finite element code in which the homogenisation technique has been implemented. From the practical point of view, the analysis highlights the major fluid-structure interaction effects on the dynamic behaviour of the steam generator; from the theoretical point of view, the study demonstrates the efficiency of the homogenisation method for periodic fluid-structure problems modelling in industrial configurations.     

考虑地基岩土参数不确定性的核电厂结构随机地震反应分析

在考虑土-结构相互作用(SSI)效应的情况下,引入随机地震反应分析方法,探讨地基岩土参数的不确定性对核电厂地震响应的影响.基于ANSYS程序,采用常数阻抗法,通过设置边界弹簧和阻尼来考虑地基土的作用,并通过设置弹簧和阻尼参数的不确定性,来模拟岩土动态参数的不确定性.针对某1000MW级压水堆核电站反应堆厂房结构,进行随机地震反应的数值仿真分析,并将随机反应结果与确定论分析结果进行了对比.结果表明,随机分析方法是确定论分析方法的有益补充,二者结合能更合理地反映参数的不确定性对结构地震响应的影响.     

Elastic–plastic analysis of nuclear structures with millions of DOFs using the hierarchical domain decomposition method

The hierarchical domain decomposition method (HDDM) proposed by Comp. Sys. Eng. 4 (1993) 495 is applied to the large scale elastic–plastic finite element (FE) analysis of nuclear structures. The HDDM is a method to implement the finite element method (FEM) on various kinds of parallel environments. The substructure-based iterative methods can effectively be used with the HDDM to solve the large scale linear algebraic equations derived from the implicit FEM. In this paper, some key techniques to parallelize the static elastic–plastic FE analysis by the HDDM are described. As illustrative examples, a support structure of the high temperature engineering test reactor (HTTR), a pressure vessel, and an internal pump of a pressure vessel are analyzed. The structure of HTTR and the pressure vessel are modeled by hexahedral solid elements whose total degrees of freedom (DOFs) are about 1.3 millions (M) and 3 M, respectively. The internal pump is modeled by quadratic tetrahedral elements whose total DOFs are about 2 M. The elastic–plastic analysis of a simple cube with 10 M DOFs is also carried out. Both the conjugate gradient method for solving the linear equations and the Newton–Raphson method for solving nonlinear problems successfully converge.     

Application of seismic analysis methodology to small modular integral reactor internals

The fluid–structure interaction (FSI) effect should be carefully considered in a seismic analysis of nuclear reactor internals to obtain the appropriate seismic responses because the dynamic characteristics of reactor internals change when they are submerged in the reactor coolant. This study suggests that a seismic analysis methodology considered the FSI effect in an integral reactor, and applies the methodology to the System-Integrated Modular Advanced Reactor (SMART) developed in Korea. In this methodology, we especially focus on constructing a numerical analysis model that can represent the dynamic behaviors considered in the FSI effect. The effect is included in the simplified seismic analysis model by adopting the fluid elements at the gap between the structures. The overall procedures of the seismic analysis model construction are verified by using dynamic characteristics extracted from a scaled-down model, and then the time history analysis is carried out using the constructed seismic analysis model, applying the El Centro earthquake input in order to obtain the major seismic responses. The results show that the seismic analysis model can clearly provide the seismic responses of the reactor internals. Moreover, the results emphasize the importance of the consideration of the FSI effect in the seismic analysis of the integral reactor.     

Dynamic characteristics of a perforated cylindrical shell for flow distribution in SMART

The System-integrated Modular Advanced ReacTor (SMART) is a small nuclear reactor under development in Korea. It is equipped with a perforated cylindrical shell, which is called a flow skirt, in the lower plenum of the reactor for uniform flow distribution and to prevent inflow of debris into the core. This perforated cylindrical shell can be excited by external forces such as seismic or pump pulsation loads. The dynamic characteristics of the perforated cylindrical shell must be identified for further dynamic analysis. This research explores the modal analysis of the scaled-down flow skirt model submerged in coolant water. For the numerical simulation, finite element analysis is carried out to extract modal characteristics of the structure considering the fluid–structure interaction and we introduce the NAVMI factor for similarity analysis. In the finite element model, the whole shape of the perforated cylindrical shell is simulated instead of using the effective material properties. In addition, a 1/12 scaled-down flow skirt is manufactured, and an experiment is designed using an exciter and waterproof accelerometers for the modal test. Due to excellent agreement between the modal test results and the finite element analysis results such as natural frequencies and mode shapes, the finite element model is validated and can be used to predict the dynamic characteristics of the real flow skirt. Moreover, the natural frequency of the real flow skirt can be calculated from the NAVMI factor and is in good agreement with the FEM result.     

核电厂中流固耦合现象数值模拟研究综述

流固耦合现象在核电厂中广泛存在，该现象引起的结构动力学问题对核电厂结构完整性和安全性有重要影响。目前，国内外对核电厂中流固耦合现象的研究给予越来越多的关注。本文介绍华北电力大学在该方面的一些研究进展，例如，快堆燃料组件抗震分析新的流体附加质量计算方法研究；蒸汽发生器换热管双管漩涡脱落的数值模拟；一个先进堆燃料组件平行板上流动引起的漩涡脱落数值模拟；由地震引起的自由表面对快堆主容器冲击现象的研究；移动粒子法求解液面晃动及晃动引起离散现象的研究等。     

堆本体抗震试验动力相似关系推导与验证

为确保堆本体抗震试验中流体对流效应、脉冲效应和堆本体结构响应的准确性,需保证重力、流体与固体惯性力、结构弹性力和结构应变的相似性。本文从固体结构的振动方程、不可压牛顿流体的动力学方程、流固交界面的边界条件和环形柱体域内液体线性晃动的动力学公式出发,基于控制方程的量纲分析法,推导了考虑液体晃动效应的堆本体地震响应动力相似关系。基于上述相似关系建立了堆容器堆内构件和堆容器内自由液面流体域的缩尺模型,通过有限体积法分析堆容器堆内构件原型和缩尺模型中液体的晃动固有频率、晃动波高、压力以及液体晃动对堆容器支承裙的倾覆力矩。结果表明本文动力相似关系具有合理性和准确性,可用于堆本体缩尺模型的抗震试验研究。     

Preliminary evaluation of the seismic response of the ELSY LFR

The main goal of the present study is the preliminary evaluation of the seismic demand of a LFR with reference to European Lead System project (ELSY) considered one of the most promising innovative Generation IV reactor. The safety aspects of the ELSY reactor in the event of a Safe Shutdown Earthquake, taking into account also the effects of the possible fluid–structure interaction, have been analyzed.To the purpose to determine the seismic demand, in according with the international rules, a non-linear dynamic analysis method was used with rather refined 3-D model of LFR for the foreseen structural analyses and simulations of the plant and of the reactor internals behaviour. In this report numerical results are presented and discussed highlighting the relevance of the fluid–structure interaction in terms of structural integrity as well as the isolation technique effectiveness, which is expected to increase the safety margin of the reactor structures during a seismic event, if the isolators frequency is far from that of the reactor.The present work has been performed within the 6th European Framework Project.     

Seismic response of reactor vessel internals for Korean standard nuclear power plant

This paper presents the development of seismic design criteria for the reactor vessel internals as a part of the standardization programme for the nuclear power plant in Korea. The seismic design loads of the reactor vessel internals are calculated using the reference input motions of reactor vessels taken from Yonggwang nuclear power plant units 3 and 4 which are being constructed in Korea. An overview of analysis related to the basic parameters and methodologies is presented. Also, the response of internal components to the reactor vessel motions is carefully investigated.