Modelling of PWR lower head failure under severe accident loading using improved shells of revolution theory

In the study of severe pressurized water reactor accidents, the scenarios that describe the relocation of significant quantities of liquid corium at the bottom of the lower head are usually investigated from the mechanical point of view. In these scenarios, the risk of a breach and the possibility of a large quantity of corium being released from the lower head exists. This may lead to an out of vessel steam explosion or to direct heating of the containment; both which have the potential to lead to early containment failure.Within the framework of the OECD Lower Head Failure (OLHF) programme, a simplified model based on the theory of shells of revolution under symmetrical loading was developed by IRSN. After successfully interpreting some other representative experiments on lower head failures, the model was recently integrated into the European integral severe accident computer ASTEC code. The model was also used to obtain the thermo-mechanical behaviour of a 900-MWe pressurized water reactor lower head, subjected to transient heat fluxes under severe accident conditions.The main objective of this paper is to present: (1) the full mathematical formulations used in the development of the model, including their matrices and integrals defined by analytical expressions; (2) the two creep laws implemented, one for the American steel SA533B1 and one for the French steel 16MND5; and (3) the various numerical interpretations of experiments using the simplified model. This paper can be considered as a theoretical manual to aid users of the simplified model during modelling of lower head failures under severe accident conditions. One of the applications presented in this paper concerns the determination of a diagram representing the vessel time to failure as a function of the pressure level and the heat flux intensity. This information has been used by IRSN in probabilistic safety assessment and severe accident management analyses.     

Semi-analytical modeling of a PWR lower head failure under severe accident conditions using an axisymetrical shell theory

The USNRC/SNL OLHF program was carried out within the framework of an OECD project. This program consisted of four one-fifth scale experiments of a reactor pressure vessel (RPV) lower head failure (LHF) under well controlled internal pressure and large throughwall temperature differentials; the objectives were to characterize the mode, timing and size of a possible PWR lower head failure in the event of a core meltdown accident. These experiments should also lead to a better understanding of the mechanical behavior of the reactor vessel lower head, which is of importance both in severe accident assessment and the definition of accident mitigation strategies. A well-characterized failure of the lower head is of prime importance for the evaluation of the quantity of core material that can escape into the containment, since this defines the initial conditions for all ex-vessel events. A large quantity of escaping corium may lead to direct heating of the containment or ex-vessel steam explosion. These are important issues due to their potential to cause early containment failure. The experiments also provide data for model development and validation. For our part, as one of the program partners, a 2D semi-analytical model has been developed and used to simulate these experiments. The aim of this effort is to develop a simplified but well predicting code that can be then implemented in European integral severe accident computer codes (ASTEC, ICARE/CATHARE). This paper presents the detailed mathematical formulation of this simplified method which is used to interpret the experimental results. The axi-symmetric shell theory under internal pressure proposed by Timoshenko has been utilised. The solution to the equilibrium equations is presented, with particular attention to the Rabotnov analytical formula. The radius and the polar angle of the deformed structure have been written as analytical expressions in order to take the large displacements and large strains into account using our mathematical formulation. The Norton type creep law and the Kachanov damage law have been used. Several failure criteria were used in the calculations and their effect on the numerical results is discussed. This 2D semi-analytical model gives very satisfactory results when compared, with the experimental and numerical results that were presented recently in the Benchmark calculations based on the first test of the OLHF program. The performance of this model is also illustrated by its capacity to accurately simulate the deformation of the lower head, including the variation of wall thickness.     

Fluid-dynamic loading during lower head failure

The containment concept of Eibl, Keβler, and Hennies for nuclear power plants equipped with large pressurised water reactors is aimed at developing passive mechanisms that are capable of safely confining core-melt consequences. Regarding this, it is important to know the ultimate loads acting on the supporting containment structures in case of core-melt accidents. In this study a large break of the reactor pressure vessel under high pressure (17 MPa) is assumed. The hydraulic load acting on the vessel supporting structure during the vessel blowdown was estimated. The results presented are based on calculations performed with the transient analysis thermal-hydraulic code RELAP5/ MOD3. The information obtained provides a force-function input for necessary structural dynamic investigations. On the assumption of a global circumferential rupture of the lower head of the pressure vessel, the computational results show a load peak of 340 MN and a continuing load of 160 MN acting on the vessel support ring.     

Study of tearing behaviour of a PWR reactor pressure vessel lower head under severe accident loadings

In PWR severe accident scenarios, involving a relocation of corium (core melt) into the lower head, the possible failure mode of the reactor pressure vessel (RPV), the failure time, the failure location and the final size of the breach are regarded as key elements, since they play an important part in the ex-vessel phase of the accident.Both the LHF and OLHF experiments as well as the FOREVER experiments revealed that initiation of the failure is typically local. For the case of a uniform temperature distribution in the lower head, crack initiation occurs in the thinnest region and for the case of a non-uniform temperature distribution, it initiates at the highest temperature region. These experimental results can be modelled numerically (but more accurately with 3D finite element codes). The failure time predictions obtained using numerical modelling agree reasonably well with the experimental values.However, the final size of the failure is still an open issue. Analyses of both the LHF and OLHF experimental data (as well as of that from the FOREVER experiments) do not enable an assessment of the final size of the breach (in relation with the testing conditions and results).Indeed, the size of breach depends on the mode of crack propagation which is directly related to the metallurgical characteristics of the RPV steel. Small changes in the initial chemical composition of the vessel material can lead to different types of rupture behaviour at high temperatures. Different rupture behaviours were observed in the LHF and OLHF experiments using the SA533B1 steel. Similar observations were previously noticed during a CEA material characterization programme on the 16MND5 steel. To determine crack propagation and final failure size, 3D modelling would thus be needed with an adequate failure criterion taking into account the variability in behaviour of the RPV material at high temperatures.This paper presents an outline of the methodology being used in a current research programme of IRSN, in partnership with CEA and INSA Lyon. The aim is to model crack opening and crack propagation in French RPV lower head vessels under severe accidents conditions. This programme was initiated in 2003 and is made up of five main sections, namely an inventory of the different French PWR lower head materials, metallurgical investigations to better understand the cause of mechanical behaviour variability that is observed and related to material microstructure, Compact Tension (CT) testing of specimens to characterize the tear resistance of the material, validation of the modelling using experiments on tube specimens and the development of a new failure criterion for the 3D finite element models.     

Overview of NRC sponsored LWR lower head failure research program

The US Nuclear Regulatory Commission (US NRC) has sponsored a research program to investigate the mode and timing of vessel lower head failure. Major objectives of the program were to identify plausible failure mechanisms and to develop a method for determining which failure mode would occur first for different light water reactor designs and accident conditions. Failure mechanisms, such as tube ejection, tube rupture, global vessel failure, and localized vessel creep rupture, were studied. Newly developed models and existing models were applied to predict which failure mechanism would occur first in various severe accident scenarios. So that a broader range of conditions could be considered simultaneously, the calculations relied heavily on models with closed-form or simplified numerical solution techniques. Finite element techniques were employed for analytical model verification and examination of more detailed phenomena. High-temperature creep and tensile data were obtained for predicting the vessel and penetration structural response. This paper summarizes major accomplishments and conclusions from research performed in the NRC sponsored lower head failure project.     

CORVIS. Investigation of light water reactor lower head failure modes

The project CORVIS (Corium Reactor Vessel Interaction Studies) is a research programme for the experimental and analytical investigation of a possible failure of the pressure vessel of a light water reactor during an assumed core melt accident. The applied methods of the experimental technique, the metallurgical investigations and the computational analysis are described. Two recent melting experiments are presented in detail. The first experiment was carried out on a steel plate 100 mm thick representing a pressure vessel lower head without penetrations. The second experiment was performed on a steel plate of the same thickness but representing a boiling water reactor lower head carrying a tube penetration in the form of a drain line. Reported are the phenomenology of these experiments, the results of the metallurgical post-test examinations and the computational reconstruction of the observed heat transfer and ablation phenomena in a stagnant and in a turbulent melt. Further, the results of three earlier tests, on a smaller scale, are presented.     

先进压水堆非能动安全系统研究进展

介绍了我国先进压水堆非能动安全系统研究进展及国内外先进压水堆非能动安全系统研究发展状况,指出我国非能动安全系统研究的发展方向是进行新一代1000MW级压水堆非能动安全系统的研究。     

The study on grid-to-rod fretting wear models for PWR fuel

The fretting wear is found to be generated at grid-to-rod contact areas by flow-induced vibration. This flow-induced grid-to-rod fretting wear may be initiated at a certain critical grid-to-rod gap that strongly depends on the extent of flow-induced vibration and grid spring designs. Three fretting wear excitation mechanisms acting on the grid-to-rod fretting wear are summarized. In order to examine the impact of grid spring designs on the fretting wear rate, the fretting wear tests for three kinds of grid spring designs were carried out for 500 h, simulating the reactor flow conditions. In parallel, three grid-to-rod fretting wear models that include constant work rate model, constant work density rate model and linear work density rate model have been developed. The three fretting wear models were used to predict the fuel rod perforation times with the use of the fretting wear test results. It is said that the constant work density rate model or the linear work density rate model is quite effective in predicting the grid-to-rod fretting-induced rod failure time observed in commercial nuclear power plants.     

压水堆吊篮下部防断支承组件流致振动分析

对秦山核电厂堆芯下腔流场、堆内下部防断支承组件振动特性及全组件的流致振动进行了分析,特别对旋涡脱落致振进行了定量分析.分析结果表明防断支承组件初始结构的整体转动振动的固有频率与旋涡脱落频率相差较大,发生大幅振动的可能性不大;只有当部分连接件松动,整体结构转动振动的固有频率下降时,才很有可能发生大幅振动.     

Developments in PWR cladding corrosion: materials and models

In pressurized water reactors Zircaloy-4 is a standard fuel cladding material. The aim of this paper is to present and evaluate corrosion data generated both in-reactor, and out-of-reactor on PWR claddings made of both Zircaloy-2 and Zircaloy-4 materials. The oxide thickness measurements of cladding tubes irradiated in the Ringhals 3 reactor, and oxide weight gain measurements carried out in Sandvik autoclaves at 400°C, 10.3 MPa clearly show that the stress relief annealed Zircaloy-2 is more corrosion resistant than Zircaloy-4 produced with an identical fabrication route. Furthermore, autoclave tests indicate that the hydrogen pickup fraction of the two alloys is very similar. The obtained data have been evaluated in regard to chemical composition and heat treatment. In addition, computer models, which simulate thermal and hydraulic reactor conditions and corrosion kinetic processes simultaneously, have been used to predict the in-reactor corrosion behaviour of the claddings.     

Thermal-hydraulics analysis during fuel element failure in an operating PWR

The fuel element failure in an operating pressurized water reactor (PWR), including fuel element breaks, has an effect on the operation safety of PWR. In this paper, the RELAP5 model of the fuel element failure is established for the safety analysis. The RELAP5 time step sensitivity analyses for the element pre-break steady and post-break transient simulation are carried out. And the variations of main thermal-hydraulics parameters related to the fuel element break are quantitatively studied, which include the internal gap pressure and the maximum fuel pellet temperature as well as the releasement of noncondensables in the gap. It is found that (1) the results by the RELAP5 code is very sensitive to the time step in a volume system with the noncondensables, and the time step sensitivity analysis is necessary if the effective time step range is unknown, (2) the larger the break area is, the more quickly the gap pressure increases and the maximum pellet temperature reaches to the stable value, (3) when the gap pressure increases and reaches to the coolant pressure, at the break the liquid inflow from coolant to gap will be turned to the vapor outflow from gap to coolant, (4) during the failure transient, the gap thermal conductivity experiences a sharp decrease in the break instant, which results in the decrease of heat transferred to cladding and the sharp decrease of cladding temperature as well as the sharp increase of minimum departure from nucleate boiling ratio (MDNBR). These conclusions can provide the basic for the operation safety analysis of PWR during the fuel element failure.     

Analysis of likelihood of lower head failure and ex-vessel fuel coolant interaction energetics for AP1000

A one-dimensional model is formulated to assess the thermal response of the Westinghouse Advanced Plant (AP1000) lower head based on two bounding melt configurations. Melt Configuration I involves a stratified light metallic layer on top of a molten ceramic pool, and melt Configuration II represents the conditions that an additional heavy metal layer forms below the ceramic pool. The approach consists of the specification of initial conditions; determination of the mode, the size and the location of lower head failure based on heat transfer analyses; computer simulation of the fuel coolant interaction processes; and finally, an examination of the impact of the uncertainties in the initial conditions and the model parameters on the fuel coolant interaction energetics through a series of sensitivity calculations. The results of the calculations for melt Configuration I show that the heat flux remains below critical heat flux (CHF) in the molten oxide pool, but the heat flux in the light metal layer could exceed CHF because of the focusing effect associated with presence of the thin metallic layers. The thin metallic layers are associated with smaller quantities of the molten oxide in the lower plenum following the initial relocation into the lower head. The calculations show that the lower head failure probability due to the focusing effect of the stratified metal layer ranges from 0.04 to 0.30. On the other hand, the thermal failure of the lower head at the bottom location for melt Configuration II is assessed to be highly unlikely. Based on the in-vessel retention analysis, the base case for the ex-vessel fuel coolant interaction (FCI) is assumed to involve a side failure of the vessel involving a metallic pour into the cavity water. The FCI sensitivity calculations intended to assess the implications of the uncertainties in initial conditions and the FCI modeling parameters show that the FCI loads range from a few MPa to upward of 1000 MPa (maximum pool pressure) with corresponding impulse loads ranging from a few kPa s to a few hundred kPa s.     

Coolant flow field in a real geometry of PWR downcomer and lower plenum

Nuclear vendors and utilities perform numerous simulations and analyses in order to ensure the safe operation of nuclear power plants (NPPs). In general, the simulations are carried out using vendor-specific design codes and best-estimate system analysis codes, most of which were developed based on one-dimensional lumped parameter models. During the past decade, however, computers, parallel computation methods, and three-dimensional computational fluid dynamics (CFD) codes have been dramatically enhanced. The use of advanced commercial CFD codes is considered beneficial in the safety analysis and design of NPPs. The present work analyzes the flow distribution in the downcomer and lower plenum of Korean standard nuclear power plants (KSNPs) using STAR-CD. The lower plenum geometry of a PWR is very complicated since there are so many reactor internals, which hinders in CFD analysis for real reactor geometry up to now. The present work takes advantage of 3D CAD model so that real geometry of a PWR is used. The results give a clear figure about flow fields in the downcomer and lower plenum of a PWR, which is one of major safety concerns.     

压水堆核电厂压力容器开盖时刻主冷却剂放射性浓度控制要求研究

压水堆核电厂停堆开盖时刻主冷却剂放射性浓度限值是核电厂的重要设计参数。本文基于停堆开盖后厂内辐射风险来源分析,建立了适用于压水堆核电厂停堆压力容器开盖时刻主冷却剂中的放射性浓度控制值评估方法,并采用欧洲第三代压水堆技术方案(EPR)堆型核电厂的设计参数对建立的方法进行了验证。验证结果表明:基于此方法得出的停堆开盖限值与EPR堆型核电厂原设计较接近。     

Momentum and mass exchange during refill in scaled models of a PWR

Interfacial momentum and mass exchange between the liquid and gas phases in a PWR downcomer were investigated. A new momentum transfer correlation was developed from air-water experiments in - and models of a PWR with standard and distorted geometries. The correlation is based on the Kutateladze parameter and indicates that the overall momentum transfer between the phases does not depend on scale for geometrically similar models. Interphase mass exchange has been included by evaluating the effective gas flow for momentum transfer. Predictions of the modified correlation agree quite well with experimental results of steam-water flows in three different scaled models of PWR's.     

Theoretical predictions of failure probabilities for PWR pressure vessels subjected to accident conditions

The Second Marshall Report (1982) presented a detailed analysis of the integrity of PWR pressure vessels. As part of that study theoretical calculations of failure probabilities were made. Since the publication of that Report modifications have been made to the theoretical model to extend the failure criterion into stable crack extension, to update the knowledge of the distribution of various parameters, to more accurately represent the stress intensities and crack shapes, and to consider a different representation of pre-service detection of defects.In this paper these modifications are summarised and the application of the model to the calculation of failure frequencies for the most severe accident conditions, the large loss-of-coolant accident and the steam break, is presented. The results indicate that the probability of vessel failure is one to two orders of magnitude lower than previously predicted.     

RPV下封头熔融池换热特性数值模拟研究

熔融物堆内滞留（In-vessel Retention,IVR）指的是在核电厂严重事故发生后,通过在压力容器和保温层间隙注入冷却水防止压力容器熔穿失效。本文基于COMSOL Multiphysics软件建立了一个流-热-固耦合计算模型,对IVR技术作用下的反应堆压力容器（Reactor Pressure Vessel,RPV）下封头双层熔融池的演变过程进行了仿真研究。当前模型计算结果表明：在稳态分层的状态下,与氧化物层接触的下封头未发生明显的熔化,与金属层接触的下封头会发生明显的熔化,但在被冷却条件下依然可以保持压力容器的完整性。     

CFD analysis of PWR core top and reactor vessel upper plenum internal subdomain models

One aspect of the Westinghouse AP1000™¹ reactor design is the reduction in the number of major components and simplification in manufacturing. One design change relative to current Westinghouse reactors of similar size is that AP1000 reactor vessel has two nozzles/hot legs instead of three. With regard to fuel performance, this design difference creates a different flow field in the reactor vessel upper plenum. The flow exiting from the core and entering the upper plenum must turn toward one of the two outlet nozzles and flow laterally around numerous control rod guide tubes and support columns. Also, below the upper plenum are the upper core plate and the top core region of the 157 fuel assemblies and 69 guidetube assemblies.To determine how the lateral flow in the top of the core and upper plenum compares to the current reactors a CFD model of the flow in the upper portion of the AP1000 reactor vessel was created.Before detailed CFD simulations of the flow in the entire upper plenum and top core regions were performed, conducting local simulations for smaller sections of the domain provided crucial and detailed physical aspects of the flow. These sub-domain models were used to perform mesh sensitivities and to assess what geometrical details may be eliminated from the larger model in order to reduce mesh size and computational requirements. In this paper, CFD analysis is presented for two subdomain models: the top core region and control rod guide tube region. These models are chosen for simulation because guide tube and top core region (including top grid, top nozzle, and hold-down device) are the major components of upper plenum effecting the flow patterns and pressure distribution.The top core region, corresponding to ¼ of fuel assembly, includes components as upper part of the fuel assemblies (top grid, fuel rods, top nozzle), core component hold-down devices, and upper core plates. These components distribute the core flow to different sections of guidetube regions. Mesh sensitivity studies have been conducted for each individual part in order to determine the proper geometrical simplifications. Pressure drop measurement data are compared with the predicted CFD results and act as a guideline for the mesh selection.The guidetube region includes control rod guidetubes themselves, adjacent support columns and open regions. In this study, two models of subdomains are analyzed: (1) a ¼ section of one control rod guide tube by itself and (2) a representative unit cell containing two ¼ sections of adjacent control rod guide tubes and one ¼ section of a neighboring support column.Predicted flow rates at each of the outflow locations in conjunction with results from the mesh sensitivity studies provide guidance on (1) what geometry to preserve or remove, (2) what geometry can be simplified to reduce the required mesh, and (3) an estimate of the total mesh required to model the entire upper plenum and top fuel domain.The commercial CFD code STAR-CCM+ is employed to generate the computational mesh, to solve the Reynolds-averaged Navier–Stokes equations for incompressible flow with a Realizable k–? turbulence model, and to post-process the results.