Energy absorbers used against impact loading

In the WWER-440 reactor the primary piping consists of six horizontal loops going rapidally from the pressure vessel, each loop having a horizontal steam generator. In this reactor type the relatively long primary piping with many curved sections requires special attention in order to successfully eliminate the consequences of the design basis accident. Emergency supports are located in appropriate places to restrict the movements of the pipe. Under normal conditions there is a gap of some centimeters between the pipe and a support so that in the pipe can be deformed freely under changing loads. This paper deals with those energy-absorbing structures used at the Loviisa Nuclear Power Plant for protection against impact loading. Places and circumstances where energy-absorbing structures are employed are specified. Development and design of impact absorber elements are discussed and impact tests are described.     

Analytical studies on local damage to reinforced concrete structures under impact loading by discrete element method

This paper proposes a new analytical approach for assessing local damage to reinforced concrete structures subjected to impact load, by applying the discrete element method (DEM). It first outlines the basis concept and analytical formulation of the DEM. Next, it discusses the results of simulation analyses of concrete material tests, uni-axial compression tests and tensile splitting tests conducted to determine appropriate analytical parameters such as material constants, failure criteria and strength increase factors depending on strain rate. Finally, the adaptability of the DEM to local damage to reinforced concrete structures impacted by rigid and deformable missiles is verified through simulation analyses of various types of impact tests. Furthermore, the various impact response characteristics and failure mechanisms, such as impact forces, penetration behavior, reduction in missile velocity and energy transfer process, which are difficult to obtain experimentally, are analytically evaluated by the DEM.     

Analysis of aircraft impact to concrete structures

Analysis of aircraft impact to nuclear power plant structures is discussed utilizing a simplified model of a “fictitious nuclear building” to perform analyses using LS-DYNA software, representing the loading: (i) by the Riera force history method and (ii) by modeling the crash by impacting a model of a plane similar to Boeing 747-400 to the structure (i.e., “missile–target interaction method”). Points discussed include: (1) comparison of shock loading within the building as obtained from the Riera force history analysis versus from the missile–target interaction analysis, (2) sensitivity of the results on the assumed Riera force loading area, (3) linear versus nonlinear modeling and (4) on failure criteria.     

The use of energy analysis and efficiency indices in nuclear energy

Minatoménergoprom. Translated from Atomnaya Énergiya, Vol. 71, No. 2, pp. 91–97, August, 1991.     

Application of an impact analysis code to reinforced concrete structures

A numerical constitutive model representing the behavior of concrete material is proposed in this paper. The stress-strain relations are kept in accordance with the updated information, such as stress, strains, strain rates in the principal directions of stress, crack states, yield states, rupture states. The algorithm of the constitutive model was implemented to the explicit impact analysis code DYNA3D. The experimental tests were also held, in which a 100 kg weight with 8 m/s velocity drops onto a reinforced concrete structure. The results of the DYNA3D analysis were compared with those of the tests and show a good agreement.     

Basic ideas of a philosophy to protect nuclear plants against shock waves related to chemical reactions

There is an increasing trend to build nuclear plants, especially nuclear power plants, within the vicinity of industry (particularly chemical plants), transport ways (streets, railroads, river) and cities. This is linked to the danger for the population in this region due to an accident in connection with explosive material. Such accidents can influence the safety of the nuclear power plant, too. To avoid risks, even in cases in which such risks are not evident at the moment, appropriate safeguarding provisions have to be taken. With respect to future developments, on one side this can be done by designing the installations to withstand the loading which is caused by explosions, on the other side this can be done by defining exclusion regions around nuclear power plants within which no storage of explosive materials or transportation that is connected with high risk is allowed.The gaseous hydrocarbons (under normal conditions) - stored in a fluid state by means of pressure or deep cooling - are considered as being particularly dangerous. By theoretical considerations a load-function has been derived to describe the effect of an imaginable accident. This pressure-time diagram was deduced from the assumption that an explosion of a gas cloud would occur only in the form of a deflagration. In the case of saturated hydrocarbons this assumption is correct with a high degree of probability. On the other side, it is possible to get higher loadings after accidents in connection with unsaturated hydrocarbons. Owing to the present lack of knowledge, it is very difficult, or nearly impossible, to evaluate a pressure-time diagram for this case.A conservative and therefore safe assessment is possible if the detonation as thinkable form of an explosion is taken into account. The possibility of this form of reaction has been shown in experiments, though there have been idealized conditions, as homogeneous stoichiometric mixture in spherical shells and detonative ignition. Quasi-static pressures up to 20 bar have been measured in these experiments. It seems unrealistic to design buildings of nuclear power plants to withstand such loadings. Therefore, distances from the nuclear power plant have been calculated, in which a detonation may occur without generating a higher loading than that evaluated for the deflagration of a gas cloud. The assumptions and models to evaluate the pressure-time function in the case of deflagration and the safety distances in the case of detonation will be discussed.     

The use of nuclear energy for district heating

So far only one reactor—the Ågesta reactor, south of Stockholm has been used to supply a sizeable district heating scheme. For 10 years this pilot scheme delivered 10 MW of electricity to the grid and initially 50 later 70 MW of heat to the suburb ‘Farsta’ of Stockholm, with a very good reliability record. As yet it has had no successors anywhere in the world. Ågesta was of course too small to give good economics, but it gave valuable experience. As the citizens of Farsta had become accustomed to the smokeless nuclear heat, there were many protests from the public when Ågesta was shut down to allow the nuclear effort in Sweden to be concentrated on bigger units.Since the oil crisis, nuclear district heating schemes have, however, been studied with increasing effort in a number of countries as one of the possible ways of achieving lower heat costs, conserving the limited oil and natural gas resources, and reducing air pollution. In this article the author describes the basis for assessing the performance and economics of such schemes. To do this it has been necessary to treat not merely the nuclear plants but also the entire system of transport distribution and storage of heat. Many of the numerical examples in this area have been taken from the Swedish scene with which the author is best acquainted but also many comments on conditions in other countries are included.Also the institutional obstacles which often stand in the way of a wider use-and the manner in which they are starting to be tackled by several countries-are discussed. The subject is treated in a manner which it is hoped will be useful also to those without previous experience of district heating.     

Application of the local-to-global approach to the study of infilled frame structures under seismic loading

The seismic performance of civil engineering structures may be estimated by using two levels of modelling. At the local level, each constituent has its own constitutive law and geometric finite element support. The main phenomena such as the cracking and the crushing of concrete and masonry could be reproduced by using the continuous damage or plasticity theories. However the cost of the computations does not allow extensive or dynamic studies and thus the global level — where the constitutive laws based on empirical rules reproduce the behaviour of the structural elements — represents the unique strategy for the analysis of complete civil engineering structures under seismic loading. The present paper aims at presenting the application of these two modelling levels in order to assess the seismic performance of masonry infilled R/C frame structures. The one-bay masonry infilled frames tested at Lisbon under cyclic loading and the four-storey building tested at ELSA have been used for the validation of the modelling approach.     

An efficient static correction algorithm with application to the hydrodynamic loading of thin shell structures

This paper treats the problem of correctly accounting for the quasi-static component of the response of a thin-shell structure to a dynamic loading which originates from a pressure disturbance within the body of a contained fluid. The importance of quasi-static structure response has been observed in BWR safety/relief valve (SRV) actuation tests which produce a pressure oscillation in the suppression pool as a consequence of the expansion and contraction of bubbles formed from air expelled from the SRV pipeline. The problem is treated within the context of a finite-element methodology which has been previously developed for the coupled analysis of a linear elastic structure in contact with a linear acoustic fluid. For problems involving a large number of degrees of freedom, the efficient application of this method requires reduction to a set of normal modes approximating the response of the coupled fluid-structure system. The coupled modes are synthesized from the fluid properties and a set of normal modes describing the behavior of the structure in the absence of the fluid. The proposed solution to the problem is to append a shape function, representing the quasi-static component of the structural response, to the set of modes computed by standard eigenvalue extraction. The success of the method is demonstrated by comparison of calculated results with measured structural response from a typical SRV test.     

Elastic-plastic creep response of structures under composite time history of loading

High temperature nuclear reactor components are subject to a complex history of thermal and mechanical loading cycles. To evaluate the adequacy of such components, detailed information on the accumulated inelastic strains and strain cycling is required. This paper presents the theory, describes efficient numerical techniques accounting for plasticity, creep and overall equilibrium, describes the overall structure of the resulting computer program, and demonstrates the capability of the analysis method on a real three-dimensional structure. Starting with the principle of virtual work, exact equilibrium equations are derived for a stepwise Lagrangian formulation. The resulting equilibrium equations are then specialized to the incremental Piola-Kirchhoff stress computation and to small incremental strain formulation. Classical plasticity theory is used to develop a novel method based on the concept of ‘plastic stress’ for consideration of inelastic behavior. It is shown that the material's stress-strain curves can be followed to any desired degree of accuracy both for isotropic and kinematic hardening. It is further shown that for kinematic hardening it is necessary to base the incremental change on the state corresponding to the mean of the initial and the final states to satisfy the yield condition at the final state. The equation of state and strain hardening is used to describe the creep behavior. A novel numerical technique to describe a complex load history is developed by using time as a parameter, history breakpoint determination by scanning of various load vectors, and by linear interpolation between any two breakpoints in the load history. Efficient criteria for load incrementation in the form of a fraction of the total ‘plastic stress’ for any sequence of two load history break points are developed and made an internal function of the program. This saves the user significant hardship when faced with guessing the load increment for an unknown state of the solution at any of the load history breakpoints. The ‘plastic stress’ load vector concept is utilized with interation and extrapolation to converge to the equilibrium states with simultaneous satisfaction of the stress-strain relations for each of the iterated states. The essential features of the computer program DYPLAS-FSH, based on the theory and techniques described above, and a postprocessor program POR-FSH, based on RDT F9-5T for ratcheting and fatigue evaluation, are identified and discussed. In summary, the new results of this work are the efficient handling of an arbitrary load history, introduction of the ‘plastic stress’ concept for inelastic computation, novel implementation of classical plasticity with recognition of incrementation conditions for the kinematic hardening, use of the load incrementation algorithm based on the ‘plastic stress’ concept, and development of a computer code capable of solving practical three-dimensional problems.     

Equivalent loading due to airplaine impact taking into account the non-linearities of impacted reinforced concrete buildings

The airplane impact loading condition applied to a nuclear power plant building usually leads to very large excitations locally around the impact point and in the overall structure. This excitation is also characterized by a wide frequency content (up to 100 Hz). The state of the art of assessing the effect of an airplane impact was to apply a widely recognized rigid load function (RLF) impact force determined with Riera's Method to a linear elastic structure model and to perform calculations in order to obtain time histories and acceleration spectra. Because the real response of the building is not only governed by the elastic behaviour but also by the non-linear behaviour of the cracked and damaged concrete around the impact point the results obtained by this procedure are very conservative for the main part of the structure. The object of the paper is to present a numerical method of determining the dynamic response at characteristic points of the building taking into account the non-linear behaviour of locally impacted cracked damaged concrete.The method is based on the determination of a verified load function (VLF) which, applied to a linear elastic model of the structure, leads to the same response of the building (far from the impact point) as that due to the RLF impact force applied to a more realistic non-linear model of the reinforced concrete building. The practical advantage of using this procedure is that it avoids long and costly non-linear time integration of a full structural model.In order to obtain the VLF one only performs non-linear explicit calculations locally which include the main physical phenomenon occurring in an impacted reinforced concrete structure.     

Integrated impact failure analysis of concrete slab structures with consideration of impact load characteristics

This paper describes a method of integrating a multi-mass model, which is applied to simulate the impact load characteristics for an impact collision, to a dynamic finite element analysis for concrete slab structures through an interactive procedure. Examples of the applicability and merit of the proposed linked procedure are then discussed.     

The use of WIMS and CITATION codes in fuel loading required for the conversion of HEU MNSR core to LEU

The Nigerian Research Reactor-1 (NIRR-1) falls in the category of Miniature Neutron Source Reactors (MNSR) using a fuel of 90% HEU. It is therefore desirable to convert it from this enrichment to LEU (less than 20%) in conformity with the new global trend of making research reactor fuel as unattractive as possible to groups that may be interested in using such highly enriched cores for non-peaceful purposes. In this work, we have developed a computational scheme based on WIMS and CITATION that would theoretically achieve this objective as easily as possible. The scheme systematically reduces the enrichment from 90% (or any other initial values) to less than 20% in steps of 5% or any desired percentage variation. Two fuel types (UAl₄ and UO₂) are considered in here, while maintaining the size and geometry of the core as well as the excess reactivity (between 3.5 and 4 mk). Our results show that the U-235 loading increases sharply as enrichment decreases. It has also been noticed that at 5% enrichment the fuel loading for both types is 2505 g. However, at 90% enrichment, the loading drops sharply to 998 g for UAl₄ fuel and 946 g for UO₂ fuel. Below the enrichment of 5%, the operation of NIRR-1 with both fuel types can be considered unrealistic as this requires structural adjustment which the work tries to maintain constant.     

Theoretical study of aircraft impact on reactor containment structures

In containment design there is a requirement to protect the reactor system from the effects of external hazards and hence it is necessary to provide suitable wall thicknesses. Experimental work undertaken by the UKAEA is being carried out as a general study and this paper describes some theoretical studies for the particular case of an aircraft impact. The theoretical study utilizes a finite difference dynamic code based upon dynamic relaxation initially developed for static problems The code models concrete, reinforcement and prestressing throughout the short term non-linear range. Concrete is assumed to have a limited tensile stress capacity, coupled with a shear carrying capacity which is dependent upon the aggregate and crack size. In addition a yield condition can be specified to allow for triaxial stress states both initial and subsequent to failure. The paper briefly describes the theory and makes comparisons for different concrete thicknesses.     

Critical impact energy for the perforation of metallic plates

This paper investigates the empirical formulae used in engineering practice to predict the critical perforation energy of metallic plates struck by rigid projectiles in the sub-ordnance regime. Main factors affecting the critical perforation energy are identified and valid conditions for each empirical formula are compared. Dimensional analysis is conducted to show the dependence of the non-dimensional critical impact energy on other influential non-dimensional numbers. Available empirical formulae are re-expressed in non-dimensional forms. A modified Jowett/AEA equation is proposed to predict the critical perforation energy of a flat-ended short projectile. The present work increases the confidence of using these empirical formulae and can be regarded as a quick guide for ballistic protection design of metallic shields and steel armour plates.     

Two-group theory of noise in reflected reactors with application to vibrating absorbers

A one-dimensional semi-analytic method, based on the adjoint technique, has been developed for two-group treatment of noise in reflected reactors. The adjoint for a symmetric system is given and examined in detail. The local and global characters of noise are investigated for in-core and ex-core perturbations. Finally, the noise induced by a vibrating absorber is determined.