Axisymmetric modeling of prestressing tendons in nuclear containment dome

Simple axisymmetric modeling of a nuclear containment building has been often employed in practice to estimate structural behavior for the axisymmetric loadings such as internal pressure. In this case, the prestressing tendons placed in the containment dome should be axisymmetrically approximated, since most dome tendons are not arranged in an axisymmetric manner. Some procedures are proposed that can realistically implement the actual three-dimensional tendon stiffness and prestressing effect into the axisymmetric model. Prestressing tendons, which are arranged in two or three ways depending on a containment type, are converted into the equivalent layer to consider the stiffness contribution in meridional and hoop directions. In order to reflect the prestressing effect, the equivalent load method and the initial stress method are devised, respectively, and the corresponding loads or stresses are derived in terms of the axisymmetric model. The proposed schemes are verified through some numerical examples comparing the results of the axisymmetric models to those of the actual three-dimensional model. The examples show that the proper level of the prestressing in the hoop direction of the axisymmetric dome plays an important role in tracing the actual behavior induced by the prestressing. Finally, some correction factors are discussed that can further improve the analysis results.     

Pressures due to post-tensioned tendons on a dome of a nuclear reactor containment vessel

An approximate method is derived for analyzing forces and pressures due to post-tensioned tendons on a dome. The dome can possess any axisymmetric shape. Loss of prestress due to friction is taken into account. Use of the method is demonstrated for a sphere-torus dome, and typical distribution of pressure is presented.     

Average force along unbonded tendons: a field study at nuclear reactor containments in Sweden

The tightness and integrity of all Swedish reactor containments depend directly and indirectly on the function of the post-tensioned system. The tendon force in containments with unbonded tendons is followed up at regular in-service inspections (ISI) to ensure that the remaining force is sufficient. At the inspections, the tendon force is measured with so-called lift-off technique, where a jack is used to lift the end anchor. The interpretation of the measuring results is not obvious. One difficulty, which affects all tendons to different extents, is the influence of friction between the tendon and duct. This influence can cause a redistribution of force along the tendons after the original tensioning. The ordinary lift-off method only measures the force at the end of the tendon, which not always represents the change of force in the rest of the tendon. A method for measuring average force along a tendon is presented in this article. In this method, the elongation of the tendon is measured when the jack force is increased to a reference level with known force distribution. Measuring results from the latest ISI in Sweden show that the end force has decreased more than the average force, especially for long tendons with high influence of friction.     

Strength monitoring of a prestressed concrete containment with grouted tendons

Existing containments are all required to be checked for their strength periodically through inservice inspection programs. In China, all the containment prestress tendons are protected by cement grouting, except the sampling tendons for testing. To improve the methodology and accuracy of the present inservice inspections for grouted tendon containments, a new scheme of containment strength verification is proposed. It applies to all prestressed containments, and it can be used as a continuous monitoring tool. The greatest advantage of the new inspection scheme is that it suggests another possible way of monitoring the prestress levels in concrete when tendon force measurements become impossible in a case where all the tendons are grouted with cement. The measured quantities are the displacements of critical points in the containment cylinder and the dome. The apparatus is installed permanently outside the containment, and the data readings can be done any time. The improved accuracy of the apparatus contributes to make these measurements a meaningful source of continuous monitoring data. The application of the new scheme in Qinshan Nuclear Power Plant has verified its practicability. At the same time, it reveals that proper application of such a monitoring system requires careful beforehand arrangements.     

Bell-ring vibration response of nuclear containment vessel with attached masses under earthquake motion

There are two types of vibrations, designated as ‘beam-type’ and ‘bell-ring type’ occurring with axisymmetric thin shell nuclear containment vessel. Up to this time, the seismic analysis for such thin axisymmetric shells has mostly been carried out only for the ‘beam-type vibration’ because the response participation factor for the ‘bell-ring type vibration’ under seismic motion is zero when the shell structure is perfectly axisymmetric. However, as with nuclear containment vessels, when the thin axisymmetric shell has several attached heavy masses such as the equipment hatch or the manholes, the resulting seismic response of bell-ring type vibration is unexpectedly large and becomes remarkably more important than the beam-type vibration.For the seismic analysis of bell-ring type vibration an approximate uncoupled analysis using the natural mode shapes of unweighted perfect axisymmetric shell has been advocated on the assumption that the effect of the attached mass on their natural modes might be very small. However, application of this method to some models showed that the response of bellring type vibration calculated was noticeably smaller than the experimental results.In this paper we show the seismic response analysis of the bell-ring type vibration coupled with the beam-type vibration through the attached masses with the new consideration. These results show good agreement between the theoretical calculation and the experiment.     

Evaluation of prestress losses in nuclear reactor containments

The most critical safety barrier in a nuclear power plant, the concrete containment, is prestressed by hundreds of tendons, both horizontally and vertically. The main purpose of the containment is to prevent radioactive discharge to the environment in the case of a serious internal accident. Due to creep and shrinkage of concrete and relaxation of the prestressing steel, tendon forces decrease with time. These forces are thus measured in Swedish containments with unbonded tendons at regular in-service inspections. In this paper, the prestress losses obtained from these in-service inspections are compared to losses estimated using several prediction models for creep, shrinkage and relaxation. In an attempt to increase the accuracy of these models, existing expressions for the development of shrinkage were modified using previous findings on the humidity and temperature inside two Swedish containments. The models which were used and modified for predicting creep and shrinkage were CEB-FIP Model Codes 1990 and 1999, ACI 209, Model B3 and GL2000. Eurocode 2 was used for the prediction of relaxation. The results show that the most accurate of the models were CEB/FIP MC 99 and ACI 209. Depending on the model, the accuracy of the prediction models was increased by 0.5-1.2 percentage points of prestress losses when using the modified development of shrinkage. Furthermore, it was found that the differences between the different models depend mainly on the prediction of creep. Possible explanations for the deviation between the calculated and measured models can be the influence of reinforcement on creep and shrinkage of concrete and the influence of friction on horizontal tendons.     

Modal parameter identification of a containment using ambient vibration measurements

Ensuring and maintaining the structural integrity of the containment structure in nuclear power plants is essential for preserving the nuclear reactor and other safety-related systems as well as protecting plant workers and publics from hazardous radioactive materials. To date, the structural integrity of the containment has been evaluated periodically via various nondestructive inspection methods. However, these methods require considerable time and cost to estimate overall structural integrity. In this paper, the possibility of monitoring the structural integrity of the containment utilizing ambient vibration measurement is explored. The ambient vibration testing was selected because it can avoid the interruption of normal operation of power plants. To fulfill the objective, the ambient vibration of the containment of Ulchin Nuclear Power Plant Unit 5 in Korea was measured, and the modal parameters, i.e., resonant frequencies and corresponding mode shapes, were extracted using the modal identification techniques in the frequency domain, i.e., the peak picking and the frequency domain decomposition methods. Using the extracted modal parameters and the finite element model, the elastic modulus of the concrete was estimated based on the sensitivity-based system identification method.     

Heat transfer of a nuclear reactor containment spray drop

Heat transfer rates to spray droplets under the conditions of a LOCA in a LWR have been evaluated by systematic solution of the governing partial differential equations subject to appropriate initial and boundary conditions. The numerical calculations are based on new correlations. The computations have been facilitated through the use of an efficient hybrid-difference scheme.Results have been provided for the average heat transfer and for the effects of the drop-size, droplet spray angle, initial injection velocity, the containment temperature and pressure on the heat transfer to the drop. The drop fall-heights before attaining thermal equilibrium with the containment atmosphere have been predicted for various conditions. The importance of accurately calculating the drag associated with a moving drop experiencing condensation has been discussed in the context of developing the results.     

Thermal shock in a nuclear containment wall due to loss-of-coolant accident

The safety analysis of reinforced concrete containments for nuclear reactors requires evaluation of thermal effects due to the loss-of-coolant accident. It is assumed that the inner surface of the containment is suddenly heated by the coolant getting out of the primary circuit. The wall is assumed to behave as a beam-column. Hoop forces and moments created by shell action are ignored. The plane wall section of the containment, normal to the reinforcing rods, is studied for evaluation of the stress increment due to the thermal shock. It is assumed that the section remains plane during the mechanical and thermal loading. The elastic-plastic model of material is chosen both for concrete and reinforcing steel. The section is considered cracked whereever the concrete is subjected to tensile stress. Thermal and mechanical material data are included in the program.The input-data for the computer program consist of the temperature of coolant inside the containment, the coefficient of heat transfer from the coolant to the wall, the axial force and the bending moment imposed by loading conditions before the thermal shock and the conditions of restraint for the considered wall section during the thermal shock. The computer program, based on the finite element method, consists of two sets of subroutines. The first set calculates the temperature increment after the prescribed time step. The second set calculates the elastic and plastic strain increments resulting from the increment of combined mechanical and thermal loading. The wall section of an actual containment is used, as an illustrative example, for the determination of thermal effect under various loading conditions. Results are presented in a diagram of axial force versus bending moment. A point on the diagram represents the load combination to which the wall section might be subjected. The thermal effect for various thermal loads, in form of the equivalent bending moment, it also plotted in the diagram.     

Deposition of RuO4 on various surfaces in a nuclear reactor containment

During a severe nuclear reactor accident with air ingress, ruthenium can be released from the nuclear fuel in the form of ruthenium tetroxide. Hence, it is important to investigate how the reactor containment is able to reduce the source term of ruthenium. The aim of this work was to investigate the deposition of gaseous ruthenium tetroxide on aluminium, copper and zinc, which all appear in relatively large amounts in reactor containment. The experiments show that ruthenium tetroxide is deposited on all the metal surfaces, especially on the copper and zinc surfaces. A large deposition of ruthenium tetroxide also appeared on the relatively inert glass surfaces in the experimental set-ups. The analyses of the different surfaces, with several analytical methods, showed that the form of deposited ruthenium was mainly ruthenium dioxide.     

Aging management of containment structures in nuclear power plants

Research is being conducted by Oak Ridge National Laboratory under US Nuclear Regulatory commission (USNRC) sponsorship to address aging management of nuclear power plant containment and other safety-related structures. Documentation is being prepared to provide the USNRC with potential structural safety issues and acceptance criteria for use in continued service evaluations of nuclear power plants. Accomplishments include development of a Structural Materials Information Center containing data and information on the time variation of 144 material properties under the influence of pertinent environmental stressors or aging factors, evaluation of models for potential concrete containment degradation factors, development of a procedure to identify critical structures and degradation factors important to aging management, evaluations of non-destructive evaluation techniques, assessments of European and North American repair practices for concrete, review of parameters affecting corrosion of metals embedded in concrete, and development of methodologies for making current condition assessments and service life predictions of new or existing reinforced concrete structures in nuclear power plants.     

Modelling of water sump evaporation in a CFD code for nuclear containment studies

During the course of a hypothetical severe accident in a pressurized water reactor (PWR), water can be collected in the sump containment through steam condensation on walls and spray systems activation. This water is generally under evaporation conditions. The objective of this paper is twofold: to present a sump model developed using external user-defined functions for the TONUS-CFD code and to perform a first detailed comparison of the model results with experimental data. The sump model proposed here is based on energy and mass balance and leads to a good agreement between the numerical and the experimental results. Such a model can be rather easily added to any CFD code for which boundary conditions, such as injection temperature and mass flow-rate, can be modified by external user-defined functions, depending on the atmosphere conditions.     

An experimental investigation of a passive cooling unit for nuclear plant containment

A set of condensation experiments in the presence of noncondensables (e.g. air, helium) was conducted to evaluate the heat removal capacity of a passive cooling unit in a post-accident containment. Condensation heat transfer coefficients on a vertically mounted smooth tube have been obtained for total pressure ranging from 2.48×10⁵ Pa(abs) to 4.55×10⁵ Pa(abs) and air mass fraction ranging from 0.30 to 0.65. An empirical correlation for heat transfer coefficient (h), has been developed in terms of a parameter group made up of steam mole fraction (Xs), total pressure (P_t), temperature difference between bulk gas and wall surface (dT). This correlation covers all data points within 20%. All data points are also in good agreement with the prediction of the diffusion layer model (DLM) with suction and are approximately 2.2 times the Uchida heat transfer correlation. Experiments with an axial shroud around the test tube to model the restriction on radial flow experienced within a tube bundle demonstrated a reduction of the heat transfer coefficient by a factor of about 0.6. The effect of helium (simulating hydrogen) on the heat transfer coefficient was investigated for helium mole fraction in noncondensable gases (X_He/X_nc) at 15, 30 and 60%. It was found that the condensation heat transfer coefficients are generally lower when introducing helium into noncondensable gas. The difference is within 20% of air-only cases when X_He/X_nc is less than 30% and total pressure is less than 4.55×10⁵ Pa(abs). A gas stratification phenomenon was clearly observed for helium mole fraction in excess of 60%.     

Failure pressure evaluation of the containment building of a large dry nuclear power plant

The evaluation of the failure pressure of the containment building of a large dry PWR-W three loops nuclear power plant, based on computer numerical simulation, is described in this paper. The proposed method considers fully three-dimensional finite element models in order to take into account the effect of the most significant structural characteristics (presence of three buttresses, penetrations, additional reinforcement around the penetrations, etc.), the lack of symmetry of the forces generated by the prestressing system, as well as the nonlinear behaviour of the materials and the sensitivity of the results to uncertainties associated with several parameters. The computational model is completely described, including the constitutive equations for the concrete, the reinforcing steel and prestressing tendons, the spatial discretization—isoparametric elements including the reinforcement are used. The structural models and the analyses performed for their calibration are also described. The influence on the failure pressure of incorporating the foundation slab in the structural model, and the influence of the thermal effects, are discussed. One of the conclusions of the numerical study is that the failure process can be appropriately simulated by means of a structural model which does not include either the foundation slab or the thermal effects. Finally, results of a probabilistic simulation of the failure pressure are given.     

Thermohydrodynamic calculation of the subdome part of the containment envelope of a nuclear power plant

Main Scientific Center of the Russian Federation — Physics and Power Engineering Institute. Translated from Atomnaya énergiya, Vol. 78, No. 2, pp. 172–176, March, 1995.     

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.     

Differential determination of leaks in the containment shell of a nuclear power plant by the gas-indicator method

Scientific-Research Institute of Hygiene and Preventive Pathology, Ministry of Health of the Russian Federation. Kola Nuclear Power Plant. Translated from Atomnaya énergiya, Vol. 77, No. 1, pp. 25–29, July, 1994.     

Forced vibration tests and simulation analyses of a nuclear reactor building

Forced vibration tests were carried out at the Hamaoka (BWR) Unit 4 R/B (reactor building) in Japan in April and May of 1992. Fundamental dynamic characteristics of the R/B were obtained, including its interaction with the adjacent T/B (turbine building) and the soil–structure interaction. Results for the preceding R/Bs are compared, and probable causes for fluctuations in the resonance curve around the 1st peak are discussed. Furthermore, simulation analyses of the fundamental dynamic characteristics of the soil–structure system were conducted, using a basic lumped-mass soil–structure model (lattice model), and strong correlation with the measured data was obtained. Other detailed simulation models were employed to investigate the effects of simultaneously induced vertical response and response of the adjacent turbine building on the lateral response of the reactor building.     

Direct containment heating integral effects tests in geometries of European nuclear power plants

The DISCO test facility at Forschungszentrum Karlsruhe (FZK) has been used to perform experiments to investigate direct containment heating (DCH) effects during a severe accident in European nuclear power plants, comprising the EPR, the French 1300 MWe plant P’4, the VVER-1000 and the German Konvoi plant. A high-temperature iron–alumina melt is ejected by steam into scaled models of the respective reactor cavities and the containment vessel. Both heat transfer from dispersed melt and combustion of hydrogen lead to containment pressurization. The main experimental findings are presented and critical parameters are identified.The consequences of DCH are limited in reactors with no direct pathway between the cavity and the containment dome (closed pit). The situation is more severe for reactors which do have a direct pathway between the cavity and the containment (open pit). The experiments showed that substantial fractions of corium may be dispersed into the containment in such cases, if the pressure in the reactor coolant system is elevated at the time of RPV failure. Primary system pressures of 1 or 2 MPa are sufficient to lead to full scale DCH effects. Combustion of the hydrogen produced by oxidation as well as the hydrogen initially present appears to be the crucial phenomenon for containment pressurization.