The leakbeforebreak(LBB) concept is difficult to apply to a structure with a thin tube that is immersed in a water environment. A heat exchanger in a nuclear power plant is such a structure. The present paper addresses an application of the LBB concept to a heat exchanger in a nuclear power plant. The minimum leaked coolant amount containing the radioactive material which can activate the radiation detector device installed in near the heat exchanger is assumed. The postulated initial flaw size that can not grow to the critical flaw size within the time period to activate the radiation detector is justified. In this case, the radiation detector can activate the warning signal caused by coolant leakage from initially postulated flaws of the heat exchanger. The nuclear plant can safely shutdown when this occurs. Since the postulated initial flaw size can not grow to the critical flaw size, the structural integrity of the heat exchanger is not impeded. Particularly the informational scenario presented in this paper discusses an actual nuclear plant.
Ignalina NPP contains RBMK-1500 type reactor. RBMK reactor is graphite-moderated with a water-cooled reactor core. The fuel cell assembly is located in the centre of the moderator column and consists of a pressure tube into which the fuel element assembly is inserted and through which the coolant flows. As a constructional material for manufacturing of pressure tubes zirconium alloys Zr + 2.5 % Nb are used. The hydrogen absorbed by zirconium alloy during corrosion process is one of the factors determining lifetime of pressure tube. When hydrogen concentration in pressure tube exceeds solubility limit initiation and development of delayed hydride cracking (DHC) can take place. The formation of hydrides under certain conditions can reduce resistance to brittle fracture. In this work the evaluation of the influence of hydrides on the fracture of pressure tube and application of leakbeforebreak (LBB) for these tubes with DHC was performed. The deterministic analysis of the pressure tube employing LBB concept was carried out using experimental data. Performed deterministic LBB analysis confirms that the pressure tube comply with LBB requirements.
A finiteelement model which utilizes the extended finiteelementmethod (XFEM) to model leaks through cracks is presented in this paper. Preliminary calculations using Ecrevisse in Code Aster indicates there is a case to include thermo-mechanical effects in Leak-before-Break analysis. This is because the leak rate can reduce due to crack closure effects. The preliminary work motivated the development of a specific finiteelement which incorporated a leak rate model and was coupled to the structure through a convection law and pressure boundary condition. Convergence studies were performed on the XFEM thermal model to validate its suitability and optimum convergence rates were seen. The mechanical model was validated by comparing the finiteelement approximated crack opening displacement with analytical solutions and the errors were less than 1% for a relative element size of more than 0.01. Thermo-mechanical simulations were then carried out using a simple 2D plate with a central crack. The leak rate was shown to decrease by about 30% when the fluid was 10 o C hotter than the
Abstract. Smoothed FiniteElementMethod (SFEM) was introduced by application of the stabilized conforming nodal integration in the conventional nite elementmethod. In this method, integration is performed on \smoothing domains" rather than elements. Smoothing domains are created based on cells, nodes, or edges for two-dimensional problems. Based on the smoothing domain creation method, dierent types of SFEM are developed that have dierent properties. It has been shown that these methods are insensitive to mesh distortion and are generally more computationally ecient than mesh- free and nite element methods for the same accuracy level. Because of their interesting features, they have been used to solve dierent problems. This paper investigates the performance of these methods in coupled hydro-mechanical (consolidation) analysis by solution to some problems using a developed SFEM/FEM code. Biot's consolidation theory is reviewed, and after introduction of the idea and formulation of SFEMs, discretized form of equations is given. Requirements for creation of stable coupled hydro-mechanical models are discussed and based on them, two methods for creation of stable SFEM models are introduced. To investigate the eectiveness of the methods, a number of examples are solved and results are compared with the nite element and analytical ones.
Structure of this paper can be summarized as follows. Section overviews some related methods brieﬂy. In Section we express the model problem as an inequality and Laplacian constrained variational optimization problem. In the same section, we present a theorem which shows the connection between the optimization problem and the second kind vari- ational inequality problems. We discretize the VI problems using a ﬁnite elementmethod. We complete the paper with a conclusion section where we discuss the method presented in this paper and point some possible future extensions.
The CANDU industry has claimed that leak detection systems installed at the CANDU plants are more sensitive compared to those at other types of nuclear plants as a result of the costs associated with upgrading of heavy water and the presence of tritium in the primary coolant. Economic considerations lead to the initiation of shutdowns due to unidentified leaks from the primary heat transport system circuit at rates of less than 360 kg/hr and station procedures are typically more conservative using rates of about 100 kg/hr or less Three different methods for leak detection are employed: (i) heat transport system inventory monitored via storage tank level, (ii) vapour recovery systems utilizing drier collection and powerhouse exhaust, and (iii) liquid detection systems using beetles (liquid collection trays) and the D 2 O recovery
The finiteelementmethod is a numerical solution technique. It’s used to solve complex problems. This method becomes popular over the last decade. The scientists and engineers have used the finiteelementmethod (FEM) for the modeling of the complex problem. This method having applicability in many areas of engineering, physical problem (stiffness, density and more) and physics such heat transfer (conduction, convection and radiation), fluid flow, electrical potential problem and many more. Finiteelement is a mathematical technique for obtaining approximate numerical solutions to the abstract equations of calculus that predicts the response of physical systems subjected to external influence.
The limitation of the two flux model is that only the propagation of diffuse intensities, but not of a collimated source can be described, because the loss of intensity of the collimated beam due to scattering will not completely be converted into backward flux, but be dispersed over all directions due to the scattering characteristics of the medium. In the four flux theory the flow of intensity is broken up into a forward and backward collimated flux and F^., and a forward and backward diffuse flux F+ and F.. All four fluxes decrease due to absorption, but scattering causes a permanent conversion from collimated to diffuse fluxes. We will not go deeper into the theory of multiple flux theory here. The main advantage of these models is their simplicity which allows to find analytical solutions in good agreement with experimental data, but they are limited to simple plane-parallel geometries. In the following we concentrate on the diffusion equation on which our finiteelement model for light transport is based. Although analytical solutions of the diffusion equation are also restricted to simple cases, numerical approaches allow the application to arbitrarily complex and inhomogeneous media.
The LBB concept was used for the Main Vessel (MV) and pipings of the SPX ( to ) and PHENIX plants. As far as the MV is concerned, the LBB approach has been applied to verify the absence of risk as regards the core supporting function and to help in the definition of the In-Service Inspection (ISI) program. Generally speaking, the low level of membrane primary stresses, which is favourable for the integrity of the vessel, makes the application of LBB more difficult due to small crack opening areas.
The test specimen is filled with water introducing a cover gas space in the upper portion of the straight vertical pipe attached with the Tee. By connecting the cover gas space to the constant nitrogen pressure tanks, the required internal pressure is sustained in the specimen, even under leaked condition in the course of test (Fig.4). The required bending moment is imposed on the specimen by applying cyclic vertical force at the end of the straight horizontal pipe welded to the Tee. Servo controlled hydraulic actuators with computerized control system is used for the application of cyclic loads.
If the piping system fails to satisfy either the Level 1 acceptance criteria or all of the elements of the Level 1 specific screening criteria, the applicant’s next logical step would be to try to demonstrate LBB using the Level 2 approach. As an illustrative example, when a Level 1 analysis was applied to an actual surge line (using data gleaned from an actual LBB submittal), it was found that the Level 1 margin on crack size was less than 2.0, i.e., the critical crack size was less than twice the postulated leakage crack sizes, . As such, this piping system failed to meet one of the acceptance criteria for a Level 1 application 1 . However, when this same piping system was analyzed using the Level 2 criteria, it was found that the resultant margin on crack size was approximately 3, which easily satisfies this element of the acceptance criteria.
The leak-before-break (LBB) analysis of pressurized piping and vessels, which is developed during the past three decades, is an important rule for assessing pressure vessels,especially nuclear equipment. LBB is an advanced technology for the safety and dependability of structures in nuclear reactors, as well as in the petrochemical industry. This paper introduced the concept of leak-before-break with its analytical process, and enumerating the some LBB analytical methods,then introduces the theories of Fuzzy reliability to evaluation the reliability of structures. LBB technology has a good prospect in development and application, which is of great importance to the modern industry.
Leak-before-break (LBB) has been widely accepted as a technical approach to eliminate pipe- whip restraints and jet-impingement shields in many nuclear power plants (NPPs). Concerns related to the application of this philosophical concept to nuclear reactors in United States were discussed by Wichman and Lee (1990). This alternative option is permitted by most regulatory bodies as long as it is ensured that all the 3 levels of LBB have actually been implemented in the plant. Level-1 is inherent in the design philosophy of ASME section III (2010) which is generally followed to design the primary coolant piping. In level-2 analysis, fatigue crack growth calculations are performed for a postulated surface crack that would be permitted by the acceptance criteria of ASME section XI (2010). The surface crack is usually postulated at locations at which the highest stresses coincident with poorest material properties occur for base materials, weldments and safe-ends. The objective of level-2 analysis is to demonstrate that a small flaw that might have gone undetected in the non-destructive examination would not become through thickness during the life time of the component. Finally, in level-3 LBB analysis it is necessary to demonstrate, at the design stage, that a postulated leakage size crack, in a piping system, would not become unstable even under extreme loading conditions (NUREG-1061, 1984).
In this paper, an efficient numerical model for solution of the two-dimensional unsteady dam- break problem is described. The model solves the shallow water equations through Characteristic-Based Split (CBS) finiteelementmethod. The formulation of the model is based upon the fractional time step technique primarily used in the finite difference method for the incompressible Navier-Stokes equations. In addition to well-known advantages of the finiteelement discretization in introducing complex geometries and making accurate results near the boundaries, the CBS utilizes interesting advantages. These include the ability of the method to simulate both compressible and incompressible flows using the same formulation. Improved stability of the CBS algorithm along with its capability to simulate both sub- and super-critical flows are other main advantages of the method. These useful advantages of the algorithm introduce the CBS as a unique procedure to solve fluid dynamics problems under various conditions. Since dam-break problem has principally a high non-linear nature, the model is verified firstly by modeling one-dimensional problems of dam-break and bore formation problems. Furthermore, application of the model to a two-dimensional hypothetical dam-break problem shows the robustness and efficiency of the procedure. Despite the high non-linearity nature of the solved problems, the computational results, compared with the analytical solutions and reported results of other numerical models, indicate the favorable performance of the used procedure in modeling the dam-break problems.
Abstract: Finiteelementmethod is a popular computer aided numerical method based on the discretisation of the domain, structure or continuum into number of elements and obtaining the solution. It converts a infinite number of degree problem to a finite number of degree problem using discretization. On the other hand, finite strip method is of semi-numerical and semi-analytical nature. The finite strip method is applicable to problems which may have complex geometry in their cross-section, but are simple along the length. the application of this method has been extended to thin and thick rectangular and annual sector plates, cylindrical shells, straight and curved box girders and folded plates etc. In this paper, the behaviour of plate subjected to different loading condition with various boundary conditions is studied.
The use of LeakBeforeBreak (LbB) arguments is well established in the nuclear industry. A 'detectable leakage' LbB procedure, similar to that of NUREG 1061, is commonly used. Such a procedure is included in the UK R6 defect assessment procedures and involves achieving an adequate margin between the evaluated critical crack length and the detectable leakage crack length. However, experience in applying LbB methods with the effects of creep included in the analysis is still limited. This paper contains results of calculations aimed at assessing how these influences impact upon the safety margins achieved in a low temperature application.
The authors proposed an elasto-plastic COD assessment method applicable to thin wall pipes with large diameter made of modified 9Cr-1Mo steel  based on the conventional GE/EPRI method . Parametric finiteelement analyses (FEA) were conducted to determine the coefficients using the finiteelement nonlinear structural analysis system “FINAS” . For the material which has a small work hardening coefficient, such as modified 9Cr-1Mo steel, COD produced before fully plastic condition is relatively large. Therefore, the local plastic COD should be taken into account explicitly in the assessment. The local plastic COD δ LP was calculated using the following
Further improvements are foreseen in order to calculate thoroughly the COA, at internal and external sides, and by considering inelastic deformations. Recent development of eXtended FiniteElement techniques shows quite interesting results as it allows accounting for complex geometries of cracks and structures.
It should be pointed out that the works mentioned above all gave one order accuracy in time increment Δt. That is to say, the first order characteristic method in time was analyzed. As for higher order characteristic method in time, Rui and Tabata 12 used the second order Runge-Kutta method to approximate the material derivative term for convection- diﬀusion problems. The scheme presented was of second order accuracy in time increment Δt, symmetric, and unconditionally stable. Optimal error estimates were proved in the framework of L 2 -theory. Numerical analysis of convection-diﬀusion-reaction problems with
(leading to mass conservation and flux continuity) and in particular the approach from  for a posteriori error estimates in mixed methods without flux continuity. We first build a flux reconstruction that is globally H(div, Ω)-conforming and locally conservative in each mesh element. In a first stage, a simple coarse balancing problem, with one unknown per interface and two unknowns (in two space dimensions) per each subdomain boundary lying in 𝜕Ω, is solved. Then we adopt the construction of [39, Section 3.5.2] and solve a local Neumann problem in a band around the interfaces in each subdomain by the mixed finiteelementmethod. Finally, two 𝐻 0 1 (Ω)-conforming potential reconstructions are built. One