Analytical studies of four-inch pipe whip tests under BWR LOCA conditions

The purpose of pipe rupture studies in JAERI is to perform model tests on pipe whip, restraint behavior, jet impingement and jet thrust force, and to establish a computational method for analyzing these phenomena. This report presents the analytical results of 4-inch pipe whip tests under BWR LOCA conditions.Dynamic response analyses were performed using the general-purpose finite element program ADINA. The test pipe was modelled by straight beam elements and the four restraints were modelled by a single truss element. The analytical results were compared with the experimental results. Impact time and maximum total restraint force showed good agreement with experimental results. On the other hand, pipe strain and pipe deflection could not be predicted so well. The reason for this is that the sliding of the restraint during the pipe whip movement cannot be considered in the analyses.     

Characterising plastic collapse of pipe bend structures

Two recently proposed design by analysis criteria of plastic collapse based on plastic work concepts, the plastic work (PW) criterion and the plastic work curvature (PWC) criterion, are applied to a strain hardening pipe bend arrangement subject to combined pressure and in-plane moment loading. Calculated plastic pressure–moment interaction surfaces are compared with limit surfaces, large deformation analysis instability surfaces and plastic load surfaces given by the ASME Twice Elastic Slope criterion and the tangent intersection criterion. The results show that both large deformation theory and material strain hardening have a significant effect on the elastic–plastic response and calculated static strength of the component. The PW criterion is relatively simple to apply in practice and gives plastic load values similar to the tangent intersection criterion. The PWC criterion is more subjective to apply in practice but it allows the designer to follow the development of the gross plastic deformation mechanism in more detail. The PWC criterion indicates a more significant strain hardening strength enhancement effect than the other criteria considered, leading to a higher calculated plastic load.     

Application of plastic analysis to the pipe whip problem

The problem of design against pipe whip is briefly reviewed and some methods of calculation applicable to the problem are considered. Emphasis is given to two methods of analysis.The first makes use of the ‘FRUSTA’ programme; this method only considers the moment deflections so that it can only be regarded as a simplified approach leading to approximate results.As an alternative, a fully 3-D plastic element method is considered (the PAPS element), the basic hypotheses being briefly reviewed. Comparisons between the two approaches are provided. Finally, a model including restraint aspects is discussed which allows the consideration of V bars, plastic elements, dampers and friction type restraints.Typical examples are given and discussed.     

A comparison of plastic collapse and limit loads for single mitred pipe bends under in-plane bending

This paper presents a comparison of the plastic collapse loads from experimental in-plane bending tests on three 90° single un-reinforced mitred pipe bends, with the results from various 3D solid finite element models. The bending load applied reduced the bend angle and in turn, the resulting cross-sectional ovalisation led to a recognised weakening mechanism. In addition, at maximum load there was a reversal in stiffness, characteristic of buckling. This reversal in stiffness was accompanied by significant ovalisation and plasticity at the mitre intersection. Both the weakening mechanism and the post-buckling behaviour are only observable by testing or by including large displacement effects in the plastic finite element solution. A small displacement limit solution with an elastic-perfectly plastic material model overestimated the collapse load by more than 40% and could not reproduce the buckling behaviour.     

An elasto-plastic finite element for steel pipelines

An efficient finite element for the modeling of inelastic behaviour of three-dimensional pipe systems is presented. The formulation is based on a two-node pipe element with 12 degrees of freedom. The element consists of an elastic portion and two potentially plastic 3D hinges of zero-length lumped at both nodes. The behaviour of the plastic hinges is characterized using recently derived and experimentally validated plastic interaction relations for pipe sections. The normality condition of plasticity is applied to the analytically derived yield hyper-surface at the stress resultant level in order to approximately simulate material elasto-plastic behaviour. The element models shear deformation effects both in the elastic and plastic ranges. Thus, it is suitable for predicting pipe behaviour subjected to high shearing forces. The model captures the essential features of pipe behaviour using a remarkably small number of degrees of freedom and is particularly suited for the analysis of long pipeline systems. Solutions for simple problems are provided and compared to several other well-established elements in the ABAQUS library in order to assess the validity of the results and demonstrate their scope of applicability.     

Notch sensitivity of circular rings subjected to impact loading

‘Notch-sensitive regions’ have been observed during a series of experimental investigations into the dynamic plastic behaviour and failure of thin-walled metallic radially notched circular rings with arc-shaped supports subjected to concentrated impact loads. The experimental results show that the exterior notches at some regions have no effect on the deformation of the rings, but do have effect at the remaining regions. The notch-sensitive region is theoretically determined by using the equivalent structures technique; fairly good agreement has been reached between the simple theory and the experimental results. Both dimensional and theoretical analyses prove that whether a plastic hinge formed or not at the notched section does not depend on the mean radius of the ring and the input kinetic energy. It depends on the weak coefficient of the notched section and the angle of the support. Generally speaking, there are mainly three failure modes for a notched circular ring with arc-shaped support under impact loading: Mode I, large inelastic deformation when the notch is outside the sensitive region, in this case the ring deforms as a normal one; Mode II, large inelastic deformation only at some part of the ring and tearing occurred at the notched sections; mode III, large inelastic deformation and total rupture occurred at the notched sections. It is believed that the present study could assist the understanding of the dynamic behaviour and failure of other kinds of nonstraight components with macroscopic imperfections under impulsive loading.     

Effect of geometry change on the creep failure life of a thick-walled CrMoV pipe with a circumferential weldment

The influence of the geometry change on the failure life during creep of an internally pressurised thick-walled main steam pipe with a circumferential weldment was investigated, using finite element creep damage analyses. The pipe is subjected to a realistic internal pressure and a range of end (system) load levels, which are within the limits allowed by design codes. Actual material properties were used which were obtained from creep testing for a CrMoV pipe weldment at 640 °C. Damage calculations were conducted to investigate the deformation and strain behaviour and to obtain the failure life of the welded pipe. The plain pipe behaviour obtained previously is briefly reviewed. The results obtained from the welded pipe are compared with those obtained from the corresponding plain pipe. For the particular weldment properties used, the results obtained show that the life reduction, due to geometry change, for the welded pipe, is in the range 4.6–6.1%, which is much less significant than that for the corresponding plain pipe. The practical significance of these results is discussed.     

Prediction of force–deflection behaviour of pressurised pipes subjected to axially long radial indentation

The force–deflection behaviour of pressurised pipes, due to radial indentation loading, was investigated using Finite Element (FE) and analytical methods. Seven different materials, three different pipe geometries, seven different pressure levels and five different support conditions were used to investigate their effects on the force–deflection behaviour. The comparisons of the FE and analytical solutions indicate that an energy-based, analytical approach can accurately predict the force–deflection behaviour in both the elastic and elastic–plastic states.     

Generalization of response number for dynamic plastic response of shells subjected to impulsive loading

A dimensionless number, termed as response number in Zhao [Archive of Applied Mechanics 68 (1998) 524], has been suggested for the dynamic plastic response of beams and plates made up of rigidly perfect plastic materials subjected to dynamic loading. Many theoretical and experimental results can be reformulated into new concise forms with the response number. The concept of a new dimensionless number, response number, termed as Rn(n), is generalized in Zhao [Forschung im Ingenieurwesen 65 (1999) 107] to study the elastic, plastic, dynamic elastic as well as dynamic plastic buckling problems of columns, plates as well as shells. The response number Rn(n) is generalized to the dynamic behaviour of shells of various shapes in the present paper.     

Heat transfer performance in 3D internally finned heat pipe

An experimental study of heat transfer performance in 3D internally finned steel-water heat pipe was carried out in this project. All the main parameters that can significantly influence the heat transfer performance of heat pipe, such as working temperature, heat flux, inclination angle, working fluid fill ratio (defined by the evaporation volume), have been examined. Within the experimental conditions (working temperature 40 °C–95 °C, heat flux 5.0 kw/m²–40 kw/m², inclination angle 2–90°), the evaporation and condensation heat transfer coefficients in 3D internally finned heat pipe are found to be increased by 50–100% and 100–200%, respectively, as compared to the smooth gravity-assisted heat pipe under the same conditions. Therefore, it is concluded that the special structures of 3D-fins on the inner wall can significantly reduce the internal thermal resistance of heat pipe and then greatly enhance its heat transfer performance.     

Investigation into the performance of a micro gravitational heat pipe and a micro gravitational heat pipe with artery

The performance of a normal micro gravitational heat pipe was investigated using the analytical and numerical models previously developed. An innovative structure of the heat pipe, i.e. the micro gravitational heat pipe with artery, was then proposed in an attempt to overcome some of the drawbacks of the normal pipe. The thermal behaviour of the new type of heat pipe was simulated, and this was compared with that of a normal micro heat pipe. A performance estimation of both pipes was carried out based on the simulation results. Copyright © 2002 John Wiley & Sons, Ltd.     

Transition of nanofluids flow in an inclined heated pipe

A numerical investigation is carried out to investigate the transitional flow behaviour of nanofluids flow in an inclined pipe using both single and multi-phase models. Two different nanofluids are considered, and these are Al₂O₃–water and TiO₂–water nanofluids. Moreover, SST κ − ω transitional model is implemented to study the nanofluids flow in inclined pipe. Gravitational force is also adopted by considering Boussinesq approximation in the momentum equation. Results reveal that Buoyancy force play a significant role on the degeneration of heat transfer rate with the increase of Reynolds number for different inclination angles. It indicates that mixed convection has opposite effect on the inclined pipe than the forced convection on the horizontal pipe. Moreover, some deformation of the flow and temperature fields near the upstream region is observed with the increase of inclination angle due to Buoyancy force.     

核电站高中能管道断管影响探讨

在设计核电站时,须对安全壳内外的高能与中能管道进行发生假想性断管事件及其后续效应的设计分析。这些管道一旦发生破裂,泄漏的高能量流体将对管道施加很大的横向力,使管道产生高速运动,即管道甩动。这种高速运动的管道可能会对周围结构造成严重破坏,因而引起世界上各主要发展核电国家的重视,并开展了大量的研究工作。详细叙述常规岛侧高中能管道断管位置的判定准则、假想破口的类型、断管的后续影响及其防护等。还进一步介绍有关管道断裂甩动问题的各种计算方法,如力矩平衡法、能量平衡法、有限元法等。     

NONLINEAR DYNAMIC BEHAVIOR OF A PIEZOTHERMOELASTIC LAMINATE CONSIDERING THE EFFECT OF TRANSVERSE SHEAR

Nonlinear dynamic behavior of a piezothermoelastic laminate subjected to mechanical, thermal, and electrical loads is analyzed. Nonlinear deformation of the laminate is analyzed based on the von Kármán strains and the first-order shear deformation theory using the Galerkin method. The buckling temperature, the large static deflection, and the natural frequencies of infinitesimal or finite oscillation are discussed. The effect of transverse shear on nonlinear behavior and the methods to raise the buckling temperature, and linearize thermal deflection and the natural frequencies, by applying the electrical voltage to piezoelectric actuators, are investigated.     

Parametric survey of upper and lower bound limit in-plane bending moments for single mitred pipe bends of various geometries

The problem of limit analysis for a cylinder–cylinder intersection forming a single mitred pipe bend subject to in-plane bending has been investigated. Lower bound analysis with new equations of force and moment equilibrium together with a higher number of parameters resulted in more stability as compared to a previous analysis of the same problem [PhD Thesis, The University of Manchester, 1991]. Concurrently, abaqus finite element plastic collapse moments were obtained as upper bounds to the problem. Two sets of results were compared, showing good agreement with each other. It could be finally concluded that the true limit moments are bounded in between.     

Limit moment of local wall thinning in pipe under bending

In engineering practice, pipe containing local wall thinning may be subjected to bending load. The existence of local wall thinning on pipe surface impairs the load-carrying capacity of pipe. In order to maintain the integrity of the pipe containing local wall thinning, it is very important to develop a method to evaluate such a pipe with local wall thinning under bending. In this paper, the limit moment of local wall thinning pipe under pure bending is computed employing 3D elastic–plastic finite element analysis. The results show that the limit moment of pipe is affected not only by the width of defect but also by the longitudinal length of defect. When the longitudinal length of defect overpasses some critical value, the results from net-section collapse criterion (NSC) are in very reasonable agreement with the results from finite element analysis. Therefore, the NSC formula can conservatively be used to assess the limit load-carrying capability of local wall thinning pipe under bending.     

The integrally hydro-forming process of pipe elbows

In this paper, a hydro-bulging technology for manufacturing pipe elbows is proposed to overcome difficulties in manufacturing large diameter elbows using traditional technology. The section profile variation of the toroidal shell during the forming process is discussed. It is demonstrated experimentally that manufacture of a pipe elbow using integrally hydro-bulging technology is feasible.     

Plastic collapse of pipe bends under combined internal pressure and in-plane bending

Plastic collapse of pipe bends with attached straight pipes under combined internal pressure and in-plane closing moment is investigated by elastic–plastic finite element analysis. Three load histories are investigated, proportional loading, sequential pressure–moment loading and sequential moment–pressure loading. Three categories of ductile failure load are defined: limit load, plastic load (with associated criteria of collapse) and instability loads. The results show that theoretical limit analysis is not conservative for all the load combinations considered. The calculated plastic load is dependent on the plastic collapse criteria used. The plastic instability load gives an objective measure of failure and accounts for the effects of large deformations. The proportional and pressure–moment load cases exhibit significant geometric strengthening, whereas the moment–pressure load case exhibits significant geometric weakening.     

Improved integrity assessment equations of pipe bends

Pipe bend or elbow is one of the important components in any piping system. Accurate integrity assessment of these pipe bends is very important for reliable operation of all types of plants including nuclear plants. While considerable research has been done in the last few decades to develop accurate integrity assessment procedures of straight pipe with or without cracks, similar efforts were missing for pipe bend or elbow. Reactor Safety Division, Bhabha Atomic Research Centre in collaboration with MPA, University of Stuttgart had embarked upon a comprehensive component integrity test program (CITP) in around 1998 to develop improved integrity assessment methods of piping components in general and elbow in particular. As a part of this program, detailed analytical, numerical and experimental investigations for so many years have generated large number of new equations for improved integrity assessment of elbows. Mainly three aspects of the integrity assessment procedure are focused – development of improved plastic collapse moment equations, proposing new elastic–plastic J-integral and crack opening displacement (COD) estimation schemes to simplify leak-before-break (LBB) analysis and presenting new eta and gamma expressions to evaluate J–R curve from test data. All these newly proposed equations have been validated with the findings of the test data, generated as a part of the CITP. A reasonably good to excellent matching between predictions of the newly proposed equations and test results have been observed in all the cases. The present paper enumerates these research findings in a consolidated yet brief manner.