Modelling techniques for pipe whip analysis

The dynamic model used to describe the pipe and the restraint to predict their behaviour during the accident transient is described. The pipe is simulated by means of a series of finite elements, having a complex elasto-plastic behaviour. Each element can be subdivided in to a number of subelements whose flexibilities are computed and internally condensed at the element level. The strain energy is the main parameter in describing the stiffness characteristics of each subelement; the material is assumed to behave elastically provided that the strain energy is less than a given amount; afterwards a plastic flow of the type σ = A^m is assumed (σ = stress, = strain). Elastic unloading is assumed. For each subelement the complete behaviour can be derived from its energy. Ovalization of the pipe is assumed when the maximum strain is larger than a given amount; a relationship = const. × thickness/diameter is used to determine the critical strain. The instability of the pipe is simulated by means of unloading followed by the formation of a hinge.Crushing of the pipe as a consequence of its impact on a hard surface can be considered and the consequent absorption of energy in the pipe is simulated by means of a fictitious restraint. The restraining action can be simulated by either a restraint or a damper. For the first, a bilinear characteristic after a no load phase is assumed, elastic unloading is provided. For the damper a restraining force proportional to the velocity is assumed. A step-by-step integration procedure is used, a plastic stepwise elastic approach is followed and the constant average acceleration scheme is used. At each step in which a change in the characteristics (from elastic to plastic or vice versa) takes place a check is made to make sure that no excessive difference between the theoretical and actual value of the moment results as a consequence of the integration procedure. The maximum value of this ratio is recorded. Typical examples are studied and are reported.     

Dynamic analysis of nonlinear pipe whip restraints

A pipe whip restraint utilizing the dissipative capacity of a plastically deforming element has been developed. The transient dynamic behavior of the pipe and the restraint is studied using a discrete mathematical model consisting of nonlinear spring, mass, and damper elements. The forcing function is a fluid dynamic transient resulting from a break in a main steam line which is part of a Westinghouse pressurized water reactor (PWR) nuclear plant. An extensive parametric study shows the relative influence of gap, restraint support rigidity, the elastic and plastic behavior of pipe, break opening time, and finally the change in restraint mass on the behavior of the pipe restraint system.     

On finite element analysis of pipe whip problems

The nonlinear dynamic finite element solution of pipe whip problems is presented. The finite element modelling used, the step-by-step incremental solution of the nonlinear equations of motion and design considerations are discussed. The influence of various physical parameters on the response of the pipe and the restraint, and the effects of using different finite element models are considered. Specific emphasis is directed to the verification of the accuracy of the solutions obtained using energy balance checks.     

Nonlinear dynamic analysis of high energy line pipe whip

This paper describes a nonlinear dynamic analysis of TVA high energy line pipe whip tests using the ABAQUS-EPGEN code. The analysis considers the effects of large deformation and strain rate on resisting moment and energy absorption capability. The numerical results of impact forces, impact velocities, pipe strains, and reaction forces at pipe supports are compared to the TVA test data. The calculated pipe whip impact time and forces are also compared with those predicted using current industry practice.The calculated pipe support reaction forces are found to be in good agreement with the TVA test data except for some peak values at the very beginning of the pipe break. These peaks are believed to be due to stress wave propagation which cannot be addressed by the ABAQUS code. Both elbow crushing and strain rate have been approximately simulated. The effects are found to be important for pipe whip impact evaluation.     

Evaluation of pipe whip impacts on neighboring piping and walls of the Ignalina Nuclear Power Plant

Stress corrosion cracks have been discovered in Group Distribution Headers (GDH) at the Ignalina and Chernobyl Nuclear Power Plants. This increases the probability that a guillotine pipe break can occur that creates a whipping pipe (GDH) with the potential to damage surrounding structures—i.e. adjacent GDH and its attached piping or adjacent reinforced concrete compartment wall. The GDH is the most important component for reactor safety in case of an accident. Emergency Core Cooling System (ECCS) piping is connected to the GDH piping such that, during an accident, coolant passes from the ECSS into the GDH.Presented in this paper is the transient analysis of a Group Distribution Header following a guillotine break at the blind end of the header. Using a very conservative force loading function, the transient response of a whipping RBMK-1500 GDH along with neighboring concrete walls and pipelines is obtained using finite element methodology.The results of the study, assuming that the impacted GDH does not suffer stress corrosion cracking, indicate that the structural integrity of the compartment should be maintained and failure should not propagate from GDH to GDH.     

Large rotation, large strain analysis of pipe whip with flow choking

Numerical techniques employed to analyse pipe whip movement involving large rotations and large strains that take into account the reduction in blowdown force due to flow choking in the whipping pipe are briefly described. The numerical instability (flutter) encountered in using beam type finite elements proposed earlier by Hibbitt [4] are discussed. It is shown that in dynamic analysis the use of non-linear in-elastic elements give more realistic and stable solution as compared to the use of non-linear elastic elements suggested by Hibbitt [4].     

Moment-rotation relationship considering flattening of pipe due to pipe whip loading

It is important to take flattening of pipe into consideration in order to obtain pipe deformation due to pipe whip loading. An experimental relationship between the flattening of pipe and the pipe surface strain was used to derive the moment-rotation relationship of whipping pipe. The derived moment-rotation relationship was used to calculate the pipe strain in the pipe whip tests using a simplified energy balance method. A comparatively good agreement was obtained between the analytical and experimental results.     

Experimental and analytical studies of pipe whip tests under PWR LOCA conditions

A series of pipe rupture tests has been performed at the Japan Atomic Energy Research Institute (JAERI) to demonstrate the safety of primary coolant circuits in the event of pipe rupture in nuclear power plants. Pipe whip tests and jet discharge tests have been conducted under boiling water reactor (BWR) and pressurized water reactor (PWR) loss-of-coolant accident (LOCA) conditions. The present paper describes the experimental and analytical results of the pipe whip tests performed under PWR LOCA conditions using 4, 6 and 8-inch test pipes. The tests were carried out at an initial pressure and temperature of 15.7 MPa and 325°C, respectively. Moreover, a dynamic analysis of pipe whip tests was carried out using the general purpose finite element program ADINA.     

Experimental studies of 4-inch pipe whip test under BWR loca conditions

Pipe whip tests or jet discharge tests have been performed at the Japan Atomic Energy Research Institute, which simulate the instantaneous circumferential guillotine break of primary coolant piping in nuclear power plants. The present paper describes the results of the pipe whip tests using test pipes of 4 inch diameter, under the BWR LOCA conditions, which were performed from 1979 to 1981. The tests were carried out at an initial pressure of about 6.8 MPa and an initial temperature of about 285°C.The test pipe was 114.3 mm (4 in) in diameter, 8.6 mm in thickness and 4500 mm in length. The four pipe whip restraints used in the tests were the U-bar type of 8 mm in diameter and fabricated from Type 304 stainless steel. The experimental parameters were the clearance (30, 50 and 100 mm) and the overhang length (250, 400, 550 and 1000 mm).The main purpose of these tests is to investigate the effects of the clearance and the overhang length on the pipe whip behavior. It has been clarified from the test results that a smaller clearance and a shorter overhang length causes the deformation of the pipe and restraints to be minimized, and the test pipe collapses near the setting point of the restraints with the overhang length of 1000 mm.     

Pipe whip analysis for nuclear reactor applications

The main problems encountered in pipe whip analysis are discussed and the way the authors tried to solve them is described. Such problems are:

1. (a) Breakage locations: AEC criteria are presented and discussed.

2. (b) Force computations: The jet force intensities during the accident are computed following Moody's theory. A computer program makes such an analysis automatically. Forces consequent to a longitudinal and a circumferential break are calculated; The forces consequent to the longitudinal break are computed as a sum of the forces consequent to two circumferential breaks, a mitigation coefficient is assumed.

3. (c) Preliminary analysis: Provided that a ‘restraint solution’ is necessary (and the related criteria are briefly discussed), a tentative distribution of the restraints is computed by means of a simple energy balance between the work done by the jet forces and the work absorbed both in the pipe and the restraint. A computer program makes such an analysis automatically.

4. (d) Final solution appraisal: The tentative solution obtained in the initial step is re-evaluated by means of a detailed dynamic elastoplastic code (FRUSTA, which is described in the companion paper).

A typical example is given, the jet forces and a tentative restraint distribution are computed; the various models used in the final appraisal solution are described and the results are evaluated mainly in order to check the validity of the preliminary criterion.     

Simplified analysis of shrinkage in pipe to pipe butt welds

Generally some shrinkage is typical of butt welding of pipes. Shrinkage due to butt welding could be more pronounced and significant in thin wall stainless steel pipes because the thermal expansion coefficient is roughly one and half times that of carbon steel. An axisymmetric finite element evaluation of hoop shrinkage associated with circumferential butt welds in thin wall stainless steel pipes was performed. Actual shrinkage data for a larger (24 in. diameter, 0.375 in. wall thickness) pipe and a smaller (4 in. diameter, 0.237 in. wall thickness) pipe were utilized. The results indicate that very localized residual stresses in excess of yield strength produced during cooldown of metal in the weld and heat affected zones cause redistribution of the stresses. A simplified elastic–plastic analysis approach was developed with adjustments for section modulus and Poisson’s ratio, and the strains due to radial shrinkage were calculated for inside and outside surfaces of the pipe at the weld center line. From the strain point of view, the strain values in the circumferential direction were about 1.4% for the larger size pipe and 3.4% for the smaller size pipe. The strain values in the axial direction were 2.5% for the larger pipe and 5.9% for the smaller pipe. It is concluded that these levels of strains are not detrimental in nature. However, for the smaller pipe they are on the high side and it is recommended not to use the pipe for elevated temperature service. Residual stresses were also calculated for inside and outside surfaces of the pipe at weld center line using a simplified elastic–plastic approach and a bilinear stress–strain curve and compared with published data indicating a general agreement.     

Thin shell analysis of non-circular pipe bends

The equations of Novozhilov's linear thin shell theory are applied to the in-plane bending and pressurising of non-circular pipe bends with lateral symmetry. Neglecting end effects, results are given for deflection and stress factors with wall thicknesses up to 0.3 of the minimum radius of the non-circular shape. Methods for determining the decay constants of end effects and for simulating built-in end conditions are presented for both circular and non-circular pipe bends but no results are given.     

Reliability analysis of shutdown system

This paper presents the results of reliability analysis of Shutdown System (SDS) of Indian Prototype Fast Breeder Reactor. Reliability analysis carried out using Fault Tree Analysis predicts a value of 3.5 × 10⁻⁸/de for failure of shutdown function in case of global faults and 4.4 × 10⁻⁸/de for local faults. Based on 20 de/y, the frequency of shutdown function failure is 0.7 × 10⁻⁶/ry, which meets the reliability target, set by the Indian Atomic Energy Regulatory Board. The reliability is limited by Common Cause Failure (CCF) of actuation part of SDS and to a lesser extent CCF of electronic components. The failure frequency of individual systems is <1 × 10⁻³/ry, which also meets the safety criteria. Uncertainty analysis indicates a maximum error factor of 5 for the top event unavailability.     

Reliability analysis of dispersion nuclear fuel elements

Taking a dispersion fuel element as a special particle composite, the representative volume element is chosen to act as the research object. The fuel swelling is simulated through temperature increase. The large strain elastoplastic analysis is carried out for the mechanical behaviors using FEM. The results indicate that the fission swelling is simulated successfully; the thickness increments grow linearly with burnup; with increasing of burnup: (1) the first principal stresses at fuel particles change from tensile ones to compression ones, (2) the maximum Mises stresses at the particles transfer from the centers of fuel particles to the location close to the interfaces between the matrix and the particles, their values increase with burnup; the maximum Mises stresses at the matrix exist in the middle location between the two particles near the mid-plane along the length (or width) direction, and the maximum plastic strains are also at the above region.     

向上倾斜管内气-水两相流流型转变分析

对管径15 mm,管长6 m的有机玻璃管,在两种不同的向上倾斜角度(15°、30°)下,同向通过的气水两相流流型转变进行了分析,列出相应的转变准则关系式。结果显示,弹状流向泡状流转变界限的实验值与计算符合较好,间歇流向环状流的转变界限在低液体流速下符合较好。     

Comparisons between finite-element analysis predictions and pipe fracture experiments

This paper presents the results of ten finite-element analyses of cracked pipe subjected to bending loads compared to the corresponding experimental results produced from full-scale tests. As part of the presentation, detailed results from two international round-robin problems are presented. In all, nine through-wall cracked pipe and one surface cracked pipe is considered. The cracked pipe includes stainless, carbon, and welded pipe.     

Reliability analysis for stiff versus flexible piping

The overall objective of this research project is to develop a technical basis for flexible piping designs which will improve piping reliability and minimize the use of pipe supports, snubbers, and pipe whip restraints. The current study was conducted to establish the necessary groundwork based on the piping reliability analysis.A confirmatory piping reliability assessment indicated that removing rigid supports and snubbers tends to either improve or affect very little the piping reliability. We then investigated a couple of changes to be implemented in Regulatory Guide (RG) 1.61 and RG 1.122 aimed at more flexible piping design. We concluded that these changes substantially reduce calculated piping responses and allows piping redesigns with significant reduction in number of supports and snubbers without violating ASME code requirements. Furthermore, the more flexible piping redesigns are capable of exhibiting reliability levels equal to or higher than the original stiffer design.An investigation of the malfunction of pipe whip restraints confirmed that the malfunction introduced higher thermal stresses and tended to reduce the overall piping reliability. Finally, support and component reliabilities were evaluated based on available fragility data. Our result indicated that the support reliability usually exhibits a moderate decrease as the piping flexibility increases. Most on-line pumps and valves showed an insignificant reduction in reliability for a more flexible piping design.     

Reliability analysis of electronic modules with digital inputs

Electronic modules which are simultaneously triggered by several digital inputs are used, for example, in protection systems of nuclear power plants for actuating positioning elements. As these control chains are not constructed self-checking, like most other parts, they substantially influence the reliability of the whole system. It becomes apparent that failure modes and failure rates of such control chains can be determined best by means of the fault tree method. As the set-up of fault trees is rather time-consuming, this task is best fulfilled by a digital computer. The mode of operation of the program, the course and results of a reliability analysis, are explained by the examination of a control chain for the actuation of a positioning driver.     

中国实验快堆通风控制系统的可靠性分析

介绍中国实验快堆通风控制系统的功能和组成结构,并本文以故障模式影响分析(FMEA)和FTA为基础进行了可靠性分析,采用故障树进行定量分析和计算,得到该故障树的失效概率和最小割集,从而为中国实验快堆通风系统风险管理提供数据支持。