Pipe Whip Research Articles

Pipe Whip: In-Plane Whipping of Bent Cantilever Pipes

The dynamic elastic-plastic behavior of a bent cantilever pipe subjected to an in-plane force pulse at its tip is described. A theoretical model based on a large deflection formulation of dynamic beam theory is described. This takes into account the plastic hardening-softening behavior which is characteristic of a pipe when it is subjected to large changes in curvature. This beam model was first formulated and applied by Reid et al. (1995b, 1996), who demonstrated that it was able to describe quite accurately the characteristics of freely whipping, straight cantilever pipes. The present paper extends this model to enable it to be applied to bent cantilever pipes and covers cases in which the bend angle is opened or closed. Previous attempts (Wang, 1991) to analyze these problems using a rigid, perfectly plastic model were not completely successful due to the inability to identify admissible modes of deformation for all circumstances. A systematic program of pipe whip tests has been carried out in UMIST on right-angled bent pipes. To illustrate the validity and use of the theoretical model, two typical cases are considered and the results compared with the experimental data extracted from high-speed films of the tests. Excellent agreement between the two is demonstrated.

An elastic–plastic hardening–softening cantilever beam subjected to a force pulse at its tip: a model for pipe whip

A theoretical model is proposed to simulate the large deflection dynamic behaviour of an elastic–plastic, hardening–softening cantilever beam with an attached end mass subjected to a suddenly applied force pulse at its free end. The model is a development of a previous one by the present authors which was based on a small deflection formulation. Numerical examples are given to illustrate the effects of the softening parameter, α , the ratio of the end mass to the mass of the beam and the intensity of the force pulse on the dynamic reponse of a beam. The changes in shape of the beams, the growth of the softening region and the possible onset of local collapse are examined. The model, though applicable generally to beams with elastic–plastic hardening–softening characteristics, was developed primarily to describe the phenomenon of pipe whip, the large deflection behaviour of a high–pressure piping system following a sudden rupture of the pipe. During the motion and deformation of a whipping pipe, softening can occur in the local bending characteristic and this in turn can lead to severe localization of the deformation, i.e. the formation of a ‘kink’. Following initial elastic behaviour, the local bending behaviour of the pipe involves sequential hardening and softening phases as the pipe deforms plastically. This results from the interaction between the material properties of the pipe and the ovalization of its cross–sections as it undergoes large plastic deformations. It has been demonstrated recently that the model can accurately predict the transient deformation of the centre lines of freely whipping pipes (Reid et al . 1996). The practical issues associated with applying the theory to tubular beams (pipes) and the mesh sensitivity of the numerical solution of the governing equations are discussed herein. However, the main aim of the paper is to add to the range of beam models available for the solution of dynamic structural plasticity problems.

Crack-opening-area analyses for circumferential through-wall cracks in pipes—Part I: analytical models

Leak-before-break (LBB) analyses for circumferentially cracked pipes are currently being conducted in the nuclear industry to justify elimination of pipe whip restraints and jet impingement shields which are present because of the expected dynamic effects from pipe rupture. The application of the LBB methodology requires calculation of leak rates. The leak rates depend on the crack-opening area of the through-wall crack in the pipe. In addition to LBB analyses which assume a hypothetical flaw size, there is also interest in the integrity of actual leaking cracks corresponding to current leakage detection requirements in NRC Regulatory Guide 1.45, or for assessing temporary repair of Class 2 and 3 pipes that have leaks, as are being evaluated in ASME Section XI. The objectives of this study were to review, evaluate, and refine current predictive models for performing crack-opening-area analyses of circumferentially cracked pipes. A three-phase effort was undertaken to accomplish this goal. It is described here in a series of three papers generated from this study. In this first paper (Part I — Analytical models), a comprehensive review is performed to determine the current state-of-the-art in predicting crack-opening displacements for circumferentially cracked pipes under pure bending, pure tension, and combined bending and tension loads. Henceforth, new and improved analytical models and some preliminary results are presented for cases where current methods are inadequate or there are no available methods. Also, based on this review, a number of appropriate predictive models are identified for a systematic evaluation of their accuracy. The results of their evaluations will be presented and examined in the forthcoming companion papers (Part II — Model validations [1] and Part III — Off-center cracks, restraint of bending, thickness transition, and weld residual stresses) [2].

Demonstration of piping integrity with SMA technology

The safe function of a new pipe whip restraint device has been demonstrated in a full scale test. The restraint is based on using a shape memory alloy to protect a pipe and its environment in the event of a double-ended-guillotine-break. The evaluation test has been performed at boiling water reactor (BWR) operating pressure and temperature using a pipe representing BWR primary piping.

Dynamic elastic-plastic behaviour of whipping pipes: experiments and theoretical model

This paper is concerned with the problem of pipe whip, the dynamic response of a high pressure piping system subjected to an end force as the result of a pipe break which releases a jet of fluid from the broken section. Both experimental and theoretical results are presented concerning the dynamic elastic-plastic behaviour of cantilever pipes subjected to a transverse force pulse at the free end. Comparisons between experimental data and theoretical predictions are made for mild-steel pipes with outer diameter-to-thickness ratios of 19.5, 28 and 32. It is demonstrated that, for these geometries, the whipping pipes display three characteristically different responses, viz. elastic, plastic hardening behaviour for thick pipes, elastic, plastic hardening-softening behaviour for moderately thick pipes and elastic, plastic hardening-softening-collapse behaviour for thinner pipes. The experimental data taken from a series of high-speed films are compared with the predictions of the instantaneous shapes of the whipping pipes derived from both a rigid, perfectly-plastic, large deflection, dynamic beam model and a more comprehensive model which incorporates the effects of elasticity and plastic hardening and softening, the details of which are presented in the paper.

Supercomputer application to structural dynamic analysis of PWR piping system

A suite of computer programs has been developed to analyse the structural dynamic response of the coolant circuit of the PWR Nuclear Steam Supply System in the event of an extremely hypothetical Loss of Coolant Accident or LOCA in short. This paper firstly introduces the computational procedures and steps of the programs to analyse the structural effects of this event. These programs calculate the thermo hydraulic response of the two phase fluid and the propagation of the depressurising wave through the complex geometry of the pipe system and equipment internals. From these time dependent thermal hydraulic quantities, the forces arising from the depressurising wave are calculated and translated into time history forces and moments. These forces act on the structures and are input to a structural lumped mass model and analysed by a dynamic piping analysis code. Resulting from this analysis are the time dependent impact forces at pipe whip restraints and system internals and supports upon which the integrity of the system must be assessed. This paper also discusses the modelling of the nonlinear supports and restraints, and the sensitivity analysis to find a computationally acceptable and sufficiently precise model for the design qualification of these structures. The nonlinear modal superposition technique used is of recent interest as being the computationally efficient and is gradually being used in conventional plant piping analysis. However, this method for the structural dynamic transient analysis of a large number of degrees of freedom structural model with nonlinearities is still computationally intensive.

Results of reliability test program on light water reactor piping

The Japan Atomic Energy Research Institute has conducted a piping reliability test program to demonstrate the safety and reliability of light water reactor primary piping. In this program, pipe fatigue test, leak-before-break (LBB) verification test and pipe rupture test were carried out to examine the integrity of piping, to verify the LBB and to demonstrate the effectiveness of protective measures against jet impingement and pipe whip loads under a pipe rupture event. In the pipe fatigue test, a procedure to predict the fatigue crack growth was developed, and the integrity of piping during the plant service life was evaluated. In the LBB verification test, the pipe fracture test and the leak rate test were performed to verify the LBB in the primary piping. In the pipe rupture test, the influence of jet impingement on the target disk and the deformation behavior of whipping pipe and restraint were investigated. Using the test results, the jet impingement behavior and the effectiveness of pipe whip restraint were demonstrated.

Behaviour of nonlinear supports on a PWR coolant system during a postulated LOCA: Part 1: Effect of modelling methods

A 4-loop Pressurised Water Reactor (PWR) primary coolant system has been analysed for the postulated Loss of Coolant Accident (LOCA) event in order to derive peak dynamic loads for qualifying the design of equipment supports and pipe whip restraints. Pipe whip restraints as well as pipe and equipment supports are nonlinear by nature because of the presence of gaps and the different directional stiffnesses arising from snubber, steelwork and geometric and material interaction at the concrete to steel embedment. The different structural idealisations for the supports and restraints have an influence on the dynamic response of the structure. In the first of the two part paper a range of idealisation models for the Steam Generator and Reactor Coolant Pump vertical columns ranging from elastic stiffnesses to bilinear stiffnesses with or without preload were examined. Due to both structural and loading complexity, the behaviour of these supports were analysed by the Nonlinear Modal Superposition Method [1] and [2]. Analyses with the different models that are within the capabilities of the WESTDYN [3] piping analysis code enabled variations in the peak dynamic loads at the supports, restraints and equipment nozzles and other parameters to be determined and the design acceptability of the hardware established.

軽水炉１次冷却系配管信頼性実証試験の成果概要

Upon request by the Science and Technology Agency of Japanese Government, the Japan Atomic Energy Research Institute has conducted Piping Reliability Test Program to demonstrate the safety and reliability of light water reactor primary pipings. In this report, the results of the program are summarized. In the test program, pipe fatigue tests, Leak-Before-Break (LBB) verification tests and pipe rupture tests were carried out to examine the integrity of pipings, to verify the LBB concept and to demonstrate the effectiveness of the protective measures against jet impingement and pipe whip under pipe rupture event, respectively. In the pipe fatigue tests, a procedure to predict the fatigue crack growth was developed and the integrity of piping during plant service life was demonstrated. In the LBB verification tests, pipe fracture tests and leak rate tests were performed using cracked pipes. Based on the test results, LBB in the primary pipings was demonstrated. In the pipe rupture tests, the influence of jet impingement on the target plate and the interaction between whipping pipe and restraint were investigated. Using the test results, the effect of jet impingement and the effectiveness of pipe whip restraints were demonstrated.

Combined beam elements for large dynamic motion of whipping pipes with fluid-structure interaction

The paper gives comprehensive details of how a finite element computer code was developed to analyse the dynamic plastic collapse behaviour of a pipe undergoing large rotation with large strain during a pipe whip motion involving fluid-induced forces. A combined beam-type finite element model is developed which takes account of the elastic behaviour of the pipe structure and the localised plastic collapse of the section. The combined element is comprised of an elastic beam with non-linear inelastic (rotational) springs on either one or both of its ends. The rotational springs not only account for plasticity in the flexure behaviour of the pipe but also model the non-linear effect of the local plastic collapse of the pipe section due to large rotation about a plastic hinge. A numerical procedure uses the current deformed shape of the pipe to obtain the fluid reactions along the length of the pipe and estimates any reduction in the blowdown force due to flow area restrictin at the collapsed section. To validate the combined beam element for its application to the pipe whip problem with fluid structure interaction, details of the experimental tests and comparison with the finite element analysis is given.

Application of leak-before-break to primary loop piping to eliminate pipe whip restraints in a Spanish nuclear power plant

The Spanish plant described in this study is a 982 MWe PWR plant with a three-loop primary circuit of piping made from centrifugally-cast stainless steel SA351 CF8A. The licensee requested an exemption to GDC-4, from CSN, so as to avoid the postulation of guillotine rupture of the primary loop piping. The request was based on the generic work performed for a US PWR plant group to have such exemption to GDC-4. As the piping material in the Spanish plant is different from that in the plants included in the generic work, CSN performed a review of the applicability of the generic results to the Spanish plant. Also, aspects such as fatigue evaluation, net section collapse, crack growth and leak detection, specifically analyzed for the Spanish plant, were reviewed. CSN found that fracture toughness test results from generic work are applicable to the Spanish plant; sufficient margin exists against unstable crack extension, and adequate leak detection capability exists with the leakage detection systems available in the plant. Exemption to GDC-4 was approved and CSN authorized the licensee to remove protection devices against dynamic loads from guillotine breaks in the primary coolant loops.

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

Abstract 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.

Pipe whip: A summary of the damage observed in BNL pipe-on-pipe impact tests

This paper describes examples of the damage resulting from the impact of a whipping pipe on a nearby pressurised pipe. The work is a by-product of a study of the motion of a whipping pipe. The tests were conducted with small-diameter pipes mounted in rigid supports and hence the results are not directly applicable to large-scale plant applications where flexible support mountings are employed. The results illustrate the influence of whipping pipe energy, impact position and support type on the damage sustained by the target pipe.

Integrity of feedwater and main steam piping in KWU light water reactor plants

New standard catalogs for piping, supports, and valves have been introduced by Kraftwerk Union (KWU) for the first time in its Convoy series of PWR plants. These catalogs, underlying regulatory codes, and newly developed KWU specifications are described. Feedwater and main steam piping systems within the containment, including pipe supports and valves, are used to demonstrate the high quality level of piping technology achieved in the Federal Republic of Germany. Such quality standards ensure the integrity of single components as well as of the entire system, so that, under certain conditions, pipe whip restraints against postulated breaks have become unnecessary. The quality aspects apply basically for both PWR and BWR plants of KWU.

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].

Evaluation and Prediction of Critical Overhang Length Under Pipe Whip Accident

When the pipe length between break exit and restraint is long in the pipe whip accident, the pipe will undergo a plastic collapse as the moment increases. The length at which plastic collapse may occur is called the critical overhang length, (OH)cr. The experimental results of (OH)cr show good agreement with the prediction by a static simplified estimation method for (OH)cr although the pipe whipping is a dynamic phenomenon. The diagrams of (OH)cr are also described for a range of sizes of stainless steel pipe under the loss of coolant accident conditions of light water reactors.

Experience in the replacement of safety related piping in German boiling water reactors

In the German boiling water reactors (BWR) of the 69 series and their forerunner plant, high-strength low-alloy ferritic materials were used for a large number of pipings both inside and outside the pressure boundary (PB). The choice of this type of material led to comparatively thin-walled piping which, at that time, had been designed and manufactured in accordance with the codes and standards applying in the Federal Republic of Germany. Due to material properties resulting from production in a conventional manner, design features which did not sufficiently meet the requirements for nondestructive testability, and defects caused during processing, mainly in the area of circumferential welds, the ferritic pipings inside the PB were replaced in the course of a plant upgrading by new piping designed and manufactured according to the basis safety concept. The improvements and experience gained during backfitting of five German BWR plants are part of the German safety strategy and can be summarized as follows: 1. (1) Exclusion of large fractures on the basis of an optimized quality level for the piping. 2. (2) Elimination of need for the pipe whip restraints which existed in the former piping. 3. (3) Limited reduction of the former scope of inservice inspections, mainly as a consequence of improved weld quality and optimized weld performance. 4. (4) Reduction of personnel radiation exposure, e.g. by reduced number of welds and by manufacture of welds using automatic equipment, as well as by improved nondestructive testing. 5. (5) Availability values for backfitted BWR comparable to German PWR values. The pipings made of stabilized austenitic materials, which are arranged inside and outside the containment of the BWR plants, were not replaced since their quality level has been proved to be sufficient even on the basis of the present standards.

A leak-before-break strategy for CANDU primary piping systems

Recent advances in elastic-plastic fracture mechanics have made it possible to assess the stability of cracks in ductile piping systems. These technological developments have been used by Ontario Hydro as the nucleus of an approach for demonstrating that CANDU primary heat transport piping systems will not break catastrophically; at worst they would leak at a detectable rate. This leak-before-break approach has been taken on the Darlington nuclear generating station as a design stage alternative to the provision of pipe whip restraints on large diameter, primary heat transport system piping. Positive conclusions reached via this approach are considered sufficient to exclude the requirement to provide protective devices, such as pipe whip restraints. In arriving at the proposed leak-before-break approach a review of current and proposed leak-before-break licensing positions of other jurisdictions (particularly those in the United States and the Federal Republic of Germany) was carried out. The approach presented makes use of recent American developments in the area of elastic-plastic fracture mechanics. It also gives consideration to aspects which are unique to the pressurized heavy water (CANDU) reactors used by Ontario Hydro. The present paper describes the proposed leak-before-break approach and illustrates its use by applying it to the Darlington generating station primary heat transport system pump suction piping.

Pipe Whip—Bounding the Required Restraint Capacity

Energy balance methods commonly in use for the design of pipe whip restraints are based on the solution for the motion of a rigid-plastic pipe before impact against the restraint, with the assumption that after impact, the whipping portion of the pipe continues to rotate about the plastic hinge location determined for conditions before impact. Such energy balance methods are not necessarily conservative because: 1) the plastic hinge which forms in the pipe moves after impact on the restraint; and 2) elastic pipe deformations are not considered. Here, upper and lower bounds to the required restraint capacity are derived. In contrast to finite element methods, which are very time-consuming, the upper and lower bounds can be evaluated by simple hand calculations. Another advantage is that the required restraint capacity is calculated directly. No trial and error design is required. A numerical example shows that for a typical pipe and restraint, the upper and lower bounds differ by as little as 20 percent.

Piping response testing associated with pipe rupture

EPRI has sponsored an experimental program in the pipe whip impact and pipe rupture and depressurization areas. Sixteen pipe whip tests were performed with 3 in Schedule 80 (or 10) carbon steel pipes impacting on rigid target or concrete slab. The major testing parameters include distance, impact location, pipe rupture location, and concrete slab thickness and strength. The piping crushing at impact correlates with impact force and target response behavior. Conservatism was established by comparing measured and calculated impact forces. The pipe rupture and depressurization tests were carried out using 6 in stainless steel and carbon steel pipes under either PWR or BWR fluid conditions. These tests are of axial crack with initial machined-in surface flaw. It was found that pipe rupture would occur only if a long unstable through-wall crack was embedded in a sufficiently long unstable part-through crack (in the pipe wall). All other flaw configuration tested led to pipe leakage only. Reaction forces were measured which show conservatism of simplified method for fully ruptured condition. No good crack propagation information was obtained.