Pipe Whip Research Articles

Energy absorption characteristics of novel bionic H-type whip restraints for nuclear power plants

To enhance the efficiency of energy absorption in H-type whip restraints for nuclear power plants, this study takes inspiration from the asymmetric twisted lines observed in the Nautilus shell, introducing the Nautilus Bionic Hierarchical Multi-Cell (NBHMC) structure. For different high-energy pipeline sizes and energy absorption quantities, the proposed structures are miniaturized and can be combined into H-type whip restraint by multiple tubes to meet the requirements. The NBHMC structures are investigated based on the validated finite element method, the results demonstrate that the energy absorption per unit mass of the new structure can reach up to 180% of that of the hollow tube, with the maximum enhancement in energy absorption efficiency being 47%. Through parameter analysis of the cross-sectional wall thickness, the highest energy absorption efficiency obtained is 99.62%, with a specific energy absorption of 31.29J/g. Furthermore, utilizing the TOPSIS method, all proposed parameter combinations are ranked, leading to the determination of the optimal parameter combination. Additionally, a theoretical model predicting the mean crushing force is introduced, exhibiting good agreement with numerical simulations. The results presented in this work provide innovative insights for the design of efficient pipe whip restraints.

Applications of the FEM to pipe whip analysis using coupled modelling technique

Pipelines in Nuclear Power Plants (NPPs) work under high pressure and temperature which may cause a guillotine rupture on the highly pressurized pipe during a sudden fracture due to a failure of any working component. Owing to the serious safety concerns resulting from such failures, it becomes important to understand the behaviour of these pipe structures under dynamic loading, particularly, the pipe whipping effect. Therefore, this research study deals with understanding the structural response of pipe whip with a computationally efficient Finite Element (FE) model.The complete three-dimensional (3D) FE model is modified and coupled with a one-dimensional (1D) FE model (coupled 1D/3D FE model) and solved under the exact transient conditions, and compared with the complete 3D FE model. The computational time of the complete 3D approach was reduced to about 10 times using the coupled 1D/3D model without compromising on the accuracy of the numerical results. Furthermore, the numerical results were found to be in close agreement with the referenced experimental data. This research provides justifiable results from the FE models where the dynamic behaviour of high-pressure pipes under transient conditions can be simulated by using the proposed coupled 1D/3D modelling approach.

Modeling of Pipe Whip Phenomenon Induced by Fast Transients Based on Fluid–Structure Interaction Method Using a Coupled 1D/3D Modeling Approach

The sudden increase in the operating pressure of nuclear power plants (NPPs) is due to the water hammer phenomenon, which tends to produce a whipping effect that causes serious damage to the pipes and their surroundings. The mechanical response of these pipelines under the influence of such fast fluid transients can be estimated using the fluid–structure interaction (FSI) method. The computational time and expense are predominantly dependent on the number of finite elements developed in the model. Hence, an effective modeling technique with limited and efficient nodes and elements is desired to obtain the closest possible results. A coupled 1D/3D finite element modeling approach using the FSI method is proposed to determine the influence of fast transients on the mechanical pipe whipping behavior of gas pipelines in NPPs. The geometric coupled modeling approach utilizes the presence of both the 3D solid elements and the 1D beam elements sharing a local conjunction. The computational model is modelled for a pipe-to-wall impact test scenario taken from the previously conducted French Commissariat a l’Energie Atomique (CEA) pipe whip experiments. The results of displacement, stresses, and impact velocity at the 3D section featuring the elbow are compared for the change in the 3D solid length varied at the juncture of the elbow. The computed results from the Ansys FSI coupling method using the Fluent and Transient Structural modules provides fair validation with the previously conducted experimental results and correlates with the CEA pipe whip tests on pipe-to-wall impact models. Thus, the 1D/3D coupled modeling approach, which minimizes the area of the solid region by constricting it to the impact area with appropriate contact modeling at the junctures, can be considered in the future for decreasing the computational time and the creation of finite elements.

In-plane pipe whip: Post-failure dynamic response

Pressurised pipes are ubiquitous in chemical, nuclear and power plants. A sudden failure and release of high-speed fluid cause large inelastic displacements characterised by a whipping-type motion, which can ultimately hinder the surrounding structural and functional systems. In this paper, a beam user element has been developed, implemented and applied to analyse the in-plane flexural dynamic response of pipe whip. The two-dimensional Euler–Bernoulli beam element is based on the corotational kinematic formulation and elastoplastic constitutive models that include metal plasticity and moment–curvature relationships obtained from numerical bending tests, which highlighted the existence of two new dimensionless groups that govern the flexural response of slender pipes and enable the creation of moment–curvature master curves for thick and thin pipes. The corotational beam element formulation is compared against an analytical rigid-perfectly plastic model, numerical simulations employing shell elements and available experimental results, showing very good accuracy in the prediction of the inelastic deformation response of pipe whip and its hazardous area of influence. Furthermore, parametric studies are performed to investigate the effect of load intensity, cross-sectional geometry and concentrated tip mass on the post-failure deformation modes, plastic hinge formation and extension of the hazard zone. The presented results represent valid tools to assess the safety of industrial piping systems undergoing failure, and to optimally design pipe whip restraints.

Finite Element Analysis and Test Study on Restraint of High-energy Pipe Whip in Conventional Island

The effects of high-energy pipe whipping after rupturing are very important in an AP1000 nuclear power plant’s conventional island and restraints of pipe whipping should be considered in the design. It is the first time in the country when reinforced concrete shear walls are used as restraint services. In this paper, the behaviors of walls and restraint services subjected to pipe whipping are analyzed through static and dynamic methods in the finite element software (ABAQUS), in which all kinds of nonlinearities are considered. In addition, a test study on the restraint of pipe whipping is conducted. The results show that the wall and the restraint service can prevent pipe whipping effectively under the design load, and anchor plates arranged around the wall opening can improve the local concrete compression performance of concrete to reduce the damage of concrete. Meanwhile, the study also provides the valuable reference for wall designing to prevent from pipe whipping.

THEORETICAL OF DYNAMIC LOADING AGAINST WATER-FILLED SIMPLY SUPPORTED PIPES

The primary aim of this study had been to investigate the effects of water-filled flow on the transient response of a simply supported pipe subjected to dynamically applied loading. The importance of this study is manifested in numerous applications, such as oil and gas transportations, where dynamic loading can be the result of an accident. The classical Bernoulli-Euler beam theory was adopted to describe the dynamic behavior of an elastic pipe and a new governing equation of a long pipe transporting gas or liquid was derived. This governing equation incorporated the effects of inertia, centrifugal, and Coriolis forces due to the flowing water. This equation can be normalized to demonstrate that only two non-dimensional parameters governed the static and the dynamic responses of the system incorporating a pipe and flowing water. The transient response of this system was investigated based on a standard perturbation approach. Moreover, it had been demonstrated that the previous dynamic models, which largely ignored the internal flow effects and interactions between the flow and the structure, normally produced a large error and are inapplicable to the analysis of many practical situations. One interesting effect identified was that at certain flow ratio, the system became dynamically unstable and any, even very small, external perturbation led to a growing unstable dynamic behavior. Such behavior, which is called pipe whip, is well-known to everyone who waters a garden using a flexible long hose.

Leak-Before-Break Under Beyond Design Basis Seismic Loading

The Atucha II nuclear power plant is a unique pressurized heavy water reactor (PHWR) being constructed in Argentina. The original plant design was by Kraftwerk Union (KWU) in the 1970's using the German methodology of break preclusion. The plant construction was halted for several decades, but a recent need for power was the driver for restarting the construction. The United States Nuclear Regulatory Commission (US NRC) developed leak-before-break (LBB) procedures in standard review plan (SRP) 3.6.3 Revision 1 for the purpose of eliminating the need to design for dynamic effects that allowed the elimination of pipe whip restraints and jet impingement shields. This SRP was originally written in 1987. The US NRC is currently developing a draft Regulatory Guide on what is called the transition break size (TBS). However, modeling crack pipe response in large complex primary piping systems under seismic loading is a difficult analysis challenge due to many factors. The initial published work (Wilkowski et al., “Robust LBB Analysis for Atucha II Nuclear Plant,” 2011 ASME PVP Conference, July 17–21, Baltimore, MD) on the seismic evaluations for the Atucha II plant showed that even with a seismic event with the amplitudes corresponding to the amplitudes for an event with a probability of 1 × 10−6 per year, that a double-ended guillotine break (DEGB) was pragmatically impossible due to the high leakage rates and total loss of make-up water inventory. The critical circumferential through-wall flaw size in that case was 94% of the circumference. This paper discusses further efforts to show how much higher the applied accelerations would have to be to cause a DEGB for an initial circumferential through-wall crack that was 33% around the circumference. This flaw length would also be easily detected by leakage and loss of make-up water inventory. These analyses showed that the applied seismic peak-ground accelerations had to exceed 25 g's for the case of this through-wall-crack to become a DEGB during a single seismic loading event. This is a factor of 80 times higher than the 1 × 10−6 seismic event accelerations, or 240 times higher than the safe shutdown earthquake (SSE) accelerations.

Out-of-Plane Pipe Whip for a Bent Cantilever Pipe: Comparison Between Experiment and FEM Models

The three-dimensional, dynamic, elastic-plastic response of a right-angle bent cantilever pipe, with an initially uniform, circular cross section, subjected to out-of-plane loading is examined using finite element beam and shell models in ABAQUS. The large-deflection behavior involves both bending and torsional elastoplastic deformations of the pipe, phenomena which have not been previously studied in the context of the dynamic problem of pipe whip. Initially, neglecting ovalization and local collapse (kinking), the bent pipe is modeled as a beam, using spatial beam elements in ABAQUS. This enables the basic three-dimensional kinematic behavior of the pipe to be analyzed. A similar, but potentially more accurate, analysis was then performed using shell elements. It is shown that there is no significant difference in the global dynamic plastic response. However the ovalization of the pipe cross section and formation and movement of the plastic zones (hinges) can be captured by using shell elements. This provides data which could form the basis for examining local failures in the pipe run. Previously unpublished experimental results, obtained in an earlier study by some of the present authors, are compared with the simulated results. Good agreement is observed and it is concluded that a nonlinear dynamic model using finite elements provides a rigorous approach for estimating the hazard zone (HZ) and, also, for treating the kinematics of a whipping pipe for this complex three-dimensional situation.

Structural modelling and testing of failed high energy pipe runs: 2D and 3D pipe whip

The sudden rupture of a high energy piping system is a safety-related issue and has been the subject of extensive study and discussed in several industrial reports (e.g. [2–4]). The dynamic plastic response of the deforming pipe segment under the blow-down force of the escaping liquid is termed pipe whip. Because of the potential damage that such an event could cause, various geometric and kinematic features of this phenomenon have been modelled from the point of view of dynamic structural plasticity. After a comprehensive summary of the behaviour of in-plane deformation of pipe runs [9,10] that deform in 2D in a plane, the more complicated case of 3D out-of-plane deformation is discussed. Both experimental studies and modelling using analytical and FE methods have been carried out and they show that, for a good estimate of the “hazard zone” when unconstrained pipe whip motion could occur, a large displacement analysis is essential. The classical, rigid plastic, small deflection analysis (e.g. see [2,8]), is valid for estimating the initial failure mechanisms, however it is insufficient for describing the details and consequences of large deflection behaviour.

Effect of flowing medium for a simply supported pipe subjected to impulse loading

The primary aim of this study is to investigate the effects of a flowing medium on the transient response of a simply supported pipe subjected to dynamically applied loading. The importance of this study is manifested in numerous applications such as oil and gas transportation where dynamic loading can be the result of an accident. The classical Bernoulli-Euler beam theory is adopted to describe the dynamic behaviour of an elastic pipe and a new governing equation of a long pipe transporting gas or liquid is derived. This governing equation incorporates the effects of inertia, centrifugal and Coriolis forces due to the flowing medium. This equation can be normalised to demonstrate that only two non-dimensional parameters govern the static and dynamic response of the system incorporating a pipe and flowing medium. The transient response of this system is investigated based on a standard perturbation approach. Further, a numerical method utilising the finite difference method is developed and applied to investigate the dynamic response of a simply supported pipe. It is demonstrated that the previous dynamic models which largely ignore the internal flow effects and interactions between the flow and structure normally produce a large error and are inapplicable to the analysis of many practical situations. One interesting effect identified in the numerical study is that at certain flow ratio the system becomes dynamically unstable and any, even very small, external perturbation leads to a growing unstable dynamic behaviour. Such behaviour, which is called pipe whip, is well known to everyone who waters a garden using a flexible long hose.

Analytical modelling of a pipe with flowing medium subjected to an impulse load

Pipes transporting gas or liquid can be subjected to impulse loading as a result of an accident. In many previous studies the effects of the flowing media on the transient response of pipes were largely ignored or considered to be negligible. This paper aims to shed light on the significance of these effects. First, we present a simplified mathematical model of a pipe filled with a flowing liquid or gas and subjected to dynamic loading. This model is based on the well-known Bernoulli–Euler beam theory, but also incorporates forces generated by the internal flow which follows the pipe lateral deflections and generates the inertia, centrifugal and Coriolis flow accelerations. Further, we develop asymptotic analytical and numerical methods for the analysis of the governing equation. Finally, as example, we investigate in detail the effect of the flow parameters on the dynamic response of a cantilever pipe subjected to impulse loading. Special attention is given to the pipe whip phenomenon, which causes growing unlimited displacements of the pipe regardless of how small the value of the applied loading is. The developed theoretical methods provide a framework for analysis of many other dynamic problems of pipes with flowing media subjected to arbitrary boundary and loading conditions.

Reproducing kernel collocation method applied to the non-linear dynamics of pipe whip in a plane

A windowed collocation method, based on a moving least squares reproducing kernel particle approximation of functions, is explored for spatial discretization of the strongly non-linear system of partial differential equations governing large, planar whipping motion of a cantilever pipe subjected to a follower force pulse (the blow-down force) normal to the deflected centreline at its tip. This problem was discussed by Reid et al. [An elastic–plastic hardening–softening cantilever beam subjected to a force pulse at its tip: a model for pipe whip. Proc R Soc London A1998;454:997–1029] where a space–time finite difference discretization was employed to solve the governing partial differential equation of motion. It was shown that, despite the deflected shape predictions being accurate, numerical solutions of these equations might exhibit problematic (possibly spurious) steep localized gradients. The resolution of this problem in the context of structural mechanics is novel and is the subject of this paper. In particular, it is demonstrated that it is possible to reduce significantly such spurious and localized numerical instabilities through a windowed collocation approach with a suitable choice of the window size. The collocation procedure presently adopted is based on the moving least squares reproducing kernel particle method. Material and structural non-linearity in the beam (pipe) model is incorporated via an elastic–plastic-hardening–softening moment–curvature relationship. The projected ordinary differential equations are then integrated in time through a fifth order, explicit Runge–Kutta method with adaptive step sizes. The whipping motion of a pipe is often associated with the formation of one or more so-called moving plastic ‘hinges’ (regions). Depending on the magnitude and duration of the follower load pulse, plastic hinges may form at intermediate positions along the pipe. In such cases numerical solutions, especially those for curvatures and their derivatives, obtained through central difference or classical finite element methods may exhibit considerable fluctuations in space and time and may even ‘blow up’ following the formation of a kink at the location of the plastic hinge. However, it is shown that the presently adopted windowed collocation strategy has a far superior numerical performance, arresting these fluctuations to a great extent. Indeed, as demonstrated in this paper, there is a band of window sizes for which such fluctuations may nearly vanish.

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.

06/01191 Reliability analysis of pipe whip impacts: Dundulis, G. et al. Nuclear Engineering and Design, 2005, 235, (17–19), 1897–1908

06/01191 Reliability analysis of pipe whip impacts: Dundulis, G. et al. Nuclear Engineering and Design, 2005, 235, (17–19), 1897–1908

Application of probabilistic methods to validate NPP pipewhip impact simulations

Piping in nuclear power plants is vital to the proper operation and safety of these facilities. To assure safety in the unlikely event of a pipe break, it is necessary to evaluate the consequences from the resulting whipping pipe on neighboring components and structures. Numerical simulations allow for rapid evaluation of these consequences. Before simulations can be accepted, however, the methodology and computer codes must be validated against experimental results. This paper uses a probabilistic approach to validate pipe whip simulations against limited experimental results. Probabilistic analysis software was developed and coupled to existing deterministic finite element software. An example of a whipping pipe impacting against a reinforced concrete slab was simulated. The described probabilistic approach was used to validate the numerical simulations. The conclusions obtained were that the numerical simulations of whipping pipe impact were validated, even though the numerical results did not exactly agree with experimental results. The chosen points of comparison – namely, time-to-impact and total reaction force – were within the 95% confidence interval.

Reliability analysis of pipe whip impacts

A probability-based approach is presented as the integration of probabilistic methods and deterministic modelling based on the finite element method. An existing finite element software package was linked to an existing probabilistic package to analyse the complex mechanics that occur during the transient non-linear analysis of impact problems. This methodology is applied to a pipe whip analysis of a group-distribution-header, which results from a guillotine break, and subsequent impact with the adjacent building wall; this is a postulated accident for the Ignalina Nuclear Power Plant RBMK-1500 reactors. The uncertainties of material properties, component geometry data and loads were taken into consideration. The probabilities of failure of the impacted header and of the header support-wall were estimated given uncertainties in material properties, geometrical parameters and loading. The software ProFES was used for the probabilistic analysis and the finite element software NEPTUNE for deterministic structural integrity evaluation. The Monte Carlo Simulation, First Order Reliability method and Response Surface method were used in the probabilistic analysis.

Structural integrity evaluation of fuel test loop submerged in water subjected to postulated pipe rupture

The structural integrity of the fuel test loop (FTL) in a Korean experimental reactor is evaluated when the FTL, submerged in a water environment, is subjected to a postulated pipe rupture. The analyses are performed under static and dynamic conditions, imposing the thrust force history at each postulated pipe rupture section. Through analysis the following results are found: 1) A double ended guillotine can not be expected based on the toughness of the material, 2) the structural integrity of the chimney surrounding the FTL would not impede the structural integrity by the pipe whip. All analyses are performed by finite element methods.

Application of LBB to high energy pipings of a pressurized water reactor in Korea

The application of the leak before break (LBB) technology to the newly constructed pressurized water reactors (PWRs) has been approved in Korea for several high energy systems that can meet rigorous acceptance criteria. The LBB application in Korea is based on the US Nuclear Regulatory Commision (USNRC) requirements. The purpose of the LBB evaluation is to eliminate the dynamic effects associated with the postulated double-ended guillotine break (DEGB) from design basis loads, as well as to eliminate pipe whip restraints and jet impingement barriers. There were several issues on the application of LBB to the primary coolant loop and the pressurizer surge line. Of concern were the material properties for the carbon steel for the primary coolant loop, estimation of the crack opening area at the pipe-to-nozzle interface considering the asymmetry, and the leakage crack size which barely meets the required margin of 2 for the surge line, etc. Some additional work was required by the safety authority to maintain the global safety of the plant at a sufficient level. This paper describes the regulatory application of LBB in Korea, and the issues encountered during the regulatory review.

Non-linear dynamic analysis of cantilever whipping pipes

This paper presents the results of numerical dynamic analyses of a number of pipe whip problems based on non-linear shell theory using the DYNA3D (version 6.0) finite element code. The calculations are mainly concerned with the transient deformation of the pipes during the whipping process. The main purpose of the study is to check the efficacy of a recently published theoretical elastic-plastic, hardening-softening (e-p-h-s) model for pipe whip developed by Reid et al. [1, 2]. This model is based upon beam theory but allows for the effects of ovalization of the pipe cross-section on the moment-curvature constitutive behaviour of the pipe. It is shown that the results using DYNA3D are in good agreement with both experimental data and the e-p-h-s model predictions and confirms the accuracy of the latter. While the DYNA3D study is not exhaustive, the localized shell bending deformation of whipping pipes in which ‘kinks’ are formed is reproduced with reasonable accuracy and it has permitted the effect of the strain-rate sensitivity of the yield stress of the pipe material to be examined in a preliminary manner.

Response spectrum analysis of piping systems with elastic-plastic gap supports

A new seismic support device and its application in piping systems is described. The device, E-BAR (patented), can be cost effectively used for snubber replacement programs, mitigation of hydraulic transients, pipe whip and as a thermal stop. The device has pre-set gaps to allow free thermal movement. During a seismic or other dynamic load event, if the pipe movement exceeds the gap dimension, the device acts as an elastic or elastic-plastic restraint. The device also has a unique design feature for not exceeding the restraint force beyond a specified limit design value. To analyze piping systems with gap supports having elastic-plastic characteristics, modal analysis procedures for both response spectrum and time history methods are developed. The comparison of responses obtained from the procedures with nonlinear time history analysis and test results available in the literature shows excellent correlation. A pilot program conducted for snubber replacement with E-BARs demonstrates that the limit force feature of E-BAR makes them very attractive for snubber replacement. This is because a particular E-BAR with a specified limit design force can be selected, such that, the E-BAR replacing the snubber does not require any modifications be made to the existing support steel and hardware.