Non-linear 3D piping analysis under stochastic dynamic loads

A new analytical method is presented for non-linear 3D piping systems subjected to stochastic dynamic loadings. First, the paper describes the development of an empirical formulation for the strength and deformation characteristics of piping systems based on a detailed finite-element shell analysis of various pipebends. Five structural parameters are selected to characterize a typical nuclear power piping design in the formulation. Second, the use of a simplified plastic hinge model is proposed in which the non-linear behavior of pipebends under stochastic loadings is accounted for by using an orthotropic biaxial hysteretic model. A numerical example and comparison with other methods are illustrated in terms of computational time and practicality of the method.     

Further development of the load coefficient method, lcm, for rational seismic design of nuclear facilities

The purpose of this paper is to present the results of a study conducted to compare the results of the Load Coefficient Method, LCM, proposed for seismic load determination, to modal analysis and the equivalent static load methods as defined in Section 3.7.2 of the U.S. Nuclear Regulatory Commission Standard Review Plan. The comparison is conducted using a number of nuclear power plant piping systems which used response spectra modal analysis input in their original design.The real piping systems studied are considered to be representative of ASME Section III nuclear Class 2 and 3 piping systems required to be designed to resist currently defined seismic loadings. Section 2 of this paper provides numerical comparisons of the application of LCM, Response Spectrum and Equivalent Static Load Methods.     

Pipe rupture and steam/water hammer design loads for dynamic analysis of piping systems

The design of restraints and protection devices for nuclear Class I and Class II piping systems must consider severe pipe rupture and steam/water hammer loadings. Limited stress margins require that an accurate prediction of these loads be obtained with a minimum of conservatism in the loads. Methods are available currently for such fluid transient load development, but each method is severely restricted as to the complexity and/or the range of fluid state excursions which can be simulated. This paper presents a general technique for generation of pipe rupture and steam/water hammer design loads for dynamic analysis of nuclear piping systems which does not have the limitations of existing methods. Blowdown thrust loadings and unbalanced piping acceleration loads for restraint design of all nuclear piping systems may be found using this method. The technique allows the effects of two-phase distributed friction, liquid flashing and condensation, and the surrounding thermal and mechanical equipment to be modeled. A new form of the fluid momentum equation is presented which incorporates computer generated fluid acceleration histories by inclusion of a geometry integral termed the “force equivalent area” (FEA). The FEA values permit the coupling of versatile thermal-hydraulic programs to piping dynamics programs. Typical applications of the method to pipe rupture problems are presented and the resultant load histories compared with existing techniques.     

Failure probability assessment of wall-thinned nuclear pipes using probabilistic fracture mechanics

The integrity of nuclear piping system has to be maintained during operation. In order to maintain the integrity, reliable assessment procedures including fracture mechanics analysis, etc., are required. Up to now, this has been performed using conventional deterministic approaches even though there are many uncertainties to hinder a rational evaluation. In this respect, probabilistic approaches are considered as an appropriate method for piping system evaluation. The objectives of this paper are to estimate the failure probabilities of wall-thinned pipes in nuclear secondary systems and to propose limited operating conditions under different types of loadings. To do this, a probabilistic assessment program using reliability index and simulation techniques was developed and applied to evaluate failure probabilities of wall-thinned pipes subjected to internal pressure, bending moment and combined loading of them. The sensitivity analysis results as well as prototypal integrity assessment results showed a promising applicability of the probabilistic assessment program, necessity of practical evaluation reflecting combined loading condition and operation considering limited condition.     

Development of stress indices for nonradial branch connections

This paper presents a brief summary of the technical basis for the recommended stress indices for 45 degree lateral connections under internal pressure and in-plane moment loadings.Starting with the historical background of the Pressure Vessel Research Committee's (PVRC) long range program on lateral connections, this paper highlights the various aspects intrinsic to this program such as model selection, analysis technique, finite element discretization, loading conditions, material properties and boundary conditions.A discussion of the stress index method and its application to the pressure vessel and piping design is offered as a prelude to the recommended code indices. Proposed changes to Par. NB-3338.2(C) (1) of Subsection NB of the ASME Code pertaining to lateral nozzles in cylindrical vessels and Par. NB-3650 relative to branch connections in piping systems are presented and discussed in detail.Besides, this paper discusses the need to develop additional data in the range of geometric parameters, 0.5 ≤ d/D ≤ 1.0 and 10 ≤ D/T ≤ 50, and under other remaining loading conditions to broaden the application of the stress index method.     

Dynamic load effects on gate valve operability and snubber performance

The Idaho National Engineering Laboratory (INEL) participated in an internationally sponsored seismic research program conducted at the decommissioned Heissdampfreaktor (HDR) located in the Federal Republic of Germany. An existing piping system was modified by installation of 200-mm, naturally aged, motor-operated gate valve from a U.S. nuclear power plant and a piping support system of U.S. design. Using various combinations of snubbers and other supports, six other piping support systems of varying flexibility from stiff to flexible were also installed and tested. Additional valve loadings included internal hydraulic loads and, during one block of tests, elevated temperature. The operability and integrity of the aged gate valve and the dynamic response of the various piping support systems were measured during 25 representative simulations of seismic events.     

Fracture mechanics and full scale pipe break testing for the Department of Energy's new production reactor-heavy water reactor

Oak Ridge National Laboratory (ORNL) has completed a major task for the US Department of Energy (DOE) in the demonstration that the primary piping of the proposed new production reactor-heavy water reactor (NPR-HWR), with its relatively moderate temperature and pressure, should not suffer an instantaneous double-ended guillotine break (DEGB) under design basis loadings and conditions. The growth of possible small pre-existing defects in the piping wall was estimated over a plant life of 60 years. This worst-case flaw was then evaluated using fracture mechanics methods. It was calculated that this worst-case flaw would increase in size by at least 14 times before pipe instability during a safe shutdown earthquake (SSE) would even begin to be possible. The approach to showing the improbability of an instantaneous DEGB for HWR primary piping required a major facility (pipe impact test facility, PITF) to apply all possible design loads, including an equivalent major earthquake (called the SSE earthquake). The facility was designed and built at ORNL in 6 months. The test article was 6.1 m long, 406 mm diameter, 13 mm thick pipe of stainless steel 316LN material that was fabricated to exacting standards and inspections following the nuclear industry standard practices. A flaw was machined and fatigued into the pipe at a tungsten inert gas (TIG) butt weld (ER316L weld wire) as an initial condition. The flaw-crack was sized to be beyond the worst-case flaw that HWR piping could see in 60 years of service—if all leak detection systems and if all crack inspection systems failed to notice the flaw's existence. Starting October 1991, the first test article was subjected to considerable overloadings. The pipe was impacted 104 times at levels equal to and well beyond the SSE loadings. In addition, over 560 000 fatigue cycles and numerous purposeful static overloads were applied in order to extend the flaw to establish the data necessary to confirm fracture mechanics theories, and more importantly, to demonstrate simply that instantaneous DEGB is highly improbable for the relatively moderate energy system.     

Coolant cavitation in dynamic containment loading

After a brief introduction to the subject of cavitation in subcooled liquids and a survey of what is known regarding the key parameters in the cavitation process for water and for sodium, the basic equations of the SIMON cavitation model for use with Lagrangian containment codes and the assumptions behind them are reviewed.Some calculations using this model are then presented which show the dissipative effect of cavitation both in uncavitated liquids transmitting tension waves and in cavitated liquids transmitting pressure waves. The cavitation which develops when pressure waves are reflected at free surfaces is also examined, and some calculated results are compared with an experiment involving this phenomenon found in the literature. The role of cavitation in the containment loading process is then discussed, and examples taken from model test calculations are adduced to show that cavitation occurs at all stages of the loading process and involves a high proportion of the total liquid volume. Again by example the point is made that in certain simple circumstances a crude pressure cut-off model of cavitation is adequate but that for other major aspects of the containment loading process such as roof impact pressures and structural deformations a more refined model is necessary.     

Performance of a piping system and equipment in the HDR simulated seismic experiments

This paper describes a portion of the analysis and results of the United States Nuclear Regulatory Commission/Idaho National Engineering Laboratory (USNRC/INEL) participation in the SHAG (Shakergebaude) Seismic Research Program conducted by Kernforschungszentrum Karlsruhe (KfK) at the Heissdampfreaktor (HDR), a decommissioned nuclear reactor. The program analyzed the responses of a piping system and associated line-mounted equipment when subjected to various seismic and hydraulic loadings. Of interest was to evaluate the influence that piping support system flexibility has on piping system responses. The results of the studies will contribute to the technical basis for assessing the responses of light water reactor (LWR) piping and fine-mounted equipment to earthquakes.     

Analysis of the capability of system codes to model cavitation water hammers: Simulation of UMSICHT water hammer experiments with TRACE and RELAP5

The capabilities of the nuclear system transient codes TRACE and RELAP5 to model coupled two-phase flow and pressure wave propagations in a pipe are assessed by analyzing the UMSICHT PPP cavitation water hammer experiments 329 and 135 after valve closure. Time-dependent pressure, flow behaviour, and the generation and collapse of vapor bubbles at the valve and the first bridge are discussed. We show that both codes are able to model the flow behaviour of the water hammer for the high pressure and high temperature case 329 (initially 10–13 bar and 420 K), however condensation heat transfer for the base case needed to be increased in order to accurately model the magnitude of the first pressure excursion. The experimental broadening and damping of the subsequent pressure peaks by Fluid-Structure Interaction (FSI) phenomena arising from the interaction of the flow with the vibrations of the piping structure are not considered in the modeling results. For the lower pressure and temperature case 135 (initially 1–4 bar and 294 K), the TRACE code provides a good approximation of the propagation of the pressure wave and the void fraction behaviour, already with base case conditions, while RELAP5 overpredicts the vapor generation along the pipe and, as a result, considerably underpredicts the pressure amplitudes and overpredicts the water hammer frequency.     

多级节流孔板在核级管道中的应用

针对大亚湾核电站安全壳喷淋系统(EAS)试验管线节流孔板气蚀引起的管道剧烈振动和噪音,以及支管疲劳破坏这一事例,研究了气蚀引起管道振动的分析方法,以及采用多级节流孔板减小气蚀的设计方法.对气蚀引起的管道振动,采用计算流体动力学(CFD)方法分析孔板附近的流动特性和压力分布,确定节流孔板下游是否发生气蚀现象;对于发生气蚀现象的节流孔板,提出采用多级节流孔板来减弱气蚀,并采用各级节流孔板气蚀数相近的原则确定节流孔径.通过对改造后的EAS试验管线的试验证实,采用本文的设计分析方法设计的多级节流孔板能够有效地减小节流孔板气蚀引起的管道系统振动和噪音.     

Probabilistic fracture assessment of piping systems based on FITNET FFS procedure

A probabilistic method based on the fracture module of the FITNET FFS procedure is developed to perform the structural integrity analysis for piping systems. Monte Carlo simulation is used to calculate the failure probability of the whole piping system, as well as that of separate defects by considering the random variables in the method. Both the sensitivity of uncertainties of variables and the model sensitivity are analyzed to identify the most important parameters that affect the failure probability of piping systems, thereby providing an insight into the countermeasures against the failure risk. The results show that the outer diameter of the pipe has the strongest influence on the failure probability of a piping system having a circumferential crack of 0.757 rad, followed by the bending moment, the piping wall thickness, the fracture toughness, the crack angle, the axial force, the ultimate tensile strength and the yield stress.     

Decreasing snubber inservice inspection costs through snubber reduction and improved test limits

Snubber inservice inspection (ISI) requirements, along with a history of snubber malfunctions, has made inspection and maintenance of snubbers a significant part of a nuclear power plant's ISI budget. These expenses can be minimized through snubber reduction and the use of improved test limits for snubber functional testing. This paper presents a snubber overview and reviews snubber ISI requirements. Examples are given of the high cost that maintaining a snubber in an operating nuclear plant represents.Snubber reduction refers to reducing a plant's snubber population by eliminating snubbers shown not to be required to restrain piping for design basis dynamic loadings, and by replacing snubbers with other types of restraints, such as rigid struts. Snubber reduction is discussed in terms of what makes removing snubbers practical along with approaches to, and results of recently implemented snubber reduction programs.Improved or increased test limits for snubber functional testing are discussed along with an approach to, and results of an Electric Power Research Institute sponsored program to develop improved limits that would not significantly affect piping response. Improved piping acceptance criteria can be used to justify the use of increased test limits provided by snubber manufacturers. An additional use is to justify the operability of piping on which faulty snubbers were found.     

The steamhammer problem: dynamic shock loading of critical reactor piping systems

In the course of both pre-operational testing and power operation of commercial nuclear power plants, relatively large amplitude transient vibrations of steam piping systems have been experienced with damage to the piping supports in at least one recent case. These transient vibrations result from ‘steamhammer’ or dynamic shock loading induced by pressure and momentum transient conditions generated in the piping by sudden changes to the flow conditions, such as are produced by sudden valve opening or closure. In particular, vibrations have been experienced in by-pass and discharge lines as a result of relief valve discharge, and in main steam lines as a result of sudden main stop valve closure. Piping in both BWR and PWR reactor systems has been found to be susceptible to these conditions.This paper is concerned with the evaluation of the pressure and momentum transients resulting from sudden valve operation, and the determination of the dynamic response of the piping to the induced transient loading. The characteristics of the transient conditions existing immediately following both sudden valve opening and closure as encountered in BWR and PWR plants are discussed. The procedures used to calculate the transient time history functions are outlined. The derivation of the loading induced in the piping by the pressure and momentum transients is discussed and the determination of the dynamic response of the piping is presented. The procedures described in the paper are illustrated by actual examples from BWR and PWR plants, and the significance of steamhammer effects relative to other loading conditions is discussed.     

Positive use of damping devices for piping systems — Some experiences and new proposals

An increase of the damping ratio is known to be very effective for the seismic design of a piping system. It is reported that the energy dissipation in piping supports contributes to increase the damping ratio of the piping system. In this paper, with regard to increasing the damping and reducing the seismic response of the piping system, three application methods of damping devices used in other engineering fields are reviewed: (1) direct damper, (2) dynamic vibration absorber, and (3) connecting damper. Based on the results of this review, the following three types of damping devices for piping systems are introduced: (1) visco-elastic dampler (direct damper), (2) elasto-plastic damper (direct damper), and (3) compact dynamic absorber (dynamic vibration absorber). The dynamic characteristics of these damping devices are investigated by a component test and the applicability of them to the piping system was confirmed by the vibration test using a three-dimensional piping model. These damping devices are more effective than mechanical snubbers to suppress the vibration of the piping system.     

Fluid dynamic interaction between water hammer and centrifugal pumps

Centrifugal pumps generate in piping systems noticeable pressure pulsations. In this paper the dynamic interaction between water hammer and pressure pulsations is presented. The experimental investigations were performed at a piping system with nominal diameter DN 100 (respectively NPS 4) and 75 m total length, built at the Institute for Process Technology and Machinery. Different measurements at this testing facility show that pulsating centrifugal pumps can damp pressure surges generated by fast valve closing. It is also shown that 1-dimensional fluid codes can be used to calculate this phenomenon. Furthermore it is presented that pressure surges pass centrifugal pumps almost unhindered, because they are hydraulic open.     

Network Analysis of Turbine and Feedwater Systems of the ‘Fugen’ Nuclear Power Plant

The present study describes the thermal-hydraulic network analysis of the turbine and feedwater systems of the ‘Fugen’ reactor. Turbines, feedwater heaters, and corresponding piping systems are modeled using the network calculation code NETFLOW++ and thermal-hydraulic conditions are calculated using the coupled numerical model. As a result of the calculation, distributions of important characteristics of the single-phase flow and two-phase flow in the piping such as pressure and void fraction are clarified. Flow patterns in the piping were investigated using the calculated result. It was found that the state of the coolant in the drainpipe changes from saturated liquid at the inlet to a two-phase flow with a large void fraction at the connection to the feedwater heaters. This is attributed to the pressure difference between the inlet and outlet of the drainpipes. Even the drainpipe from the moisture separator to the shell of feedwater heater #4 shows a similar behavior, and the flow pattern changes from single phase to slug flow. The steam quality in the extraction line is very high, although a large number of droplets are contained in the flow. Contrary to expectation, these droplets do not completely evaporate in spite of the low-pressure conditions.     

管道系统的功能性评定准则研究

管道系统的功能性是不同于管道系统压力边界完整性的一项要求，美国核管理委员会（NRC）提出了管道系统功能性的2种评定准则。为了探讨功能性评定准则的来源以及应用，通过研究经典文献中有关功能性评定准则的内容，阐述了2种评定准则的来历和依据，分析了2种功能性评定准则的特点，指出了使用功能性评定准则的注意事项。通过一个管道系统功能性评定的实例，提出2种功能性评定准则在不同的核电厂设计阶段的应用策略。对于新建的核电厂，尽量使用C级限值来保证管道系统的功能性，如果是已建造的核电厂，则可以用D级限值附加5个条件来保证管道系统的功能性。      

Response of piping system on friction support to bi-directional excitation

Installation of friction devices between a piping system and its supporting medium is an effective way of energy dissipation in the piping systems. In this paper, seismic effectiveness of friction type support for a piping system subjected to two horizontal components of earthquake motion is investigated. The interaction between the mobilized restoring forces of the friction support is duly considered. The non-linear behavior of the restoring forces of the support is modeled as an elastic-perfectly plastic system with a very high value of initial stiffness. Such an idealization avoids keeping track of transitional rules (as required in conventional modeling of friction systems) under arbitrary dynamic loading. The frictional forces mobilized at the friction support are assumed to be dependent on the sliding velocity and instantaneous normal force acting on the support. A detailed systematic procedure for analysis of piping systems supported on friction support considering the effects of bi-directional interaction of the frictional forces is presented. The proposed procedure is validated by comparing the analytical seismic responses of a spatial piping system supported on a friction support with the corresponding experimental results. The responses of the piping system and the frictional forces of the support are observed to be in close agreement with the experimental results validating the proposed analysis procedure. It was also observed that the friction supports are very effective in reducing the seismic response of piping systems. In order to investigate the effects of bi-directional interaction of the frictional forces, the seismic responses of the piping system are compared by considering and ignoring the interaction under few narrow-band and broad-band (real earthquake) ground motions. The bi-directional interaction of the frictional forces has significant effects on the response of piping system and should be included in the analysis of piping systems supported on friction supports. Further, it was also observed that the velocity dependence of the friction coefficient does not have noticeable effects on the peak responses of the piping system.     

Experimental evaluation of ability of Relap5, Drako, Flowmaster2™ and program using unsteady wall friction model to calculate water hammer loadings on pipelines

Mechanical loadings on pipe systems caused by water hammer (hydraulic transients) belong to the most important and most difficult to calculate design loadings in nuclear power plants. The most common procedure in Sweden is to calculate the water hammer loadings on pipe segments, according to the classical one-dimensional (1D) theory of liquid transient flow in a pipeline, and then transfer the results to strength analyses of pipeline structure. This procedure assumes that there is quasi-steady respond of the pipeline structure to pressure surges—no dynamic interaction between the fluid and the pipeline construction. The hydraulic loadings are calculated with 1D so-called “network” programs. Commonly used in Sweden are Relap5, Drako and Flowmaster2—all using quasi-steady wall friction model. As a third party accredited inspection body Inspecta Nuclear AB reviews calculations of water hammer loadings. The presented work shall be seen as an attempt to illustrate ability of Relap5, Flowmaster2 and Drako programs to calculate the water hammer loadings. A special attention was paid to using of Relap5 for calculation of water hammer pressure surges and forces (including some aspects of influence of Courant number on the calculation results) and also the importance of considering the dynamic (or unsteady) friction models. The calculations are compared with experimental results. The experiments have been conducted at a test rig designed and constructed at the Szewalski Institute of Fluid Flow Machinery of the Polish Academy of Sciences (IMP PAN) in Gdansk, Poland. The analyses show quite small differences between pressures and forces calculated with Relap5, Flowmaster2 and Drako (the differences regard mainly damping of pressure waves). The comparison of calculated and measured pressures and also a force acting on a pre-defined pipe segment shows significant differences. It is shown that the differences can be reduced by using unsteady friction models in calculations. Recently, such models have been subjects of works of several researches in the world.