Transient cavitation effects in fluid piping systems

An accurate prediction of pressure transients and associated loadings in nuclear power plant piping systems requires a treatment of cavitation. A technique for calculating this effect in a general fluid-hammer analysis by the method of characteristics is developed. Cavitation is treated by a modified column separation model and is assumed to be a local phenomenon occurring whenever the pressure drops below the vapor pressure of the fluid. While the model is a simplification of the actual phenomena it reproduces the essential features of transient cavitation. Computational results obtained for a variety of piping arrangements demonstrate the versatility of the approach, and clearly illustrate the fact that neglecting cavitation leads to erroneous pressure-time loadings in the piping systems. Comparisons of calculated results with available experimental data, for a simple piping arrangement, show good agreement and provide validation for the computational cavitation model.     

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.     

An implicit three-dimensional finite-element formulation for long-duration structural analysis of piping systems

This paper describes an implicit three-dimensional finite-element formulation for the structural analysis of reactor piping systems. The numerical algorithm considers hoop, flexural, axial, and torsion modes of the piping structures. It is unconditionally stable and can be used for calculation of piping response under static or long duration dynamic loads.The method uses a predictor-corrector, successive iterative scheme which satisfies the equilibrium equations. A set of stiffness equations representing the discretized equations of motion are derived to predict the displacement increments. The calculated displacement increments are then used to correct the element nodal forces. The algorithm is fairly general, and is capable of treating large displacements and elastic-plastic materials with thermal and strain-rate effects.The implicit-time integration scheme described herein has been incorporated into the three-dimensional piping code SHAPS. Two sample problems are presented to illustrate the analysis. The first problem deals with a dynamic analysis of a pipe-elbow loop. The second problem studies the piping response to seismic excitation. The results are discussed in detail.     

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.     

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.     

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.     

The effects of reactor coolant system pipe rupture motion on tributary piping and attached equipment

This paper presents a rigorous analysis of a pressurized water reactor coolant system (RCS) to determine time-history excitations of intact equipment and tributary piping attached to the RCS caused by a postulated guillotine rupture in the primary coolant piping. Reactor control rods and drive mechanisms, in core instrumentation guide tubes and reactor coolant pump motor appurtenances are examples of attached equipment which is excited by RCS LOCA induced motions. The surge line, mainsteam lines and emergency core cooling lines are examples of tributary piping similarly affected by RCS LOCA induced motions. The methods described herein include structural and dynamic modeling and analytical techniques used in the non-linear transient dynamic time-history analysis of a 3-D coupled model of the RCS. The results of this analysis are generated for the purpose of defining the excitation for subsequent analysis of intact tributary systems attached to the reactor coolant system in order to evaluate their response to those LOCA induced motions. This paper also presents results of analyses for intact tributary piping subjected to LOCA induced motions and assesses the severity of the response compared to typical seismic response.     

Computer modelling of piping components for transient hydrodynamic-structural response

The paper describes three new piping components that are coupled with existing pipe and elbow models so that transient hydrodynamic-structural response analysis of general piping systems is possible. The three models are: a generalized piping component model, a tee-branching junction model, and a surge tank model. Optional interior rigid wall simulation and heat exchanger tube bundle representation in the generalized piping component model makes possible its use in modelling valves, pipe expansions and reducers, and heat exchangers. Two-dimensional implicit continuous-fluid Eulerian finite difference technique is utilized in the hydrodynamics calculations. A convected coordinates finite element method is used in the structural analysis which considers both the membrane and bending strengths of the thin axisymmetric shells representing the walls.     

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.     

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.     

Numerical fluid-hammer analysis by the method of characteristics in complex piping networks

This paper describes the method of characteristics as used to calculate fluid-hammer problems in complex piping networks. The formulation is based on the one-dimensional Navier-Stokes equation that contains the viscous term expressed as wall friction. A stepwise solution procedure is constructed from compatibility relations along characteristics and appropriate boundary conditions describing various types of pipe joints.The close agreement between the numerical result and the acoustic solution validates the boundary conditions for sudden area change based on steady-state flow conditions. A non-reflecting far-end boundary condition is devised that enables certain portions of a complex system to be analyzed. A dummy-junction boundary condition proved useful in treating systems containing long pipe sections in comparison to other pipes of the system. The numerical results obtained for the sodium-loop piping arrangement of the experimental breeder reactor II with the sodium-water reaction as the pressure disturbance are presented and discussed.     

Probabilistic fracture failure analysis of nuclear piping containing defects using R6 method

Failure analysis of in-service nuclear piping containing defects is an important subject in the nuclear power plants. Considering the uncertainties in various internal operating loadings and external forces, including earthquake and wind, flaw sizes, material fracture toughness and flow stress, this paper presents a probabilistic assessment methodology for in-service nuclear piping containing defects, which is especially designed for programming. A general sampling computation method of the stress intensity factor (SIF), in the form of the relationship between the SIF and the axial force, bending moment and torsion, is adopted in the probabilistic assessment methodology. This relationship has been successfully used in developing the software, Safety Assessment System of In-service Pressure Piping Containing Flaws (SAPP-2003), based on a well-known engineering safety assessment procedure R6. A numerical example is given to show the application of the SAPP-2003 software. The failure probabilities of each defect and the whole piping can be obtained by this software.     

A three-dimensional method for integrated transient analysis of reactor-piping systems

A three-dimensional method for integrated hydrodynamic, structural, and thermal analyses of reactor-piping systems is presented. The hydrodynamics are analyzed in a reference frame fixed to the piping and are treated with a two-dimensional Eulerian finite-difference technique. The structural responses are calculated with a three-dimensional co-rotational finite-element methodology. Interaction between fluid and structure is accounted for by iteratively enforcing the interface boundary conditions.A thermal transient capability has been developed. A system energy equation is used to compute the coolant temperatures due to convection. A radial heat-conduction equation is employed to establish the temperature profile throughout the pipe-wall thickness. The constitutive equation used for the thermal-mechanical stress calculation is suited for a large number of materials under various loading conditions, such as those having thermal, plastic, and viscous effects. The flow surface, which defined the purely elastic regime, can be arbitrarily small; an associated flow rule is utilized for regimes of material plasticity.Three sample problems are presented to illustrate this method. The first one calculates the piping response under the seismic excitation. The second one validates the heat-conduction model. The third problem deals with a coupled hydrodynamic-structural-thermal analysis of a piping system. Results are discussed in detail.     

Extended applications of LBB piping evaluation diagrams for a new plant design

Plant specific data, such as pipe geometry, material properties and pipe loads, are required to apply leak-before-break (LBB) to a piping system. Thus, LBB evaluation cannot be done until piping design and routing are completed. A simple method for evaluating LBB for piping systems during design process considering the effects of nozzle and the change in local and global compliance in cracked piping system is developed in this paper. This method produces piping evaluation diagrams for intermediate pipe locations and pipe-nozzle interface locations which defines the LBB requirements to the piping designer for use during the design process and is independent of pipe routing. Piping evaluation diagrams can be used for the LBB evaluation for a new plant design.     

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.     

Analysis of piping with hysteretic supports using response spectra

This paper introduces a response spectra-based method for analyzing piping with hysteretic nonlinear supports. The method is developed to be as simple and versatile as possible, yet accurate enough to model the essential nonlinear behavior of the supports. The required data is the hysteresis loops of the supports, the linear properties of the piping, and the linear acceleration response spectra. The supports are modeled by equivalent linear stiffness and damping, and the combined piping/support system is analyzed using complex modal properties that account for high-damping effects. The final peak response is obtained by a mode combination rule which is a new generalization of Complete Quadrature Combination (CQC) that accounts for nonlinear properties and complex modes. Sensitivities that indicate the degree of nonlinear behavior and support interaction are also determined. The method is used to analyze two three-dimensional piping systems with multiple nonlinear supports, which have been tested on a shaking table. Comparisons between experimental and analytical results show good agreement.     

Automated analysis of multiple-support excitation piping problems

An automated solution algorithm is presented for the treatment of multiple-support excitation piping problems. The method is an extension of the well-known response spectrum analysis method which is routinely used for seismic analysis of structural systems. The new algorithm was incorporated in Kraftwerk Union's proprietary computer code KWUROHR for static and dynamic analysis of piping systems.In this paper the numerical results from the use of envelope and multiple-support acceleration input spectra are presented for two typical piping systems in nuclear power plants. From the comparison of these results it becomes obvious that the multiple-support excitation method should be recommended as standard analysis procedure for systems attached to support points which are subjected to different acceleration spectra. The additional computer cost is negligible.     

Stochastic prediction of maximum seismic response of light secondary systems

A stochastic model is presented for predicting the elastic response of light multi-degree-of-freedom secondary systems to strong motion earthquakes. Secondary systems may include light mechanical or electrical equipment, piping, or other light systems attached at one or several points to walls or floors of the supporting or primary structures. The critical functions of these secondary systems in nuclear power plants make the accurate prediction of their maximum responses important. The response of such secondary structures may be obtained by a direct time-history analysis, or more approximately, by the response spectrum method. The time-history solution is, of course, expensive; moreover, there is no single representative earthquake and thus a number of possible earthquake ground motions have to be considered. On the other hand, the response spectrum method applied to secondary systems can lead to unreliable results.Within the framework of the normal mode method, a decoupled stationary random vibration model is developed based on the assumption of Gaussian response process and Poisson barrier crossings. The accuracy of the proposed model is verified by comparing the calculated responses, at the 10 and 50% probability of exceedance level, with the second highest and average of the time-history responses from eight normalized accelerograms. The influence of decoupling, i.e. ignoring the dynamic interaction between the primary and the secondary systems, on the response is examined.The influence of nonstationarity is also evaluated. It is observed that nonstationarity is unimportant for earthquakes of relatively long duration, and that for a given damping most of the error can be accounted for by a simple scaling. It is also shown that one aspect of the proposed method constitutes the basis for some of the approximations in the response spectrum method; however, the proposed method yields results that are consistently more reliable than the response spectrum method. Moreover, results obtained with the proposed method represent maximum response statistics from an ensemble of earthquakes rather than a single earthquake.     

Structural safety and reliability of primary system pressure boundaries for water cooled power reactors: Panel Discussion at the Second International Conference on Structural Mechanics in Reactor Technology, Berlin, Germany, 10–14 September, 1973

A stochastic model is presented for predicting the elastic response of light multi-degree-of-freedom secondary systems to strong motion earthquakes. Secondary systems may include light mechanical or electrical equipment, piping, or other light systems attached at one or several points to walls or floors of the supporting or primary structures. The critical functions of these secondary systems in nuclear power plants make the accurate prediction of their maximum responses important. The response of such secondary structures may be obtained by a direct time-history analysis, or more approximately, by the response spectrum method. The time-history solution is, of course, expensive; moreover, there is no single representative earthquake and thus a number of possible earthquake ground motions have to be considered. On the other hand, the response spectrum method applied to secondary systems can lead to unreliable results.Within the framework of the normal mode method, a decoupled stationary random vibration model is developed based on the assumption of Gaussian response process and Poisson barrier crossings. The accuracy of the proposed model is verified by comparing the calculated responses, at the 10 and 50% probability of exceedance level, with the second highest and average of the time-history responses from eight normalized accelerograms. The influence of decoupling, i.e. ignoring the dynamic interaction between the primary and the secondary systems, on the response is examined.The influence of nonstationarity is also evaluated. It is observed that nonstationarity is unimportant for earthquakes of relatively long duration, and that for a given damping most of the error can be accounted for by a simple scaling. It is also shown that one aspect of the proposed method constitutes the basis for some of the approximations in the response spectrum method; however, the proposed method yields results that are consistently more reliable than the response spectrum method. Moreover, results obtained with the proposed method represent maximum response statistics from an ensemble of earthquakes rather than a single earthquake.