Natural circulation with two-phase flow is a nonlinear dynamical systems, which can show a very complex and strange behavior under specific conditions. The application of stability analysis requires a large computational effort and is cumbersome in case of prediction the dynamical behavior by system codes alone. Therefore, model order reduction techniques are used to compensate this disadvantage by coupling with a bifurcation code such as MatCont. A reduced order model is derived by employing the POD-method to analyze the stability landscape of a low pressure natural circulation system representing passive safety systems such as the containment cooling condenser. The required full order model contains a classical natural circulation loop with a heated section and a riser. The two-phase region is modeled by a drift-flux mixture model. The reliability of the FOM is investigated by comparison with a reference model by the validated system code ATHLET.

Steam generating boilers in gas cooled nuclear reactors in the UK operate at high temperatures and some of them have been in service for more than 30 years and are now facing the challenges from long term operation extension demand. The tubular components experience surface metal losses due to exposure to oxidation and corrosive environment and as a result, some tubes suffer from restricted flow which may lead to an increased creep-fatigue crack initiation damage. To maintain or recover boiler heat transfer efficiency, internal chemical cleaning of selected boiler tubes is carried out, which introduces additional metal loss in the tube wall, weakening its load bearing capacity. Some boiler components are subject to high temperature, pressure and mechanical loadings in large number of operating cycles through life, introducing creep in addition to cyclic fatigue damage. In support of an operational safety case and plant long term operation extension requirements, structural integrity assessments have been carried out on a critical boiler component — bifurcation, taking into account tube wall metal loss for extended long term services, including the effects of possible future chemical cleaning operations. This paper presents the finite element analyses and R5 Volume 2/3 assessment work carried out for the structural integrity substantiation of a stainless steel boiler tube bifurcation. The bifurcation is a tubular component subject to significant applied displacement due to long range thermal expansion of the neighbouring components. The initial study following normal industry practice using a decoupled analysis approach showed that the strain ranges obtained would exceed the creep-fatigue crack initiation capacity and plastic ratchetting would occur which would lead to short term, incremental plastic collapse, hence a safety case could not be made. To meet the challenge, the analysis and assessment processes have been examined. A coupled FE analysis approach was used to remove the pessimism associated with the decoupled analysis approach. This approach captures the displacement-controlled nature of the system loads and allows a more realistic assessment. In addition, the plant life has been divided into a number of assessment periods such that the more realistic metal loss appropriate for each period could be used. Furthermore, segregated temperature zones have been considered in the assessment, leading to a significant reduction in the creep-fatigue crack initiation damage and a satisfactory extended long term operation safety case.

The AP1000 ® Containment Vessel (CV) is a freestanding steel containment designed to protect the public from radiation release. The CV consists of 2 ellipsoidal heads connected by a cylindrical shell and is constructed of carbon steel. The AP1000 plant design has four large penetrations (two airlocks and two equipment hatches) located in approximately the same quadrant of the circumference of the shell which imposes asymmetric effects in the shell structure. The CV is designed and constructed in accordance with ASME Boiler and Pressure Vessel Code, Section III, Subsection NE. Traditionally, the local and global stability of freestanding steel containments have been designed by use of formulae using conservative assumptions based on an axisymmetric structure. ASME Code Case N-284 “Metal Containment Shell Buckling Design Methods, Class MC Section III, Division 1” outlines methodology for satisfying the stability of the CV using two approaches. Section 1710 provides a stress based buckling approach using detailed formulae that assumes an axisymmetric structure. The second approach provides guidance and acceptability based on a linear bifurcation analysis (2D (1720) or 3D (1730)). Due to the asymmetric structure of the CV, the 3D linear bifurcation method delivers the most accurate results. The methodology and assumptions implemented by Westinghouse to qualify stability of the CV via Code Case N-284 are outlined. Also, the procedure to properly amplify the stresses as required by N-284 is included as justification of the methods used. This justification was thoroughly investigated by the Nuclear Regulatory Commission (NRC) and deemed acceptable.

The spent fuel dry-storage system of High Temperature Reactor-Pebble bed Modules (HTR-PM) in China is designed to consist of 3 separate regions, with each composed of multiple storage wells. Cold air is distributed to 8 parallel wells in the interim region from a bifurcation chamber, and then heated by vertical placed canisters in each well before gathering in a mixture chamber. In accident condition, the decay heat in interim region will be discharged by open-cycle natural ventilation. In this paper, thermal performance of the interim region by natural ventilation was investigated by a step-by-step scheme. Firstly, the resistance characteristics of wells loaded with different numbers of canisters and bifurcation chamber were studied with CFD code, and were formulated into momentum sources of porous media. Then, equivalent model of the system with porous media regions was employed to simulate the flow distribution of the system. Two different operation conditions (half-loaded condition and full-loaded condition) were studied in this step and hottest well were located. Finally, a refined model of the hottest well with minimized and necessary assumption was employed to investigate the conjugate heat transfer coupled with thermal radiation process, and to obtain the internal temperature profile of the hottest well. The results showed that the total mass flow of natural ventilation is 5.53 kg/s under half-loaded condition (20 canisters, 156.72 kW of decay heat) and 4.83 kg/s under full-loaded condition (40 canisters, 192.37 kW of decay heat). Hottest well was the well-1 th under half-loaded condition, where maximal temperatures of concrete walls, steel barrel, canisters and spent fuel pebble bed inside the canister were 86.5 °C, 142.2 °C, 279.5 °C, 484.9 °C, respectively. The results demonstrate that the interim region of dry-storage system satisfies the temperature limitation of component materials in accident condition.

In order to study the vortex-induced vibration, the three-dimensional unsteady, viscous, incompressible Navier-Stokes equation and LES turbulence model are solved with the finite volume approach, and the dynamic equilibrium equations are discretized by the finite element theory. A three-dimensional numerical model for flexible tube vibration induced by cross flow is proposed. The model realized the fluid-structure interaction with solving the fluid flow and the structure vibration simultaneously. Based on this model, the dynamic behavior and response characteristic of the tube are investigated. Meanwhile, the limit cycle and bifurcation of lift coefficient and displacement are analyzed. Amplitude response, trajectory, phase difference, fluid force coefficient and vortex shedding frequency are obtained. The results reveal that, a quasi-upper branch is found in the present fluid-flexible tube coupling system with high mass-damping and low mass ratio. The three-dimensional flexible tube has a broader synchronization range and the amplitude is higher than elastically mounted two-dimensional rigid tube. In the quasi-upper branch and lower branch regime, the “lock-in” begins. In quasi-upper branch, the lateral amplitude increases with reduced velocity increasing. While in lower branch, the amplitude keeps almost constant. The drag force reaches its peak value before lift. The lift coefficient reaches its maximum value at the switch from initial branch to quasi-upper branch. The phase angle reaches zero under “lock-in” and the dynamic behavior is a periodic motion. There is no bifurcation of lift coefficient and lateral displacement occurred in three dimensional flexible tube submitted to uniform turbulent flow.

Interface-System Loss-of-Coolant Accident (ISLOCA) occurs by failure of isolation valves in piping systems. In this study, transient behavior of pressure propagation in piping systems after ISLOCA has been estimated. At first, capability of TRACG code to predict pressure propagation in a simple pipe line, which has expansion, contraction and bifurcation, has been investigated. Then, sensitivity analysis of valve opening period has been performed to investigate the behavior of pressure propagation in a simple pipe line. Finally, pressure propagation inside piping systems after ISLOCA has been simulated for Hitachi-GE standard Advanced boiling water reactor (ABWR) plant. Maximum pressure inside High Pressure Core Flooder (HPCF) systems has been less than 7.8MPa. TRACG code has been shown to be useful to predict transient behavior of pressure propagation in complicated network of piping systems after ISLOCA.

The possibility of instabilities in future nuclear reactors cooled by supercritical water is a matter of concern due to sharp changes in thermodynamic properties of coolant within the core. In the present work, a lumped parameter dynamic model of supercritical water-cooled reactor has been developed for analysis of coupled neutronic-thermohydraulic instabilities. The coolant channel is divided into two nodes with a moving boundary between them. The heater wall dynamics is described by a lumped parameter energy balance. Point neutron kinetics with one group of delayed neutrons has been used to model the power dynamics. Simple non-dimensional equations of state have been obtained for evaluating thermodynamic properties. Stability analysis has been done for various values of parameters such as the reactor power, coolant mass flow rate and inlet temperature. Stability maps have been plotted in the parameter planes. Dynamic simulations have been performed in the time domain to study the nature of operating transients. The stability analysis with neutronics is found to be more conservative. Transient simulations without neutronics indicate a supercritical Hopf bifurcation and the existence of a stable limit cycles in the unstable region. However, simulations with coupled neutronics indicate a subcritical Hopf bifurcation and the existence of unstable limit cycles in the stable region. Therefore, the analysis with neutronics is more conservative and shows that the system can be unstable for large perturbations, even if it is stable for small perturbations.

Behavior of a water column oscillator with a cover gas system was studied experimentally and analytically. One of the free water surfaces was sealed with the cover gas, while the other was open to the atmosphere. The cover gas was supplied with a constant rate, and it was ejected through a valve when the water level reached a certain point. As soon as the level reached another point, the valve closed and the cover gas quantity increased again. In the experiment, a bifurcation-like phenomenon was observed; the valve closed period usually had single value, while it took two values under certain conditions. In order to examine the cause of this bifurcation-like phenomenon, a numerical analysis model was developed which described the system behavior precisely. The analytical result revealed that the bifurcation-like phenomenon was not bifurcation. Very small noise superimposed on the singular characteristic of the system was found to cause the two duration values under the conditions; the duration changed abruptly by an uncontrollable slight variation of the system conditions. It is likely to be confused with bifurcation by observers who could not perceive the uncontrollable noise.

Stability and bifurcation analyses of nuclear-coupled thermal hydraulic instability in BWR has been performed using a semi-analytical method. The BWR model used in this study consists of three parts: neutron kinetics, fuel rod heat conduction and single and two-phase heated channel thermal hydraulics. Point reactor model is currently being used for neutron kinetics and will be extended in the future to higher order lambda or omega-mode. In the heat conduction part, a piecewise quadratic approximation to radial temperature distribution in fuel pellet and cladding is assumed. ODEs for the expansion coefficients of the quadratic spatial profiles are developed by applying variational principle. Similar to the heat conduction model, the spatial enthalpy distribution in the single phase region and steam quality in the two-phase region in the BWR core are approximated by quadratic polynomials. Two-phase flow is modeled using the homogeneous equilibrium model. A bifurcation analysis code, BIFDD, is then used to perform the analysis for the stability boundary (SB) and the nature of Poincare´-Andronov-Hopf bifurcation (PAH-B). Results in control-rod-induced-reactivity—inlet-subcooling-number space show that both super or sub-critical bifurcation can occur along the SB—the subcritical bifurcation occurs for very small or very large subcooling number values; super-critical PAH-B occurs for intermediate values of subcooling number.

Nonlinear boiling water reactor (BWR) studies are generally pursued by employing large system codes, like RAMONA and RETRAN. However, detailed investigations using this approach in which parametric studies are to be carried out over large regions of parameter space are very expensive and time consuming. Therefore, it is necessary to use the so-called reduced order models containing a “manageable” number of system equations incorporating the essential features of the physical phenomena. Since the thermal-hydraulic model determines the main feedback gain and the associated time delay (void feedback reactivity), the modelling of the fluid dynamics is of paramount importance for the reduced order model analyses for BWRs. For a certain set of hydraulic parameter values, the system of nonlinear differential equations describing the fluid dynamics generates the so-called self-sustained density wave oscillations (DWO), which is a typical two-phase flow instability.

This paper presents a study in which the bifurcation analysis is carried out using the system code RAMONA. As a first step, a correspondence hypothesis is proposed to underline the relationship between a stable (unstable) limit cycle solution and the occurrence of supercritical (subcritical) Hopf bifurcation in the modeling of boiling water reactor stability behaviour. A detailed local bifurcation analysis is then carried out in the narrow environment of one representative operational point for the Leibstadt NPP. Based on the experience acquired during stability and bifurcation analyses using our reduced order model, the results found using RAMONA could be explained. As a result, this is the first time that the occurrence of a subcritical Hopf bifurcation has been identified using RAMONA, or any other system code.

The thermal-hydraulic stability of a uniformly heated channel at supercritical water pressure has been investigated to help understand the system instability phenomena which may occur in Supercritical Water Nuclear Reactors (SCWR). We have extended the modeling approach often used for Boiling Water Nuclear Reactor (BWR) stability analysis to supercritical pressure operation conditions. We have shown that Ledinegg excursive instabilities and pressure-drop oscillations (PDO) will not occur in supercritical water systems. The linear stability characteristics of a typical uniformly heated channel were computed by evaluating the eigenvalues of the model. An analysis of non-linear instability phenomena was also performed in the time domain and the dynamic bifurcations were evaluated.