Thermo-hydraulics during start-up in natural circulation boiling water reactors

The transient behavior of natural circulation for boiling two-phase flow was investigated by simulating normal and abnormal start-up conditions to research the feasibility of natural circulation BWRs such as the SBWR. It was found that the instabilities, which are out-of-phase geysering, in-phase natural circulation oscillation and out-of-phase density wave instability, may occur during the start-up when the vapor generation rate is insufficient. In this paper, the mechanism of in-phase natural circulation oscillation induced by hydrostatic head fluctuation in steam separators, which has never been understood well enough, is experimentally clarified. Next, the effect of system pressure on the occurrences of the geysering and the natural circulation oscillation are investigated. Finally, from the results, a recommendation is provided to establish the rational start-up procedure and reactor configuration for natural circulation BWRs.     

Startup transient simulation for natural circulation boiling water reactors in PUMA facility

In view of the importance of instabilities that may occur at low-pressure and -flow conditions during the startup of natural circulation boiling water reactors, startup simulation experiments were performed in the Purdue University Multi-Dimensional Integral Test Assembly (PUMA) facility. The simulations used pressure scaling and followed the startup procedure of a typical natural circulation boiling water reactor. Two simulation experiments were performed for the reactor dome pressures ranging from 55 kPa to 1 MPa, where the instabilities may occur. The experimental results show the signature of condensation-induced oscillations during the single-phase-to-two-phase natural circulation transition. The results also suggest that a rational startup procedure is needed to overcome the startup instabilities in natural circulation boiling water reactor designs.     

Experimental and theoretical noise analysis investigations in boiling water reactors

The stochastic neutron flux fluctuations in boiling water reactors represent a significant source of informations about thermohydraulic parameters. In this paper, experimental results of a series of in core measurements are described together with the development of a theoretical model.     

Nodal analysis of density-wave oscillations in boiling water nuclear reactors

This work presents a model for density-wave oscillations in boiling water nuclear reactors (BWRs). A nodal approach is adopted to describe the power generation in the core. The nodal equations are derived within the framework of Avery's coupled-core kinetics theory. This method enables us to evaluate easily the internodal coupling coefficients using steady-state flux and importance distributions. Particular care is taken in treating the heater wall dynamics by using a distributed parameter model for the fuel rod. The flow is described by the homogeneous equilibrium conservation equations.A steady-state calculation is performed to determine the flow distribution and the neutronic coupling parameters in a core constituted by three hydrodynamic channel types and two neutronic radial nodes. The dynamics solution is based on linearization and use of the Nyquist stability criterion. The stability margin is found to be significantly affected by the coupling effect. The importance of a detailed representation of the neutronic behavior in BWR stability studies is demonstrated.     

Advances on the research on nonlinear phenomena in boiling natural circulation loop

The state-of-the-art of theoretical investigations on the flow oscillations that occur in a boiling natural circulation loop has been presented here. Motivation behind the work is to develop a high-fidelity model that is capable of predicting nature of flow instabilities more accurately. At the low pressures and low heat fluxes conditions, the major four types of instabilities may occur in boiling natural circulation loop depending on operating conditions: Flow excursion, Geysering instability, Flashing-induced instability and Type I density-wave oscillations. The characteristics of different instabilities as well as the effects of different operating and geometric parameters on them have been reviewed. The objective of this review is to gather the research findings on the nonlinear stability phenomena in various boiling flow channel systems over a period of several years. This review indicates that most of the theoretical predictions of amplitudes and periods of the sustained oscillations are carried out using two models, namely, homogeneous equilibrium model (HEM) (still debatable) and drift-flux model (DFM) (more realistic) and are validated by experimental findings. This review work on theoretical investigations presented in this paper indicates that there are enough scopes for improving mathematical formulations of the natural circulation boiling loop (NCBL) for thermohydraulic instabilities.     

Steam drum level dynamics in a multiple loop natural circulation system of a pressure-tube type boiling water reactor

Advanced Heavy Water Reactor (AHWR) is a pressure tube type boiling water reactor employing natural circulation as the mode of heat removal under all the operating conditions. Main heat transport system (MHTS) of AHWR is essentially a multi-loop natural circulation system with all the loops connected to each other. Each loop of MHTS has a steam drum that provides for gravity based steam–water separation. Steam drum level is a very critical parameter especially in multi-loop natural circulation systems as large departures from the set point may lead to ineffective separation of steam–water or may affect the driving head. However, such a system is susceptible to steam drum level anomalies under postulated asymmetrical operating conditions among the different quadrants of the core like feedwater flow distribution anomaly among the steam drums or power anomaly among the core quadrants. Analyses were carried out to probe such scenarios and unravel the underlying dynamics of steam drum level using system code RELAP5/Mod3.2. In addition, a scheme to obviate such problem in a passive manner without dependence on level controller was examined. It was concluded that steam drums need to be connected in the liquid as well as steam space to make the system tolerant to asymmetrical operating conditions.     

Numerical simulation and artificial neural network modeling of natural circulation boiling water reactor

Numerical simulation of natural circulation boiling water reactor is important in order to study its performance for different designs and under various off-design conditions. Numerical simulations can be performed by using thermal-hydraulic codes. Very fast numerical simulations, useful for extensive parametric studies and for solving design optimization problems, can be achieved by using an artificial neural network (ANN) model of the system. In the present work, numerical simulations of natural circulation boiling water reactor have been performed with RELAP5 code for different values of design parameters and operational conditions. Parametric trends observed have been discussed. The data obtained from these simulations have been used to train artificial neural networks, which in turn have been used for further parametric studies and design optimization. The ANN models showed error within ±5% for all the simulated data. Two most popular methods, multilayer perceptron (MLP) and radial basis function (RBF) networks, have been used for the training of ANN model. Sequential quadratic programming (SQP) has been used for optimization.     

Influence of subcooled boiling on out-of-phase oscillations in boiling water reactors

In this paper, we develop a reduced order model with modal kinetics for the study of the dynamic behavior of boiling water reactors. This model includes the subcooled boiling in the lower part of the reactor channels. New additional equations have been obtained for the following dynamics magnitudes: the effective inception length for subcooled boiling, the average void fraction in the subcooled boiling region, the average void fraction in the bulk-boiling region, the mass fluxes at the boiling boundary and the channel exit, respectively, and so on. Each channel has three nodes, one of liquid, one with subcooled boiling, and one with bulk boiling. The reduced order model includes also a modal kinetics with the fundamental mode and the first subcritical one, and two channels representing both halves of the reactor core. Also, in this paper, we perform a detailed study of the way to calculate the feedback reactivity parameters. The model displays out-of-phase oscillations when enough feedback gain is provided. The feedback gain that is necessary to self-sustain these oscillations is approximately one-half the gain that is needed when the subcooled boiling node is not included.     

Performance improvement analysis of boiling water reactors by incorporation of hydride fuel

The feasibility of improving the neutronic characteristics of boiling water reactors (BWR) by using U–Zr hydride fuel is studied. Several modified BWR fuel assembly designs are considered. These include designs in which hydride fuel rods replace water rods only, replace water rods and a fraction of the oxide fuel rods, replace oxide fuel in the upper half of all the fuel rods, and replace all the oxide fuel in the assembly. It is found that replacement of at least half of the oxide fuel rods in the fuel assembly by U–ZrH_1.6 fuel might simultaneously improve the performance of BWR in three ways: (a) Increasing the energy extracted per fuel assembly and the cycle length by up to 10%. (b) Reducing the uranium ore and SWU requirements by approximately 10%. (c) Reducing the negative void coefficient of reactivity by, at least, 50%. It is also found that replacement of all the oxide fuel by hydride fuel opens interesting new options for the design of BWR fuel assemblies. The net result might be simplified assembly designs that can generate significantly more energy while featuring small negative void coefficient of reactivity. U–ThH₂ fuel appears to be even more promising than U–ZrH_1.6. For the potential benefits from hydride fuel to be realized, a clad material that is not permeable to hydrogen and is not as neutron absorbing as stainless steel needs to be developed.     

Analytical modeling of flashing-induced instabilities in a natural circulation cooled boiling water reactor

A dynamic model for natural circulation boiling water reactors (BWRs) under low-pressure conditions is developed. The motivation for this theoretical research is the concern about the stability of natural circulation BWRs during the low-pressure reactor start-up phase. There is experimental and theoretical evidence for the occurrence of void flashing in the unheated riser under these conditions. This flashing effect is included in the differential (homogeneous equilibrium) equations for two-phase flow. The differential equations were integrated over axial two-phase nodes, to derive a nodal time-domain model. The dynamic behavior of the interface between the one and two-phase regions is approximated with a linearized model. All model equations are presented in a dimensionless form. As an example the stability characteristics of the Dutch Dodewaard reactor at low pressure are determined.     

Mass flow rate sensitivity and uncertainty analysis in natural circulation boiling water reactor core from Monte Carlo simulations

Our aim was to evaluate the sensitivity and uncertainty of mass flow rate in the core on the performance of natural circulation boiling water reactor (NCBWR). This analysis was carried out through Monte Carlo simulations of sizes up to 40,000, and the size, i.e., repetition of 25,000 was considered as valid for routine applications. A simplified boiling water reactor (SBWR) was used as an application example of Monte Carlo method. The numerical code to simulate the SBWR performance considers a one-dimensional thermo-hydraulics model along with non-equilibrium thermodynamics and non-homogeneous flow approximation, one-dimensional fuel rod heat transfer. The neutron processes were simulated with a point reactor kinetics model with six groups of delayed neutrons. The sensitivity was evaluated in terms of 99% confidence intervals of the mean to understand the range of mean values that may represent the entire statistical population of performance variables. The regression analysis with mass flow rate as the predictor variable showed statistically valid linear correlations for both neutron flux and fuel temperature and quadratic relationship for the void fraction. No statistically valid correlation was observed for the total heat flux as a function of the mass flow rate although heat flux at individual nodes was positively correlated with this variable. These correlations are useful for the study, analysis and design of any NCBWR. The uncertainties were propagated as follows: for 10% change in the mass flow rate in the core, the responses for neutron power, total heat flux, average fuel temperature and average void fraction changed by 8.74%, 7.77%, 2.74% and 0.58%, respectively.     

Numerical investigations on power ramping procedure for a natural circulation boiling water reactor

Startup of a natural circulation boiling water reactor (NCBWR) is studied numerically, using a thermal-hydraulic system code RELAP5. A number of numerical experiments are carried out using various power ramps, and a suitable heat-up rate is identified to pressurize the reactor to the desired operating conditions in a reasonable time without considerable void generation in the core. It is observed that the occurrence of flashing in the riser section is unavoidable. Although flashing helps in steam production, the amplitude of flow oscillations induced by flashing is the event of concern, as in the case of the pressure tube type NCBWR studied here. Therefore, the feasibility of a complete single-phase startup is also examined and found not attractive. A new startup procedure, which completely bypasses the unstable two-phase region, is conceptualized, and the method to take the system to the operating condition without encountering flow oscillations is numerically investigated.     

The development and validation of a natural circulation analysis code for marine reactors

A code PNCMC (Program for Natural Circulation under Motion Conditions) has been developed for natural circulation simulation of marine reactors. The code is based on one-dimensional two-fluid model in noninertial frame of reference. The body force term in the momentum equation is considered as a time dependent function, which consists of gravity and inertial force induced by three-dimensional ship motion. Staggered mesh, finite volume method, semi-implicit first order upwind scheme and Successive Over Relaxation (SOR) method are used to discretize and solve two-phase mass, momentum and energy equations. Single-phase natural circulation experiments under rolling condition performed in Institute of nuclear and new energy technology of Tsinghua University and two-phase natural circulation experiments under rolling condition performed by Tan and colleagues are used to validate PNCMC. The validation results indicate that PNCMC is capable to investigate the single-phase and two-phase natural circulation under rolling motion.     

Parametric effects on reactivity instabilities and nonlinear oscillations in a nuclear-coupled double channel natural circulation boiling system

Natural circulation boiling systems consisting of parallel channels can undergo different types of oscillations (in-phase or out-of-phase) depending on the geometric parameters and operating conditions. The coupling between the neutronics and thermal-hydraulics has a strong influence on the modes of oscillations in a multi-channel system. In the present study a natural circulation double channel system is modeled. The reactor kinetics is represented by multi-point neutron kinetics model which includes the spatial variation of neutrons. Parametric effects on stability of the system, frequency, and the oscillation modes (reactivity instabilities) are investigated. It is found that at high powers compact cores will be more stable compared to larger cores, while the opposite will be the case at low powers. Further, nonlinear analysis is carried out to investigate the parametric effects on the bifurcation characteristics, transition from one mode to the other mode and chaotic oscillations. The delay in heat transfer and strong neutron interactions between the subcores delays the occurrence of chaotic oscillations.     

Startup instability in natural circulation driven nuclear reactors

Natural circulation driven nuclear reactors are prone to flow instability during the startup transients. This paper intends to provide the state-of-the-art reviews on the theoretical analysis and experimental studies on flow instability in three types of natural circulation driven reactors, ranging from conventional nuclear reactors to small modular reactors. Brief overviews of three categories of startup flow instability, i.e., density wave oscillations, flashing instability, and Geysering instability, are provided. A critical review is conducted for the scaling analysis and design of small scaled test facility. The review of obtaining quasi-steady state stability maps in the dimensionless stability plane through frequency domain analysis and experimental tests provides the state-of-the-art methodology of analyzing the flow instability. Experimental startup instability during different initial startup procedures is reviewed. Although extensive efforts have been made to study the flow instability, further work is required to improve the scaling ability of experimental investigation and the accuracy of code analysis. Some discussions for future research directions are given.     

Study on the flow-pattern-transition instability in a natural circulation heavy water moderated boiling light water cooled reactor

A mathematical model has been developed to study the flow pattern transition instability which may occur in a boiling two-phase system. The model considers flow pattern transition criteria for vertical upward and horizontal flow in pipes to identify the flow pattern transition and flow pattern specific pressure drop models. It also considers the drift flux model to estimate the void fraction in the two-phase region. The model has been applied to predict the flow pattern transition instability in a natural circulation heavy water moderated boiling light water cooled reactor. It is found that the instability characteristics is similar to that of the Ledinegg-type instability. However, the number of multiple steady states for a given operating power can be much larger in the flow pattern transition instability as compared to that of the Ledinegg-type instability. Stability maps were plotted and compared for both the flow pattern transition instability and that of the Ledinegg-type instability. The influence of various geometric and operating parameters on this instability were investigated.     

Study on the stability behaviour of a natural circulation pressure tube type boiling water reactor

The stability behaviour of a natural circulation pressure tube type boiling water reactor (BWR) has been investigated analytically. The analytical model considers homogeneous two-phase flow, a point kinetics model for the neutron dynamics and a lumped heat transfer model for the fuel dynamics. The results indicate that both Type I and Type II density-wave instabilities can occur in the reactor in both in-phase and out-of-phase mode of oscillations in the boiling channels of the reactor. The delayed neutrons were found to have strong influence on the stability of Type I and Type II density-wave instabilities. Also, the stability of the reactor is found to increase with increase in negative void reactivity coefficient unlike that observed previously in vessel type BWRs. Decay ratio map was predicted considering the effects of channel power, channel inlet subcooling, feed water temperature and channel exit quality, which are useful for the design of the reactor.