Study of startup transients and power ramping of natural circulation boiling systems

Numerical models of a natural circulation test facility and its prototype have been developed with RELAP5/MOD3.4 code and verified for their grid independence by nodal sensitivity studies. The model of the test facility has been validated for its steady state as well as transient predictions with the help of experimental observations. The transient predictions and parametric trends obtained by the numerical model of the prototype have been compared with those of the numerical model of the test facility. Thus, the ability of RELAP5 code to predict the transients during startup of a natural circulation boiling water reactor is verified. A powering procedure for the test facility has been conceptualized with the help of its RELAP5 model and demonstrated experimentally. Based on this, a similar powering procedure for the prototype has been proposed and simulated numerically with its RELAP5 model.     

Study of flow instabilities in double-channel natural circulation boiling systems

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. Disturbances in one channel affect the flow in other channels, which triggers thermal–hydraulic oscillations. In the present work, the modes of oscillation under different operating conditions and channel-to-channel interaction during power fluctuations and on-power refueling in a double-channel natural circulation boiling system are investigated. The system is modeled using a lumped parameter mathematical model and RELAP5/MOD3.4. Parametric studies are carried out for an equal-power double-channel system, at different operating conditions, with both the models, and the results are compared. Instabilities, non-linear oscillations, and effects of recirculation loop dynamics and geometric parameters on the mode of oscillations, are studied using the lumped model. The two channels oscillate out-of-phase in Type-I region, but in Type-II region, both the modes of oscillation are observed under different conditions. Channel-to-channel interaction and on-power refueling studies are carried out using the RELAP model. At high powers, disturbances in one channel significantly affect the stability of the other channel. During on-power refueling, a near-stagnation condition or low-velocity reverse flow can occur, the possibility of reverse flow being higher at lower pressures.     

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.     

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.     

Characteristics of two-phase natural circulation in freon-113 boiling loop

A freon-113 flow visualization loop for simulating the hot-leg U-bend natural circulation flow has been constructed and hot-leg two-phase flow behavior has been studied experimentally. From the present experiments, an understanding of the basic mechanisms of the two-phase natural circulation and flow termination were obtained. The power input, loop friction and the liquid level in the simulated steam generator played key roles in the overall flow behavior. Experimental results show that the flow behavior strongly depends on phase changes and coupling between hydrodynamic and heat transfer phenomena. Non-equilibrium phase-change phenomena such as flashing create unstable hydrodynamic conditions which lead to cyclic or oscillatory flow behaviors.     

Stability analysis and nonlinear dynamics of natural circulation boiling water reactors

Numerous experimental and numerical investigations have been reported in literature on the effect of various parameters on the dynamics of natural circulation boiling water reactors (NCBWRs). Different findings were reported in literature regarding the effect of void reactivity coefficient and fuel time constant on Type-I and Type-II instabilities. The present work contains stability analysis and nonlinear dynamics of NCBWR using a lumped parameter model. The purpose of the stability analysis is to resolve different, seemingly contradictory parametric trends reported by previous authors. Stability analysis for three different system configurations has been done using the same mathematical model and compared with the findings reported in literature. It has been observed that the effects of void reactivity coefficient and fuel time constant are influenced by geometrical parameters and are different for different systems. Nonlinear dynamics and bifurcations have been studied numerically, for one of the system configurations, for boiling channels with and without riser. The possibility of existence of stable and unstable limit cycles, period doublings, and chaotic oscillations has been investigated. The effect of void reactivity coefficient on the nonlinear dynamics has been studied in both Type-I and Type-II regions. In the Type-I region, subcritical Hopf bifurcation leading to unstable limit cycle, as well as supercritical Hopf bifurcation leading to stable limit cycle have been found. The boiling channels with and without riser have been observed to undergo chaotic oscillations under strong reactivity feedback in the Type-II region. It has been found that the presence of riser aggravates chaotic oscillations.     

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.     

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.     

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.     

Analysis of chaotic instabilities in boiling systems

An analytic model for the investigation of non-linear dynamics in boiling systems has been developed. This model is comprised of a nodal formulation that uses one-dimensional homogeneous equilibrium assumptions for diabatic two-phase flow, a lumped parameter approach for heated wall dynamics, and point neutron kinetics for the consideration of nuclear feedback in a boiling water reactor (BWR) loop. This model indicates that a boiling channel coupled with a riser may experience chaotic oscillations. In contrast, a boiling channel without a riser that is subjected to a constant pressure drop (i.e. a parallel channel) may undergo a supercritical bifurcation (i.e. may experience a limit cycle), but chaos was not found. Flow instabilities in a two-phase natural circulation loop have been verified using the model presented in this paper. The predictions of the effects of the channel inlet resistance, outlet resistance and liquid level in the downcomer agree with the data of Kyung and Lee. Finally, an analysis of nuclear-coupled density-wave instabilities in a simplified BWR (SBWR) was performed. Significantly, even for low pressure conditions, a simplified SBWR appears to be stable during start-up and normal operations; however, a limit cycle may occur for abnormal operating conditions.     

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.     

Experimentaland numerical investigation of liquid metal boiling in fuel subassemblies under natural circulation conditions

Boiling of Na-K eutectic alloy (22% Na; 78% K) in parallel channels under the natural circulation condition has been investigated at the AR-1 facility of IPPE. Hydrodynamics and heat transfer data have been obtained at this facility for various experiment set-ups of both single and parallel sections. A thermohydraulic code system based on the subchannel analysis code SABENA-3D has been developed and used to simulate these experiments. Comparisons show that the code system can reproduce the boiling phenomena in the test section with sufficient accuracy, correctly predicting the heat transfer conditions prior to and during the boiling.     

低流速自然循环过冷沸腾汽泡脱离点实验研究

针对低流速环形通道中自然循环过冷沸腾汽泡脱离点特性进行了实验研究,运用Saha-Zuber模型、Bowring模型、Forster模型和Levy模型测算汽泡脱离点的位置,与实验值进行比较,发现由于流速较低,上述模型不适用于计算本实验条件下的汽泡脱离点。以Levy模型为基础,修正了浮力项的影响系数,修正后的模型与实验结果符合良好。     

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.     

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.     

Thermo-hydraulic instability of boiling natural circulation loop induced by flashing (analytical consideration)

An analytical study is presented on the thermo-hydraulic stability of a boiling natural circulation loop with a chimney at low pressure start-up. The effect of flashing induced by the pressure drop in the channel and the chimney due to gravity head on the instability is considered. A method to analyze linear stability is developed, in which a drift-flux model is used. The analytical result of a stability map agrees very well with the experimental one obtained in a previous report. Instability does not occur when the heater power is too low to generate voids in the chimney and only natural circulation of single phase can be induced. Instability tends to occur when boiling occurs only near the chimney exit due to flashing. This instability phenomenon has some similarities with density wave oscillation, such as the phase difference of temperature between the boiling region and non-boiling region, and the oscillation period which is near to the time required for fluid to pass through the chimney. However, there are also some differences from density wave oscillation, such as the boiling region is very short, and pressure fluctuation can affect void fraction fluctuation.     

Experimental investigations on steady state natural circulation behavior of multiple parallel boiling channel system

In some industrial applications, including nuclear power plants, natural circulation flow is often employed as a reliable heat transport method. A common characteristic of many industrial two-phase natural circulation systems is the presence of a large number of parallel boiling channels. Sensitivity of the steady state behavior of such a two-phase natural circulation system to different system parameters has many implications vis-à-vis performance of the system as per the design intent under various operating conditions. This article reports the results of experimental studies carried out on the characteristics of a low pressure two-phase natural circulation system with parallel boiling channels having their individual heat sources. The work covers the study of dependence of system behavior on operational history, down-comer resistance and channel power. In view of its particular significance in nuclear industry, a special system condition with zero power in one of the parallel channels was also studied. An experimental setup consisting of 10 transparent parallel channels was designed and constructed for conducting these experimental investigations.     

Experimental study of natural circulation instability with void reactivity feedback during startup transients for a BWR-type SMR

The natural circulation boiling type SMR can experience flow instability during the startup transients due to the void reactivity feedback. A BWR-type natural circulation test loop has been built to perform the nuclear coupled startup transient tests for Purdue Novel Modular Reactor (NMR). This test loop is installed with different instruments to measure various thermal hydraulic parameters. The testing process can be monitored and controlled through PC with the assistance of LabVIEW procedure. The effects of power ramp rate on the flow instability during the nuclear coupled tests were investigated by controlling the power supply based on the point kinetics model with coolant void reactivity feedback. Two power ramp rates were investigated and the results were compared with those of the thermal hydraulic startup transients without void reactivity feedback. The time trace of power supply, system pressure, natural circulation rate, and void fraction profile are used to determine the flow stability during the transients. The results show that nuclear coupled startup transients also experience flashing instability and density wave oscillations. The power curves calculated from point kinetics model for startup transients show some fluctuations due to void reactivity feedback. However, the void reactivity feedback does not have significant effects on the flow instability during the startup procedure for the NMR.     

Analytical study of nuclear-coupled density-wave instability in a natural circulation pressure tube type boiling water reactor

An analytical model has been developed to study the nuclear-coupled density-wave instability in the Indian advanced heavy water reactor (AHWR) which is a natural circulation pressure tube type boiling water reactor. The model considers a point kinetics model for the neutron dynamics and a lumped parameter model for the fuel thermal dynamics along with the conservation equations of mass, momentum and energy and equation of state for the coolant. In addition, to study the effect of neutron interactions between different parts of the core, the model considers a coupled multipoint kinetics equation in place of simple point kinetics equation. Linear stability theory was applied to reveal the instability of in-phase and out-of-phase modes in the boiling channels of the AHWR. The results indicate that the stability behavior of the reactor is greatly influenced by the void reactivity coefficient, fuel time constant, radial power distribution and channel inlet orificing. The delayed neutrons were found to have a strong influence on the Type I and Type II instabilities observed at low and high channel powers, respectively. Also, it was found that the coupled multipoint kinetics model and the modal point kinetics model predict the same threshold power for out-of-phase instability if the coupling coefficient in the former model is half the eigen value separation between the fundamental and the first harmonic mode in the latter model. Decay ratio maps were predicted considering various operating parameters of the reactor, which are useful for its design.