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.     

The development of a closed-form analytical model for the stability analysis of nuclear-coupled density-wave oscillations in boiling water nuclear reactors

A state-of-the-art one-dimensional thermal-hydraulic model has been developed to be used for the linear analysis of nuclear-coupled density-wave oscillations in a boiling water nuclear reactor (BWR). This model accounts for phasic slip, distributed spacers, subcooled boiling, space/time-dependent power distributions and distributed heated wall dynamics. In addition to a parallel channel stability analysis, a detailed model was derived for the BWR loop analysis of both the natural and forced circulation modes of operation.The model for coolant thermal-hydraulics has been coupled with the point kinetics model of reactor neutronics. Kinetics parameters for use in the neutronics model have been obtained by utilizing self-consistent nodal data and power distributions.The computer implementation of this model, NUFREQ-N, was used for the parametric study of a typical BWR/4, as well as for comparisons with existing in-core and out-of-core data. Also, NUFREQ-N was applied to analyze the expected stability characteristics of a typical BWR/4.     

Conditions for the existence of chaotic oscillations in nuclear reactors

It is shown on the basis of point kinetics equations with delayed neutrons that if the impulse feedback function is negative, nonmonotonic, and possesses several maxima and the coefficient of amplification of feedback is sufficiently large, then chaotic self-excited oscillations of the following type arise in nuclear reactors. Neutron bursts with random intensity occur in random time interals in the reactor, and the neutron density between the bursts oscillates at a low level. The mechanism for the appearance of chaos is described and one-dimensional mappings which approximately determine the chaotic dynamics are constructed. Three types of reactors (boiling water, with gaseous core, pulsed) where such chaotic oscillations can arise are indicated. The results obtained point the way to determining other types of reactors with stochastic behavior. 4 figures, 10 references. This work is supported by a grant (No. 87 Gr-98) in fundamental studies in the field of power engineering and electronics (Ministry of Education, Moscow Power-Engineering Institute) “Chaotic dynamics of nuclear reactors” and a grant in fundamental studies in the field of automatics and telemechanics, computer technology, information technology, cybernetics, metrology, and communication (Ministry of Education, St. Petersburg State Electrical Engineering University) “Chaotic dynamics of nonlinear control systems.” Scientific-Research Institute of Mechanics at Nizhnii Novgorod State University. Translated from Atomnaya énergiya, Vol. 88, No. 6, pp. 432–438, June, 2000.     

Flow and pressure drop fluctuations in a vertical tube subject to low frequency oscillations

Heat transfer and other equipment mounted on off-shore platforms may be subjected to low frequency oscillations. The effect of these oscillations, typically in the frequency range of 0.1–1 Hz, on the flow rate and pressure drop in a vertical tube has been studied experimentally in the present work. A 1.75 m-long vertical tube of inner diameter 0.016 m was mounted on a plate and the whole plate was subjected to oscillations in the vertical plane using a mechanical simulator capable of providing low frequency oscillations in the range of 8–30 cycles/min at an amplitude of 0.125 m. The effect of the oscillations on the flow rate and the pressure drop has been measured systematically in the Reynolds number range 500–6500. The induced flow rate fluctuations were found to be dependent on the Reynolds number with stronger fluctuations at lower Reynolds numbers. The effective friction factor, based on the mean pressure drop and the mean flow rate, was also found to be higher than expected. Correlations have been developed to quantify this Reynolds number dependence.     

Analytical study of coupled neutronic and thermodynamic instabilities in a boiling channel

Linear stability analysis in the frequency domain is performed to reveal the basic mechanism of coupled nuclear-thermal instabilities in a boiling channel. It is found that the Ledinegg instability will not occur due to the coupling of the void-reactivity feedback and the hydrodynamic feedback. Besides the phase-change number N_p and Jacob number Ja, the Froude number Fr and the fuel-time-constant τ_M are found to be the parameters determining the density-wave instability. It is also found that the Froude number effect on the density-wave stability becomes stronger when the void-reactivity feedback is involved, and that the lower the Fr number the less stable the system. The result reveals that there exists a region in which the void-reactivity feedback loop is unstable, and this has a strong effect on the stability of the system. A non-dimensional fuel-time-constant number is proposed, with which the stability boundary is better presented in the range of Froude numbers of interest.     

Thermo-hydraulic instabilities in parallel boiling channel systems: Part 1. A non-linear and a linear analytical model

Two analytical models are proposed to analyze density wave instability. One is a non-linear analytical model (PARALLEL) solved for the time elapsed and is applicable to systems with more than three channels with the same flow conditions or different flow conditions between channels. The other is a linear model (PARCOMP) solved on a complex plane and is applicable to two channel systems with or without different flow conditions. The results obtained by these models are compared with the density wave instability occurring in a twin parallel boiling channel system. The PARALLEL is applied to systems with more than three channels with the same flow conditions, and the results are compared with those in a twin channel system. Finally, the effects of the different flow conditions on the stable flow limit in a system with more than three channels are investigated analytically using PARALLEL. The approximation method by a linear model is examined and proposed to evaluate the stable flow limit in this case.     

Photographic study on transitions from non-boiling and nucleate boiling regime to film boiling due to increasing heat inputs in liquid nitrogen and water

The behavior of vapor bubbles and vapor film during the transition from non-boiling regime such as natural convection or transient conduction regime to film boiling regime on a 1.2-mm diameter platinum horizontal cylinder in liquid nitrogen and in water due to exponentially increasing heat inputs, ranging from a quasi-steady state heat input to a very rapidly increasing one, were examined by photographs taken by a high-speed video camera. The experiments for water were performed for the two cases without and with pre-pressurization before each experimental run. It was confirmed by the observation of vapor behavior that the direct transitions in liquid nitrogen and in water which is pre-pressurized before each run occur due to the explosive-like heterogeneous spontaneous nucleation (HSN) in originally flooded cavities not only in the transient conduction regime, but also in quasi-steadily increasing natural convection regime without the vapor bubbles from active cavities entraining vapor. It was also confirmed that the semi-direct transition from conduction regime to film boiling with nucleate boiling due to the rapidly increasing heat inputs in water occurs due to the HSN with nucleate boiling at around the lower limit of HSN surface superheat in subcooled water even for the non-prepressure case. The lower limit of HSN surface superheat was measured as an initial boiling surface superheat caused by a quasi-steadily increasing heat input for the case with pre-pressurization before each experimental run.     

On the occurrence of burnout downstream of a flow obstacle in boiling two-phase upward flow within a vertical annular channel

If a flow obstacle, such as a spacer is placed in a boiling two-phase flow within a channel, the temperature on the surface of the heating tube is severely affected by the existence of the spacer. Under certain conditions, a spacer has a cooling effect, and under other conditions, the spacer causes dryout of the cooling water film on the heating surface. The burnout mechanism, which always occurs upstream of a spacer, however, remains unclear.In a previous paper [Fukano, T., Mori, S., Akamatsu, S., Baba, A., 2002. Relation between temperature fluctuation of a heating surface and generation of drypatch caused by a cylindrical spacer in a vertical boiling two-phase upward flow in a narrow annular channel. Nucl. Eng. Des. 217, 81–90], we reported that the disturbance wave has a significant effect on dryout and burnout occurrence and that a spacer greatly affects the behavior of the liquid film downstream of the spacer.In the present study, we examined in detail the influences of a spacer on the heat transfer and film thickness characteristics downstream of the spacer by considering the result in steam–water and air–water systems. The main results are summarized as follows:

(1) The spacer averages the liquid film in the disturbance wave flow. As a result, dryout tends not to occur downstream of the spacer. This means that large temperature increases do not occur there. However, traces of disturbance waves remain, even if the disturbance waves are averaged by the spacer.

(2) There is a high probability that the location at which burnout occurs is upstream of the downstream spacer, irrespective of the spacer spacing.

(3) The newly proposed burnout occurrence model can explain the phenomena that burnout does occur upstream of the downstream spacer, even if the liquid film thickness t_F m is approximately the same before and behind the spacer.

Influence of a flow obstacle on the occurrence of burnout in boiling two-phase upward flow within a vertical annular channel

When a flow obstruction such as a cylindrical spacer is set in a boiling two-phase flow within an annular channel, the inner tube of which is used as a heater, the temperature on the surface of the heating tube is severely affected by its existence. In some cases, the cylindrical spacer has a cooling effect, and in the other cases it causes the dryout of the cooling water film on the heating surface resulting in the burnout of the heating tube.In the present paper, we have focused our attention on the influence of a flow obstacle on the occurrence of burnout of the heating tube in boiling two-phase flow.The results are summarized as follows:

(1)When the heat flux approaches the burnout condition, the wall temperature on the heating tube fluctuates with a large amplitude. And once the wall temperature exceeds the Leidenfrost temperature, the burnout occurs without exception.

(2)The trigger of dryout of the water film which causes the burnout is not the nucleate boiling but the evaporation of the base film between disturbance waves.

(3)The burnout never occurs at the downstream side of the spacer. This is because the dryout area downstream of the spacer is rewetted easily by the disturbance waves.

     

Decoherence of beam oscillations in the SSC due to beam-beamcollisions

Computer simulations were made to study the decoherence of beam oscillations in the SSC collider due to the tune shift generated by the head-on beam-beam interaction. Our simulation results on the average tune shift and the RMS tune spread were compared with previous theoretical estimates and excellent agreement was found. Our simulations also confirmed the expectation that the decoherence time increases with decreasing tune spread in the beam. A simple procedure was presented to quantify the decoherence time from the simulated growth of the beam emittance relative to the beam centroid     

Nonlinear analysis of nuclear coupled density wave instability in time domain for a boiling water reactor core undergoing core-wide and regional modes of oscillations

The objective of the paper is to develop a nuclear coupled thermal-hydraulic model in order to simulate core-wide (in-phase) and regional (out-of-phase) stability analysis in time domain within the limitation of desktop research facility for a boiling water reactor subjected to operational transients. The integrated numerical tool, which is a combination of thermal-hydraulic, neutronic and fuel heat conduction models, is used to analyze a complete boiling water reactor core taking into account the strong nonlinear coupling between the core neutron dynamics and primary circuit thermal-hydraulics via the void-temperature reactivity feedback effects. The integrated model is validated against standard benchmark and published results. Finally, the model is used for various parametric studies and a number of numerical simulations are carried out to investigate core-wide and regional instabilities of the boiling water reactor core with and without the neutronic feedback effects. Results show that the inclusion of neutronic feedback effects has an adverse effect on boiling water reactor core by augmenting the instability at lower power for same inlet subcooling during core-wide mode of oscillations, whereas the instability is being suppressed during regional mode of oscillations in presence of the neutronic feedback. Dominance of core-wide instability over regional mode of oscillations is established for the present case of simulations which indicates that the preclusion of the former will automatically prevent the latter at the existing working condition.     

A second order turbulence model based on a Reynolds stress approach for two-phase boiling flow. Part 1: Application to the ASU-annular channel case

High-thermal performance PWR (pressurized water reactor) spacer grids require both low pressure loss and high critical heat flux (CHF) properties. Numerical investigations on the effect of angles and position of mixing vanes and to understand in more details the main physical phenomena (wall boiling, entrainment of bubbles in the wakes, recondensation) are required.In the field of fuel assembly analysis or design by means of CFD codes, the overwhelming majority of the studies are carried out using two-equation eddy viscosity models (EVM), especially the standard K-? model, while the use of Reynolds Stress Transport Models (RSTM) remains exceptional.But extensive testing and application over the past three decades have revealed a number of shortcomings and deficiencies in eddy viscosity models. In fact, the K-? model is totally blind to rotation effects and the swirling flows can be regarded as a special case of fluid rotation. This aspect is crucial for the simulation of a hot channel in a fuel assembly. In fact, the mixing vanes of the spacer grids generate a swirl in the coolant water, to enhance the heat transfer from the rods to the coolant in the hot channels and to limit boiling.First, we started to evaluate computational fluid dynamics results against the AGATE-mixing experiment: single-phase liquid water tests, with Laser-Doppler liquid velocity measurements upstream and downstream of mixing blades. The comparison of computed and experimental azimuthal (circular component in a horizontal plane) liquid velocity downstream of a mixing vane for the AGATE-mixing test shows that the rotating flow is qualitatively well reproduced by CFD calculations but azimuthal liquid velocity is underestimated with the K-? model.Before comparing performance of EVM and RSTM models on fuel assembly geometry, we performed calculations with a simpler geometry, the ASU-annular channel case. A wall function model dedicated to boiling flows is also proposed.     

竖直矩形窄流道内过冷沸腾汽泡生长特性及对换热的影响

在一个大气压下以水为工质研究了竖直矩形窄流道内过冷沸腾的汽泡生长特性。采用Laplace数(La)和时间因子(ξ)无量纲化汽泡半径和汽泡生长时间,得到了不同工况下的无量纲汽泡生长曲线。通过分析质量流速和热流密度变化对无量纲汽泡生长的影响,发现增加质量流速会抑制汽泡生长;增加热流密度则会促进汽泡生长。汽泡的生长行为会严重影响核态沸腾换热系数hNB,从而影响总沸腾两相流动换热系数htp。采用与雷诺数(Re)相关的无量纲时间(t*)的1/3次方模型来预测无量纲汽泡生长,发现此模型能较好地预测本研究中所得到的无量纲汽泡生长数据。     

Heat transfer modeling in the vertical tubes of the passive containment cooling system of the simplified boiling water reactor

The long term containment cooling of GE's passive BWR design is based on a new safety system called PCCS (passive containment cooling system). Performance of this system relies on the pressure difference between the drywell and wetwell in case of an accident and on the condensation of steam moving downward inside vertical tubes fully submerged in a water pool initially at room temperature. In this paper a model based on the resolution of momentum equations of both phases, the application of the heat and mass transfer analogy, and the consideration of the presence of a noncondensable gas by diffusion theory in a boundary layer is presented. Assumptions and approximations taken resulted in new methods to estimate film thickness and heat transport from the gas to the interface. Influence of phenomena such as suction, flow development, film waviness, and droplet entrainment has been accounted for. Based on this formulation, a computer programme called HVTNC (heat transfer in vertical tubes with noncondensables) has been built up. HVTNC results have been compared to the experimental data available. Experimental trends have been reproduced. Heat transfer has been found to be severely degraded by the presence of noncondensables whereas high Reynolds numbers of gas flow have been seen to enhance shear stress and therefore, heat transmission. The average error of HVTNC is essentially located at regions where only a residual fraction of heat remains to be transferred, so that minor deviations can be anticipated in the overall heat transfer in the tube. Comparison of HVTNC to other models show a substantial gain of accuracy with respect to earlier models.     

An interface redesign for the feed-water system of the advanced boiling water reactor in a nuclear power plant in Taiwan

A well-designed human-computer interface for the visual display unit in the control room of a complex environment can enhance operator efficiency and, thus, environmental safety. In fact, a cognitive gap often exists between an interface designer and an interface user. Therefore, the issue of the cognitive gap of interface design needs more improvement and investigation. This is an empirical study that presents the application of an ecological interface design (EID) using three cases and demonstrates that an EID framework can support operators in various complex situations. Specifically, it analyzes different levels of automation and emergency condition response at the Lungmen Nuclear Power Plant in Taiwan. A simulated feed-water system was developed involving two interface styles. This study uses the NASA Task Load Index to objectively evaluate the mental workload of the human operators and the Situation Awareness Rating Technique to subjectively assess operator understanding and response, and is a pilot study investigating EID display format use at nuclear power plants in Taiwan. Results suggest the EID-based interface has a remarkable advantage over the original interface in supporting operator performance in the areas of response time and accuracy rate under both normal and emergency situations and provide supporting evidence that an EID-based interface can effectively enhance monitoring tasks in a complex environment.     

Incorporation of the procedure for monitoring coolant boiling in a VVER-1000 core into the in-reactor noise diagnostics system

A method for performing diagnostics of coolant boiling in a VVER-1000 core is described. This method was developed at the Russian Science Center Kurchatov Institute and is based on monitoring the increase of the sensitivity of neutron flux noise to the fluctuations of the coolant parameters. This procedure is intended to be used as part of the in-reactor noise diagnostics system. It is now in commercial operation of the No. 3 unit of the Kalinin and two units of the Tianwan (China) nuclear power plants. Translated from Atomnaya énergiya, Vol. 105, No. 2, pp. 79–82, August, 2008.     

A contribution to the hydrodynamics of boiling crisis in a forced flow of water

A physical approach is presented for defining the mechanisms responsible for the ‘departure from nucleate boiling’, DNB, in cooling water under forced convection.Based on experimental observations, a hydrodynamic model is proposed. It considers the flow of vapour bubbles away from the heated surface and the counter-current of liquid coolant streaming towards it. The general DNB correlation derived from this model is compared with numerous experimental results reported in literature and with well-known empirical DNB equations. The application to critical heat flux in uniformly heated round tubes and annuli; as well as to non-uniform heat flux profiles, is examined.Due to the scatter inherent at the onset of the boiling crisis, the proposed correlation has been set to fit the lower conservative limit of heat flux density, where DNB is observed rather than to a most probable mean value.