“Delta-Wrinkly Zone” Observed Near Crack of Ductile Zircaloy-2 Cladding during Impact Loading Test

An equivalent linearization method has been introduced for density-wave oscillation analysis. Unlike the frequency domain approach with linearized equations assuming an infinitely small amplitude, the present method can deal with large amplitude oscillations with the nonlinearity effect on limit cycle amplitudes taken into account in the frequency domain.

Equivalent linear equations have been derived based on a one-dimensional separated flow model. A profile fit model was adopted for subcooled boiling. The characteristics of the equivalent linear equations and factors to limit the amplitudes were phenomenologically examined.

Analyses of the experimental data by Saha et al. using the present method revealed that, given an appropriate set of two-phase flow correlations, the equivalent linearization method can predict limit cycle amplitudes after instability initiation as well as the stability boundary.     

Stability analysis of parallel-channel systems with forced flows under supercritical pressure

The flow in the core of supercritical water reactors (SCWRs) experiences drastic change in its thermodynamic properties and transport properties near the pseudo-critical temperature, thus the core flow may be susceptible to density wave oscillation instability, which is a challenge to the system safety and must be studied carefully. This paper studies the dynamic stability characteristics of the fast-spectrum zone of a newly designed mixed-spectrum SCWR (SCWR-M), which is characterized as a parallel-channel system. A frequency-domain model has been developed for linear stability analysis, and marginal stability boundaries under several conditions for the parallel-channel system are generated, which indicate that the system normal operational condition is in the stable region. The stability of parallel-channel systems is dominated by the hottest channel. The higher the power density of the hottest channel is, the less stable the system will be. Increasing mass flow is beneficial for the system stability. Systems with uniformly axial power distribution are less stable than those with cosine-shaped or stair-shaped axial power distributions. In the time-domain, a single-phase one-dimensional model has been developed for non-linear analysis, and several perturbation transients are calculated. The results of analysis show a good agreement with that of the frequency-domain analyses, and the existence of transitional stable region has been verified.     

Turning points and sub- and supercritical bifurcations in a simple BWR model

Stability and semi-analytical bifurcation analyses of BWRs have been performed using a dynamical system approach. A reduced order model of a BWR that includes simple neutronics as well as thermal hydraulics has been used. Analyses have been carried out using a bifurcation analysis code, BIFDD, that carries out analytic–numeric stability and bifurcation analyses of set of ordinary differential equations and ODEs with delays. A large segment of the parameter space has been investigated using this very efficient tool. Stability boundaries are obtained in several two-dimensional parameter spaces. In addition, the nature of bifurcation along these stability boundaries has also been determined. Results indicate that both subcritical as well as supercritical Poincaré–Andronov–Hopf bifurcations are likely to occur in regions of interest in parameter space.In addition to the semi-analytical bifurcation studies, the governing equations have also been integrated numerically. Results confirm the findings of the stability and bifurcation analyses. Numerical integrations, carried out for parameter values away from the stability boundary, further show that the bifurcation curves, in many cases of subcritical bifurcations, have a turning point. The bifurcation curve in these cases extends back into the unstable region. These results show that it is possible to experience large amplitude stable oscillations in the unstable region infinitesimally close to the stability boundary. Moreover, large amplitude stable oscillations are also possible, following large but finite perturbations, in the stable region of the parameter space near the stability boundary. These findings provide alternate explanation for the experimental and operational observations in BWRs that indicate the existence of stable limit cycle oscillations and the possibility of growing amplitude oscillations.Results obtained here using a simple model suggest that further work along these lines, with more detailed models, is needed to identify operating conditions and perturbation amplitudes that might lead to stable limit cycles or growing amplitude oscillations in current and next generation of BWRs.     

Experimental investigation of natural circulation in a symmetrical loop under large scale rolling motion conditions

In ocean environment, the ship motion significantly affects the natural circulation behavior in ship-based integrated-type reactor. This paper theoretically and experimentally investigated natural circulation characteristics in symmetrical loops under rolling condition. Experiments were carried out on a test loop with a symmetrical configuration by simulating the structure of an accrual reactor. The theoretical results revealed that only angular acceleration contributes to the resultant force under zero power rolling condition. In a closed circuit with a uniform cross-section area, the angular acceleration force integral is proportional to the angular acceleration and the area enclosed by the circuit. The integral value varies over time and causes flow oscillations. However, the angular acceleration force does not influence the flow status in the shared part of the two symmetrical neighbor circuits due to force interactions. Rolling experiments with a zero power load confirmed these results. Full power experiments under rolling condition exhibited observable flow rate and temperature oscillations in each branch of the flow channel. The oscillations in the side flow channels had the same values for both the period and the phase with the variation of rolling angle. The angular acceleration force was the main cause of this. The oscillations in the middle channel had a period half the value of the rolling period. The periodical variation of the vertical component of gravity caused this. The horizontal component of gravity was out-phasing with angular acceleration. Therefore, it alleviated oscillation in the side channels. The experimental results showed that for the same rolling period, as the rolling angle increased, the average flow rate decreased and oscillation amplitudes increased. Also, as the power load increased, the oscillations in the middle channel increased and the oscillation in the side channel decreased.     

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.     

Impact of Pseudocolloid Formation on Migration of Nuclides within Fractures

Numerical simulation of boiling of Na-K eutectic alloy (22% Na; 78% K) in a parallel channel system under natural circulation conditions is presented in this work. The calculations pertain to an experimental analysis conducted at the AR-1 facility of IPPE (Russia), analyzing the reactor core coolabilty under severe thermal conditions. The geometrical and operational characteristics reproduce those typical of Russian FBRs. A thermohydraulic code system based on a subchannel analysis code has been developed and adopted for the simulation. Comparisons show that the adopted numerical procedure is capable of reproducing the boiling phenomena inside the parallel bundle test section, correctly predicting the heat transfer conditions prior to and during the boiling. Experimental as well as computational results show the marked influence of the parallel channel interaction, evidenced by the appearance of severe flow oscillations. The results confirm that stable heat removal is provided throughout the entire transient.     

Simulation Study on the Self-Sustained Oscillations in DC Driven Glow Discharges at Atmospheric Pressure Under Different Gas Gaps

In this paper,a one-dimensional plasma fluid model is employed to study the selfsustained oscillations in DC-driven helium glow discharges at atmospheric pressure under different gas gaps.Our simulation results indicate that a harmonic current oscillation with tiny amplitude always occur at the onset of instability and transits into a relaxation one as the conductivity of the semiconductor is decreased.It is found that the dynamics of the oscillations are dependent on the gas gaps.The discharge can only exhibit a simple oscillation with unique amplitude and frequency at smaller gas gaps(2 mm) while it can exhibit a more complex oscillation with several different amplitudes and frequencies at larger gas gaps(2 mm).The discharge modes in these current oscillations have also been analyzed.     

Startup scheme optimization and flow instability of natural circulation lead-cooled fast reactor SNCLFR-100

Owing to the inherent instability of the natural circulation system,flow instability can easily occur during the operation of a natural circulation lead-cooled fast reactor,especially during the startup phase.A compre-hensive startup scheme for SNCLFR-100,including pri-mary and secondary circuits,is proposed in this paper.It references existing more mature startup schemes in various reactor types.It additionally considers the restriction con-ditions on the power increase in other schemes and the characteristics of lead-based coolant.On this basis,the multi-scale coupling code ATHLET-OpenFOAM was used to study the flow instability in the startup phase under different power-step amplitudes and power duration times.The results showed that obvious flow instability phenom-ena were found in the different startup schemes,such as the short-term backflow phenomenon of the core at the initial time of the startup.Moreover,an obvious increase in the flow rate and temperature to the peak value at the later stage of a continuous power rise was observed,as well as continuous oscillations before reaching a steady state.It was determined that the scheme with smaller power-step amplitude and a longer power duration time requires more time to start the reactor.Nevertheless,it will be more conducive to the safe and stable startup of the reactor.     

Experimental study on two-phase natural circulation and flow termination in a loop

In order to study the two-phase natural circulation and flow termination during a small break loss of coolant accident in LWR, a hot leg U-bend simulation loop has been built based on the two-phase flow scaling criteria developed under this program. The nitrogen-water system has been used to isolate the key hydrodynamic phenomena from heat transfer problems. Various tests were carried out to establish the basic mechanism of the flow termination and reestablishment as well as to obtain essential information on scale effects of various parameters such as the loop frictional resistance, thermal center, U-bend curvature, and inlet geometry. It was found that the permanent termination of the natural circulation was related to the head balance between the hot and cold legs. The local flow condition at the inverted U-bend could produce intermittent flow, however was not related to the permanent flow termination. The void distribution in a hot leg, flow regime, and natural circulation rate have been measured in detail for various conditions. Significant effects of the inlet geometry on these were observed. Near the flow termination condition, large amplitude flow oscillations occurred. The occurrence of this type of flow instability is important for safety analyses, because it may lead to loop-to-loop oscillations or flow excursions in a prototype system which has a multi-loop configuration.     

流动不稳定性对CHF的影响

本文成功地训练了一个用于预测流动不稳定性条件下CHF的人工神经网络,利用所训练的人工神经网络,分析了流动不稳定性对无量纲因子F的影响规律.分析结果表明,系统压力对F的影响是非单值的;平均质量流速增大,总体上F也增大.还分析了流动不稳定性条件下系统主要参数对临界热流密度的影响.结果表明:当质量流速的振幅与平均质量流速的比增加时,CHF 减小;质量流速的振幅与平均质量流速的比不变时,随着周期增大,CHF减小.     

非对称加热下摇摆对并联双通道管间脉动特性的影响

采用理论分析与RELAP5/MC程序计算相结合的方法,研究了非对称加热条件下摇摆运动对并联双通道管间脉动特性的影响。结果表明,摇摆运动会引起周期等于摇摆周期以及1/2摇摆周期的流量波动,当摇摆引起的流量波动周期与系统固有热工水力振荡周期接近时,会发生共振效应,从而使密度波振荡提前发生。增大摇摆幅度及通道到摇摆中心的距离可增强流量波动幅度,降低系统稳定性。     

Nonlinear effects in two-phase flow dynamics

Thermally induced two-phase flow oscillations in uniformly heated boiling channels have been analyzed numerically using a one-dimensional model of two-phase flow. Two different approaches to modeling of subcooled boiling have been considered: a mechanistic model and a profile-fit model. The overall model has been numerically implemented as a computer code, DYNOBOSS, which has been validated against a linear stability analysis code and experimental data.The effects of both modeling assumptions and numerical methods of solution have been studied. It has been shown that the calculated transient response of the boiling channel may be very sensitive to the numerical scheme and spatial discretization, especially for operating conditions in the linearly unstable region. For the range of operating parameters studied, phasic slip has shown a significant stabilizing effect on the system, whereas subcooled boiling has indicated smaller influence. Furthermore, it has been shown that the rate of increase of limit cycle amplitude with channel exit quality is higher for low than high inlet subcoolings.     

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.     

An experimental-stochastic and theoretical analysis of the density wave instability in a helical monotube vapour generator

Some of the AGR Nuclear Power Plants in the UK contain helical forced-flow once-through steam generators. The design of these plants and their associated control policies and systems to ensure stable operation over an adequate range of operating conditions has proved a difficult task, and has required a close study of the dynamic performance of helical two-phase systems, and particularly of instability mechanisms.A combined theoretical and experimental study has been carried out to investigate the dynamics of two-phase flow in such arrangements, with special reference to density wave oscillations.An “Arcton-113” closed loop comprising a helical, electrically heated, once-through tube in a parallel channel design has been constructed and operated.The inherent noise of the flowrate signal with the hidden periodicities present in the vapour generator have been recorded and analysed using stochastic facilities and techniques in order to determine the dynamic behaviour of the system.The observed density wave oscillations are compared with the analytical predictions from a computerised distributed parameter time-varying linearised analysis of the conservation equations of the two phases. We consider the slip between the two phases, variable friction factors, as well as variable heat flux by taking into account the dynamics of the heater wall.The experimental-stochastic analysis gives insight into the phenomenon and meaningful results which are in accordance with the theoretical predictions.     

The propagation dynamics and stability of an intense laser beam in a radial power-law plasma channel

By containing ponderomotive self-channeling,the propagation behavior of an intense laser beam and the physical conditions are obtained theoretically in a radial power-law plasma channel.It is found that ponderomotive self-channeling results in the emergence of a solitary wave and catastrophic focusing,which apparently decreases the region for stable propagation in a parameter space of laser power and the ratio of the initial laser spot radius to the channel radius(RLC).Direct numerical simulation confirms the theory of constant propagation,periodic defocusing and focusing oscillations in the parameter space,and reveals a radial instability which prevents the formation of bright and dark solitary waves.The corresponding unstable critical curve is added in the parameter space numerically and the induced unstable region above the unstable critical curve covers that of catastrophic focusing,which shrinks the stable region for laser beams.For the expected constant propagation,the results reveal the need for a low RLC.Further study illustrates that the channel power-law exponent has an obvious effect on the final stable region and laser propagation,for example increasing this exponent can enlarge the stable region significantly,which is beneficial for guiding of the laser and increases the lowest RLC for constant propagation.Our results also show that the initial laser amplitude has an apparent influence on the propagation behavior.     

A comparative study of water boiling in a vertical tube under temperature-controlled or power-controlled boundary conditions

The Simulant Boiling Flow Visualization (SBFV) loop is an experimental facility where natural-convection boiling of water was accomplished in a transparent vertical tube by using hot glycerine; thus, direct observation was possible. As a result, heating was obtained through a temperature-controlled rather than a power-controlled boundary condition. To compare the SBFV data with previous experiments using a stainless steel test section and a power-controlled boundary condition, a comparative study of the effect on water boiling with the two different boundary conditions was performed. The computer program LOOP-W was used for this purpose. This program has been used successfully in analyzing data from the SBFV, and it was modified so that analogous cases could be run with the two different boundary conditions.The period and the amplitude of the oscillations calculated by the computer code using either boundary condition were essentially the same. Calculations also predicted the effect on the boiling process of using different test section materials (glass and stainless steel). Important differences were noted in the calculated periods and amplitudes. These calculations suggest that the SBFV loop can adequately simulate a power-controlled experimental facility.     

Modeling and analysis of hydrodynamic instabilities in two-phase flow using two-fluid model

Because of the practical importance of two-phase flow instabilities, especially in boiling water nuclear reactor technology, substantial efforts have been made to date to understand the physical phenomena governing such instabilities and to develop computational tools to model the dynamics of marginally-stable/unstable boiling systems. The purpose of this paper is to present an integrated methodology for the analysis of flow-induced instabilities in boiling channels and systems. The major novel aspects of the proposed approach are: (a) it is based on the combined frequency-domain and time-domain methods, the former used to quantify stability margins and to determine the onset of instability conditions, the latter to study the nonlinear system response outside the stability boundaries identified using the nearly-exact results of the frequency-domain analysis; (b) the two-fluid model of two-phase flow has been used for the first time to analytically derive the boiling channel transfer functions for the parallel-channel and channel-to-channel instability modes. In this way, the major characteristics of a boiling system, including the onset-of-instability conditions, can be readily evaluated by using the qualitative frequency-domain approach, whereas the explicit time-domain integration is performed, if necessary, only for the operating conditions that have already been identified as unstable. Both methods use the same physical two-fluid model that, in one case, is linearized and used to derive a rigorous analytical solution in the complex domain, and, in the other case, is solved numerically using an algorithm developed especially for this purpose. The results using both methods have been compared against each other and extensively tested. The testing and validation of the new model included comparisons of the predicted steady-state distributions of major parameters and of the transient channel response against experimental data.     

Instabilities in Parallel Channel of Forced-Convection Boiling Upflow System, (V)

The density wave instability in a parallel boiling channel system heated electrically has been studied experimentally and analytically by the authors. In our country, the steam generator for LMFBR has been investigated with Power Reactor and Nuclear Fuel Development Corp. as the central figure for its development, and many results of this instability were reported. Their results were different from our ones as regard to the governing factor of the period of flow oscillation in the unstable region and to the effect of the slip ratio on the stability in analysis. A new linear analytical model is proposed in this paper and the analytical results are compared with ones of two-phase analyses based on the same linear method as this model. Subsequently, the effect of the slip ratio on the stability is studied analytically by this model. The parallel boiling channel system is studied experimentally and analytically, using Freon-113 as test fluid heated by hot water as simulation of the SG for LMFBR. The governing factor of the period of flow oscillation is made clear.     

A stability analysis of ventilated boiling channels

A mathematical model has been developed for the linear stability analysis of a system of ventilated parallel boiling channels. This model accounts for subcooled boiling, an arbitrary heat flux distribution, distributed and local hydraulic losses, heated wall dynamics, slip flow, turbulent mixing and arbitrary flow paths for transverse ventilation. The digital computer program MAZDA-NF was written for numerical evaluation of the mathematical model.Comparison of MAZDA-NF results with those obtained form both a closed form analytical solution and experiment, showed good agreement. A parametric study revealed that such phenomena as subcooled boiling, the transverse coupling between channels (due to cross-flow and mixing) and power skewing can have a significant impact on predicted stability margins. An analysis of an advanced BWR fuel, of the ASEA-ATOM SVEA design, has indicated that transverse ventilation may considerably improve channel stability.     

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.