Two-Phase Flow Instability at Low Flow Rate Conditions

Instability of two-phase flow at low flow rate conditions is investigated analytically and experimentally. By applying the drift flux model, a linear analysis is conducted to study the effect of slip which is considered to play an important role at low flow rate conditions. Results obtained are compared with those of other analytical works and the reason for apparent variations is discussed. Some notes are also given on the lumped parameters which govern instability characteristics, and on the often-observed relation between the period of oscillation and the transit time.

Experiments are conducted using R-113 at the test fluid. The results are analyzed in terms of the stability boundary and the period of oscillation. In the analysis it must be assumed that the flow is laminar. It is found that the instability observed experimentally is typical in the gravity term of the heated section is the dominant destabilizing term in the momentum equation.     

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.     

低压自然循环复合流量脉动实验研究

在低压流动沸腾不稳定性实验中,研究了自然循环流动在不同入口过冷度下的演化过程。对实验中的流动沸腾不稳定性入口流量信号进行快速傅里叶变换,基于振幅和频率特性区分了3种流动脉动模式：小幅流量脉动、复合流量脉动和逆流。分析了加热功率和入口过冷度对自然循环不稳定性的影响。根据加热段出口水温变化得到了出口的流型变化,当流量波动振幅较小时加热段出口流体始终是饱和状态,而当流量波动振幅较大时,加热段出口为单相液体和两相混合物交替通过。给出了这3种流量脉动的边界图,分析了热流密度和入口过冷度对流量脉动模式的影响。结果表明：出口含气率大于0时发生流动不稳定性,热流密度达到间歇干涸型临界热流密度时发生逆流。     

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.     

并联双通道密度波不稳定性实验研究

采用两个相同的加热通道构成试验段,进行并联双通道密度波不稳定性实验研究。主要研究系统压力、质量流速和入口过冷度对流动不稳定性的影响,并给出过冷度-相变数边界。     

5MW核供热堆自然循环两相流流动特性分析

实验研究在５ＭＷ核供热堆热工水力学模拟系统ＨＲＴＬ－５上进行。计算分析采用带有质量,蒸汽质量,能量及动量守恒方程的一维两相流漂移模型。用Ｃｌａｕｓｉｕｓ－Ｃｌａｐｅｙｒｏｎ方程计算上升段中闪蒸起始点。通过在过冷沸腾区,饱和沸腾区及上升段中推导守恒方程,得到可描述自然循环两相流系统特性的常微分方程组。用时域法求解。研究表明过冷沸腾及空泡的闪蒸对空泡分布,系统循环流量及流动稳定性都有很大影响,且系统压力越低,过冷沸腾及闪蒸的影响越大;在相当宽的两相流动条件下,加热段中只发生过冷沸腾;揭示了两相流不稳定时振荡的传播特性。在５ＭＷ核供热堆条件下理论分析与实验结果吻合得很好。     

基于RELAP5的两管平行通道流动不稳定性研究

利用RELAP5程序对垂直并联管中汽液两相流不稳定性实验装置进行了模拟,并与实验工况进行比较,结果表明：RELAP5程序的非平衡态两流体模型的计算结果与实验数据符合较好。并在此基础上研究了主要运行参数对两管平行通道管间脉动流动不稳定性的影响。结果表明：入口欠热度对管间脉动的影响并非线性关系;系统压力的增加可提高系统的稳定性并减小管间脉动的振幅;进口节流增加,系统的稳定性明显提高;入口不均匀节流时两管总的极限热负荷升高;不均匀加热时两管总的极限热负荷降低。     

An equivalent linearization technique for two-phase flow instability analysis

An equivalent linearization technique has been developed to analyze two-phase flow instability oscillation with finite amplitude in the frequency-domain. A one dimensional slip flow model has been used to formulate equivalent linear equations, and implemented into a computer program.A simple boiling channel has been analyzed by the program. Results for very small amplitude oscillations agreed well with results by a detailed linear frequency-domain program.Analyses for larger amplitude oscillations gave more stable results. Limit cycle amplitudes have been calculated from the amplitudes at which channel characteristics change from unstable to stable as the amplitude is increased.     

Two-phase flow instability in a parallel multichannel system

The two-phase flow instabilities observed in through parallel multichannel can be classified into three types, of which only one is intrinsic to parallel multichannel systems. The intrinsic instabilities observed in parallel multichannel system have been studied experimentally. The stable boundary of the flow in such a parallel-channel system are sought, and the nature of inlet flow oscillation in the unstable region has been examined experimentally under various conditions of inlet velocity, heat flux, liquid temperature, cross section of channel and entrance throttling. The results show that parallel multichannel system possess a characteristic oscillation that is quite independent of the magnitude and duration of the initial disturbance, and the stable boundary is influenced by the characteristic frequency of the system as well as by the exit quality when this is low, and upon raising the exit quality and reducing the characteristic frequency, the system increases its instability, and entrance throttling effectively contributes to stabilization of the system.     

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.     

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, (II)

The instabilities observed in a parallel-channel system carrying boiling fluid in forced upward flow have been studied theoretically and experimentally, using water as test fluid.

The limits of the stable flow in such a parallel-channel system (the stable boundary) are sought, and the nature of inlet flow oscillation in the unstable region has been examined experimentally under various conditions of inlet velocity, heat flux, liquid temperature, cross section of channel and entrance throttling.

The results obtained are compared with calculations based on the mathematical model reported in a companion paper, and good agreement is seen between analysis and experiment in respect of the stable boundary. The experimental results are further examined through phase analysis using the same model.     

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.     

气空间对自然循环两相流动系统稳定性影响实验研究

微沸腾工况运行是核供热堆实现热电联供的关键性问题之一，微沸腾运行工况下，两相流系统稳定性更加不利和复杂。通过实验研究，揭示了气空间对两相流系统稳定性的影响，研究提出通过气空间改性来抑制系统不稳定。实验结果表明，在气空间加装隔离孔板，对两相流系统不稳定振幅有明显的抑制作用，对两相流系统不稳定边界也有改善。      

Density Wave Instability in Once-Through Boiling Flow System, (I)

Density wave instability in a once-through boiling flow system was systematically observed using a uniformly joule-heated water loop operated at system pressures ranging from 20 to 43 ata. The test section consisted of two heated tubes connected in parallel and further paralleled by an unheated by-pass. The oscillatory behavior is analyzed as well as the effects brought on the threshold of instability by changes in the operating variables—mass velocity, system pressure, inlet resistance, inlet subcooling, by-pass ratio and exit quality. The experimental data are also presented in form convenient for verifying various analytical methods devised to predict the stability boundary.     

Linear Analysis of Thermo-hydraulic Instabilities of the Advanced Heavy Water Reactor (AHWR)

Analysis was carried out to predict the threshold of instability for Ledinegg type and density wave oscillations for the Indian Advanced Heavy Water Reactor (AHWR) which is a Natural Circulation Pressure Tube Type Boiling Water Reactor. The mathematical model considers homogeneous two-phase flow and the conservation equations are solved analytically to obtain the steady state thermo-hydraulic characteristics and flow stability map. The model was applied for the AHWR concept after it had been validated with the test data obtained from a simple forced circulation loop with small parallel boiling channels and from the High Temperature Loop (PNC). The results indicate that the proposed design configuration of the AHWR may experience both Ledinegg type (static instability) and Type-I and Type-II density wave oscillations depending on the operating condition. The effects of various geometric and operating parameters on these types of instabilities were studied. It can be seen from the results that the Ledinegg type instability is suppressed with an increase in pressure and disappears when the operating pressure is higher than 0.7MPa. But the density wave instability may occur even at 7 MPa. In addition, it is found that for parallel multiple channels operating under natural circulation condition, the stability of density wave instability is not always enhanced by increasing the throttling coefficients at the inlet of channels.     

基于RELAP5的单通道自然循环流动不稳定性分析

针对某一自然循环实验,利用RELAP5程序对其建模,并进行数值分析,得出了该系统的流动不稳定性边界。对不同压力和不同上升段结构尺寸下的流动不稳定性边界及流量振动曲线进行了比较,分析了原因。最后,讨论了欠热沸腾对自然循环流动不稳定性的影响。研究结果可为自然循环系统的工程设计提供一定的借鉴。     

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.     

Interface Waves Excited by Vertical Vibration of Stratified Fluids in a Circular Cylinder

The excitation of interface waves by vertical vibration of stratified immiscible fluids in a circular cylinder is studied experimentally and analytically. The excitation of linear capillary-gravity waves by the time-dependent fluid acceleration combined with the fluid-wall relative motion is considered in the analysis. The analytical results show that the interface responses are dominated by the modes predicted by the Mathieu equation when the excitation amplitude and frequency lie in an unstable region of the Mathieu equation governing the acceleration-driven interface oscillation. Otherwise, symmetrical harmonic modes are excited by the capillary force associated with the fluid-wall relative motion. These changes in the instability modes agree to those observed in the experiments conducted with oil (kerosene) and water in an acrylic pipe. The amplitudes of the symmetrical harmonic waves in the experiments are well predicted by using the contact line model of Miles. The interface motion in the experiments, however, is found to include cyclic formation of a thin film of oil on which the oil-water interface behaves as if it “slips” without being much affected by the capillary force, and thus to be far more complicated than assumed by the model.     

加热双通道密度波流动不稳定性数值研究

密度波流动不稳定性是影响换热设备安全性和可靠性的重要因素之一,其发生机理十分复杂。本工作基于RELAP5程序对加热通道密度波脉动进行了动态计算分析,揭示了脉动期间流体密度、流量及压降等参数的变化规律,并与两种经典机理进行比较分析。结果表明：密度波脉动期间,通道内流量、密度（空泡）及压降呈周期性脉动,加热通道内轴向不同位置流量不同,进出口流量反相脉动,单向段压降和两相段压降基本反相;加热通道密度波脉动的发生与两相段流量波动传播的延迟性有着密切的关系。