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.     

Study on the stability behaviour of two-phase natural circulation systems using a four-equation drift flux model

Theoretical investigations were carried out to study the influence of two-phase flow parameters such as friction factor multiplier, drift velocity and void distribution parameter on the stability of boiling two-phase natural circulation systems. The theoretical model considers a four-equation drift flux model which solves the linearised conservation equations of mass, momentum and energy applicable to boiling two-phase natural circulation systems. The model was applied to three boiling natural circulation loops wherein Type I and Type II instabilities were observed over a wide range of operating pressures. The two-phase friction loss was predicted using different friction factor multiplier models available in literature. It was found that these models influence the steady state and threshold powers for stability, especially the Type II instabilities in natural circulation significantly. Since the void fraction depends on the drift velocity and the void distribution parameter in two-phase flow, these parameters were varied and their effects on the natural circulation flow stability were investigated. It was found that an increase in either the drift velocity or the void distribution parameter reduces the unstable regions observed in the Type I or Type II flow instabilities in two-phase natural circulation systems.Further, investigations were carried out to study the effect of loop diameter on the Type I and Type II instabilities in natural circulation. This study is important to reveal the capability of the reduced diameter scaled facilities of the prototype systems to simulate natural circulation instabilities. The results indicate that with increase in the loop diameter, the threshold power of the Type I instability and the Type II instability increases. Moreover, the stability of natural circulation greatly enhances with increase in the diameter of the loop.     

A 2D numerical simulation of sub-cooled flow boiling at low-pressure and low-flow rates

The main purpose of this study is to apply a two-fluid mathematical model to numerical simulation of two-phase flow at low-pressure condition. Although models of sub-cooled boiling flow at one-dimension and high-pressure have been studied extensively, there are few equivalent studies for numerical simulation at two-dimension and low-pressure (1-2 bar) conditions. Recent literature studies on sub-cooled boiling flow at low-pressure have shown that empirical models developed for high-pressure situations are not valid at low-pressures. Since the mathematical model used in this study is accomplished at low-pressure, the transport equations for the variables of each phase are substituted in low-pressure. The governing equations of two-phase flow with an allowance to inter-phase transfer of mass, momentum and heat, are solved using a two-fluid; non-equilibrium model. The finite volume discretization scheme is used to create a linearized system of equations that are solved by SIMPLE staggered grid solution technique for a rectangular channel. Improvement of the void fraction prediction of our model for the case of low-pressure sub-cooled flow boiling conditions was achieved. It is found that the heat transfer due to evaporation and surface quenching is higher than that by convection. Good agreement is achieved with the predicted results against the experimental data’s available in the literatures for a number of test cases.     

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.     

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.     

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.     

平行通道密度波不稳定性研究

本文针对套管式直流蒸汽发生器传热管环隙窄缝通道的流动,采用RELAP5程序对强迫循环并联通道的流动不稳定现象进行研究,指出在进口欠热度较低的条件下,并联通道系统会发生两种完全不同的不稳定现象,即同相密度波不稳定性和管间脉动不稳定性。对密度波不稳定性的发生条件进行研究,在较大的参数范围内确定了各系统参数的影响规律,最终得出流动不稳定边界。并对不同流量条件和不同压力条件下的不稳定性区间进行了比较。     

Analysis of low-heat-flux sodium boiling test in a 37-pin bundle by the two-fluid model computer code SABENA

This paper summarizes the development of a new detailed multi-dimensional multi-field computer code SABENA and its application to an out-of-pile low-heat-flux sodium boiling test in a 37-pin bundle. The semi-implicit numerical method employed in the two-fluid six-equation two-phase flow model has proved in solving a wide spectrum of sodium boiling transients in a rod bundle under low pressure conditions. The code is capable of predicting the spatial incoherency of the boiling, dryout on fuel cladding surfaces and fuel pin heat transfer. Essential to the successful application of such a mechanistic model computer code are validational efforts aimed at the LMFBR accident phenomenology analyses. Through the simulation of the natural circulation boiling conditions, this study provides a consistent analytical interpretation of the experimental data. The important influences of such parameters as the inlet flow restriction and bundle geometry have been examined through interpretations of two-phase flow analysis including considerations of the flow instability induced dryout mechanism.     

Numerical simulations of basic interfacial instabilities with incompressible two-fluid model

The incompressible two-fluid model for stratified flow was improved. The interface of the stratified two-phase flow was successfully recognized and sharpened within the two-fluid model. After the advection step of volume fraction the numerical diffusion of the interface was reduced in such a way that the thickness of the interface is kept constant during the simulation. The surface tension force was implemented in the system of the two-fluid model equations. The two basic instabilities of stratified flows: Rayleigh-Taylor and Kelvin-Helmholtz instability were used to validate the proposed two-fluid model. The proposed two-fluid model with interface sharpening presents a step towards the simulations of mixed flows, where locally dispersed flow or stratified flow will be simulated with appropriated submodels within the two-fluid model.     

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.     

两流体模型在环形窄缝内的应用研究

采用EPRI最新开发的Chexal-Harrison相壁相间摩擦模型和简化的相壁相间传热模型,构造了适用于环形窄缝内沸腾传热和流动的两流体模型,并编制了热工水力计算程序——THYME程序.与实验数据比较,分析了环形窄缝套管在不同负荷下Relap5/Mod3.2程序和本文程序的计算结果.计算结果表明,Relap5/Mod3.2低估了环形蒸发管的蒸汽温度,本文计算结果与实验数据较为一致.     

Flow excursion instability in downward flow systems: Part I. Single-phase instability

A procedure for predicting the onset of flow excursion instability in downward flows at low-pressure and low-flow conditions without boiling is presented. It is generally accepted that the onset of significant void in subcooled boiling precedes, and is a precondition to, the occurrence of static flow instability. A detailed analysis of the pressure drop components for a downward flow in a heated channel reveals the possibility of unstable transition from single-phase flow to high-quality two-phase flow, i.e. flow excursion. Low flow rate and high subcooling are the two important conditions for the occurrence of this type of instability. The unstable transition occurs when the resistance to the downward flow caused by local (orifice), frictional, and thermal expansion pressure drops equalizes the driving force of the gravitational pressure drop. The inclusion of the thermal expansion pressure drop is essential to account for this type of transition. Experimental data have still to be produced to verify the prediction of the present analysis.     

并行双通道内超临界水流动不稳定性数值分析

采用时域法对超临界水冷堆(SCWR)中可能出现的并行通道流动不稳定性进行分析,建立适用于并行双通道内超临界水流动不稳定性分析的数值计算模型,对质量、动量及能量方程进行隐式差分离散求解,自行编制计算程序SCIA。采用SCIA分析双通道结构堆芯流动特性,计算得到超临界条件下的水动力曲线,研究了系统参数对超临界水流动稳定性的影响规律。结果表明:静态流动不稳定性在SCWR中很难发生;超临界下的系统参数影响规律与亚临界具有相似性。     

Sabena: Subassembly boiling evolution numerical analysis

This paper describes the computer code SABENA that has been used in subassembly sodium boiling evolution numerical analysis as a contribution to fast breeder reactor safety analysis. SABENA is a two-fluid model subchannel code system to calculate coolant boiling and two-phase flow in a rod bundle together with external loop characteristics which affects the overall boiling behavior in the bundle section. With the use of relatively simple but reasonable constitutive models, the SABENA code has been applied to and validated against many multi-pin sodium boiling problems. The results have shown excellent agreement with the experiments. The numerical methods and models employed in the code have proven to be robust and efficient in light of the extreme severity of the conditions characterizing low-pressure sodium boiling.     

Dynamic analysis of multiple nuclear-coupled boiling channels based on a multi-point reactor model

This work investigates the non-linear dynamics and stabilities of a multiple nuclear-coupled boiling channel system based on a multi-point reactor model using the Galerkin nodal approximation method. The nodal approximation method for the multiple boiling channels developed by Lee and Pan [Lee, J.D., Pan, C., 1999. Dynamics of multiple parallel boiling channel systems with forced flows. Nucl. Eng. Des. 192, 31–44] is extended to address the two-phase flow dynamics in the present study. The multi-point reactor model, modified from Uehiro et al. [Uehiro, M., Rao, Y.F., Fukuda, K., 1996. Linear stability analysis on instabilities of in-phase and out-of-phase modes in boiling water reactors. J. Nucl. Sci. Technol. 33, 628–635], is employed to study a multiple-channel system with unequal steady-state neutron density distribution. Stability maps, non-linear dynamics and effects of major parameters on the multiple nuclear-coupled boiling channel system subject to a constant total flow rate are examined. This study finds that the void-reactivity feedback and neutron interactions among subcores are coupled and their competing effects may influence the system stability under different operating conditions. For those cases with strong neutron interaction conditions, by strengthening the void-reactivity feedback, the nuclear-coupled effect on the non-linear dynamics may induce two unstable oscillation modes, the supercritical Hopf bifurcation and the subcritical Hopf bifurcation. Moreover, for those cases with weak neutron interactions, by quadrupling the void-reactivity feedback coefficient, period-doubling and complex chaotic oscillations may appear in a three-channel system under some specific operating conditions. A unique type of complex chaotic attractor may evolve from the Rossler attractor because of the coupled channel-to-channel thermal-hydraulic and subcore-to-subcore neutron interactions. Such a complex chaotic attractor has the imbedding dimension of 5 and the fractal dimension ranging from 1.26 to 1.35.     

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.     

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.     

Wall function approach for boiling two-phase flows

One of the important goals of the NURESIM project is to assess and improve the simulation capability of the three-dimensional two-fluid codes for prediction of local boiling flow processes. The boiling flow is strongly affected by local mechanisms in the turbulent boundary layer near the heated wall. Wall-to-fluid transfer models for boiling flow with the emphasis on near-wall treatment are being addressed in the paper. Since the computational grid of the 3D two-fluid models is too coarse to resolve the variable gradients in the near-wall region, the use of wall functions is a common approach to model the liquid velocity and temperature profile adjacent to the heated wall.The wall function model for momentum, based on the surface roughness analogy has been discussed and implemented in the NEPTUNE_CFD code. The model has been validated on several upward boiling flow experiments, differing in the geometry, working fluid and operating conditions. The simulations with the new wall function model show an improved prediction of flow parameters over the boiling boundary layer. Furthermore, a wall function model for the energy equation, based on enhanced two-phase wall friction has been derived and validated.     

Capability of the RELAP5 code to simulate natural circulation behavior in test facilities

Many advanced reactor designs incorporate passive systems mainly to enhance the operational safety and possible elimination of severe accident condition. Some reactors are even designed to remove the nominal fission heat passively by natural circulation without using mechanical pumps e.g. ESBWR, AHWR, CHTR, CAREM, etc. while in most other new reactor concepts, the decay heat is removed passively by natural circulation following the pump trip conditions. The design and safety analysis of these reactors are carried out using the best estimate codes such as RELAP5, TRAC and CATHARE, etc. These best estimate codes have been developed for pumped circulation systems and it is not proven about their adequacy or applicability for natural circulation systems wherein the driving mechanism is completely different. Some of the key phenomena which are difficult to model but are significantly important to assess the natural circulation system performances are – low flow natural circulation mainly because the flow is not fully developed and can be multi-dimensional in nature; flow instabilities; critical heat flux under oscillatory condition; flow stratification particularly in large diameter vessel; thermal stratification in large pools; effect of non-condensable gases on condensation, etc. Though, these best estimate codes use a six equation two-fluid model formulation for the thermal-hydraulic calculation which is considered to be the best representative of two-phase flows, but their accuracies depend on the accuracies of the models for interfacial relationships for mass, energy and momentum transfer which are semi-empirical in nature. The other problem with two-fluid models is the effect of ill-posedness which may cause numerical instability. Besides, the numerical diffusion associated due to truncation of higher order terms can affect the prediction of flow instabilities. All these effects may lead to inability to capture the important physical instability in natural circulation systems and instability characteristics i.e. amplitude and frequency of flow oscillation. In view of this, it is essential to test the capability of these codes to simulate natural circulation behavior under single and two-phase flow conditions before applying them to the future reactor concepts.In the present study, one of the extensively used best estimate code RELAP5 has been used for simulation of steady state, transient and stability behavior of natural circulation based experimental facilities, such as the High-Pressure Natural Circulation Loop (HPNCL) and the Parallel Channel Loop (PCL) installed and operating at BARC. The test data have been generated for a range of pressure, power and subcooling conditions. The computer code RELAP5/MOD3.2 was applied to predict the transient natural circulation characteristics under single-phase and two-phase conditions, thresholds of flow instability, amplitude and frequency of flow oscillations for different operating conditions of the loops. This paper presents the effect of nodalisation in prediction of natural circulation behavior in test facilities and a comparison of experimental data in with that of code predictions. The errors associated with the predictions are also characterized.     

单棒通道流动振荡诱发沸腾临界可视化实验研究

为深入分析沸腾两相流动振荡诱发沸腾临界的影响特性,本文以去离子水为工质,横截面19 mm×19 mm、中心为外径9.5 mm的单棒通道为研究对象,通过在不同热工参数下开展沸腾两相流动特性可视化实验研究,结合汽泡行为和汽-液界面特性,分析流动振荡诱发沸腾临界的影响特性。研究结果表明,低压力、低质量流速和低入口过冷度下,极易出现流动振荡,并导致沸腾临界提前发生,此时的临界热流密度与稳定工况下相比明显偏低;随着壁面热流密度不断增加,流道中两相流型先后出现泡状流、弹状流、合并弹状流、搅混流、剧烈搅混流、不稳定环状流;当流动出现剧烈振荡时,流道存在回流;发生沸腾临界时流道压降波动最大,对应的流型为不稳定环状流。因此,单棒通道内流动振荡可能会导致沸腾临界提前发生。