Pressure wave propagation in air-water bubbly and slug flow

Related to nuclear reactor safety problems, such as the loss of coolant accident caused by some small crevasses in nuclear reactor, choked flows after postulated breaks of hot and cold legs of pressurized water reactors and the boiling flow instability in parallel channels, the characteristics of pressure wave propagation were investigated experimentally for the air-water bubbly and slug two-phase flow in a vertical pipe. Pressure wave was generated from the small pressure disturbance by the up-and-down movement of piston in the test section. Air void fraction was up to 0.7 and superficial liquid velocity was up to 1.5 m/s as experimental conditions. The experimental results show that the pressure wave propagation velocity in bubbly flow decreases acutely with the increase of air void fraction from 0 to 0.05. In slug flow, it is constant when the air void fraction is less than 0.5 but increases gradually when the void fraction increases beyond 0.5. The attenuation coefficient of pressure wave increases with the increase of air void fraction in bubbly flow. The dependency of pressure wave propagation velocity on angle frequency ω in air-water flow shows the dispersion characteristic. The propagation velocity and attenuation coefficient increases gradually with the increase of angle frequency. However, the increase vanishes slowly as the angle frequency reaches 250 Hz in bubbly flow. The propagation of pressure wave in bubbly flow is independent of the superficial velocity of fluids in the range of experiment.     

Wave propagation in two-phase flow of magnetic fluid under a nonuniform magnetic field

The effect of nonuniform magnetic field on the linear and nonlinear wave propagation phenomena in two-phase pipe flow of magnetic fluid is investigated theoretically to realize the effective energy conversion system using boiling two-phase flow of magnetic fluid. Firstly, the governing equations of two-phase flow based on the unsteady thermal nonequilibrium two-fluid model are presented and the linear void wave propagation phenomena in boiling two-phase flow are numerically analyzed by using the finite volume method. Next, the nonlinear pressure wave propagation in gas-liquid two-phase flow is numerically analyzed by using the finite different method. According to these theoretical studies on the wave propagation phenomena in two-phase flow of magnetic fluid, it seems to be a reasonable proposal that the precise control of the wave propagation in two-phase flow is possible by effective use of the magnetic force.     

Frictional pressure drop of gas liquid two-phase flow in pipes

Experiments of air water two-phase flow frictional pressure drop of vertical and horizontal smooth and relatively rough pipes were conducted, respectively. The result demonstrated that the frictional pressure drop increases with increasing relative roughness of the pipe. However, the influence of the relative roughness becomes more evident at higher vapour quality and higher mass flux. A new prediction model for frictional pressure drop of two-phase flow in pipes is proposed. The model includes a new definition of the Reynolds number and the friction factor of two-phase flow. The proposed model fits the presented experimental data very well, for vertical, horizontal, smooth and rough pipes. Therefore, the reproductive accuracy of the model is tested on the experimental data existing in the open literature and compared with the most common models. The statistical comparison, based on the Friedel’s Data-Bank containing of about 16,000 measured data, demonstrated that the proposed model is the best overall agreement with the data. The model was tested for a wide range of flow types, fluid systems, physical properties and geometrical parameters, typically encountered in industrial piping systems. Hence, calculating based on the new approach is sufficiently accurate for engineering purposes.     

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。     

一体化反应堆蒸汽发生器内两相流密度波型脉动的预报模型

一体化反应堆由于其固有优越的安全性和广泛用途，受到许多国家的重视。解决两相流脉动问题是发展一体化反应堆的关键技术之一。本文利用两相流动的变密度模型，建立了一体化反应堆蒸汽发生器并联管内高压汽水两相流密度波型脉动的控制方程，运用小扰动线性化方法及拉普拉斯变换和自动控制理论的稳定性判据，提出了系统发生密度波型脉动的预报模型。利用模型，计算了系统发生脉动的界限热流密度，并分析了有关参数对脉动界限的影响，结果与试验符合较好，可用于实际蒸汽发生器的设计     

A study of acoustic wave damping in water-filled pipes with zero flow and turbulent flow

A simple, fundamental experimental study was conducted to further the understanding of acoustic wave propagation in fluid-filled pipes. Three experiments were conducted: the first with zero flow and a closed outlet end; the second with turbulent flow and an open outlet end; and the third with zero flow and an open outlet end. The intent was to obtain data at higher frequencies than those previously reported and which can be used to validate and verify numerical models. A further objective was to determine the effect of turbulent flow on the acoustic response of the system. Some new insights are obtained and presented.     

The role of interfacial friction on the shock wave propagation in stratified gas-liquid flow inside pressure tubes

The admission of the interfacial friction factor in the analysis of the shock wave propagation in the horizontal two-phase stratified flow systems is observed to weaken the shock wave travelling through the phases. A quasi-steady energy balance alludes the importance of the inclusion of the frictional loss in the shock wave phenomena in the horizontal two-phase flows. Finally the problem is dealt with a fuel bundle placed inside the pressure tube, as in a CANDU system to demonstrate experimentally the adverse effect of the pressure transients inside the fuel bundles during a LOCA (loss of coolant accident).     

Two-phase flow resistance in flexible metal hoses

This study presents the two-phase flow resistance, hence the friction factor and the pressure drop for air–water mixture flowing in flexible metal hoses. Experiments were performed under the following conditions of two-phase parameters; mass flux from 200 to 1150 kg/m² s, gas quality from 1 to 60% and system pressure from 3 to 10 bar. The inner diameters of the tested hoses were 25, 40, 50 and 65 mm with a ratio of ridge depth to inner diameter (r/d) from 0.02 to 0.1 and a ratio of pitch to inner diameter (p/d) from 0.06 to 0.3. The results demonstrate that the two-phase flow resistance, energy dissipation and friction losses in flexible metal hoses are perceptible greater than that in pipes. Therefore, the two-phase pressure drops of the hoses are two to five times greater than that in smooth pipes. The two-phase friction factor of such hoses increased from 0.035 up to 0.2 in dependence on the influencing flow and geometrical parameters. Based on the energy balance and the presented experimental results, a new model has been developed to calculate the two-phase pressure drops and hence the friction factor of flexible metal hoses. The model includes the relevant primary parameters, fit the data well and is sufficiently accurate for engineering purposes. The results reported enable practical designs with standard products and optimization of the hose geometry for specific conditions.     

垂直上升管内泡状流压力波传播

研究了垂直上升管内气液两相泡状流压力波的传播速度和衰减规律,为了提高压力波测量精度．实验中设计了不影响两相流动结构的调频式压力扰动装置．实验结果表明,随着含气率的增加,泡状流中压力波波速开始陡降,当含气率大于0．05以后波速缓慢下降;衰减系数随含气率的增加连续增加：工质的流速对压力波的传播没有影响;压力波的传播速度及其衰减与扰动频率有关．随着扰动频率的增加,波速及其衰减都增加本文实验验证了泡状流压力波色散特性的临界频率现象．即高于临界频率．压力波的色散特性消失．在本试验条件和参数范围内．临界扰动角频率为300Hz．     

Analysis of the capability of system codes to model cavitation water hammers: Simulation of UMSICHT water hammer experiments with TRACE and RELAP5

The capabilities of the nuclear system transient codes TRACE and RELAP5 to model coupled two-phase flow and pressure wave propagations in a pipe are assessed by analyzing the UMSICHT PPP cavitation water hammer experiments 329 and 135 after valve closure. Time-dependent pressure, flow behaviour, and the generation and collapse of vapor bubbles at the valve and the first bridge are discussed. We show that both codes are able to model the flow behaviour of the water hammer for the high pressure and high temperature case 329 (initially 10–13 bar and 420 K), however condensation heat transfer for the base case needed to be increased in order to accurately model the magnitude of the first pressure excursion. The experimental broadening and damping of the subsequent pressure peaks by Fluid-Structure Interaction (FSI) phenomena arising from the interaction of the flow with the vibrations of the piping structure are not considered in the modeling results. For the lower pressure and temperature case 135 (initially 1–4 bar and 294 K), the TRACE code provides a good approximation of the propagation of the pressure wave and the void fraction behaviour, already with base case conditions, while RELAP5 overpredicts the vapor generation along the pipe and, as a result, considerably underpredicts the pressure amplitudes and overpredicts the water hammer frequency.     

Development of numerical analysis method of flow-acoustic resonance in stub pipes of safety relief valves

The boiling water reactors (BWRs) have steam dryer in the upper part of the pressure vessel to remove moisture from the steam. The steam dryer in the Quad Cities Unit 2 nuclear power plant was damaged by high-cycle fatigue due to acoustic-induced vibration during extended power uprate operation. The principal source of the acoustic-induced vibration was flow-acoustic resonance at the stub pipes of the safety relief valves (SRVs) in the main steam lines (MSLs). The acoustic wave generated at the SRV stub pipes propagates throughout the MSLs and eventually reaches and damages the steam dryer. Therefore, for power uprate operation of the BWRs, it has been required to predict the flow-acoustic resonance at the SRV stub pipes. The purpose of this article was to propose a numerical analysis method for evaluating the flow-acoustic resonance in the SRV stub pipes. The proposed method is based on the finite difference lattice Boltzmann method (FDLBM). So far, the FDLBM has been applied to flow-acoustic simulations of laminar flows around simple geometries at low Reynolds number. In order to apply the FDLBM to the flow-acoustic resonance simulations of turbulent flows around complicated geometries at the high Reynolds number, we developed computationally efficient model by introducing new function into the governing equation. The proposed method was compared with the conventional FDLBM in the cavity-driven flow simulation. The proposed method was validated by comparisons with the experimental data in the 1/10-scale test of BWR-5 under atmosphere condition. The following three results were obtained; the first is that the proposed method can reduce the computing time by 30% compared with the conventional FDLBM; the second is that the proposed method successfully simulated the flow-acoustic resonance in the SRV stub pipes of the BWR-5, and the pressure fluctuations of the simulation results agreed well with those of the experimental data; and the third is the mechanism of the flow-acoustic resonance in the SRV stub pipes. Acoustic waves causing the flow-acoustic resonance in the SRV stub pipes are generated by the unsteady vortices in the SRV stub pipes.     

Analysis on transient piping pressure and force caused by high pressure steam flow disturbances

This paper presents a quantitative analysis on transient responses of pressure and its resulting force to sudden operation of a pressure relief valve on the main steam line of a pressurized water reactor plant, which is initially in a closed system at high pressure. When the valve at closed position changes to the full open position suddenly, the shock can be generated by the sudden steam flow which may reach critical velocity and then travel through the pipe line causing some damages to the piping system. The major characteristics of shock are quantitatively investigated on the basis of one dimensional pressure wave theory. Through the application to the actual transient incident occurred at the Kori unit 1 on 16 April 2005, it is found that the present approach is quite practical to predict the transient behavior of shocks caused by sudden operation of valves.     

Properties of disturbance waves in vertical annular two-phase flow

Disturbance waves play an important role in interfacial transfer of mass, momentum and energy in annular two-phase flow. In spite of their importance, majority of the experimental data available in literature on disturbance wave properties such as velocity, frequency, wavelength and amplitude are limited to near atmospheric conditions (Azzopardi, B.J., 1997. Drops in annular two-phase flow. International Journal of Multiphase Flow, 23, 1-53). In view of this, air-water annular flow experiments have been conducted at three pressure conditions (1.2, 4.0 and 5.8 bar) in a tubular test section having an inside diameter 9.4 mm. At each pressure condition liquid and gas phase flow rates are varied over a large range so that the effects of density ratio, liquid flow rate and gas flow rate on disturbance wave properties can be studied systematically. A liquid film thickness is measured by two flush mounted ring shaped conductance probes located 38.1 mm apart. Disturbance wave velocity, frequency, amplitude and wavelength are estimated from the liquid film thickness measurements by following the statistical analysis methods. Parametric trends in variations of disturbance wave properties are analyzed using the non-dimensional numbers; liquid phase Reynolds number (Re_f), gas phase Reynolds number (Re_g), Weber number (We) and Strouhal number (Sr). Finally, the existing correlations available for the prediction of disturbance wave velocity and frequency are analyzed and a new, improved correlation is proposed for the prediction of disturbance wave frequency. The new correlation satisfactorily predicted the current data and the data available in literature.     

Type of flow, pressure drop, and critical heat flux of a two-phase sodium flow

Little is known about the two-phase pressure loss, the flow pattern, and the critical heat flux conditions for boiling sodium under forced convection. The specific thermohydraulic properties of sodium prohibit extrapolation to sodium of experimental data obtained for other liquids. Therefore, some new test series were carried out in a sodium loop with an induction heated test section of 9 mm inner diameter and 200 mm heated length. The two-phase pressure loss and the film thickness were measured up to the critical cooling conditions. The experimental results are compared with values predicted by known models on annular flow and annular mist flow, respectively. Satisfactory predictions of the flow pattern and the critical heat flux conditions could only be obtained using the measured two-phase pressure losses.     

Interfacial measurements in horizontal stratified flow patterns

The interfacial characteristic parameters of horizontal stratified wavy flow patterns were experimentally investigated for a mixture of air and water two-phase flow by using the double-sensor, parallel wire conductance probe method. The experiments were conducted in a horizontal flow loop 15.4 m long consisting of Pyrex glass tubing of 50.3 mm i.d. The range of gas superficial velocities was from 0.85 to 31.67 ms⁻¹ and the liquid superficial velocities ranged from 0.014 to 0.127 ms⁻¹. Several interfacial wave patterns as described by Andritsos and Hanratty (Int. J. Multiphase Flow 13 (1987a) 583–603) were identified and their characteristic parameters such as wave height, most dominant frequency, mean propagation velocity and mean wavelength were investigated in terms of liquid and gas flow rates. The interfacial shear stress calculated from the experimental measurements was used to evaluate the most widely used interfacial shear models.     

LBB泄漏率计算与热力学非平衡效应影响评估

裂纹泄漏率计算是破前漏（LBB）在核电站管道和设备上应用的基础。在Fauske模型基础上,整个裂纹内流体流动假设为等焓过程且充分考虑摩擦效应对裂纹临界泄漏率的影响,利用Mathcad计算得到了管道裂纹两相泄漏率,与已有文献中实验数据进行对比,将其发展成为可准确计算裂纹泄漏率的计算机程序。同时根据两相流动不平衡理论,对模型进行热力学不平衡参数影响修正。结果表明：随裂纹长径比(L/D)增大,两相泄漏率减小;随裂纹入口滞止压力增大,两相泄漏率增大;裂纹入口流体过冷度增大,两相泄漏率增大,数学模型计算结果与实验结果趋势一致,但忽略热力学非平衡效应,数学模型计算得到的临界流量小于实验流量。对于热力学不平衡参数修正后模型,模型计算得到的结果均与实验数据符合很好,故由修正后模型编制的Mathcad程序可完成裂纹泄漏率的准确计算,为LBB在核电站管道上的应用提供基础。     

Experimental and numerical simulation of air-water two-phase flow in the rod bundle with grid spacer

1 Introduction Grid spacer is the key part of reactor fuel assem-bly. The presence of spacers in fuel assemblies affectsvarious thermal-hydraulic characteristics of the reactorcore. The grid spacer with fine performance can im-prove thermal-hydraulic performance of the core fuelassembly and enhance the critical heat flux withouttoo much augment of the pressure loss. As a result,the implementation of grid spacer with high thermalperformance provides more thermal margin, then in-creases s…     

Development of the analysis tool for the water cooling type passive residual heat removal system of Chinese pressurized reactor

An innovative design for Chinese pressurized reactor is the steam generator (SG) secondary side water cooling passive residual heat removal system (PRHRS). The new design is expected to improve reliability and safety of the Chinese pressurized reactor during the event of feed line break or station blackout (SBO) accident. The new system is comprised of a SG, a cooling water pool, a heat exchanger (HX), an emergency makeup tank (EMT) and corresponding valves and pipes. In order to evaluate the reliability of the water cooling PRHRS, an analysis tool was developed based on the drift flux mixture flow model. The preliminary validation of the analysis tool was made by comparing to the experimental data of ESPRIT facility. Calculation results under both high pressure condition and low pressure condition fitted the experimental data remarkably well. A hypothetical SBO accident was studied by taking the residual power table under SBO accident as the input condition of the analysis tool. The calculation results showed that the EMT could supply the water to the SG shell side successfully during SBO accident. The residual power could be taken away successfully by the two-phase natural circulation established in the water cooling PRHRS loop. Results indicate the analysis tool can be used to study the steady and transient operating characteristics of the water cooling PRHRS during some accidents of the Chinese pressurized reactor. The present work has very important realistic significance to the engineering design and assessment of the water cooling PRHRS for Chinese NPPs.     

Two-phase flow in a full-scale loop seal facility

An experimental program has been carried out to study two-phase behaviour of a PWR cold leg loop seal during loss-of-coolant accidents. The experimental facility comprises a full-scale cold leg with a reactor coolant pump simulator. Three separate air/water test series were performed to determine the onset of slugging in the horizontal pipe, the residual water mass and the total two-phase pressure drop in the loop seal.The results of flow regime transition experiments have been compared with smaller-scale experiments and with theoretical predictions to evaluate scaling criteria. The strong hysteresis of transitions found between the stratified and slug flow regimes depends on the loop seal geometry and U-tube oscillations.     

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.