Numerical study on shock phenomena and void wave propagation in horizontal stratified flow

Void wave propagation and the related numerical instability in the two-fluid model of horizontal stratified flow have been investigated, focusing on the interfacial pressure force. First, shock phenomena, which are predicted by the two-fluid model when taking into account the interfacial pressure force, are discussed to clarify their physical meaning. Second, numerical instability is investigated through the calculation of void disturbance propagations. The Von Neumann stability analysis is applied to these problems. It has been found that the results explain the nature of the instabilities produced in the calculations. The relationship between the stability limit of the discretized equation set and the ill-posed limit of the field equation set is clarified.     

HRTL-5轴向空泡份额计算

基于一维两相四方程漂移流模型,并考虑加热段欠热沸腾、上升段冷凝以及上升段闪蒸的影响,采用数值模拟的方法对5 MW低温核供热堆热工模拟回路(HRTL-5)的轴向空泡分布进行模拟计算,分析HRTL-5轴向参数分布的特性及其参数效应。结果表明:1)在HRTL-5条件下,考虑欠热沸腾、冷凝、闪蒸等因素影响的计算结果更接近实际情况;2)是否考虑加热段的欠热沸腾对于加热段出口的空泡份额以及出口的状态确定有重要影响;3)冷凝过程对于闪蒸区以及自然循环驱动力的计算有一定的影响;4)闪蒸对低压低干度自然循环系统轴向空泡份额的分布有重要影响,尤其在低压情况下。     

Measurement and modeling of average void fraction, bubble size and interfacial area

The local void fraction, bubble size and interfacial area concentration for co-current air-water bubbly flow through a horizontal pipe of 50.3 mm internal diameter were investigated experimentally using the double-sensor resistivity probe method. The local and area-averaged void fractions and interfacial area concentrations were analyzed as a function of liquid and gas flow rates. These parameters were found to increase systematically with decreasing liquid flow and increasing gas flow. However, variations with the liquid flow were not as significant as with the gas flow. A consistent variation of the gas phase drift velocity and distribution parameter with the liquid flow rate was observed. It was demonstrated that presentation of the average void fraction in terms of flowing volumetric concentration was more appropriate for horizontal bubbly flow. Several bubble break-up mechanisms were discussed. It was concluded that average pressure fluctuations generated by the turbulent liquid fluctuations acting across a bubble diameter are the only mechanism which causes distortion of a bubble. Based on this force and the competing surface tension force, a theoretical model was developed for mean bubble size and interfacial area concentration. The theoretically predicted mean bubble size and interfacial area concentration were found to agree reasonably well with those measured by the double-sensor resistivity method.     

Development of one-dimensional two-fluid model with consideration of void fraction covariance effect

Accurate evaluation of gas-liquid two-phase flow behavior within rod bundle geometry is crucial for the safety assessment of the nuclear power plants. In safety assessment codes, two-phase flow in rod bundle geometry has been treated as a one-dimensional flow. In order to obtain the reliable one-dimensional two-fluid model, it is essential to utilize proper area-averaged models for governing equations and constitutive relations. The area-averaged interfacial drag term utilized to evaluate two-phase interfacial drag force is typically given by the drift-flux parameters which consider the velocity profile in two-phase flow fields. However, in a rigorous sense, the covariance due to void fraction profile is ignored in traditional formulations. In this paper, the rigorous formulation of one-dimensional momentum equation was derived by taking consideration of void fraction covariance, and a new set of one-dimensional momentum equation and constitutive relations for interfacial drag was proposed. The newly obtained set of formulations was embedded into TRAC-BF1 code and numerical simulation was performed to compare against the traditional model without covariance. It was found that effect of covariance was almost negligible for steady-state adiabatic conditions, but for high void fraction condition with added perturbation, the traditional model underpredicted the damping ratio at around 8%.     

Classification of flooding data according to type of tube-end geometry

Flooding data are partitioned according to type of entrance and exit geometry by applying the entropy minimax principle. It is found that the effect of exit geometry on flooding is great in the low liquid velocity region, while that of entrance geometry is great in the high liquid velocity region. Two flooding correlations having second order polynomial form are suggested with ±20% uncertainty bands for smooth exit and sharp exit geometries, respectively. It is found that flooding gas velocities predicted by most previous correlations are close to those predicted by the smooth exit correlation.     

Experimental investigation of natural circulation instability in a BWR-type small modular reactor

The Purdue NMR (Novel Modular Reactor) represents a BWR-type small modular reactor with a significantly reduced reactor pressure vessel (RPV). Specifically, the NMR is one third the height and area of a conventional BWR RPV with an electrical output of 50 MWe. Experiments are performed in a well-scaled test facility to investigate the thermal hydraulic flow instabilities during the startup transients for the NMR. The scaling analysis for the design of natural circulation test facility uses a three-level scaling methodology. Scaling criteria are derived from non-dimensional field and constitutive equations. Important thermal hydraulic parameters, e.g. system pressure, inlet coolant flow velocity and local void fraction, are analyzed for slow and fast normal startup transients. Flashing instability and density wave oscillation are the main flow instabilities observed when system pressure is below 0.5 MPa. And the flashing instability and density wave oscillation show different type of oscillations in void fraction profile. Finally, the pressurized startup procedure is recommended and tested in current research to effectively eliminate the flow instabilities during the NMR startup transients.     

竖直圆管内低压过冷沸腾相分布特性实验研究

实验采用双探头光学探针对内径24 mm竖直圆管内低压过冷沸腾局部空泡份额、界面面积浓度及汽泡尺寸等局部相界面参数径向分布特性进行了研究。实验结果表明：竖直圆管内过冷沸腾相分布形态呈现轴对称特性,随着热流密度的增大,相分布形态出现近壁峰值并逐渐向中间峰值分布形态的发展,较高热流密度工况下出现轴心峰值分布;随着质量流速的增加,局部空泡份额减小,并出现中间峰值向近壁峰值分布形态的转变;随着压力的增大,局部相界面参数减小。     

Code performance with improved two-group interfacial area concentration correlation for one-dimensional forced convective two-phase flow simulation

In gas–liquid two-phase flow simulation for reactor safety analysis, interfacial momentum transfer in two-fluid model plays an important role in predicting void fraction. Depending on flow conditions, a shape of the two-phase interface complicatedly evolves. One of the proposed approaches is to quantify the gas–liquid interface information using interfacial area transport equation. On the other hand, a more simplified and robust approach is to classify bubbles into two-groups based on their transport characteristics and utilize constitutive equations for interfacial area concentration for each group. In this paper, interfacial drag model based on the two-group interfacial area concentration correlations is implemented into system analysis code, and void fractions were calculated for the evaluation of numerical behaviors. The present analysis includes (1) comparison of one-group and two-group relative velocity models, (2) comparison with separate effect test database, (3) uncertainty evaluation of drag coefficient, (4) numerical stability assessment in flow regime transition, and (5) transient analysis for simulating the prototypic condition. Results showed that utilization of interfacial drag force term using constitutive equations of two-group interfacial area concentration yields satisfactory void fraction calculation results. The proposed solution technique is practical and advantageous in view of reducing the computational cost and simplifying the solution scheme.     

Void fraction estimation within rod bundles based on three-fluid model and comparison with x-ray CT void data

An interfacial shear stress equation in the dispersed-annular two-phase flow regime has been developed, which is based on a three-fluid model consisting of a liquid film on a rod, vapor and entrained liquid associated with a vapor flow. It is an extension of J.G.M. Andersen's procedure that provides a two-fluid interfacial shear stress equation using the drift flux parameters C₀ and V_gj. This interfacial shear stress equation can take into account a phase and velocity distribution through an equivalence between the drift flux parameters and the interfacial shear stress.

Using the three-fluid subchannel analysis code TEMPO with the three-fluid interfacial shear stress model, the capability of a three-fluid calculation using the drift flux parameters C₀ and V_gj that reproduce a measured void fraction is demonstrated. A comparison was made with advanced X-ray computed tomography (CT) void fraction data within a 4×4 rod bundle in diabatic 1 MPa pressure conditions. The three-fluid velocity field was estimated to be in good agreement with the experimental result of a void fraction.     

Effects of non-uniform inlet boundary conditions and lift force on prediction of phase distribution in upward bubbly flows with Fluent-IATE

This study investigates the profile effects of the boundary conditions in two-phase flows, such as the inlet void fraction, interfacial area concentration, and phase velocity, on the predictions of flow behaviors downstream. Simulations are performed for upward air-water bubbly flows in a 48.3-mm inner diameter pipe by employing Fluent's two-fluid model together with an interfacial area transport equation (IATE) model. The IATE was developed in the literature to model the interfacial area concentration by taking into account the bubble coalescence and disintegration, and phase change effects.In this study, two types of inlet boundary conditions are considered, one being a uniform-profile boundary condition in the radial direction with area-averaged experimentally measured values while the other being a non-uniform profile condition based on the actual measured profiles at the inlet. The numerical predictions of downstream profiles of the phase distributions indicate that the two types of boundary conditions yield similar results for the downstream flow behaviors for the bubbly flow conditions investigated. In addition, the results with and without the lift force demonstrated that the lift force is essential to obtain accurate lateral phase distribution.     

Modeling of distribution parameter,void fraction covariance and relative velocity covariance for upward steam-water boiling flow in vertical rod bundle

In order to improve the prediction accuracy of one-dimensional interfacial force formulated by ‘Andersen’ approach, the distribution parameter in a drift–flux correlation, void fraction covariance, and relative velocity covariance has been modeled for dispersed boiling two-phase flow in a vertical rod bundle. The distribution parameter has been derived by a bubble-layer thickness model. The correlations of void fraction covariance and relative velocity covariance have been developed based on prototypic 8 × 8 rod bundle data. The correlation of void fraction covariance agrees with the bundle data with the mean absolute error, standard deviation, mean relative deviation, and mean absolute relative deviation being 0.00120, 0.0415, ?0.173%, and 1.80%, respectively. The correlation of relative velocity covariance agrees with the bundle data with the mean absolute error, standard deviation, mean relative deviation, and mean absolute relative deviation being ?0.00241, 0.0452, ?0.0316%, and 2.52%, respectively. In view of the great importance of void fraction covariance and relative velocity covariance on the one-dimensional interfacial drag force formulation, it is highly recommended to include the void fraction covariance and relative velocity covariance in the one-dimensional formulation of interfacial drag force used in nuclear thermal-hydraulic system analysis codes.     

Experimental and numerical studies of void fraction distribution in rectangular bubble columns

Bubbly flow is encountered in a wide variety of industrial applications ranging from flows in nuclear reactors to process flows in chemical reactors. The presence of a second phase, recirculating flow, instabilities of the gas plume and turbulence, complicate the hydrodynamics of bubble column reactors.This paper describes experimental and numerical results obtained in a rectangular bubble column 0.1 m wide and 0.02 m in depth. The bubble column was operated in the dispersed bubbly flow regime with gas superficial velocities up to 0.02 m/s. Images obtained from a high speed camera were used to observe the general flow pattern and have been processed to calculate bubble velocities, bubble turbulence parameters and bubble size distributions. Gas disengagement technique was used to obtain the volume averaged gas fraction over a range of superficial gas velocities. A wire mesh sensor was applied, to measure the local volume fraction at two different height positions. Numerical calculations were performed with an Eulerian–Eulerian two-fluid model approach using the commercial code CFX.The paper details the effect of various two-fluid model interfacial momentum transfer terms on the numerical results. The inclusion of a lift force was found to be necessary to obtain a global circulation pattern and local void distribution that was consistent with the experimental measurements. The nature of the drag force formulation was found to have significant effect on the quantitative volume averaged void fraction predictions.     

窄矩形通道内搅混流和环状流相界面参数的计算方法

空泡份额和界面浓度是两相流动中重要的相界面参数,准确获取窄矩形通道内搅混流和环状流工况下空泡份额和界面浓度是构建和完善两流体模型的关键。本文针对横截面为65 mm×2 mm的矩形通道开展了气液两相流动特性可视化实验研究,气相折算速度j_g＝1～9 m/s,液相折算速度j_f＝0.1～1.5 m/s,流型包含搅混流和环状流。提出了基于高速摄像法获取搅混流和环状流下空泡份额和界面浓度的分析计算方法,利用该方法所得空泡份额与窄矩形通道内经验关系式计算值的相对偏差约在10%以内。此计算方法可为研究复杂流型下窄矩形通道内的相界面参数提供理论依据。     

基于竖直圆管空气-水两相流实验的相间曳力模型研究

研究两相流相间阻力特性对系统程序关键本构模型封闭具有重要意义。本文基于竖直圆管开展了空气-水两相流实验,采用四探头电导探针对空泡份额、气泡弦长和界面面积浓度等气泡参数的径向分布进行了测量。结果表明空泡份额和气泡弦长呈现“核峰型”分布,而界面面积浓度并没有表现出随流速的单调关系。进一步开发了泡状流和弹状流的相间曳力模型,考虑了液相表观流速与管径对气泡尺寸分布的影响,建立了临界韦伯数与不同液相流速的关系。计算得到的空泡份额和界面面积浓度与实验数据整体符合较好,验证了模型的可靠性,为两相流相间阻力特性研究提供参考意义。     

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．     

Development of drift–flux correlation for predicting void fraction in downcomer regions

Accurate prediction of interfacial drag in the downcomer annulus is crucial for the assessment of downcomer void fraction for the loss of coolant accident analysis. The downcomer annulus is the gap between reactor pressure vessel (RPV) exterior and the inner wall of pressure containment vessel (PCV). Based on the previous research, occurrence of the nonuniform two-phase flow in downcomer section is reported, which is partly due to the large wall temperature difference between RPV exterior and the inner wall of PCV. In RELAP5, interfacial drag term in downcomer section is calculated using Kataoka–Ishii and churn-turbulent drift–flux correlations. It has been pointed out that this traditional calculation approach for calculating downcomer void fraction needs modification. The purpose of the current study is to assess the behaviors of drift–flux parameters in downcomer section and to propose an improved distribution parameter model that is suitable for donwcomer boiling analysis.     

Modeling of low-pressure subcooled boiling flow of water via the homogeneous MUSIG approach

Applying a three-dimensional two-fluid model coupled with homogeneous multiple size group (MUSIG) approach, numerical simulations of upward subcooled boiling flow of water at low pressure were performed on the computational fluid dynamics (CFD) code CFX-10 with user defined FORTRAN program. A modified bubble departure diameter correlation based on the Unal's semi-mechanistic model and the empirical correlation of Tolubinski and Kostanchuk was developed. The water boiling flow experiments at low pressure in a vertical concentric annulus from reference were used to validate the models. Moreover, the influences of the non-drag force on the radial void fraction distribution were investigated, including lift force, turbulent dispersion force and wall lubrication force. Good quantitative agreement with the experimental data is obtained, including the local distribution of bubble diameter, void fraction, and axial liquid velocity. The results indicate that the local bubble diameter first increases and then decreases due to the effect of bubble breakup and coalescence, and has the maximum bubble diameter along the radial direction. Especially, the peak void fraction phenomenon in the vicinity of the heated wall is predicted at low pressure, which is developed from the wall repulsive force between vapor bubbles and heated wall. Nevertheless, there is a high discrepancy for the prediction of the local axial vapor velocity.     

摇摆对过冷沸腾相分布特性的影响机理分析

采用双探头光学探针测量了摇摆条件下圆管内过冷沸腾局部空泡份额、界面面积浓度及汽泡尺寸等局部相界面参数径向分布特性,根据实验及计算结果,从汽液相界面作用力角度对摇摆运动条件下过冷沸腾相分布机理进行了分析。结果表明：摇摆条件下,浮力径向分量、升力、湍流分散力和壁面润滑力量级约为10³ N/m³,附加惯性力与其余诸力相比小2～3个量级。因此摇摆条件下过冷沸腾相分布特性主要取决于周期性波动的升力、湍流分散力、壁面润滑力及浮力径向分量之间的平衡关系。     

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.     

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.