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.     

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。     

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。     

Simultaneous measurement of void fraction and fundamental bubble parameters in subcooled flow boiling

Visualization was performed for the vapor bubbles in water subcooled flow boiling in a vertical heated tube to measure simultaneously the void fraction and the four fundamental bubble parameters: nucleation site density, bubble release frequency, bubble lifetime and bubble size. Using the mass flowrate and liquid subcooling as the experimental parameters, the changes of void fraction and bubble parameters with the wall heat flux were measured. The results of image analysis showed that the vapor void fraction could be approximated by the function of nucleation site density and bubble lift-off diameter; the bubble lift-off diameter was more influential than the nucleation site density. It was hence concluded that the bubble lift-off diameter could be regarded as the key parameter to determine the vapor void fraction under the present experimental conditions. The strong relation of bubble lift-off diameter to superheated liquid layer thickness was indicated for the future model development studies of bubble lift-off diameter.     

Analysis of subcooled boiling flow with one-group interfacial area transport equation and bubble lift-off model

To enhance the multi-dimensional analysis capability for a subcooled boiling two-phase flow, the one-group interfacial area transport equation was improved with a source term for the bubble lift-off. It included the bubble lift-off diameter model and the lift-off frequency reduction factor model. The bubble lift-off diameter model took into account the bubble's sliding on a heated wall after its departure from a nucleate site, and the lift-off frequency reduction factor was derived by considering the coalescences of the sliding bubbles. To implement the model, EAGLE (elaborated analysis of gas-liquid evolution) code was developed for a multi-dimensional analysis of two-phase flow. The developed model and EAGLE code were validated with the experimental data of SUBO (subcooled boiling) and SNU (Seoul National University) test, where the subcooled boiling phenomena in a vertical annulus channel were observed. Locally measured two-phase flow parameters included a void fraction, interfacial area concentration, and bubble velocity. The results of the computational analysis revealed that the interfacial area transport equation with the bubble lift-off model showed a good agreement with the experimental results of SUBO and SNU. It demonstrates that the source term for the wall nucleation by considering a bubble sliding and lift-off mechanism enhanced the prediction capability for the multi-dimensional behavior of void fraction or interfacial area concentration in the subcooled boiling flow. From the point of view of the bubble velocity, the modeling of an increased turbulence induced by boiling bubbles at the heated wall enhanced the prediction capability of the code.     

过冷流动沸腾中汽泡脱离直径的理论研究

汽泡脱离直径模型是壁面沸腾计算中的一个重要子模型。为了正确预测过冷流动沸腾中的壁面传热情况,研究结合新改进的汽泡生长模型,采用力平衡方法对过冷流动沸腾中的汽泡脱离直径进行了模拟。汽泡生长模型同时考虑了微液层、过热层和汽泡顶部过冷液体层对汽泡生长所做的贡献,并采用饱和沸腾与过冷沸腾2个实验对其进行了验证,结果表明预测曲线与实验值吻合良好。另外,选取了3个过冷流动沸腾实验来验证汽泡脱离直径模型,模拟结果均在可接受的误差范围内。      

低压下水欠热流动沸腾的两相CFD数值模拟研究

采用两流体(汽相和液相)基本数学模型,结合汽相和液相之间的界面传热、传质和动量交换封闭模型、汽泡平均直径模型、汽泡脱离直径模型、汽泡成核模型、汽泡脱离频率模型、欠热沸腾起始点模型和壁面热流密度分配模型,在CFD软件CFX4.4中采用用户自定义函数将相变引起的传热、传质和动量交换作为源项分别添加到汽相和液相的能量、质量和动量守恒方程中,对低压下内管加热外管绝热的环形通道内的欠热沸腾进行了数值研究,得到了欠热流动沸腾下汽相体积份额、液相速度、汽相速度分布等。采用Lee等的环形通道内低压下欠热沸腾体积份额实验数据对计算结果进行了验证,吻合良好。     

基于CFD方法的矩形窄缝通道内过冷流动沸腾模型研究

板状燃料元件中的矩形窄缝通道具有宽高比大的几何特征,高度方向速度梯度大、分布陡峭,发生过冷沸腾时,近壁面汽泡运动行为将受其影响而改变,其中汽泡滑移现象对沸腾换热影响较大。本文针对矩形窄缝通道中的汽泡滑移行为,构建了包含滑移热流的壁面热流分配模型,并建立机理性的汽泡受力模型和滑移模型计算汽泡脱离直径、浮升直径和滑移距离等辅助参数,开发了一套适用于矩形窄缝通道内向上流动沸腾的壁面沸腾模型。选用Nuthel窄缝通道沸腾实验进行数值模拟验证,结果表明：本文模型可以较好地预测1～4 MPa中低压工况窄缝通道向上流动沸腾的壁面过热度,最大误差相比RPI模型由80%降低至17%;蒸发热流份额和近壁面空泡份额相比RPI模型更低。     

Flow Structure of Subcooled Boiling Water Flow in a Subchannel of 3 × 3 Rod Bundles

In this paper, the interfacial flow structure of subcooled water boiling flow in a subchannel of 3 × 3 rod bundles is presented. The 9 rods are positioned in a quadrangular assembly with a rod diameter of 8.2mm and a pitch distance of 16.6 mm. Local void fraction, interfacial area concentration, interfacial velocity, Sauter mean diameter, and liquid velocity have been measured using a conductivity probe and a Pitot tube in 20 locations inside one of the subchannels. A total of 53 flow conditions have been considered in the experimental dataset at atmospheric pressure conditions with a mass flow rate, heat flux, inlet temperature, and subcooled temperature ranges of 250–522 kg/m s, 25–185 kW/m², 96.6–104.9°C, and 2–11 K, respectively. The dataset has been used to analyze the effect of the heat flux and mass flow rate on the local flow parameters. In addition, the area-averaged data integrated over the whole subchannel have been used to validate some of the distribution parameter and drift velocity constitutive equations and interfacial area concentration correlations most used in the literature.     

管内过冷流动沸腾CFD模型参数敏感性研究

采用CFD方法对燃料组件进行过冷流动沸腾数值模拟研究是反应堆热工水力分析的一项重要内容。本研究使用STAR CCM+基于欧拉双流体模型结合壁面沸腾模型对管内过冷流动沸腾进行数值模拟,得到了壁面温度、主流温度及空泡份额的分布。基于实验结果对网格模型、湍流模型、壁面沸腾模型及相间作用力模型的参数设置进行了敏感性分析。研究结果表明,对于欧拉双流体模型,并非网格量越多结果越准确,加热面第1层网格的高度对结果影响显著。湍流模型和曳力模型对计算结果影响较小,非曳力中的湍流耗散力及升力对结果影响较大。Li Quan或Hibiki Ishii汽化核心密度模型与Kocamustafaogullari气泡脱离直径模型组合对壁面温度及空泡份额的计算较准确。本研究可为反应堆燃料组件内过冷流动沸腾数值模拟提供参考依据。     

Influence of subcooled boiling on out-of-phase oscillations in boiling water reactors

In this paper, we develop a reduced order model with modal kinetics for the study of the dynamic behavior of boiling water reactors. This model includes the subcooled boiling in the lower part of the reactor channels. New additional equations have been obtained for the following dynamics magnitudes: the effective inception length for subcooled boiling, the average void fraction in the subcooled boiling region, the average void fraction in the bulk-boiling region, the mass fluxes at the boiling boundary and the channel exit, respectively, and so on. Each channel has three nodes, one of liquid, one with subcooled boiling, and one with bulk boiling. The reduced order model includes also a modal kinetics with the fundamental mode and the first subcritical one, and two channels representing both halves of the reactor core. Also, in this paper, we perform a detailed study of the way to calculate the feedback reactivity parameters. The model displays out-of-phase oscillations when enough feedback gain is provided. The feedback gain that is necessary to self-sustain these oscillations is approximately one-half the gain that is needed when the subcooled boiling node is not included.     

基于气泡动力学的过冷流动沸腾边界层模型研究

过冷流动沸腾中的流动和传热特性对反应堆的安全运行和经济性都具有重要意义。过冷流动沸腾起始于ONB点,结束于Tsat点,中间被OSV点划分为高过冷流动沸腾段和低过冷流动沸腾段,不同阶段流场情况以及气泡行为存在较大区别。目前关于过冷流动沸腾过程的研究主要基于宏观实验、理论研究和数值模拟,随着气泡动力学的发展,从微观层面揭示沸腾机理变得可行。本文基于气泡动力学和气泡边界层模型,提出了一套预测过冷流动沸腾的理论模型,采用分相模型,将流场在径向上划分为多个区域,通过1组准二维控制方程,将各区域内的气泡行为,区域间的质量、动量和能量交换以及两相参数沿轴向的变化情况考虑在内,利用获得的边界层流场信息,可确定ONB点和OSV点。模型与空泡份额和流体温度的实验结果符合良好,并成功应用于核反应堆燃料元件通道的过冷流动沸腾计算。     

Interfacial area measurements in subcooled flow boiling

The purpose of the present study was to measure two-phase parameters in subcooled flow boiling. These parameters include void fraction distribution, interfacial area concentration distribution, Sauter mean diameter, and the interfacial velocity. A literature review was conducted and the results show that only three researchers have made local measurements in the subcooled boiling region. None of the previous have included results for interfacial area concentration distribution. To make these measurements an experimental facility was constructed that allows insertion of advanced local two-phase flow instrumentation. Experiments were performed for a number of conditions at atmospheric pressure.     

Numerical Simulation on Subcooled Boiling Heat Transfer Characteristics of Water-Cooled W/Cu Divertors

In order to realize safe and stable operation of a water-cooled W/Cu divertor under high heating condition,the exact knowledge of its subcooled boiling heat transfer characteristics under different design parameters is crucial.In this paper,subcooled boiling heat transfer in a water-cooled W/Cu divertor was numerically investigated based on computational fluid dynamic(CFD).The boiling heat transfer was simulated based on the Euler homogeneous phase model,and local differences of liquid physical properties were considered under one-sided high heating conditions.The calculated wall temperature was in good agreement with experimental results,with the maximum error of 5%only.On this basis,the void fraction distribution,flow field and heat transfer coefficient(HTC)distribution were obtained.The effects of heat flux,inlet velocity and inlet temperature on temperature distribution and pressure drop of a water-cooled W/Cu divertor were also investigated.These results provide a valuable reference for the thermal-hydraulic design of a water-cooled W/Cu divertor.     

Experimental investigation of local two-phase flow parameters of a subcooled boiling flow in an annulus

As a series of subcooling boiling flow tests, local two-phase flow parameters were obtained at SUBO (subcooled boiling) test facility under steam–water flow conditions. The test section is a vertical annulus of which the axial length is 4.165 m with a heater rod at the center of a channel. The inner and outer diameters of the test section and the heater rod are 35.5 mm and 9.98 mm, respectively. The test was performed by a two-stage approach. Stage-I for the measurement of local bubble parameters has been already done (Yun et al., 2009). The present work focused on the stage-II test for the measurement of local liquid parameters such as a local liquid velocity and a liquid temperature for a given flow condition of stage-I. A total of six test cases were chosen by following the test matrix of stage-I. The flow conditions are in the range of the heat flux of 370–563 kW/m², mass flux of 1110–2100 kg/(m² s) and inlet subcooling of 19–31 °C at pressure condition of 0.15–0.2 MPa. From the test, local liquid parameters were measured at 6 elevations along the test section and 11 radial locations of each elevation in addition to the previously obtained local void fraction, interfacial area concentration, Sauter mean diameter and bubble velocity. The present subcooled boiling (SUBO) data completes a data set for use as a benchmark, validation and model development of the Computational Fluid Dynamics (CFD) codes or existing safety analysis codes.     

压水堆子通道欠热沸腾数值验证及交混翼研究

为改善压水堆交混翼格架在欠热沸腾工况下的热工水力特性,以子通道为研究对象验证了所使用的欠热沸腾数值模型在不同工况下的有效性。基于已验证的数值模型,对含不同偏折角交混翼格架的子通道模型在不同工况下进行了两相流数值模拟,研究交混翼及其偏折角对子通道中两相流动、传热及气泡分布的影响。结果表明：交混翼在增大压降的同时明显强化了冷却剂的交混、降低了近壁面气泡份额、提高了换热效率,且在一定范围内偏折角越大影响越明显。相对较高的气泡份额将导致更大的压力损失、减弱冷却剂的交混、降低传热效率。当交混翼偏折角达25°时,继续增大其偏折角对降低近壁面气泡份额和提高传热效率的作用不再明显,反而造成压降的快速增大,因此建议其偏折角在25°左右。     

蒸汽发生器传热管束过冷沸腾区两相流动数值模拟

基于两流体欧拉数学模型结合RPI壁面沸腾模型,利用大型商用CFD软件ANSYS CFX 12.0对蒸汽发生器传热管束过冷沸腾区一次侧、壁面和二次侧耦合传热过程进行了数值模拟。研究了三叶梅花孔支撑板和不同入口过冷度条件下蒸汽发生器传热管束内的流动沸腾现象,得到一、二次侧流场与温度场,二次侧空泡份额分布,支撑板梅花孔局部的流动状况及不同入口过冷度对蒸汽发生器热工水力特性的影响。数值模拟结果表明,三叶梅花孔支撑板的存在及不同入口过冷度对蒸汽发生器传热管束过冷沸腾区域的热工水力特性影响显著。     

A mechanistic critical heat flux model for wide range of subcooled and low quality flow boiling

A mechanistic model to predict a critical heat flux (CHF) over a wide operating range in the subcooled and low quality flow boiling has been proposed based on a concept of the bubble coalescence in the wall bubbly layer. The conservation equations of mass, energy and momentum, together with appropriate constitutive relations, are solved analytically to derive the CHF formula. The model is characterized by an introduction of the drag force due to wall-attached bubbles roughness in the momentum balance, which determines the limiting transverse interchange of mass flux crossing the interface of the wall bubbly layer and core. Comparison between the predictions by the proposed model and the experimental CHF data shows good agreement over a wide range of parameters for both light water and fusion reactors operating conditions. The model correctly accounts for the effects of flow variables such as pressure, mass flux and inlet subcooling as well as geometry parameters.     

Void distribution and bubble motion in bubbly flows in a 4×4 rod bundle. Part I: Experiments

Lack of local void fraction data in a rod bundle makes it difficult to validate a numerical method for predicting gas–liquid two-phase flow in the bundle. Distributions of local void fraction and bubble velocity in each subchannel in a 4×4 rod bundle were, therefore, measured using a double-sensor conductivity probe. Liquid velocity in the subchannel was also measured using laser Doppler velocimetry (LDV) to obtain relative velocity between bubbles and the liquid phase. The size and pitch of rods were 10 and 12.5 mm, respectively. Air and water at atmospheric pressure and room temperature were used for the gas and liquid phases, respectively. The volume fluxes of gas and liquid phases ranged from 0.06 to 0.15 m/s and from 0.9 to 1.5 m/s, respectively. Experimental results showed that the distributions of void fraction in inner and side subchannels depend not only on lift force acting on bubbles but also on geometrical constraints on bubble dynamics, i.e. the effects of rod walls on bubble shape and rise velocity. The relative velocity between bubbles and the liquid phase in the subchannel forms a non-uniform distribution over the cross-section, and the relative velocity becomes smaller as bubbles approach the wall due to the wall effects.     

Void distribution and bubble motion in bubbly flows in a 4×4 rod bundle. Part II: numerical simulation

Numerical simulations of bubbly flows in a four by four rod bundle are carried out using a multi-fluid model to examine effects of the numerical treatment of phase distribution and drag model. The transport equations of bubble number density and void fraction are used as the continuity equation of the gas phase. Two drag models are tested: one of them accounts for the bubble deformation (aspect ratio), whereas the other does not. The rod diameter, the rod pitch and the hydraulic diameter of the rod bundle are 10, 12.5 and 9.1 mm, respectively. The gas and liquid volume fluxes are J_G = 0.06 m/s and J_L = 0.9 and 1.5 m/s, respectively. The bubble diameter ranges from 1 to 5 mm. Comparisons between the numerical and measured data show that (1) the restriction on bubble lateral motion due to the presence of rods can be taken into account by using the transport equation of bubble number density, whereas that of the void fraction cannot deal with the restriction and causes large errors in the distribution of void fraction and (2) the reduction in the bubble-relative velocity near the wall is predictable by using the drag model accounting for the bubble deformation effect.