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.     

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.     

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。     

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.     

An application of the method of moments to the modeling of bubbly flow

Bubbly flows are relevant in nuclear reactors thermalhydraulics and safety analysis. Regularly, empirical constitutive laws are required to close the two-fluid equations, particularly in relating the interfacial area and the bubble number densities to the local void fraction. In this article, starting from a generalized Boltzmann transport equation for the bubble size spectrum, a convection equation for the bubble number density is derived using the method of moments. The equation is analyzed for a vertical bubbly flow in stagnated liquid, showing excellent agreement with experimental data. The model is useful as a mean to provide conservation-based correlations to complement the existing two-fluid models.     

Model evaluation of two-group interfacial area transport equation for confined upward flow

The bubble interaction mechanisms have been analytically modeled in the first paper of this series to provide mechanistic constitutive relations for the two-group interfacial area transport equation (IATE), which was proposed to dynamically solve the interfacial area concentration in the two-fluid model. This paper presents the evaluation approach and results of the two-group IATE based on available experimental data obtained in confined upward flow, namely, 11 data sets in or near bubbly flow and 13 sets in cap-turbulent and churn-turbulent flows. The two-group IATE is evaluated in steady-state, one-dimensional (1D) form. To account for the inter-group bubble transport, the void fraction transport equation for Group-2 bubbles is also used to predict the void fraction for Group-2 bubbles. Agreement between the data and the model predictions is reasonably good and the average relative difference for the total interfacial area concentration between the 24 data sets and predictions is within 7%. The model evaluation demonstrates the capability of the two-group IATE focused on the current confined flow to predict the interfacial area concentration over a wide range of flow regimes.     

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。     

竖直下降两相流相界面结构输运特性

竖直下降两相流具有与竖直上升两相流不同的相界面结构特征及输运特性。本文对竖直下降管内的气水两相流进行了实验研究,运用微型四头电导探针对7.5、31.5及55.5倍管径横截面处的空泡份额、相界面浓度、气泡直径、气泡频率及气泡速度等相界面结构参数的局部分布进行了测量。分析获得了相界面结构参数的沿程变化规律,并研究了气相表观流速对相界面结构发展的影响及一维相界面结构输运特性。发现竖直下降泡状流的升力指向管中心,导致相界面结构参数基本呈中心峰值分布;气相表观流速的增大会提高空泡份额和相界面浓度分布的峰度;竖直下降两相流在距入口31.5倍管径处基本达到充分发展。     

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。     

Horizontal bubbly flow with elbow restrictions: Interfacial area transport modeling

The present study develops an interfacial area transport equation applicable to an air-water horizontal bubbly flow, along which two types of horizontal elbows are installed as flow restrictions. Two sets of experiments are performed in a round glass tube of 50.3 mm inner diameter. Along the test section, a 90-degree elbow is installed at L/D = 206.6 from the two-phase mixture inlet and then a 45-degree elbow is installed at L/D = 353.5. In total, 15 different flow conditions in the bubbly flow regime for each of the two flow restriction experiments are studied. Detailed local two-phase flow parameters are acquired by a double-sensor conductivity probe at four different axial locations in the 90-degree experiment and three different axial locations in the 45-degree experiment. The effect of the elbows is found to be evident in the distribution of local parameters as well as in the development of interfacial structures. It is clear that the elbows make an effect on the bubble interactions resulting in significant changes to both the void fraction and interfacial area concentration. In the present analysis, the interfacial area transport equation is developed in one-dimensional form via area averaging. In the averaging process, characteristic non-uniform distributions of the flow parameters in horizontal two-phase flow are treated mathematically through a distribution parameter. The mechanistic models for the major bubble interaction phenomena developed in vertical flow analysis are employed in the present study. Furthermore, the change in pressure due to the minor loss of an elbow is taken into consideration by using a newly developed correlation analogous to Lockhart and Martinelli's. In total, 105 area-averaged data points are employed to benchmark the present model. The present model predicts the data relatively well with an average percent difference of approximately ±20%.     

Characteristics of two-phase condensing flow by visualization using computed image processing

The mechanics of the condensing behavior of vapor bubbles in a subcooled bulk flow is complicated and influenced by both heat and mass transfer. To examine the characteristics of such thermal-nonequilibrium two-phase flow, experimental and analytical researches have been made. In the experiment, the movement of each vapor bubble in a flowing channel was recorded on video tapes and analyzed by an image processing system. As result, the distributions of void fraction along the test section were obtained. In the analysis, a simple analytical model was introduced to predict the distributions of void fraction and liquid subcooling temperature. By considering the rate of vapor condensation along the flow direction, the differential equation of energy balance between two phases was obtained. Integration of this equation yielded the void fraction and bulk liquid subcooling at any position. The condensation rate was estimated as a function of the local liquid subcooling, interfacial area and mass velocity. Finally, a close fit between calculated results and experimental data was obtained.     

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.     

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.     

竖直大圆管内两相流动界面输运过程研究

采用光纤探针测量方法研究了垂直上升管中空气-水两相流动的局部界面面积浓度（IAC）和空泡份额等分布规律。实验选用的圆管直径为100 mm,气相、液相表观速度的范围分别为0～0.1 m/s和0～1.0 m/s。结果发现,影响径向IAC分布的因素主要为气泡通过频率。基于Ishii-Kim界面输运模型,对轴向IAC进行了计算;通过分析4种气泡间相互作用对IAC的影响,发现工作压力是影响轴向IAC变化的主要因素,最后给出了引入工作压力影响的轴向IAC计算关联式。     

Modeling and validation of interfacial area transport equation in subcooled boiling flow

The first comprehensive validation of the interfacial area transport equation in subcooled boiling is presented and shown to perform exceptionally when compared with experimental data. The formulation and closure of the bubble layer averaged interfacial area transport equation is reviewed along with the treatment of the two-fluid model in subcooled boiling. Interfacial area concentration source and sink terms in subcooled boiling are presented including the bubble interaction mechanisms (random collision and turbulent impact), as well as phase change terms (wall nucleation and condensation). Additionally, the volume source terms from phase change are described and discussed in terms of their significance to the interfacial area transport equation. The validation of the interfacial area transport equation with a recently proposed wall nucleation source term is shown to have excellent prediction at low and elevated pressure, as well as a wide range of mass flux. With new confidence in the wall nucleation source term, the interfacial area concentration in subcooled boiling can be accurately predicted. Due to its strong dependence in the modeling of active nucleation site density, bubble departure frequency, and departure diameter, the calculation is shown to be very sensitive to wall temperature.     

流动欠热水中空泡份额变化的实验研究

对垂直向上流动过程的欠热水中汽泡的凝结及空泡份额沿流动方向的变化问题做了实验研究和理论分析。给出了欠热水中空泡份额沿流动方向变化的试验研究结果。通过对汽泡冷凝过程的传热机理分析,给出了垂直向上流动欠热水中计算空泡份额的公式,此公式与试验结果吻合较好。     

Local measurement of bubbly flow in helically coiled tubes using double-sensor conductivity probe

ABSTRACT

The two-phase flow in helically coiled tubes (HCTs) is rather important in many industries, such as the heat exchange facility in nuclear power plant. In this work, a double-sensor conductivity probe was used to study the air/water bubbly flow in HCTs. The cross-sectional distribution profile of the interfacial parameters (void fraction, interfacial area concentration, bubble size, etc.) of air–water bubbly flow were systematically studied. Through carefully processing the raw data collected by the double-sensor conductivity probe, the distribution of the void fraction, interfacial area concentration, the bubbles number frequency over the cross-section are demonstrated, as well as the bubble velocities and sizes vertically in the dense region. Some statistical parameters of cross-sectional-averaged quantities, coefficients of variation, and bubble aggregation core coordinates are defined to quantitatively describe the distribution characteristics of interfacial parameters. The measured data are helpful for improving the understanding of two-phase flow characteristics in HCTs.     

A unified model considering force balances for departing vapour bubbles and population balance in subcooled boiling flow

Population balance equations combined with a three-dimensional two-fluid model are employed to predict subcooled boiling flow at low pressure in a vertical annular channel. The MUltiple-SIze-Group (MUSIG) model implemented in CFX4.4 is extended to account for the wall nucleation and condensation in the subcooled boiling regime. A model considering the forces acting on departing bubbles at the heated surface is formulated. This model provides the capacity of complex analyses on the bubble growth and departure for a wide range of wall heat fluxes and flow conditions.Comparison of model predictions against local measurements is made for the void fraction, bubble Sauter mean diameter and gas and liquid velocities covering a range of different mass and heat fluxes and inlet subcoolings. Good agreement is achieved with the local radial void fraction, bubble Sauter mean diameter and liquid velocity profiles against measurements. However, significant weakness of the model is evidenced in the prediction of the vapour velocity. Work is in progress to circumvent the deficiency of the MUSIG boiling model by the consideration of additional momentum equations to better represent the momentum forces acting on the range of bubble sizes in the bulk subcooled liquid.     

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.     

Implementation and evaluation of one-group interfacial area transport equation in TRACE

The present study implements the one-dimensional interfacial area transport equation into the TRACE code, being developed by the U.S. Nuclear Regulatory Commission. The interfacial area transport equation replaces the conventional flow regime dependent correlations and the regime transition criteria for furnishing the interfacial area concentration in the two-fluid model. This approach allows dynamic tracking of the interfacial area concentration by mechanistically modeling bubble coalescence and disintegration mechanisms. Thus, it eliminates potential artificial bifurcations or numerical oscillations stemming from the use of conventional static correlations. To implement the interfacial area transport equation, a three-field version of TRACE is utilized, which is capable of tracking both the continuous liquid and gas fields as well as a dispersed gas field. To demonstrate the feasibility of the present approach, the steady-state one-group interfacial area transport equation applicable to adiabatic air-water bubbly two-phase flow is first tested in the present study. Data obtained in 18 different flow conditions from two vertical co-current upward air-water bubbly two-phase flow experiments performed in round pipes (25.4 mm and 48.3 mm) are used to help evaluate the implementation. Results obtained from TRACE with the interfacial area transport equation (TRACE-T) and those from TRACE without the transport equation (TRACE-NT) are compared to demonstrate the enhancement in prediction accuracy. The predictions made by TRACE-T agree well with the data with an average percent difference of approximately ±8%. It is also evident from the results that while TRACE-T accounts for dynamic interaction of bubbles along the flow field, the predictions made by TRACE-NT are attributed primarily to the pressure change.