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.     

Critical Heat Flux Prediction Method Based on Two-Phase Turbulence Model

In this paper, we present an analytical methodology to predict forced convective CHF (Critical Heat Flux) for DNB (Departure from Nucleate Boiling) type boiling transition that occurs inside of uniformly heated round tubes. Axial directional two-phase flow analysis was conducted based on one-dimensional two-fluid model and typical constitutive models. At the same time, the radial directional distribution of void fraction at any axial location was calculated based on the bubble diffusion model, which was coupled with two-phase turbulence model for boiling bubbly flow. The calculated void fraction showed the wall peak distribution, and was compared with experimental data, which was derived from subcool boiling experiments. IPNVG (Incipient Point of Net Vapor Generation), which means the starting point of two-phase flow analysis, was also investigated well, since it was revealed that IPNVG had a significant influence on CHF prediction. By using this methodology for calculating radial directional void fraction distribution, we carried out CHF prediction for water on the assumption that DNB would occur when the local void fraction near the heated wall exceeds a critical value. The predicted CHF agreed well with experimental data, and the accuracy was within about 20%.     

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.     

中压沸腾工况相径向分布实验研究

采用高温高压单探头光学探针．在中压沸腾工况下进行了局部空泡率与汽泡频率径向分布特性实验研究,并根据探针信号对两相流流型进行了识别,分析了中压沸腾工况下空泡率径向分布与流型的关系。研究结果表明：随热平衡含汽率增加,整个直径方向上空泡率分布从近U形向鞍形和弧形发展;汽泡频率则以近U形分布为主;泡状流工况下,空泡率呈U形或近壁区显著高于中心区的鞍形分布,弹状流工况下,中心区空泡率略低于近壁区。整个直径上空泡率呈弧形分布。     

倾斜管内上升泡状流界面参数分布特性实验研究

采用双头光纤探针对倾斜圆管内空气-水两相泡状流界面参数分布特性进行了实验研究,包括局部空泡份额、气泡通过频率、界面面积浓度及气泡当量直径径向分布特性。实验段内径为50 mm,液相表观速度为0.144 m/s,气相表观速度为0~0.054 m/s。结果表明倾斜管内向上泡状流气泡明显向上壁面聚集。局部界面浓度、空泡份额及气泡通过频率径向分布相似。倾斜条件下局部界面参数分布下壁面附近峰值相对于竖直状态被削弱甚至消失,上壁面附近峰值被加强,中间区域从下壁面往上逐渐增大,且随倾斜角度的增加变化更加剧烈。气泡等价直径随径向位置、气相速度及倾斜角度的不同无明显变化,气泡聚合和破碎现象较少发生。通过气泡受力分析解释了倾斜对泡状流局部界面参数分布的影响机理。     

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。     

竖直圆管内泡状流界面参数分布特性

采用双头光纤探针对内径为50 mm竖直圆管内空气-水两相泡状流界面参数径向分布特性进行了实验研究。气液两相表观速度变化范围分别为0.004～0.05 m/s和0.071～0.283 m/s。结果表明,竖直管内向上泡状流局部界面面积浓度（IAC）、空泡份额及气泡频率径向分布相类似,即气相流速较低时管道中间很大范围内以上3个局部界面参数几乎恒定,近壁区迅速下降到较低值;随气相流速的增加,局部界面参数在管道中心出现峰值。本实验中气泡聚合与破碎现象较少发生,索特平均直径沿径向近似均匀分布,且随气液两相流速变化很小。通过气泡横向受力解释了局部界面参数分布的影响机理。     

Void fraction distribution in low flow rate subcooled boiling

Experimental data are presented for the void fraction distribution in low flow rate forced convection subcooled boiling of water in a heated vertical tube at steady-state conditions. The measurements are based on gamma attenuation and X-ray radiography techniques. The measured local equilibrium quality at the point of net vapor generation and the void fraction profiles are compared with theoretical and empirical models of subcooled boiling. A close fit to the experimental results is obtained by the Levy model and by the Saha and Zuber correlation.     

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.     

流动欠热沸腾空泡份额的研究

影响欠热沸腾传热的主要因素是含汽率和系统压力。系统压力直接影响加热面上汽泡的大小,从而影响壁面向液体的传热量。欠热沸腾区任一点的热平衡含汽率可由通道内的热工参数和流动参数求出,然后据此求出通道中某点的空泡份额。文中给出了计算加热通道内流动欠热沸腾区空泡份额的计算关系式,该关系式在给定的参数范围内与实验结果符合较好。     

Flow structure and bubble characteristics of steam–water two-phase flow in a large-diameter pipe

The flow structure and bubble characteristics of steam–water two-phase upward flow were observed in a vertical pipe 155 mm in inner diameter. Experiments were conducted under volumetric flux conditions of J_G<0.25 m s⁻¹ and J_L<0.6 m s⁻¹, and three different inlet boundary conditions to investigate the developing state of the flow. The radial distributions of flow structure, such as void fraction, bubble chord length and gas velocity, were obtained by horizontally traversing optical dual void probes through the pipe. The spectra of bubble chord length and gas velocity were also obtained to study the characteristics of bubbles in detail. Overall, an empirical database of the multi-dimensional flow structure of two-phase flow in a large-diameter pipe was obtained. The void profiles converged to a so-called core-shaped distribution and the flow reached a quasi-developed state within a relatively short height-to-diameter aspect ratio of about H/D=4 compared to a small-diameter pipe flow. The PDF histogram profiles of bubble chord length and gas velocity could be approximated fairly well by a model function using a gamma distribution and log–normal distribution, respectively. Finally, the correlation of Sauter mean bubble diameter was derived as a function of local void fraction, pressure, surface tension and density. With this correlation, cross sectional averaged bubble diameter was predicted with high accuracy compared to the existing constitutive equation mainly being used in best-estimate codes.     

Performance Analysis of Mesh-Packed Cold Traps

SIMMER-IV, a three-dimensional version of SIMMER-III, has been developed at JNC to study the safety of fast reactors mechanistically. SIMMER-IV was applied to the experimental analysis of bubbly flow to verify the models. The results of an experiment performed by Valukina et al. showed that the radial distribution of void fraction changes suddenly as the bubble size changes. In the present work, the analysis focuses on reproducing the change of the radial void distribution. The diffusion term, “lateral lift force,” and “wall force” were introduced in sequence into its momentum conservation equation. Naturally, the diffusion term improved the radial distribution of vertical velocity but did not explain the change of the radial void distribution in the experiment. Subsequent introduction of the lateral lift force increased the void fraction along the wall, but it did not change the radial void distribution as the bubble size changed. Finally, the wall force was introduced and, in accordance with the experimental results, the dependence of radial void distribution on the bubble size was proved. The behavior of a molten pool that is bubbly with steel steam plays an important role in the evaluation of LMFR severe accidents. This study is expected to improve the evaluation.     

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。     

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。     

Experimental study of vapor local characteristics in upward low pressure boiling tube

Radial distribution of vapor local parameters, including local void fraction, interfacial velocity, bubble size, bubble frequency and interfacial area concentration, are investigated through the measurement in an upward boiling tube using dual-sensor optical probe. In addition, a new local parameter -"local bubble number concentration" is developed on the basis of bubble frequency. The analysis shows that this parameter can reflect bubble number density in space, and has clear physical meaning.     

竖直圆管中泡状流含汽率径向分布的统计测量方法

为了研究竖直圆管中高含汽率泡状流的含汽率径向分布,设计了一种测量含汽率径向分布的方法.该方法通过统计投影视图中的像素信息得到泡状流的投影含汽率,根据汽泡投影重叠概率计算出截面含汽率在投影面上的边缘分布;再基于竖直圆管中含汽率分布轴对称的假设,使用改进的傅里叶级数展开方法求解Abel逆变换,计算出含汽率沿圆管径向的分布.为验证该方法的有效性,测量了较低含汽率时的泡状流径向含汽率,并与匹配方法的测量结果进行比较.实验结果表明:此方法能得到高含汽率或含汽率近壁分布等其他方法难以测量的含汽率分布.     

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.     

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.     

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。