CFD modelling of most probable bubble nucleation rate from binary mixture with estimation of components’ mole fraction in critical cluster

The employment of different mathematical models to address specifically for the bubble nucleation rates of water vapour and dissolved air molecules is essential as the physics for them to form bubble nuclei is different. The available methods to calculate bubble nucleation rate in binary mixture such as density functional theory are complicated to be coupled along with computational fluid dynamics (CFD) approach. In addition, effect of dissolved gas concentration was neglected in most study for the prediction of bubble nucleation rates. The most probable bubble nucleation rate for the water vapour and dissolved air mixture in a 2D quasi-stable flow across a cavitating nozzle in current work was estimated via the statistical mean of all possible bubble nucleation rates of the mixture (different mole fractions of water vapour and dissolved air) and the corresponding number of molecules in critical cluster. Theoretically, the bubble nucleation rate is greatly dependent on components’ mole fraction in a critical cluster. Hence, the dissolved gas concentration effect was included in current work. Besides, the possible bubble nucleation rates were predicted based on the calculated number of molecules required to form a critical cluster. The estimation of components’ mole fraction in critical cluster for water vapour and dissolved air mixture was obtained by coupling the enhanced classical nucleation theory and CFD approach. In addition, the distribution of bubble nuclei of water vapour and dissolved air mixture could be predicted via the utilisation of population balance model.     

A fractal analysis of subcooled flow boiling heat transfer

A fractal model for the subcooled flow boiling heat transfer is proposed in this paper. The analytical expressions for the subcooled flow boiling heat transfer are derived based on the fractal distribution of nucleation sites on boiling surfaces. The proposed fractal model for the subcooled flow boiling heat transfer is found to be a function of wall superheat, liquid subcooling, bulk velocity of fluid (or Reynolds number), fractal dimension, the minimum and maximum active cavity size, the contact angle and physical properties of fluid. No additional/new empirical constant is introduced, and the proposed model contains less empirical constants than the conventional models. The proposed model takes into account all the possible mechanisms for subcooled flow boiling heat transfer. The model predictions are compared with the existing experimental data, and fair agreement between the model predictions and experimental data is found for different bulk flow rates.     

A two-fluid model for critical vapour-liquid flow

One-dimensional two-fluid equations are used to calculate the mass flux of initially saturated or subcooled water discharging from a pipe in critical flow. The model allows in a general way for thermal non-equilibrium between the liquid and vapour bubbles, and for interphase relative motion. The theory is shown to be in good agreement with the measured critical flow-rates of pressurised water over a wide pressure range for a single choice of parameters characterising (i) the density of nucleation sites in the liquid, (ii) the liquid superheat required to cause bubble nucleation. Predictions are made of the critical mass flux of initially saturated water in pipes of the range of sizes of interest in water-reactor blowdown safety analysis. Results indicate that for pipes up to ten diameters in length flows will be significantly higher than values obtained from conventional homogeneous thermal equilibrium flow theory.     

Axial development of subcooled boiling flow in an internally heated annulus

For the main purpose of database construction in order to develop the interfacial area transport equation, axial developments of local void fraction, interfacial area concentration, bubble Sauter mean diameter, interfacial velocity, and bubble number density were measured in boiling water bubbly flows in a vertical-upward internally heated annulus using a double-sensor conductivity probe. The annulus channel consisted of an inner rod with a diameter of 19.1 mm and an outer round tube with an inner diameter of 38.1 mm, and the hydraulic equivalent diameter was 19.1 mm. A total of 11 data sets were acquired consisting of four inlet liquid velocities, 0.500, 0.664, 0.987 and 1.22 m/s, two heat fluxes, 100 and 150 kW/m², and two inlet liquid temperatures, 95.0 and 98.0°C. The axial developments of the flow parameters were discussed based on the measured data in detail. In addition to the database construction, the measured data validated recently proposed constitutive equations for the distribution parameter, drift velocity, and bubble Sauter mean diameter, which will improve the accuracy of the drift-flux model in subcooled bubbly flow.     

The role of nucleation in the initial phases of a rapid depressurization of a subcooled liquid

A two-fluid model with zero slip between the phases but which allows for unequal phase temperatures, changing interfacial area and the effect of heterogeneous nucleation has been used to evaluate the initial depressurization of a subcooled or saturated light. The results compare favourably with existing water and dichlorodifluoromethane experiments and suggest that the algorithm, in association with well-tabulated data, could be used to evaluate the heterogeneous nucleation factor.     

The interaction of background ocean air bubbles with a surface ship

A two-fluid model suitable for the calculation of the two-phase flow field around a naval surface ship is presented. This model couples the Reynolds-averaged Navier–Stokes (RANS) equations with equations for the evolution of the gas-phase momentum, volume fraction and bubble number density, thereby allowing the multidimensional calculation of the two-phase flow for monodisperse variable size bubbles. The bubble field modifies the liquid solution through changes in the liquid mass and momentum conservation equations. The model is applied to the case of the scavenging of wind-induced sea-background bubbles by an unpropelled US Navy frigate under non-zero Froude number boundary conditions at the free surface. This is an important test case, because it can be simulated experimentally with a model-scale ship in a towing tank. A significant modification of the background bubble field is predicted in the wake of the ship, where bubble depletion occurs along with a reduction in the bubble size due to dissolution. This effect is due to lateral phase distribution phenomena and the generation of an upwelling plume in the near wake that brings smaller bubbles up to the surface. © 1998 John Wiley & Sons, Ltd.     

两相临界流

由于两相临界流在压水反应堆安全分析中的重要性，在过去的４０年内，两相临界流一直是一个活跃的分支学科。本文对压水堆失水事故常用的两相临界流均匀平衡模型、滑移模型、考虑相间热力学非平衡效应的简化模型及两流体模型做了综述。结论是到目前为止，没有一个数学模型能准确预测各种参数范围、各种通道形状的临界流量。特定的模型只能适用于特定的情况。本文对非平衡两相流中汽泡成核、汽泡生长、相界面间质量、动量、能量交换的机理给予了更多的关注。     

Experimental study of pool temperature effects on nucleate pool boiling

Nucleate pool boiling experiments with constant wall temperature were performed using pure R113 for subcooled, saturated, and superheated pool conditions. A microscale heater array and Wheatstone bridge circuits were used to maintain the constant wall temperature and to measure the instantaneous heat flow rate accurately with high temporal and spatial resolutions. Images of bubble growth were taken at 5000 frames per second using a high-speed CCD camera synchronized with the heat flow rate measurements. The bubble geometry was obtained from the captured bubble images. The effect of the pool conditions on the bubble growth behavior was analyzed using dimensionless parameters for the initial and thermal growth regions. The effect of the pool conditions on the heat flow rate behavior was also examined. The bubble growth behaviors during subcooled, saturated, and superheated pool boiling were analyzed using a modified Jakob number that we newly defined. Dimensionless time and bubble radius parameters with the modified Jakob number characterized the bubble growth behavior well. These phenomena require further analysis for various pool temperature conditions, and this study will provide good experimental data with precise constant wall temperature boundary condition for such works.     

一种模拟气液两相流的格子波尔兹曼改进模型

基于格子波尔兹曼自由能模型,提出了一种模拟黏性流场中大密度比气液两相流的改进模型. 为了提高模型的精度,在原始模型的基础上计入了邻近点间粒子数密度的传递速率控制,考虑了碰撞项的差分松弛;为了避免两相间大密度比造成的数值不稳定问题,分别采用六点和九点差分格式求解?和?2. 同时,与传统格子波尔兹曼方法不同,实现了由单步碰撞操作到两步操作的转化. 通过对无重力场中气泡的模拟及与已有模型的计算结果的对比分析,表明该模型具有更高的数值精度. 成功模拟了重力作用下,单个上浮气泡的形变和尾涡形成过程,以及水平和竖直方向上两个气泡的相互作用过程,并验证了其质量守恒和体积不可压缩性.      

Thermal hydraulic modeling of a natural circulation loop

 The experiment was carried out on the test loop HRTL-5, which simulates the geometry and system design of a 5 MW nuclear heating reactor. The analysis was based on a one-dimensional two-phase flow drift model with conservation equations for mass, steam, energy and momentum. Clausius–Clapeyron equation was used for the calculation of flashing front in the riser. A set of ordinary equations, which describes the behavior of two-phase flow in the natural circulation system, was derived through integration of the above conservation equations for the subcooled boiling region, bulk boiling region in the heated section and for the riser. The method of time-domain was used for the calculation. Both static and dynamic results are presented. System pressure, inlet subcooling and heat flux are varied as input parameters. The results show that subcooled boiling in the heated section and void flashing in the riser have significant influence on the distribution of the void fraction, mass flow rate and flow instability of the system, especially at low pressure. The response of mass flow rate, after a small disturbance in the heat flux is shown, and based on it the instability map of the system is given through experiment and calculation. There exists three regions in the instability map of the investigated natural circulation system, namely, the stable two-phase flow region, the unstable bulk and subcooled boiling flow region and the stable subcooled boiling and single phase flow region. The mechanism of two-phase flow oscillation is interpreted. Received on 24 January 2000     

A method of concurrent thermographic–photographic visualization of flow boiling in a minichannel

A method is developed to capture the distribution of surface temperature while simultaneously imaging the bubble motions in diabatic flow boiling in a horizontal minichannel. Liquid crystal thermography is used to obtain highly resolved surface temperature measurements on the uniformly heated upper surface of the channel. High-speed images of the flow field are acquired simultaneously and are overlaid with the thermal images. The local surface temperature and heat transfer coefficient can be analyzed with the knowledge of the nucleation site density and location, and bubble motion and size evolution. The horizontal channel is 1.2 mm high × 23 mm wide × 357 mm long, and the working fluids are Novec 649 and R-11. Optical access is through a machined glass plate which forms the bottom of the channel. The top surface is an electrically heated 76 μm-thick Hastelloy foil held in place by a water-cooled aluminum and glass frame. The heat loss resulting from this construction is computed using a conduction model in Fluent. The model is driven by temperature measurements on the foil, glass plate and aluminum frame. This model produces a corrected value for the local surface heat flux and enables the computation of the bulk fluid temperature and heat transfer coefficient along the channel. The streamwise evolution of the heat transfer coefficient for single-phase laminar flow is compared to theoretical values for a uniform-flux boundary condition. Examples of the use of the facility for visualizing subcooled two-phase flows are presented. These examples include measurements of the surface temperature distribution around active nucleation sites and the construction of boiling curves for locations along the test surface. Points on the curve can be associated with specific image sequences so that the role of mechanisms such as nucleation and the sliding of confined bubbles may be discerned.     

An evaluation of a 3D free‐energy‐based lattice Boltzmann model for multiphase flows with large density ratio

In this paper, the 3D Navier–Stokes (N–S) equation and Cahn–Hilliard (C–H) equations were solved using a free‐energy‐based lattice Boltzmann (LB) model. In this model, a LB equation with a D3Q19 velocity model is used to recover continuity and N–S equations while another LB equation with D3Q7 velocity model for solving C–H equation (Int. J. Numer. Meth. Fluids, 2008; 56 :1653–1671) is applied to solve the 3D C–H equation. To avoid the excessive use of computational resources, a moving reference frame is adopted to allow long‐time simulation of a bubble rising. How to handle the inlet/outlet and moving‐wall boundary conditions are suggested. These boundary conditions are simple and easy for implementation. This model's performance on two‐phase flows was investigated and the mass conservation of this model was evaluated. The model is validated by its application to simulate the 3D air bubble rising in viscous liquid (density ratio is 1000). Good agreement was obtained between the present numerical results and experimental results when Re is small. However, for high‐Re cases, the mass conservation seems not so good as the low‐Re case. Copyright © 2009 John Wiley & Sons, Ltd.     

海洋大气间气泡的气体输运

研究球形小气泡在理想流体的波浪场中的气体扩散过程,把小雷诺数下均匀来流绕流球形气泡的气体交换结果与气泡运动方程耦合在一起进行求解．讨论了溶解于水中的气体浓度、波浪、气泡半径、气泡初始深度对单个气泡气体扩散量的影响．由于气泡云对气体的输运,溶解于水中的气体可出现过饱和状态．对１０ｍ／ｓ风速下气泡云的气体输运量进行了计算,得到水中Ｏ２的过饱和度可达１．８９％～３９２％,与实际观测值一致．     

Measurement of heat transfer at the phase interface of condensing bubbles

Using holographic interferometry and high-speed cinematography the heat transfer at the phase interface of vapor bubbles condensing in a subcooled liquid of the same substance was measured with ethanol, propanol, refrigerant R113 and water. To evaluate the axisymmetric temperature field around the bubble from the interference fringe field, the Abel integral method is not sufficient. A correction procedure considering the light deflection caused by the local temperature gradient has been developed and applied to calculate the heat transfer coefficient. The measurements were performed in the range 2 < Pr < 15 and I < Ja < 120. Measured data could be well-correlated as functions of the Prandtl and Reynolds numbers for the heat transfer coefficient and as functions of the Reynolds, Prandtl and Jacob numbers for the bubble collapse time.     

波浪作用下直立结构物附近强湍动掺气流体运动的数值模拟

波浪破碎卷入气体易对建筑物受力产生压力振荡, 了解波浪作用下建筑物附近掺气水流的运动特性是精确计算建筑物受力的前提. 基于OpenFOAM开源程序包和修正速度入口造波方法建立三维数值波浪水槽, 模型采用S-A IDDES湍流模型进行湍流封闭, 并采用修正的VOF 方法捕捉自由液面, 数值模拟了规则波在1:10的光滑斜坡上与直立结构物的相互作用过程, 重点分析了结构物附近的水动力和掺气水流运动特性. 结果表明, 建立的数值模型能精确地捕捉波浪作用下直立结构物附近的自由液面的变化以及气泡输运过程, 较好地描述气体卷入所形成的气腔形态以及多气腔之间的融合、分裂等过程; 波浪与直立结构物相互作用产生强湍动掺气水流, 其运动过程十分复杂; 掺气流体输运过程中水气界面周围一直伴随着涡的存在, 其中, 气泡的分裂与周围正负涡量剪切作用密切相关, 且其输运轨迹主要受周围流场的影响; 研究揭示了结构物附近湍动能与掺气特性的关系, 发现波浪作用下直立结构物附近湍动能的分布与掺气水流特征参数(气泡数量、空隙率)整体呈现一定的线性关系.      

固体炸药爆轰与惰性介质相互作用的一种扩散界面模型

提出一种保持热力学一致性的扩散界面模型,用来数值模拟固体炸药爆轰与惰性介质的相互作用问题。基于混合网格内各组分物质间可以达到力学平衡状态而不能达到热学平衡状态的假设,由混合网格能量守恒以及压力相等条件,推导出每种组分物质的体积分数演化方程。由此获得的扩散界面模型包括组分物质的质量守恒方程、混合物质的动量及总能量守恒方程,同时包括组分物质的体积分数演化方程和混合物质的压力演化方程。该扩散界面模型的主要特点是考虑了化学反应以及热学非平衡的影响。提出的扩散界面模型在物质界面附近不会出现物理量的非物理振荡现象、适用于任意表达形式的物质状态方程以及任意数目的惰性介质。     

Transient behavior of boiling bubbles generated on the small heater of a thermal ink jet printhead

The fundamental behavior of boiling bubbles generated on a small film heater used for thermal ink jet (TIJ) printers is investigated experimentally under the condition of a single pulse heating in a pool of water. The pulse power and the pulse width are varied in wide ranges that include the printing conditions. As the pulse power is increased or the pulse width increased at a fixed high pulse power, numerous fine bubbles appear simultaneously on the heater and then coalesce into a thin vapor film to grow to a vapor bubble, before collapsing at the center of the heater. For a long pulse width sequence, the coalesced bubble repeats the growth and collapse. Bubble behavior is also studied in the same heat flux range using a platinum film heater enabling surface temperature measurement. From a comparison of the two heaters, the dominant mechanism of nucleation on the TIJ heater is believed to be spontaneous nucleation at around the heating rate for printing. The dependence of the size and lifetime of the coalesced bubble on pulse power and pulse width are examined. Based on the analytical model presented by Asai [J. Heat Transfer 113 (1991) 973], the pressure impulse arising during the rapid evaporation of the superheated liquid, presumed to dominate the subsequent growth of the coalesced bubble, is estimated from the measured size of the coalesced bubble. The relationship between the pressure impulse and the superheat energy in the liquid is discussed.