垂直圆管内湍流泡状流的数值研究

在经典Euler/Euler型水动力模型基础上,引入考虑不同直径气泡的种群平衡方程来描述气液两相泡状流,对液相和气相分别建立了基本方程,通过对气泡的受力分析并考虑气泡之间聚合和破碎效应后给出了本构方程,建立了封闭的双流体模型并用于垂直管道湍流泡状流的三维数值模拟.模型预测值与实验数据的比较结果表明该模型能较好地模拟垂直管道湍流泡状流中的相含率分布、速度分布、湍动能分布、气泡直径分布以及气泡直径分布的演变过程.     

Modeling of bubble-column flows with quadrature-based moment methods

Bubble-column reactors are frequently employed in the biological, chemical and petrochemical industries. This paper presents a novel approach to model bubble-column flows using quadrature-based moment methods (QBMM). A fully two-way coupled flow solver is developed that solves the incompressible Navier-Stokes equation for the liquid phase and moment transport equations for the dispersed bubble phase. The moment transport equations for the dispersed bubble phase are solved using a kinetic theory approach. Contributions from the liquid-phase pressure gradient, vorticity, drag, virtual mass and gravity are accounted for in the bubble-phase force balance. The solution algorithm and coupling procedure are described in detail, and results are presented for a 2-D bubble column with two different gas flow rates (1.6 and 8.0 l/min).     

Determination of the transfer coefficient of natural turbulence occurring near the solid-propellant gasification zone. I. Two-phase model of the gasification zone

A model for solid propellant gasification is proposed which contains a two-phase medium in an intermediate stage. The formation of the gas phase proceeds in two ways: chemical reactions result in gaseous products, which, in turn, initiate the formation of bubbles in which vapor forms from the liquid phase of the propellant. Gaseous products play an important role only in the very early stage of bubble development; their critical pressure is used to determine the minimum size of gas-phase nuclei. The bubble volume grows primarily by evaporation of the liquid phase. A kinetic equation for the bubble concentration and the necessary boundary conditions are formulated. Arguments are given suggesting that a temperature maximum cannot occur in the gasification zone and that natural turbulence can be generated by collapsing bubbles. The sound produced by solid propellant combustion is explained by the collapse of a huge number of microscopic bubbles. If the processes in the two-phase zone are neglected, the formulated system of equations is transformed into the Belyaev–Zel’dovich model equations.     

Two-phase modeling of a gas phase polyethylene fluidized bed reactor

A two-phase model is proposed for describing the behavior of a fluidized bed reactor used for polyethylene production. In the proposed model, the bed is divided into several sequential sections where flow of the gas is considered to be plug flow through the bubbles and perfectly mixed through the emulsion phase. Polymerization reactions occur not only in the emulsion phase but also in the bubble phase. Voidages of the emulsion and bubble phases are estimated from the dynamic two phase structure hydrodynamic model. The kinetic model employed in this study is based on the moment equations. The hydrodynamic and kinetic models are combined in order to develop a comprehensive model for gas-phase polyethylene reactor. The results of the model are compared with the experimental data in terms of molecular weight distribution and polydispersity of the produced polymer. A good agreement is observed between the model predictions and actual plant data. It has been shown that about 20% of the polymer is produced inside the bubble phase and as such cannot be neglected in modeling such reactors.     

Effect of bubble contamination on rise velocity and mass transfer

An apparatus where individual bubbles are kept stationary in a downward liquid flow was adapted to simultaneously (i) follow mass transfer to/from a single bubble as it inevitably gets contaminated; (ii) follow its shape; and (iii) periodically measure its terminal velocity. This apparatus allows bubbles to be monitored for much longer periods of time than does the monitoring of rising bubbles. Thus, the effect of trace contaminants on bubbles of low solubility gases, like air, may be studied.Experiments were done with air bubbles of 1-5 mm initial equivalent diameter in a water stream. The partial pressure of air in the liquid could be manipulated, allowing bubbles to be either dissolving or kept at an approximately constant diameter.Both drag coefficient and gas-liquid mass transfer results were interpreted in terms of bubble contamination kinetics using a simplified stagnant cap model. Drag coefficient was calculated from stagnant cap size using an adaptation of Sadhal and Johnson's model (J. Fluid Mech. 126 (1983) 237).Gas-liquid mass transfer modelling assumed two mass transfer coefficients, one for the clean front of the bubble, the other for the stagnant cap. Adjusted values of these coefficients are consistent with theoretical predictions from Higbie's and Frössling's equations, respectively.     

THE RESONANT SUPERCOMPRESSION AND SONOLUMINESCENCE OF A GAS BUBBLE IN A LIQUID-FILLED FLASK

The spherically-symmetric problem of the oscillations of a small gas bubble in the center of a spherical flask filled with a compressible liquid that is excited by small radial displacement of the flask's wall is considered. Two asymptotic solutions have been found for the low Mach number stage. The first one is an asymptotic solution for the field far from the bubble, and it corresponds to linear wave theory. The second one is an asymptotic solution for the boundary layer near the bubble and it corresponds to an incompressible fluid. In the analytical solution of the low Mach number step matching of these asymptotic solutions is done. A generalization of the Rayleigh = Plesset equation for a compressible liquid is given in the form of two ordinary difference-differential equations that take into account the pressure waves which are reflecting from the bubble and those that are incident on the bubble from the flask wall. The initial value problem for the initiation of the bubble oscillations due to flask wall excitation and for the evolution of these oscillations was considered. Linear and non-linear periodic bubble oscillations were analyzed analytically, and resonant frequencies were identified. Non-linear resonant and near-resonant solutions for the bubble's non-harmonic oscillations, which are excited by harmonic pressure or velocity oscillations on the flask wall, are obtained.     

On the Averaging of Equations of Change for Mass,Species Mass,Momentum and Energy – One-Dimensional Pipe Flows

The single-phase and multiphase Eulerian equations of change are derived by applying a suitable averaging procedure to the local instantaneous equations of change. In the present work, the local instantaneous equations of change for mass, species mass, momentum and energy are gross-scale averaged over the cross-sectional area. In particular, the internal energy equation is achieved by subtracting the kinetic energy equation from the total energy balance. Thus, two paths are to our disposal for deriving the cross-sectional averaged internal energy balance: (i) the averaged kinetic energy equation is subtracted from the averaged total energy equation, or (ii) the local instantaneous kinetic energy equation is subtracted from the local instantaneous energy equation and the resulting equation is averaged. The resulting Euler equations of change for internal energy are not identical for these two approaches. Approach (ii) is recommended because of its simplicity.     

Quantitative rate equations for change of phase

A new set of rate equations for gas desorption has been derived from the laws of thermodynamics and motion and the kinetic theory of gases. The equations assume that gas desorption or absorption originally represents an isothermal change at the interface, similarly to condensation or vaporization. The mass transfer in gas desorption or absorption is initially caused by external work being done on the system and takes place as work done by the system which instantly develops a concentration gradient, increases in internal energy and temperature, and a deviation from the ideal gas behaviour inside MTZ in the process of mass transfer. After cessation of external work, these conditions disappear following the transfer of a small residual mass at a constant velocity and a decrease in internal energy inside the MTZ.     

Gas–liquid mass transfer to single bubbles: Effect of surface contamination

The dissolution of single bubbles of gases of low solubility kept stationary in a downward stream of water was studied. In “clean” water, two regimes are identified. Initially, the process is fast, consistent with the theory for circulating bubbles. Then, the mass-transfer rate falls sharply to that predicted for solid spheres. Transition times and transition diameters vary widely with experimental conditions. In untreated water, only the second regime is found. Results are explained in terms of the kinetics of trace surfactant accumulation at the interface. An adaptation of the stagnant-cap model is proposed, with surface immobilization expressed in terms of interface dynamics. The model yields good prediction of the transition point for a very large set of conditions, including different gases at various concentrations in the liquid stream and a wide range of initial bubble diameters.     

Intensification of nitrous acid oxidation

An alternative solution to the reduction of a discharge of residual nitric oxide and nitrogen dioxide into atmosphere has been proposed. Instead of using methane or ammonia for SCR or gas absorption into alkali solutions, which are the most popular treatment methods of tail gases, now the use of powerful oxidant—ozone capable of transforming nitrous acid and nitric oxides into nitrogen of the highest oxidation level—could be employed for this purpose. As the intensive oxidation and ozonation of nitrous acid is the heterogeneous gas-liquid process, the solubility of oxygen and ozone in HNO₂/HNO₃ aqueous solution was necessary to be determined. Variations of reaction rates depending on temperature, ozone dose and nitrous and nitric acid concentrations were studied experimentally. The kinetic model of the reactions, 2HNO₂+O₂→2HNO₃ and HNO₂+O₃→O₂+HNO₃, were proposed and the kinetic parameters (rate constants and activation energies) were estimated on the basis of experimental data in semi-batch laboratory gas-liquid contactor with the liquid phase drawn from an absorption column in the nitric acid plant. The determined kinetic parameters were then used in designing and modeling of the oxidation of nitrous acid using ozone-oxygen mixture in a continuous bubble column. The model consists of mass transfer kinetic equations and material balance equations for the gas and liquid phases. The co-current flow of gas and liquid phases and the complex kinetics of chemical reaction in the liquid phase were taken into account. The variation of the following process conditions, flow rate, compositions of the gas and liquid phases, temperature, and pressure in the bubble column of different diameters and heights, were studied in numerical solutions of the proposed model.     

浅议浮法玻璃气泡问题的分析与解决

在生产实践中,玻璃产品中的气泡问题一直是困扰玻璃生产厂家的一大难题。本文介绍了某玻璃企业玻璃产品出现气泡以后的观察、分析和解决过程,提出气泡的形成、变化、消失、再出现的过程,是气体在玻璃熔体中溶解和扩散的结果,了解各种气体在玻璃熔体中的特性和行为方式,有针对性地确定好玻璃熔化的温度曲线和燃料分配,这对减少玻璃中气泡是很重要的。     

A comprehensive mathematical model for biomass gasification in a bubbling fluidized bed reactor

A mathematical model of biomass gasification in bubbling fluidized gasifier has been developed. It is a one-dimensional, two-phase (bubble and emulsion), two-zone (bottom dense bed and upper freeboard), steady state model. The model is based on global reaction kinetic, mass and energy balances and is capable of predicting temperature, solid hold ups and gas concentration along the reactor’s major axis. The overall model has sub-models to deal with biomass pyrolysis, gasification, bed hydrodynamics, material classification and property calculation. A sub-model for tar generation and cracking is included in this study. The model is capable of dealing with wide variety of biomasses and fluidizing agents, i.e. air, oxygen, steam or a mix of these gases. Results show that during devolatilization step, gases release and mixing are sensitive and critical parameters. They have a strong influence on the overall performance of a gasifier. A comparison with experimental data from numerous literature works was done, which showed fairly good agreement. The model can be used to study and optimize the operation of bubbling fluidized bed gasifier. However, further validation with diverse data will help to fine-tune the model.     

Equations to predict precipitation onset and bubblepoint pressures of asphaltenic reservoir fluids

A set of algebraic equations to predict upper onset‐of‐precipitation and bubble‐point pressures of asphaltene‐containing reservoir fluids in wide temperature ranges are proposed. In developing the equations, laboratory data of 11 Mexican and 12 more live oils have been analyzed, and a correlation of these data with temperature has been found. A modified least‐squares regression method has been used to develop two versions of the proposed equations. In one version, a single pressure/temperature data point is required to predict the entire onset/bubble‐point curves at any temperature. For oils with no experimental precipitation data available at all, a second version of the proposed expressions employs standard chromatographic data of the reservoir fluid to provide a reasonable prediction. The average absolute deviations in calculated onset and bubble‐point pressures by the proposed equations are 2.53 and 0.45MPa by the one‐point correlations, respectively, and 3.96 and 1.62 MPa by the compositionally‐based correlations, respectively. The developed expressions are simple and can be used to provide reasonable predictions of upper onset and bubble‐point pressures of asphaltenic live oils in cases where laboratory data are scarce. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Model based on population balance for the simulation of bubble columns using methods of the least-square type

A novel model is presented which uses mass and momentum equations based on population balances to describe the dispersed phase of bubble columns. A set of integro-differential non-linear equations constitutes the model, which can be solved directly using the least-squares methods. The implementation for these is presented.The model presents a degree of flexibility, as different density functions (number, mass and volume) and different internal coordinates (bubble diameter, volume and mass) can be used.A simplified 1D model of a bubble column is solved using the least-squares spectral element method. The results obtained for two different gas volume fluxes at the inlet are compared with experiments by several authors. The simulations show good agreement with the measured data.     

The motion of electrolytic gas bubbles near electrodes

Several reports in the literature mention oscillatory bubble motions close to, or in contact with electrodes. Such behaviour is obviously related to a time-variable force, but it was not apparent what the origin of this variable force was. Recent advances in understanding of the surfactant behaviour of gases, and in particular the gases liberated during electrolysis, have cast a new light on the underlying mechanism of these oscillations. Other unexpected, but not necessarily oscillatory bubble behaviour is discussed, and the role of electrolytic gas acting as a surfactant illuminates these non-oscillatory motions as well. Finally, the paradox of bubbles remaining attached to electrodes with zero contact angle is resolved.     

鼓泡床内气泡-液体两相湍流代数应力模型的数值模拟

现有的气泡 -液体两相流动的数值模拟中 ,或者不考虑湍流 ,或者仅仅考虑液体湍流 ,但是直接模拟和PIV测量结果都表明气泡由于尾迹的作用有强烈的湍流脉动 .本文首次推导和封闭了同时模拟气泡湍流脉动和液体湍流脉动的二阶矩输运方程两相湍流模型 ,并在此基础上建立了代数应力气泡 -液体两相湍流模型 .用代数应力模型模拟了二维矩形断面鼓泡床内气泡 -液体两相流动 .预报结果给出了气泡和液体两相速度场、两相Reynolds应力及湍动能分布和气泡体积分数分布 .模拟结果与PIV测量结果符合很好 ,表明了模型的合理性 .研究结果表明 ,原先静止的液体在气泡因浮力而产生的上升运动的作用下产生回流流动 ,而气泡则只有上升运动 .气泡速度始终大于液体速度 .在床内气泡湍流脉动确实始终很强烈 .液体则由于气泡的作用以及自身速度梯度产生的双重作用而发生湍流脉动 .气泡的脉动显著地大于液体的脉动 .两相湍流脉动都是各向异性的 ,而且气泡湍流脉动的各向异性比液体的更强烈     

Modeling the dynamics of tamponade multicomponent gases during retina reattachment surgery

Vitrectomy and pneumatic retinopexy are common surgical procedures used to treat retinal detachment. To reattach the retina, gases are used to inflate the vitreous space allowing the retina to attach by surface tension and buoyancy forces that are superior to the location of the bubble. These procedures require the injection of either a pure tamponade gas, such as C₃F₈ or SF₆, or mixtures of these gases with air. The location of the retinal detachment, the anatomical spread of the retinal defect, and the length of time the defect has persisted, will determine the suggested volume and duration of the gas bubble to allow reattachment. After inflation, the gases are slowly absorbed by the blood allowing the vitreous to be refilled by aqueous. We have developed a model of the mass transfer dynamics of tamponade gases during pneumatic retinopexy or pars plana vitrectomy procedures. The model predicts the expansion and persistence of intraocular gases (C₃F₈, SF₆), oxygen, nitrogen, and carbon dioxide, as well as the intraocular pressure. The model was validated using published literature in rabbits and humans. In addition to correlating the mass transfer dynamics by surface area, permeability, and partial pressure driving forces, the mass transfer dynamics are affected by the percentage of the tamponade gases. Rates were also correlated with the physical properties of the tamponade and blood gases. The model gave accurate predictions in humans. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3651–3662, 2017     

Interfacial area density in bubbly flow

The interfacial area per unit volume is one of the key parameters in bubbly flow. Momentum, mass and energy transfer occur through the interface between the phases. The functionality of two phase reactors with bubbly flow depends mainly on these three transfer processes. Thus, the design process of a reactor requires the prediction of interfacial area density. In the present work a simple equation for the interfacial area density is derived from the population balance, taking into account the events of coalescence and bubble break-up for each bubble fraction. The system of partial integro-differential equations is simplified. Since the integrals in these equations complicate a numerical treatment. This reduces the balance to one single partial differential equation. An approximate analytical solution is given. If the resulting equation is applied to large gas fluxes, the instability of the coalescence process causes large bubbles and gas plugs to develop. From the instability the volume fraction of the large bubbles and gas plugs may be predicted. Additives may hinder the coalescence process. Experiments show that coalescence hindrance changes the coalescence kernel only by a factor. Calculations are done for bubble columns and vertical pipe flow.     

On the possibility of diffusionally driven oscillations in two component gas bubbles in fluids

The problem of an isolated, stationary, two-component gas bubble in a fluid is analysed. The appropriate governing equations, and an approximate version of these equations, for this model system are reviewed. The qualitative differences in bubble dissolution behaviour between single- and two-component gas bubbles are elucidated. In particular, it is demonstrated that in the latter case the gas bubble radius may exhibit extrema as a function of time for certain values of the controlling parameters. The conditions under which these extrema may occur, and the maximum number of extrema which are permitted are elucidated.     

Dynamic modeling of blown‐film extrusion

Past dynamic studies of blown‐film extrusion have been confined to the stability analysis of the linearized equations. The full set of nonlinear equations comprises a system of partial differential and algebraic equations with boundary conditions that vary from author to author. In this paper, the Numerical‐Method‐of‐Lines, which combines finite‐difference methods with ordinary differential/algebraic equation integrators, is used to solve the full system. Appropriate boundary conditions are selected to give physical results that compare well with experiment. An important boundary condition is the “minimum order reduction” condition on the gradient of the bubble‐tube radius with respect to distance above the extrusion die (the axial position). Transient startups and operational disturbances are examined. Calculations show the influence of oscillations in operating conditions such as heat transfer or inflation pressure on the bubble‐tube radius and film thickness. Steady‐state results obtained by integrating the transient equations for a sufficiently long time are qualitatively in agreement with experiment, in contrast to past simulations of these equations.