DYNAMICS OF BUBBLE SIZE DISTRIBUTION IN TURBULENT GAS-LIQUID DISPERSIONS

The population balance equation coupled with the proposed breakage kernel and the previously developed breakage model is applied to the analysts of bubble size distribution for non-coalescing systems in a bench-scale airlift column. Good agreement obtained between the theoretical results and the experimental data is encouraging and indicates that the model is suitable for predicting dispersion properties such as bubble size and interfacial area in turbulent gas-liquid dispersions.     

Investigations of mixing in a fluid Jet agitated tank

Mixing can be achieved in a variety of ways including mechanical agitation, agitation by a fluid jet impingement or by static mixers. This article is concerned with mixing by a fluid jet impingement. Jet mixing can be described as a fast-moving stream of liquid being injected into a slow-moving or stationary liquid. In this study, computational fluid dynamics (CFD) is used to investigate the performance of a jet mixer. The degree of mixing has been evaluated by monitoring mixing of a hot volume of fluid in the larger tank until criteria for 95% mixing are met at a number of monitoring points. A wide range of jet injection rates has been investigated. Good agreement was shown between numerical and published experimental results. Moreover, the need to monitor mixing at more than one point, and especially at points in zones with little liquid motion, is shown to be necessary. Numerical results provided detailed plots of velocity and temperature fields and clearly showed the locations of zones with very low velocities, which require the longest time to become well mixed.     

DISPERSION OF GAS AND LIQUID IN BUBBLE COLUMNS OF HOMOGENEOUS BUBBLE FLOW REGIME

Mean gas holdup, lateral distribution of gas holdup and axial mixing of gas and liquid were measured in bubble columns of 12 and 19cm i.d. The lateral distribution of gas holdup was strongly dependent on the flow regimes in the column. The axial mixing of liquid in the homogeneous bubble flow regime was much smaller than that in the heterogeneous bubble flow regime, and was not expressed by existing correlations. The axial mixing of liquid in the homogeneous bubble flow and the intermediate flow regime was simulated with a flow model based on the lateral distribution of buoyancy force and the effective viscosity. The axial mixing of gas was larger than that of liquid.     

Multi-fluid simulation of turbulent bubbly pipe flows

Radial distributions of void fraction α_G, bubble aspect ratio E, phasic velocities V_G and V_L and turbulent kinetic energy k in bubbly pipe flows are measured using an image processing method and a laser Doppler velocimetry. Multi-fluid simulations are conducted to examine applicability of state-of-the-art closure relations to the turbulent bubbly pipe flows. The experimental results indicate that aspect ratio of bubbles in the near wall region takes a higher value than that of free rising bubbles due to the presence of wall, and that the change in the aspect ratio induces decrease in relative velocity between bubbles and liquid in the near wall region. Drag coefficient C_D of a bubble in a bubbly pipe flow tends to increase with magnitude of shear flow, and the effect of shear flow on C_D is estimated by the correlation proposed by Legendre and Magnaudet (1998). Comparison between the simulated and the measured results indicate that the effects of bubble shape and shear flow on drag force acting on bubbles should be taken into account for accurate predictions of bubbly pipe flows. The turbulence models proposed by Lopez de Bertodano et al. (1994) and by Hosokawa and Tomiyama (2004a) give good predictions for turbulence modification caused by bubbles.     

气液逆流鼓泡塔中的气含率与液速分布和数值模拟

分别采用线－线电导探针和背靠背式皮托和测定了气液逆流鼓泡塔中局部气含率和液体轴向速度的径向和轴向分布,讨论了操作条件对气含率与液体轴向速度分布的影响,利用双流体模型对塔内两相湍流流动进行了数值模拟。     

ABOUT BUBBLE BREAKUP MODELS TO PREDICT BUBBLE SIZE DISTRIBUTIONS IN HOMOGENEOUS FLOWS

We present results of a study of the equilibrium between coalescence and breakup of bubbles in homogeneous media with isotropic turbulence. The Boltzmann equation for the particle distribution function (pdf) was evaluated in steady state, using a multigroup approach. Binary bubble breakup was assumed. We used uniform function, delta function, and the model proposed by Luo and Svendsen (1996) for the bubble size distributions resulting from a breakup. The bubble breakup rate was calculated with Luo and Svendsen (1996) and Prince and Blanch (1990) models. Significant differences in bubble breakup rate, and therefore in bubble size distribution, are predicted by both models. The models were compared to the bubble size distributions measured by Boyd and Varley (1998) in air-water flow. The transient response of the bubble size distribution and interfacial area density was also analyzed. This work is of significance in the prediction of reaction rates when they are dependent on bubble size distribution.     

DYNAMICS OF BUBBLE DEPARTURE IN MICRO-GRAVITY

The effect of gravity on nucleate pool boiling is considered. The static and dynamic forces acting on a growing vapor bubble on a heating surface are evaluated and how their interaction causes the bubble to detach from the surface is presented. By using a force balance, an estimate of the bubble departure radius is calculated and compared with experimental measurements from literature under micro-gravity conditions. In addition, five well known theoretical correlations are used to predict the bubble departure radius and are compared for several gravitational accelerations.     

SIMULATION OF BUBBLE FORMATION AND HEAPING IN A VIBRATING GRANULAR BED

The Eulerian-Eulerian approach is used to simulate flow in a dense granular bed subjected to a slight, vertical, sinusoidal vibration. The bottom of the bed was subjected to a vertical vibration, ASin(ω _v t)J ₀(k _m x), where J represents the profile of the bottom wall and is the first kind of Bessel function. The governing equations of the gas phase and particle phase are described and the results of the model with different vibration frequencies and amplitudes are presented. Bubble formation and upward and downward heaping were observed at different amplitudes and frequencies. The results of the model confirm that there is a change from upward to downward heaps according to the strength of the vibration. In addition, the location of the bubble and the shape of the heaping at the interface of the bed depend on the strength of the vibration and the profile of the bottom of the container.     

鼓泡床反应器中液体循环的模拟

应用分离流概念对气液鼓泡床反应器中的两相流体动力学进行了理论分析,从而建立了一个基于机理的液体循环的数学模型。根据这个模型,对影响液体循环的诸因素及部分实例进行了模拟计算,其结果与实验结果吻合很好。     

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     

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.     

On the second-order moment turbulence model for simulating a bubble column

Two versions of the second-order moment two-phase turbulence model are proposed in this study for simulating bubble-liquid two-phase turbulent velocity fluctuations and their interactions in bubble-liquid flows under the dispersed bubble regime. One of them is a full transport equation model; the other is an algebraic stresses model. The proposed model is used to simulate liquid and gas mean velocities, gas volume fraction, liquid and gas Reynolds stresses and turbulent kinetic energy in a 2-D bubble column. Furthermore, the bubble and liquid velocities, Reynolds stresses and gas volume fraction are measured using the PIV. The simulation results are in good agreement with the PIV results and experimental data in the literature. The studies reveal the liquid recirculation and bubble up-rising flow patterns, and anisotropic liquid and bubble normal Reynolds stresses. Bubble fluctuation is observed to be stronger than liquid fluctuation. Moreover, both the liquid velocity gradient and bubble-liquid interaction are important for the generation of liquid turbulence.     

BASIC EQUATION OF TURBULENCE AND MODELING OF INTERFACIAL TRANSFER TERMS IN GAS-LIQUID TWO-PHASE FLOW

Turbulence is one of the most important phenomena in analyzing thermohydrodynamic characteristics of gas-liquid two-phase flow. For the purpose of accurate prediction of the turbulence phenomena, a basic conservation equation of Reynolds stress was derived based on the local instant formulation of mass and momentum conservations of two-phase flow. In this equation, interfacial transfer terms of turbulence appear as source terms. Detailed considerations on these transport terms were carried out. It was shown that they consist of a viscous damping term due to small scale interfacial structures, a drag induced turbulence generation term due to large scale interfacial structures and a term representing the exchange between surface energy and turbulence. Based on the mechanistic modeling and turbulence modulations, carried out were physical interpretations of interfacial area concentrations of small and large scale interfacial structures, a viscous damping term due to small scale interface and turbulence generation term due to large scale interface.     

MODELING OF THE UNMIXEDNESS IN HOMOGENEOUS REACTING TURBULENCE

A simple mathematical model is presented for the prediction of the limiting bounds of the unmixedness parameter in non-premixed homogeneous reacting turbulence. This model is based on a Beta distribution for the PDF of a conserved Shvab-Zeldovich variable and generates statistical results which show similar trends to those previously obtained by computational experiments based on direct numerical simulations.     

Determination of the collision frequency between bubbles and particles in flotation

Collision efficiency for a spherical bubble rising in a uniform concentration of small non-inertial particles is studied by direct numerical simulations (DNS). The Stokes number of the particles is negligibly small so that the particle trajectories follow the streamlines. The effect of the bubble interface contamination is studied for the flow surrounding the bubble using the spherical cap model. Numerical results are obtained for a wide range of bubble Reynolds number (based on bubble diameter d_b) ranging from 0.01 to 1000 and for different angles of contamination ranging from 0^° to 180^°. The collision efficiency is found to be increased with the Reynolds number and significantly decreased with the level of contamination. Correlations of the numerical results are proposed for efficiencies versus d_p/d_b (d_p being the particle diameter), bubble Reynolds number and interface contamination degree. For clean (respectively, fully contaminated) spherical bubbles, the efficiency evolves as d_p/d_b (respectively (d_p/d_b)²) whatever the bubble Reynolds number and the particle size. For partially contaminated bubbles, efficiency can be scaled with d_p/d_b or (d_p/d_b)² depending on both the level of contamination and the particle size.     

AXIAL DISTRIBUTION OF SOLID PARTICLES IN BUBBLE COLUMN SLURRY REACTORS IN THE BUBBLE FLOW REGIME

Physical mechanisms responsible for the suspension of solid particles in semi-batch bubble column slurry reactors in bubble flow are identified, thus allowing the classification of solids into four states: free, engaged, wake-entrained and captured particles. A theory is then presented to predict the axial distribution of solids when wake-entrained and captured particles are absent. Reasonable agreement is found between the theory and experimental data obtained in this work and those reported by otherinvestigators.     

AXIAL DISTRIBUTION OF SOLID PARTICLES IN BUBBLE COLUMN SLURRY REACTORS IN THE BUBBLE FLOW REGIME

Physical mechanisms responsible for the suspension of solid particles in semi-batch bubble column slurry reactors in bubble flow are identified, thus allowing the classification of solids into four states: free, engaged, wake-entrained and captured particles. A theory is then presented to predict the axial distribution of solids when wake-entrained and captured particles are absent. Reasonable agreement is found between the theory and experimental data obtained in this work and those reported by otherinvestigators.     

SIMULATION OF TRANSPORT DYNAMICS IN FLUIDIZED-BED DRYERS

ABSTRACT

A mathematical model for predicting three-dimensional, two-phase flow, heat and mass transfer inside fluidized-bed dryers has been developed. The model consists of the full set of partial-differential equations that describe the conservation of mass, momentum and energy for both phases inside the dryer, and is coupled with correlations concerning interphase momentum-, heat-, and mass-transfer.

It is shown that the model can predict the most important engineering aspects of a fluidized-bed dryer including pressure drop, particle holdup, temperature distribution in both phases as well as drying efficiency all over the fluidized-bed. Plug-flow conditions are predicted for the gas phase, while back-mixing is predicted for the particles.

The effect of particle mass-flow-rate on fluidized-bed dryer performance is evaluated. It is shown that the lower the particle mass flow-rate, the more intense the horizontal moisture gradients, while the higher the particle rate the more uniform the moisture distribution throughout the bed.