SIMULATION OF BUBBLE BREAKUP DYNAMICS IN HOMOGENEOUS TURBULENCE

This article presents numerical simulation results for the deformation and breakup of bubbles in homogeneous turbulence under zero gravity conditions. The lattice Boltzmann method was used in the simulations. Homogeneous turbulence was generated by a random stirring force that acted on the fluid in a three-dimensional periodic box. The grid size was sufficiently small that the smallest scales of motion could be simulated for the underlying bubble-free flow. The minimum Weber number for bubble breakup was found to be about 3. Bubble breakup was stochastic, and the average time needed for breakup was much larger for small Weber numbers than for larger Weber numbers. For small Weber numbers, breakup was preceded by a long period of oscillatory behavior during which the largest linear dimension of the bubble gradually increased. For all Weber numbers, breakup was preceded by a sudden increase in the largest linear dimension of the bubble. When the Weber number exceeded the minimum value, the average surface area increased by as much as 80%.     

鼓泡床中的气泡尺寸分布

根据气泡聚并和破裂速率模型,提出一个描述鼓泡床中气泡尺寸分布的总体平衡(Population Balance)模型。该模型可预计鼓泡床中气泡尺寸分布随床高的变化。对空气-水体系的模拟结果与实测结果吻合较好。     

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.     

IMPROVED HEAT AND MASS TRANSFER MODELS TO PREDICT GRAIN QUALITY

ABSTRACT

This paper reviews a recent development in the heat and moisture transfer modeling for drying single layes of agricultural grains. A diffusion model with time-varying boundary condition predicts the complex shape of the drying curve well. A conduction model with evaporating boundary condition, when used with the Gamson correlation for convective heat transfer coefficient, accurately predicts experimental grain surface temperature. The new modewls were tested experimentally, drying wheat and barley in a thin-layer dryer useing 40 to 175 c air and the initial moisture ranging from 0.20 to 0.40 (decimal dry basis). It is shown that grain temperatures calculated by the conduction heat equation, when used in conjunction with a probit-type germination loss model, predict germination values different from those predicted by the lump heat equation.     

IMPROVED HEAT AND MASS TRANSFER MODELS TO PREDICT GRAIN QUALITY

This paper reviews a recent development in the heat and moisture transfer modeling for drying single layes of agricultural grains. A diffusion model with time-varying boundary condition predicts the complex shape of the drying curve well. A conduction model with evaporating boundary condition, when used with the Gamson correlation for convective heat transfer coefficient, accurately predicts experimental grain surface temperature. The new modewls were tested experimentally, drying wheat and barley in a thin-layer dryer useing 40 to 175 c air and the initial moisture ranging from 0.20 to 0.40 (decimal dry basis). It is shown that grain temperatures calculated by the conduction heat equation, when used in conjunction with a probit-type germination loss model, predict germination values different from those predicted by the lump heat equation.     

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.     

AN ASSESSMENT OF EXPERIMENTAL TECHNIQUES FOR THE MEASUREMENT OF BUBBLE SIZE IN A BUBBLE SLURRY REACTOR AS APPLIED TO INDIRECT COAL LIQUEFACTION

The proper design and control of an indirect coal liquefaction process plant require an accurate knowledge of bubble sizes and size distribution. Of particular importance regarding proper design is the understanding of the complicated dependence of bubble dynamics on bubble column geometry, and of the nature of the solid-liquid phases. The nature of the products and their relative proportions, on the other hand, are seriously influenced by the bubbling characteristics of the reactor because the mass transfer behavior and mixing are dependent on the bubble size and velocity distributions. This report reviews experimental techniques that have been employed to measure bubble sizes in multiphase reactors. The methods, which fall in three different categories, namely, the photographic method, the optical probe, and the electrical conductivity (resistivity) probe, are described in a historical sequence; and in each case, their unique features and design details are discussed. A general methodology of data analysis in each category is given, together with a state-of-the-art technology assessment and, finally, relative merits and demerits of the methods.     

CHARACTERIZATION OF GAS-LIQUID FLOWS IN RECTANGULAR BUBBLE COLUMNS USING CONDUCTIVITY PROBES

Unsteady gas-liquid flows in bubble columns are comprised of various flow processes occurring with varying length and time scales and govern mixing and transport processes. In the present work, we have characterized dynamic and time-averaged properties of gas-liquid flows in rectangular bubble columns using conductivity probes. The development of a single-tip conductivity probe, data processing methodology, and photographic validation procedure is discussed in detail. The effect of superficial gas velocity and aerated liquid height-to-width (H/W) ratio on voidage fluctuations and time-averaged gas holdup was investigated. The experimental data presented here can help in understanding the dynamics of various flow processes and validating computational fluid dynamics based models.     

THE EFFECT OF SOLUTES ON BUBBLE SIZE IN AIR-WATER DISPERSIONS

Bubble size distributions in a bubble column of 200 mm diameter were measured by means of a photoelectric probe. The gas-liquid dispersion was generated by distributing air with a porous plate into aqueous solutions of electrolytes and of organic compounds (alcohols, glycols, ketones, carboxylic acids, saccharose, carboxymethyl-cellulose, detergents). For all these solutes there exists a rather narrow concentration range in which the change from quick coalescence in pure water to coalescence suppression takes place. Though rough relationships between concentrations for coalescence suppression and molecular properties can be found (ionic strength for electrolytes, number of carbon atoms in a homologous series of organic compounds), exact equations based on a theory of coalescence cannot be given.

The bubble size distributions obtained in the experiments have also been used to show the impact of coalescence phenomena on gas-liquid mass transfer. For this purpose, surface areas were calculated from measured gas hold-up and mean bubble diameters (Sauter diameters). A comparison of these data with the trends for volumetric mass transfer coefficients reported in the literature for n-alcohols (C₁-C₂i) showed good agreement, despite the fact that the mass transfer data had been obtained in a quite different gas-liquid contacting device (stirred vessel).     

THE EFFECT OF SOLUTES ON BUBBLE SIZE IN AIR-WATER DISPERSIONS

Bubble size distributions in a bubble column of 200 mm diameter were measured by means of a photoelectric probe. The gas-liquid dispersion was generated by distributing air with a porous plate into aqueous solutions of electrolytes and of organic compounds (alcohols, glycols, ketones, carboxylic acids, saccharose, carboxymethyl-cellulose, detergents). For all these solutes there exists a rather narrow concentration range in which the change from quick coalescence in pure water to coalescence suppression takes place. Though rough relationships between concentrations for coalescence suppression and molecular properties can be found (ionic strength for electrolytes, number of carbon atoms in a homologous series of organic compounds), exact equations based on a theory of coalescence cannot be given.

The bubble size distributions obtained in the experiments have also been used to show the impact of coalescence phenomena on gas-liquid mass transfer. For this purpose, surface areas were calculated from measured gas hold-up and mean bubble diameters (Sauter diameters). A comparison of these data with the trends for volumetric mass transfer coefficients reported in the literature for n-alcohols (C₁-C₂i) showed good agreement, despite the fact that the mass transfer data had been obtained in a quite different gas-liquid contacting device (stirred vessel).     

气—液鼓泡塔中流动域和气含率的分布

利用压力传感器测定了气、液两相鼓泡塔内不同轴、径向位置上压强的脉动信号,分析了压强的脉动特征,计算了各种操作条件下塔内不同轴向位置截面上的平均气含率,发现在不同操作条件下,塔内可能出现不同的流动域分布,即全塔均匀鼓泡域、全塔过渡域、全塔湍动鼓泡域以及均匀鼓泡域,过渡域和湍动鼓泡域中的相邻2种或3种流域同时出现在塔内不同高度上。提出了不同轴向位置流域转变的判据。并发现,同一截面的不同径向位置基本处于同一流域内。同时研究了鼓泡塔内气含率在轴向上的分布规律,给出了不同流动域内气含率的关系式。     

EVALUATION OF LAGRANGIAN PARTICLE DISPERSION MODELS IN TURBULENT FLOWS

This work evaluates the performance of Lagrangian turbulent particle dispersion models based on the Langevin equation. A family of Langevin models, extensively reported in the open literature, decompose the fluctuating fluid velocity seen by the particle in two components, one correlated with the previous time step and a second one randomly sampled from a Wiener process, i.e., the closure is at the level of the fluid velocity seen by the particle. We will call those models generically the “standard model.” On the other hand, the model proposed by Minier and Peirano (2001) is considered; this approach is based on the probability density function (PDF) and performs the closure at the level of the acceleration of the fluid seen by the particle. The formulation of a Langevin equation model for the increments of fluid velocity seen by the particle allows capturing some underlying physics of particle dispersion in general turbulent flows while keeping simple the mathematical manipulation of the stochastic model, avoiding some pitfalls, and simplifying the derivation of macroscopic relations. The performance of the previous dispersion models is evaluated in the configurations of grid-generated turbulence (Snyder and Lumley, 1971; Wells and Stock, 1983), simple shear flow (Hyland et al., 1999), and confined axisymmetric jet flow laden with solids (Hishida and Maeda, 1987).     

EVALUATION OF LAGRANGIAN PARTICLE DISPERSION MODELS IN TURBULENT FLOWS

This work evaluates the performance of Lagrangian turbulent particle dispersion models based on the Langevin equation. A family of Langevin models, extensively reported in the open literature, decompose the fluctuating fluid velocity seen by the particle in two components, one correlated with the previous time step and a second one randomly sampled from a Wiener process, i.e., the closure is at the level of the fluid velocity seen by the particle. We will call those models generically the “standard model.” On the other hand, the model proposed by Minier and Peirano (2001 Minier , J. P. and Peirano , E. ( 2001 ). The PDF approach to turbulent polydisperesed two-phase flows , Phys. Rep. , 352 , 1 – 214 .[Crossref], [Web of Science ®] , [Google Scholar]) is considered; this approach is based on the probability density function (PDF) and performs the closure at the level of the acceleration of the fluid seen by the particle. The formulation of a Langevin equation model for the increments of fluid velocity seen by the particle allows capturing some underlying physics of particle dispersion in general turbulent flows while keeping simple the mathematical manipulation of the stochastic model, avoiding some pitfalls, and simplifying the derivation of macroscopic relations. The performance of the previous dispersion models is evaluated in the configurations of grid-generated turbulence (Snyder and Lumley, 1971 Snyder , W. H. and Lumley , J. L. ( 1971 ). Some measurements of particle-velocity autocorrelation functions in a turbulent flow , J. Fluid Mech. , 48 , 41 – 71 .[Crossref], [Web of Science ®] , [Google Scholar]; Wells and Stock, 1983 Wells , M. R. and Stock , D. E. ( 1983 ). The effect of crossing trajectories on the dispersion of particles in a turbulent flow , J. Fluid Mech. , 136 , 31 – 62 .[Crossref], [Web of Science ®] , [Google Scholar]), simple shear flow (Hyland et al., 1999), and confined axisymmetric jet flow laden with solids (Hishida and Maeda, 1987 Hishida , K. and Maeda , M. ( 1987 ). Turbulent characteristics of gas-solids two-phase confined jet: Effect of particle density , Jpn. J. Multiph. Flow , 1 , 56 – 69 . [Google Scholar]).     

三相循环流化床中气泡大小及其分布的实验研究

用光纤探头技术对三相循环流化床中的气泡大小及其分布进行了系统研究 ,实验测定了操作条件对气泡大小及其分布的影响规律 .实验结果表明 ,三相循环流化床中气泡的大小分布可用对数正态分布表征 ,在实验条件下气泡平均直径在床中心区域较小且沿半径方向由中心向边壁逐渐增大 ,并随表观气速的增大而减小 ,随固含率的增大而增大 ,表观液速对气泡平均直径的影响较小     

THE NARROWING OF CRYSTAL SIZE DISTRIBUTIONS IN A SONICATOR-MSMPR CRYSTALLIZER SYSTEM

Obtaining small crystals of a narrow crystal size distribution is an important problem in many pharmaceutical, biotechnological, and ceramic processing applications. This paper describes the use of a two-stage system to reproducibly produce pilot-scale quantities of a ceramic precursor powder.

The population balance is used to determine the crystal size distributions obtained from a staged crystallization system. The staged crystallization system consists of two units, a mininucleator (sonicator) and an MSMPR crystallizer. Experimental and theoretical studies of this system showed that the use of the mininucleator leads to narrowing of the crystal size distribution obtained from the MSMPR crystallizer. The resulting expression for the population density distribution allows direct fitting of experimental log population density data from the second stage to determine the growth and nucleation kinetics for both the mininucleator and the MSMPR crystallizer     

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     

ANALYSIS OF TRANSIENT TEMPERATURE DISTRIBUTIONS IN A PERFUSED MEDIUM DUE TO A SPHERICAL HEAT SOURCE WITH APPLICATION TO HEAT TRANSFER IN TUMORS: HOMOGENEOUS AND INFINITE MEDIUM

The role of conduction and convection in transferring heat through a perfused medium is quantified by analyzing the transient temperature field within and around a spherical heat source embedded in the medium, using the bio-heat transfer equation. Analytical expressions for transient temperature distributions are obtained in terms of the following dimensionless variables: ξ, the relative position; τ, the Fourier number; β²;, the Peclet number, and ratios of thermal conductivities and difFusivities. The perfused medium is assumed to be infinite, isotropic and homogeneous. Frequency response of the probe to sinusoidal power input is also analyzed. The analytical expressions obtained are used to estimate heat transfer characteristics of tumors from in vivo data describing blood flow and temperature distributions around a spherical probe.