Numerical simulation of gas bubbles behaviour using a three-dimensional volume of fluid method

In this paper a three-dimensional (3D) volume of fluid (VOF) method is presented featuring (i) an interface reconstruction technique based on piecewise linear interface representation, (ii) a 3D version of the CSF model of Brackbill et al. [1992, Journal of Computational Physics 100, 335]. Our model can handle a large density and viscosity ratio and a large value of the surface tension coefficient.First the results of a number of test cases are presented to assess the correctness of the advection and interface reconstruction algorithms and the implementation of the 3D version of the CSF model. Subsequently the computed terminal Reynolds numbers and shapes of isolated gas bubbles rising in quiescent liquids are compared with data taken from the bubble diagram of Grace (1973). Finally results of two calculations are reported involving the co-axial and oblique coalescence of two gas bubbles. The computed bubble shapes compared very well with the experimentally observed bubble shapes of Brereton and Korotney [1991, In: Dynamics of Bubbles and Vortices Near a Free Surface, AMD-vol. 119. ASME, New York].     

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。     

Numerical simulations of gas–liquid flow in thermal sorption processes

Thermal storage systems, used, e.g., for domestic heating, must be able to compensate the mismatch between supply and demand. The most efficient techniques for thermal storage are based on sorption storage processes. Usually in sorption, the adsorption process occurs in combination with a solid state adsorbent, whereas absorption takes place in a liquid/gas system. During such sorption processes the flow behavior of the carrier medium is crucial for the efficiency of a falling film absorber. In this work the hydrodynamics of the falling liquid film in two geometrical setups, namely on an inclined plane and over two horizontal parallel tubes, is studied. For the simulation the Eulerian–Eulerian model of the software ANSYS CFX and the interFoam application of the open source software OpenFOAM were used. The numerical results of the two geometries were compared with each other and also with existing data from literature to predict the performance of a sorption storage regarding the specific wetted area and the needed height for gravity driven film absorption.     

微孔塑料挤出成型中气泡长大过程的数值模拟

选用广义牛顿流体等温条件下气泡长大的细胞模型,并利用Polyflow软件的用户自定义模块编制发泡成型口模中泡孔半径及熔体密度的计算模块,可实现微孔塑料挤出口模中气泡长大过程的数值模拟。     

Numerical and technological properties of bubble column bioreactors for aerobic processes

This paper describes the method of modelling and numerical simulation of bubble column bioreactors in which the process of aerobic biodegradation of carbonaceous substrate occurs. Such bioreactors belong to systems with distributed state variables. Determining steady states of such objects results in solving non-linear boundary-value problems.The bioreactors with axial dispersion and piston flow with biomass recirculation were analysed. The effectiveness of selected algorithms used to determine the steady states of such bioreactors were compared; the numerical properties of mathematical models of analysed bioreactors were specified, the branches of steady states in bioreactors with axial dispersion and piston flow were determined and the application areas of such bioreactors were defined.     

Effects of viscosity and relaxation time on the hydrodynamics of gas–liquid systems

Effects of liquid properties on the hydrodynamics of gas–liquid systems were investigated in lab-scale bubble column (BC) and internal loop airlift (ILA). Alginate solutions, a glycerol solution and a Boger fluid were adopted to separately address the effects of viscosity and of surface tension for Newtonian fluids, and the effects of relaxation time for non-Newtonian fluid characterized by approximately constant viscosity (low shear thinning). Hydrodynamic regimes were characterized in terms of overall gas holdup, gas–liquid mass transfer coefficient, drift-flux and liquid circulation velocity. The superficial gas velocities at the transition between hydrodynamic regimes (homogenous regime–vortical-spiral regime–heterogeneous regime) as a function the liquid viscosity was characterized by a maximum. The same behavior was observed for the maximum stable gas holdup and gas–liquid mass transfer coefficient in BC. Viscosity enhances homogeneous regime stability for μ<4.25 mPa s, in BC, and μ<7.68 mPa s, in ILA. For non-Newtonian fluids the transition velocity increases with liquid elasticity. The stabilization mechanism related to the relaxation time of Boger fluids has been discussed.     

聚合物发泡泡孔尺寸调控

采用核壳模型建立了描述聚合物发泡泡孔增长过程的一组控制方程，并采用有限元法而不是通过浓度边界层的积分对控制方程组进行了求解；同时考察若干影响最终泡孔尺寸的因素。计算表明对于一具体发泡过程壳层厚度主要影响最终泡孔尺寸。     

A thermodynamically consistent, nonlinear viscoelastic approach for modeling glassy polymers

A thermodynamically consistent nonlinear viscoelastic constitutive theory is derived to capture the wide range of behavior observed in glassy polymers, including such phenomena as yield, stress/volume/enthalpy relaxation, nonlinear stress-strain behavior in complex loading histories, and physical aging. The Helmholtz free energy for an isotropic, thermorheologically simple, viscoelastic material is constructed, and quantities such as the stress and entropy are determined from the Helmholtz potential using Rational Mechanics. The constitutive theory employs a generalized strain measure and a material clock, where the rate of relaxation is controlled by the internal energy that is likewise determined consistently from the viscoelastic Helmholtz potential. This is perhaps the simplest model consistent with the basic requirements of continuum physics, where the rate of relaxation depends upon the thermodynamic state of the polymer. The predictions of the model are compared with extensive experimental data in the following companion paper.     

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.     

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%.     

多孔挡板流化床气泡行为的研究

本文在内径为(?)120mm 的多孔挡板流化床中,用光导纤维法和电容法测定了 Al(OH)_3粉、铜粉和 FCC 三种不同物料体系的气泡频率和气泡速度,对操作条件和挡板参数对气泡行为的影响作了研究和分析。结果表明,在一定的气速下,挡板的开孔率、孔径和板间距(级间高径比小于3)对气泡频率和气泡速度的影响较小;对属 B 类的 Al(OH)_3粉和铜粉物料,气速对气泡频率的影响可以忽略,而对属 A 类的 FCC 物料,气泡频率随气速的增大而增大。     

Numerical simulation of elastic recovery for uncured rubber compound with a multi-mode Simhambhatla-Leonov model

Transient squeeze flow and recovery experiments are simulated for a rubber compound. The rheological behaviour of the selected compound is described with a multi-mode Leonov model developed for filled uncured elastomers. The calculation is performed with the finite element software POLYFLOW. In particular, we focus on the deformation undergone under the application of a load, and on the subsequent recovery that develop upon cessation of the squeezing force. We also try to establish a possible empirical relationship between the applied squeeze force and time interval (input data) and the resulting deformation and recovery (output quantities).     

BUBBLE MOTION IN A THREE-PHASE LIQUID FLUIDIZED BED

This paper presents results for the rise velocities of air bubbles in liquids and liquid-solid fluidized beds. The bubble sizes ranged from approximately 0.03 to 0.45 cm radius. Tap water and distilled water were used as the fluidizing liquids. The solid phase consisted of low density alginate gel beads of mean radius 0.04 cm. The gel beads were translucent which permitted observation of bubbles inside the bed even at large solids volume fractions. Experiments were conducted for solids volume fractions ranging from 15% to 52% and in clear liquids. The goal of the experiments was to determine rise velocities of bubbles and to develop and evaluate correlations of bubble rise velocity based on bubble size, solids volume fraction and liquid properties. It was determined that, for moderate solids fractions (ranging from 28% to 45% solids), a semi-empirical correlation that treated the fluidized bed as a pure liquid with a higher viscosity than the liquid phase could be used to represent the data. The Thomas effective viscosity model was used to predict the viscosity. Provided that one restricts attention to a water fluidized bed, a second empirical correlation can be used to represent the data over a broader range of solids fractions.