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].     

Numerical Simulation of Interfacial Closures for 3D Bubble Column Flows

Numerical investigation of flow hydrodynamics in a square cross‐sectioned bubble column was conducted in a transient Euler‐Euler environment by applying the simulation tool Ansys CFX 14.0. The influence of the drag coefficient (C_D) was investigated and the results were also compared with drag force models. Furthermore, three different lift force models and a defined lift coefficient were studied. All results were compared with the available experimental data. All simulations were carried out for a single‐hole sparger with given aspect ratio (H/D) and superficial gas velocity.     

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。     

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。     

Numerical Simulation of Single‐Bubble Dynamics in High‐Viscosity Ionic Liquids Using the Level‐Set Method

Two numerical models for studying the dynamics of formation and rise of single bubbles in high‐viscosity ionic liquids were implemented using the level‐set method. The models describe two stages of bubble dynamics: bubble formation at the inlet nozzle and bubble displacement across the column. The models were experimentally validated through a laboratory‐scale bubble column using water‐glycerol mixtures and two imidazolium‐type ionic liquids. The models were consistent with the experimental tests for Reynolds numbers < 5. Outside this range, the models tend to underestimate the bubble terminal velocity, which can be explained by the effect of the high velocity and pressure gradients close to the gas‐liquid interface. The models also predicted the velocity and pressure fields near the bubble surface before and after detachment.     

Characterization of Bubble Shapes in Non‐Newtonian Fluids by Parametric Equations

Based on experiments with single air bubbles rising in stagnant non‐Newtonian fluids, an innovative model containing the aspect ratio (E) and two parameters (α, β) was proposed and proved to be capable of characterizing the bubble shape from spherical/ellipsoidal to prolate/oblate‐tear with good accuracy. Several impacts on bubble deformation were investigated, involving the rheological properties of the fluids and different forces exerted on the bubble, which were quantified by multiple dimensionless numbers (e.g., Reynolds, Eötvös, and Deborah number). Within a wide range, the empirical correlations were obtained for parameter β, and between α and β. Together with the shape model, a complete system was set up for bubble shape characterization and prediction that will provide new ideas for future studies on bubble hydrodynamics.     

Bubble size modeling approach for the simulation of bubble columns

The constant bubble size modeling approach (CBSM) and variable bubble size modeling approach (VBSM) are frequently employed in Eulerian–Eulerian simulation of bubble columns. However, the accuracy of CBSM is limited while the computational efficiency of VBSM needs to be improved. This work aims to develop method for bubble size modeling which has high computational efficiency and accuracy in the simulation of bubble columns. The distribution of bubble sizes is represented by a series of discrete points, and the percentage of bubbles with various sizes at gas inlet is determined by the results of computational fluid dynamics (CFD)–population balance model (PBM) simulations, whereas the influence of bubble coalescence and breakup is neglected. The simulated results of a 0.15 m diameter bubble column suggest that the developed method has high computational speed and can achieve similar accuracy as CFD–PBM modeling. Furthermore, the convergence issues caused by solving population balance equations are addressed.     

Numerical Investigation of Three‐Dimensional Bubble Column Flows: A Detached Eddy Simulation Approach

Numerical simulations were performed employing detached eddy simulation (DES) in a three‐dimensional transient Euler‐Euler framework for bubble columns, and all the computational fluid dynamics results were compared with a k‐? model and available experimental data. The numerical results are in good agreement with the experiments in predicting the time‐averaged axial velocity and turbulent kinetic energy profiles. The flow‐resolving capabilities of the DES model are highlighted, and it is shown that the DES turbulence model can be efficiently used for simulating flow field and turbulent quantities in the case of bubble columns.     

玻璃熔体中气泡行为特征的数学模型

给出了一套描述多组分气泡在玻璃熔体内复杂行为特征的数学模型.该模型可以计算气泡的大小、所在位置、三维速度、运动轨迹、内部气体成份、压力及温度等;根据电视屏玻璃池炉内澄清段的相应工况,模拟了气泡行为;文中给出了气泡在上升过程中半径和气体成分的变化,以初步揭示气泡在玻璃液中的有关行为特征.     

Flow Regimes of Viscous Immiscible Liquids in T‐Type Microchannels

A computational and experimental study of the flow regimes of a mixture of castor and paraffin oils in a T‐type microchannel with 200 × 400 µm cross section was carried out. The ranges of parallel, slug, droplet, and rivulet flow regimes of the tested mixture were defined. According to the experimental results, a flow regime map was constructed for this mixture depending on the Weber number multiplied by the Ohnesorge number. A correlation of the length of paraffin oil slugs to the fluid flow ratio was established. The experimental data were compared with results of numerical simulation. A good agreement between calculation and experimental data was achieved in terms of reproduction of flow regimes, phase boundaries, and slug length.     

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.     

Coalescence Deformation of Bubble Pairs Generated from Twin Nozzles in CMC Solutions

A coupled level‐set/volume‐of‐fluid method, under the consideration of the rheological characteristics of a fluid, is employed to investigate numerical coalescence deformation of bubble pairs generated at two adjacent nozzles in carboxymethyl cellulose aqueous solutions. The satisfactory agreement between numerical results and experimental measurements proves the validity of this approach in predicting the surface evolution of bubbles. Simulated results show that the bubble coalescence process involves four stages of independent growth, rapid mergence, radial expansion, and vertical stretching. The various effects of surfactant concentration, gas flow rate, nozzle spacing, and nozzle diameter on the aspect ratio depend greatly on each coalescence period.     

Numerical Simulation of Dispersed Gas/Liquid Flows in Bubble Columns at High Phase Fractions using OpenFOAM®. Part II – Numerical Simulations and Results

The design of industrial gas/liquid reactors such as bubble columns requires detailed information with respect to the flow structure and characteristics of two‐ or multiphase systems in the reactor. The contribution is focused on the evaluation of the simulation results obtained by model selection. The results are further compared with those reported in literature. The simulation has been performed with the CFD software OpenFOAM®. The main focus of the numerical simulation was set on capturing the characteristic process and design parameters of bubble columns.     

Radial Profiles of Gas Bubble Behavior in a Gas‐Liquid Bubble Column Reactor under Elevated Pressures

The effects of operating conditions on radial variation of gas holdups, bubble swarm rising velocity, and Sauter mean diameter were investigated in a bubble column reactor under elevated pressures using a conductivity probe method. Air served as gas phase and tap water as liquid phase with varying gas velocity and pressure. All three parameters increased constantly with higher superficial gas velocity. Maximum holdup, velocity, and Sauter mean diameter were found at the center of the cross section. Two different cases for Sauter mean diameter distribution were observed. The gas holdups increase continuously with higher system pressure, but decrease for bubble swarm rising velocity and Sauter mean diameter. According to experimental results, an empirical correlation of the gas holdup profiles is presented.     

Models for the Numerical Simulation of Bubble Columns: A Review

This work reviews the state‐of‐the‐art models for the simulation of bubble columns and focuses on methods coupled with computational fluid dynamics (CFD) where the potential and deficits of the models are evaluated. Particular attention is paid to different approaches in multiphase fluid dynamics including the population balance to determine bubble size distributions and the modeling of turbulence where the authors refer to numerous published examples. Additional models for reactive systems are presented as well as a special chapter regarding the extension of the models for the simulation of bubble columns with a present solid particle phase, i.e., slurry bubble columns.     

Robust Direct Numerical Simulation of Viscoelastic Flows

Many technical processes involve viscoelastic flows, which makes the subject interesting for CFD. Despite the complex fluid rheology and related numerical problems in solving the constitutive equations, recent stabilization approaches allow for a robust simulation of viscoelastic flows in the technical relevant range at high degrees of fluid elasticity. A recent general‐purpose numerical stabilization framework, based on the finite‐volume method of OpenFOAM is presented and its capability for the robust simulation of viscoelastic single‐, as well as two‐phase flows is shown.     

Numerical Simulation of Dispersed Gas/Liquid Flows in Bubble Columns at High Phase Fractions using OpenFOAM®. Part I – Modeling Basics

Various chemical products are synthesized in processes using gas/liquid reactors with bubbly flows. Hence, there is a significant interest in a more efficient process design as well as in process intensification with a strong focus on this reactor class. However, the design of industrial gas/liquid reactors requires more detailed information about the flow structures and characteristics of two‐ or multiphase systems. The basic models for two‐fluid model simulations of dispersed gas/liquid flows in bubble columns at high gas fractions are presented.