Numerical simulation of bubble interactions using an adaptive lattice Boltzmann method

Bubble interactions have significant impact on the shape and motion of bubbles, and therefore the dynamics of bubbles in a swarm may be considerably different from that of an isolated bubble. This research presents a numerical study of bubble interactions using a novel lattice Boltzmann method (LBM). By using the adaptive mesh refinement (AMR) and the multiple-relaxation-time (MRT) algorithm, this technique is able to accurately capture the deformation of the interface, and can remain numerically stable for low Morton number and high Reynolds number flows. The numerical approach is briefly illustrated, and validated with the experimental results of the buoyant rise of an isolated bubble in the literature. Then the method is applied to simulate the interaction between multiple bubbles during their buoyant rise. A pair of bubbles with spherical or ellipsoidal shapes is first simulated under different configurations and rise velocities. Both attractive and repulsive interactions are observed in the simulations depending on the relative position and the Reynolds number. When the Reynolds number is sufficiently high, the bubble–wake interaction is found to be the main interaction mechanism, which results in strong attraction between the ellipsoidal bubbles in vertical or oblique arrangement. Simulations for a group of 14 bubbles are also carried out, and effects of the bubble shape and Reynolds number on the spatial distribution of the bubbles are briefly discussed. In general, a good agreement is found between the current simulation and the experimental and numerical results reported in the literature.     

Comparison of finite volume and lattice Boltzmann methods for multicomponent flow simulations

In pseudopotential lattice Boltzmann (LB) models for simulating multicomponent flows, interaction forces between the components of a mixture lead to phase separation and interfacial tension. At the macroscopic scale, such LB models solve an advection-diffusion equation for each component and the Navier-Stokes equations for the fluid mixture. In this paper, the computational efficiency of the LB method is compared with a finite volume (FV) solver for the same macroscopic-scale equations for a binary system in a two dimensional domain. The FV implementation replicates the phase separation of the LB model. Differences in the interfacial tension are due to truncation of the Taylor series expansion of the LB interaction force in the FV version. While the computations required to update the domain for each timestep can be completed faster with the FV approach, a smaller timestep is required to achieve stability, which negates the improvement in processing speed. The FV implementation, however, allows independent variation of model parameters, which is not possible in LB. For example, the viscosity can be changed without affecting interfacial tension or the extent of phase separation. Furthermore, it is possible to obtain low interfacial tensions without suppressing phase separation with the FV formulation. The significance of changing the diffusion rate of components on the deformation of a droplet in shear is also demonstrated. For three-dimensional simulations, the finite volume approach is expected to be faster than LB and would benefit from the demonstrated flexibility in specifying model parameters.     

Numerical simulation of single bubble rising in vertical and inclined square channel using lattice Boltzmann method

A lattice Boltzmann equation (LBE) model based on the Cahn–Hilliard diffuse interface approach is used to investigate the dynamics of a bubble rising in a vertical and inclined square channel with large density and viscosity ratios. Deformation parameter Δ, film thickness δ, and terminal velocity U_t of the bubble are interrelated quantities which depend on non-dimensional numbers such as Bond number Bo, Morton number Mo, and ratio between bubble diameter and channel width k as it was reported by previous experimental studies. As k is increased, higher Δ and smaller δ are exhibited. This finding is independent of the value of Bo and Mo. In addition, a relationship was established between δ and Δ with non-dimensional numbers such as Capillary number Ca and Weber number We. An evaluation was performed for inclined channels to relate the Froude number Fr with the inclination angle θ, where in each case there is a critical value of θ which corresponds to the highest value of Fr, consequently highest U_t. This finding is consistent with previous simulation and experimental results. Moreover, a relation was established between the critical value of θ and Ca and Bo. This three-dimensional study was performed using a range of Bo (1<Bo<12), Mo (10⁻⁴<Mo<10³) and the inclination of the channel is varied from 0 to 75°.     

功能性多孔介质中气泡输运调控的格子Boltzmann分析

为提高毛细蒸发海水淡化技术中的蒸发效率,多孔介质层需要维持一定的毛细压力,同时还要确保气泡能够快速通过。基于此背景,本文建立了多孔介质参数化模型,探究了气泡穿越多孔介质间隙过程的运动特征,研究在保持一定孔隙毛细压力的同时,通过调控孔道尺寸及排布从而使气泡能够更快速地通过多孔介质层。基于格子Boltzmann伪势模型分析了多孔介质孔隙率、壁面润湿特性、孔道排布及气泡水平方向初速度等对气泡形貌、上升速度、与壁面平均接触面积及孔隙毛细力的影响,获得了多孔介质的孔隙率设计范围,骨架润湿特性调控以及孔道排布方式的选择依据。同时还获得了在实际蒸发过程中,可以使气泡存在一定的水平方向初速度,从而能够更快地脱离多孔介质的策略。     

Contact line motion without slip in lattice Boltzmann simulations

We have simulated the pressure driven motion of a gas bubble immersed in a partially wetting liquid in a two-dimensional channel using the Shan and Chen multi-phase lattice Boltzmann (LB) method. Both the one-component and the two-component multi-phase models of the Shan–Chen approach have been used. The static contact angle at the fluid–solid interface was controlled by adjusting the fluid–solid interaction potential. The variation of the dynamic contact angle with the capillary number obtained from the LB simulations was compared with experimental data from the literature. Our results indicate that in the LB simulation the contact line moves over the no-slip surface due to evaporation at the nose and condensation at the tail of the bubble. This is in contrast to reality where slip at the contact line facilitates the bubble motion. We show that by controlling the extent of phase transition the simulations can be brought into close agreement with experimental data from the literature.     

Numerical simulations of bubble formation on submerged orifices: Period-1 and period-2 bubbling regimes

The process of bubble formation is involved in several gas-liquid reactors and process equipment. It is therefore important to understand the dynamics of bubble formation and to develop computational models for the accurate prediction of the bubble formation dynamics in different bubbling regimes. This work reports the numerical investigations of bubble formation on submerged orifices under constant inflow conditions. Numerical simulations of bubble formation at high gas flow rates, where the bubble formation is dominated by inertial forces, were carried out using the combined level set and volume-of-fluid (CLSVOF) method and the predictions were experimentally validated. Effects of gas flow rate and orifice diameter on the bubbling regimes and in particular, on the transition from period-1 to period-2 bubbling regime (with pairing or coalescence at the orifice) were investigated. Using the simulation data on the transition of bubble formation regimes, the bubble formation regime map constructed using Froude and Bond numbers is presented.     

Gas flow simulations in a structured packing by lattice Boltzmann method

Numerical simulations of gas flow between two sheets of plastic Mellapak^TM 250 Y are performed using Lattice Boltzmann methods in laminar and turbulent regimes. Results are compared with experimental measurements and with known correlations. They are also compared with simulations using a classical CFD code. In all cases, the agreement is very good.     

Effect of bubble deformation on stability and mixing in bubble columns

The paper deals with hydrodynamics in bubble columns. The objective of the paper is to study stability and mixing in a bubble column. The modeling of parameters such as stationary drag and added mass is addressed. In addition, the effect of bubble deformation in terms of eccentricity is highlighted. In a previous paper, the transition between homogeneous and heterogeneous regimes in bubble column without liquid flow has been shown to be driven by the deformation of the bubbles associated to drag and added mass. In the present paper, this work is generalized to bubble column with liquid flow and to the transition from bubble flow to slug flow in a vertical pipe. Numerical simulations of gas-liquid reactors are presented. The numerical simulations are validated in the case of gas plume after the Becker et al. data (Becker, S., Sokolichin, A., & Eigenberg, G. (1994) Gas-liquid flow in bubble columns and loop reactors: Part II. Comparison of detailed experiments and flow simulations. Chemical Engineering Science, 49 (24B), 5747-5762. The numerical simulations are finally applied to a bubble column. The simulations of residence time distribution coupled to transient hydrodynamics are shown to be very sensitive to the modeling of interfacial transfer of momentum from the bubbles to the liquid in terms of drag and added mass, including the effect of bubble deformation.     

Effect of solids on homogeneous-heterogeneous flow regime transition in bubble columns

Experiments were conducted to study the effect of the presence of the solid phase on the homogeneous-heterogeneous flow regime transition in a bubble column 0.14 m diameter. Air, distilled water and calcium alginate beads (2.1 mm, ) at concentrations c=0-30% (vol.) were the phases. The basic data were the voidage-gas flow rate dependences. The critical point, where the homogeneous regime loses stability and the transition begins, was evaluated by the drift flux model. The critical values of voidage and gas flow rate were the quantitative measures of the homogeneous regime stability. These were plotted against the solid phase concentration. It was found, that both the voidage and the critical values increased with the solid content at low solid loading, approx. c=0-3%, and decreased at higher loading, c>3%. The homogeneous regime was thus first stabilized and then destabilized. To explain this dual effect, possible physical mechanisms of the solid phase influence on the uniform bubble bed were discussed.     

基于多GPU并行格子Boltzmann方法的方管湍流模拟

采用CUDA (Compute Unified Device Architecture)和MPI (Message-Passing-Interface)在超级计算机Mole-8.5E上实现了格子Boltzmann方法(LBM)多GPU并行算法,通过三维顶盖驱动方腔流算例验证了多GPU并行LBM算法的准确性和有效性,利用该并行算法分别对雷诺数Reτ为300, 600, 1200下的充分发展的方管湍流进行了大规模模拟。研究发现,当计算网格尺寸小于黏性底层厚度(即Δ+<5)时,在壁面附近的相关传递特性统计误差较小,预测精度满足工程应用范围;Reτ为300, 600时,不同网格尺寸Δ+下的模拟结果表明LBM在方管流中心湍流特性统计具有网格弱相关性,Reτ为600时,与DNS (Direct Numerical Simulation)相比,Δ+=1.667, 3.750, 6.250时平均流向速度的平均误差分别是1.357%, 2.994%和4.766%;Reτ分别为300, 600和1200时,对应网格尺寸Δ+分别为0.833, 1.667和3.333时的方管湍流模拟中,成功捕捉到了二次流特性,预测得到的中心面流向速度、脉动均方根速度等的规律与文献基本吻合,进一步验证了单松弛LBM的可靠性,相关计算结果也为理解高Reτ下的方管湍流特性提供了参考。方管湍流的模拟验证了单松弛LBM多GPU并行算法在超大规模网格计算中的潜力,为进一步实现实际工程流动所需更大规模的数值模拟奠定了基础。     

Hydrodynamic characterization of a needle sparger rectangular bubble column: Homogeneous flow, static bubble plume and oscillating bubble plume

In this work a detailed experimental hydrodynamic characterization of a needle sparger rectangular bubble column has been performed. The liquid velocity profiles and bubble plume oscillation frequency have been measured by means of laser Doppler anemometry (LDA), and the bubble velocity map by particle image velocimetry (PIV). In this way, the influence of the superficial gas velocity, liquid height and aeration pattern on the column flow structure was analysed. A highly uniform upward flow structure with down flow near the walls was obtained by means of a full-length aeration pattern. This flow structure was preserved even for high gas fractions values. The partial-length aeration patterns with the aerated zone (defined as the aerated width divided by the column width) larger than 0.7 provide a bubble plume and two pure liquid vortical structures in the column bottom, although they are static in nature. With aerated zones lower than 0.6, an oscillating bubble plume is obtained. A non-dimensional analysis of bubble plume oscillation frequency shows a dependence of bubble plume behaviour with the aerated zone. In this way, two different types of bubble plume oscillations, namely confined bubble plume oscillation and free bubble plume oscillation, are introduced and analysed.     

Effect of spent grains on flow regime transition in bubble column

It is well known that two main flow regimes are present in bubble columns, being the evaluation of transition between homogeneous and heterogeneous regimes of crucial importance for reactor design. For air–water systems, several models have been satisfactorily proposed to explain this phenomenon. However when gas–liquid–solids systems are considered, solid particles influence on regime transition is not yet clear, in spite of the amount of research developed over the past years.The objective of this work is to evaluate the effect of a specific solid phase – spent grains – on homogeneous regime stability and regime transition. Spent grains are cellulose-based particles that have been used to immobilize cells on biotechnology process. These particles are wettable and have a density close to water and its influence on bubble column reactors is particularly important in order to establish the limits were both regimes prevail.A cylindrical Plexiglax BC of 18 L volume was used with air, water and spent grains at different concentrations (0–20% (wt._{WET BASIS}/vol.)) as gas, liquid and solid phases. Regime transition was determined according to the drift-flux and slip speed concept.It was found that at studied concentrations of spent grains, critical gas hold-up decreases as solids concentration increases. At the highest solids concentration and lowest gas flow rates no fluidization of the solid phase was observed. It is believed that the critical hold-up decrease was mainly due to bubble coalescence, as larger bubbles were observed when heterogeneous regime was present. This coalescence may be caused by the non-uniform distribution of solid phase on the column and the interaction of spent grains with bubbles in the liquid–gas interface     

Explorations on the multi-scale flow structure and stability condition in bubble columns

Physical understanding of heterogeneous flow structure is of crucial importance for modelling and simulation of gas-liquid systems. This article presents a review and report of recent progress in our group on exploratory application of the variational (analytical) multi-scale approach to gas-liquid systems. The work features the closure of a hydrodynamic model with the incorporation of a stability condition reflecting the compromise between the dominant mechanisms in the system. A dual-bubble-size (DBS) model is proposed to approximate the heterogeneous structure of gas-liquid systems based on a single-bubble-size (SBS) model previously established. Reasonable variation of the gas holdup and the composition of the two bubble species with operating conditions have been calculated and the regime transition can therefore be reasonably predicted for air-water system, suggesting that stability condition may provide an insightful concept to explain the general tendencies in gas-liquid systems out of their hydrodynamic complexity, and to give simple models of their overall behaviors. Of course, the diversity of the correlations for drag force and minimum bubble size and the sensitivity of the model predictions to these correlations may suggest the necessity to clarify further the essential and robust results in the current model and to reduce the uncertainties involved.     

An efficient numerical algorithm for “A novel theoretical breakup kernel function of bubble/droplet in a turbulent flow”

An efficient numerical algorithm was proposed for “A novel theoretical breakup kernel function of bubble/droplet in a turbulent flow”. In this algorithm, a recursive method was used to calculate the involved triple integral, which reduced the calculation complexity of a triple integral to a double integral.     

Influence of the lift force on the stability of a bubble column

This work investigates the role of the lift force for the stability of a homogeneous bubble column. Instabilities caused by the lift force may be one important reason for the transition from homogeneous to heterogeneous bubble column. On rising bubbles the lift force acts in a lateral direction, when gradients of the liquid velocity are present. Non-uniform liquid velocity fields may be induced if the gas fraction is not equally distributed, e.g. caused by local disturbances. This feedback mechanism is studied in the paper. It was found, that a positive lift coefficient (small bubbles) stabilizes the flow, while a negative coefficient (large bubbles) leads to unstable gas fraction distributions, and thus it favours the appearance of a heterogeneous bubble column regime. The turbulent dispersion force has always a stabilizing action, i.e., it partially compensates the destabilization induced by a negative lift coefficient. A stability analysis for a mono-dispersed system nevertheless showed, that influence of the lift force is much larger, compared to the influence of the turbulent dispersion force, if only bubble induced turbulence is considered. Thus, the stability condition is practically the positive sign of the lift force coefficient. The extension of the analysis to two bubbles classes, from which one being small enough to have a positive lift coefficient, results in a minimum fraction of small bubbles needed for stability. Finally a generalized criterion for N bubble classes and for a continuous bubble size distribution is given.     

Fluid-particle interaction from lattice Boltzmann simulations for flow through polydisperse random arrays of spheres

Fluid-solid drag force correlations, such as the Ergun relation, are widely used in many areas of chemical engineering. In many practical applications, the solid phase consist of an assembly of spheres which are, more often than not, polydisperse. In this paper we report on a study of the fluid-particle interaction by fully resolved DNS-type simulations (lattice Boltzmann) of flow through polydisperse random arrays of spheres, both for log-normal and Gaussian size distributions. In a recent paper [Van der Hoef, M.A., Beetstra, R., Kuipers, J.A.M., 2005. Lattice Boltzmann simulations of low Reynolds number flow past mono- and bidisperse arrays of spheres: results for the permeability and drag force. J. Fluid Mech. 528, 233] we have shown that a correction factor should be applied to the monodisperse drag force relations, when used for bidisperse systems. On the basis of the data reported in this paper, we conclude that the correction factor also applies to general polydisperse systems.     

Numerical simulation of periodic bubble formation at a submerged orifice with constant gas flow rate

Extensive numerical simulations were carried out to study the problem of bubble formation at submerged orifices under constant inflow conditions. A combined volume-of-fluid and level-set method was applied to simulate the formation process, the detachment and the bubble rise above the orifice in axisymmetric coordinates. On the one hand, the operating conditions of the formation process such as orifice flow rate, orifice radius and wettability of the orifice plate were investigated for the working fluids of air and water at 20 °C. On the other hand, the influence of the variation of fluid properties (liquid density and viscosity, surface tension) was examined individually. In this frame, the present work focused on low and medium flow rate conditions, at which the formation takes place in a periodic manner, in contrast to aperiodic or double periodic modes. The results of the computations provide information on the influence of various conditions on the bubble shapes, the bubble volume and the transition from a single to a double periodic formation process. The numerical results were extensively validated with experimental data available in the literature.     

Multiphase reacting flow studies of bubble column ozonation reactor for water remediation

A multiphase Volume‐of‐fluid (VOF) model was developed to gain further insights into the reactive flow parameters and electrical capacitance tomography (ECT) measurements on the remediation of hazardous organic pollutants. Low ozone bubble frequencies were obtained for high surface tension fluids, and the liquid viscosity affected the ozone bubbling frequency. The VOF model indicated that the increase of inlet gas velocity enriched the ozone bubble detachment and concomitantly generated larger ozone bubbles, decreasing the detoxification rates. VOF mappings and ECT visualizations of gas‐liquid unveiled preferential routes and highlighted the attenuation of the axisymmetric behavior of the ozonation bubble column under high‐interaction regimes.     

Free-energy lattice Boltzmann simulations of slicing of rising droplets

We performed two-dimensional simulations of the slicing of a rising droplet by a vertical knife and by two knives. We used a free-energy lattice Boltzmann method. Most simulations are for an Eötvös number of 3.96 and a Morton number of 1.24 × ${10}^{-4}$. We carefully probed effects of the spatial resolution on the rising speed and slicing process. The effect of wettability of the knife(s) was studied by varying the equilibrium contact angle of the drop on the knife in the range of 45° to 135°. Slicing time as well as fine droplet fragments staying behind on the knife depend on the knife's wettability.