Use of models for lift, wall and turbulent dispersion forces acting on bubbles for poly-disperse flows

Closure laws are needed for the qualification of CFD codes for two-phase flows. In case of bubbly and slug flow, forces acting on the bubbles usually model the momentum transfer between the phases. Several models for such forces can be found in Literature. They show, that these forces depend on the liquid flow field as well as on the size and the shape of the bubbles. A validation of consistent sets of bubble force models for poly-disperse flows is given, basing on a detailed experimental database for vertical pipe flows, which contains data on the radial distribution of bubbles of different size as well as local bubble size distributions. A one-dimensional (1D) solver provides velocity profiles and bubble distributions in radial direction. It considers a large number of bubble size classes and is used for the comparison with the experiments. The simplified model was checked against the results of full 3D simulations done by the commercial code CFX-5.7 for simplified monodisperse cases. The effects of the number of bubbles classes as well as the effect of the lateral extension of the bubbles were analyzed. For the validation of bubble force models measured bubble size distributions were taken as an input for the calculation. On basis of the assumption of an equilibrium of the lateral bubble forces, radial volume fraction profiles were calculated separately for each bubble class. In the result of the validation of different models for the bubble forces, a set of Tomiyama lift and wall force, deformation force and Favre averaged turbulent dispersion force was found to provide the best agreement with the experimental data. Some discrepancies remain at high liquid superficial velocities.     

A model for two-phase turbulent mixing in a jet bubble column

Mixing behavior of the two phase air-water turbulent flow in a jet bubble column is examined. The time evolution of the mixing behavior of a liquid tracer in a turbulent air-water flow within a jet bubble column is predicted using a model based on the fundamental governing equations of fluid motion. The predictions of the model are compared with experimental measurements. Measured residence time distributions (RTD) of the liquid tracer within the cone agree well with the predicted values given by the model. For the range of parameters considered in the study, lack of radial mixing and large axial mixing are evident within the cone of the jet bubble column. Use of fundamental mathematical models for the study of hydrodynamics in a two-phase conventional bubble column has been reported earlier (Torvik, 1990; Jakobsen et al., 1993). The present paper extends the use of such models to predict the mixing characteristics in a jet bubble column.     

Two‐Phase Flow with Mass Transfer in Bubble Columns

Bubble columns are widely used in the chemical and biochemical industries. In these reactors a gaseous phase is dispersed into a continuous liquid phase thus the rising bubble swarm induces a circulating flow field. For the dimension of these reactors the local interfacial area and the residence time of the liquid and the gaseous phase are key parameters. In this paper an Euler‐Euler approach is used to calculate the flow field in bubble columns numerically. Therefore a transport equation for the mean bubble volume based on a population balance equation approach is coupled with the balance equations for mass and momentum. The calculations are performed for three‐dimensional, instationary flow fields in cylindrical bubble columns considering the homogeneous and the heterogeneous flow regime. For the interphase mass transfer the physical absorption of the gaseous phase into the liquid is assumed. The back mixing in the gaseous and liquid phase is calculated from the local and time dependent concentration of a tracer.     

Numerical study of bubbly upflows in a vertical channel using the Euler–Lagrange two-way model

Bubbly flows exist extensively in industrial processes, so it is very meaningful to study hydrodynamic characteristics of them to improve efficiency of bubbly flow equipments. This paper introduces a numerical method of the Euler–Lagrange two-way model for the air–water bubbly flows in detail. The flow field is simulated by using direct numerical simulations (DNS) in Euler frame of reference, while the bubble dynamics are fully analyzed by integration of Newtonian equations of motion taking into account interphase interaction forces including drag force, lift force, wall lift force, pressure gradient force, virtual mass force, gravity force, buoyant force, and inertia force in Lagrange frame of reference. The coupling between phases is considered by regarding the interphase interaction forces as a momentum source term of the continuous phase. Bubbles distribution and turbulent statistics of the liquid phase are comprehensively analyzed. The results show that an overwhelming majority of bubbles cluster near the walls, and turbulent structures of the liquid phase are modified to some certain by addition of bubbles, namely, the mean streamwise velocity become increased at the core of the channel, the wall-normal and spanwise turbulent intensities and Reynolds stress are reduced. Redistribution of turbulent energy from the streamwise velocity components to wall-normal and spanwise velocity components is also suppressed due to the addition of bubbles.     

臭氧在对硝基苯酚溶液中的吸收与模拟过程

研究了鼓泡塔中臭氧在对硝基苯酚溶液中的吸收传质过程。首先探讨了pH值和气速对对硝基苯酚降解速率的影响。在 298K下,臭氧被连续通入对硝基苯酚溶液中,臭氧的传质速率因为溶解臭氧与对硝基苯酚的快速反应而大大加强。然后运用与实验条件相同的操作参数,进行了臭氧在鼓泡塔中吸收过程的模拟研究,采用MATLAB软件求解吸收过程的质量平衡方程,模拟了吸收过程中臭氧和对硝基苯酚浓度的变化,并与实验值进行了比较。结果表明,在短的鼓泡塔中,应用全混流模型来描述气相和液相的流体状态是可行的,在 80%的对硝基苯酚降解之前,模拟值和实验值能很好地一致。     

Mixing in a co‐current upflow bubble column reactors with and without internals

Liquid phase mixing is a phenomenon that results mainly due to convective and turbulent flow fields, which are generated by hydrodynamic interactions between the gas and liquid phases within a continuous co‐current upflow bubble column reactor. The extent of liquid phase mixing is usually quantified through the mixing time, or the axial dispersion coefficient. In the present work, the computational fluid dynamics (CFD) simulations for mixing and RTD in a continuous bubble column (with and without internals) are performed by using OpenFOAM 2.3.1. The superficial gas velocities were 0.014, 0.088, and 0.221 m/s and the superficial liquid velocities were 0.005 and 0.014 m/s. The simulations have been performed for three different configurations of the bubble column, that is, (a) an open bubble column, (b) a column with one vertical central rod of 36 mm diameter, (c) a column with the same central rod and four vertical additional rods of 12 mm diameter. The effects of superficial gas and liquid velocities and column internals were investigated on liquid phase mixing and the axial dispersion coefficient. Comparisons have been made between the experimental measurements and the CFD simulations.

     

Hydrodynamic Model for Horizontal Two‐phase Flow Through Porous Media

A unidirectional, two‐fluid model based on the volume‐average mass and momentum balance equations was developed for the prediction of two‐phase pressure drop and external liquid hold‐up in horizontally positioned packed beds experiencing stratified, annular and dispersed bubble flow regimes. The so‐called slit model drag force closures were used for the stratified and annular flow regimes. In the case of dispersed bubble flow regime, the liquid‐solid interaction force was formulated on the basis of the Kozeny‐Carman equation by taking into account the presence of bubbles in reducing the available volume for the flowing liquid. The gas‐liquid interaction force was evaluated by using the respective solutions of drag coefficient for an isolated bubble in viscous and turbulent flows. The proposed drag force expressions for the different flow patterns occurring in the bed associated with the two‐fluid model resulted in a predictive method requiring no adjustable parameter to describe the hydrodynamics for horizontal two‐phase flow in packed beds.     

Hydrodynamics of turbulent slurry bubble column (Ⅳ)Modeling and simulation of bubble column with vertical pipe bundles

工业浆态床反应器一般都安装有密集的换热列管,列管束的存在使得速度和气含率的径向分布趋于陡峭,形成“烟囱效应”,目前对此还缺乏合适的流体力学模型进行定量描述。本文提出两点新思路以解决列管束的模拟问题：一是将密集列管束的影响作为体积源项而不是边界条件来考虑,在标准k-ε方程中增加与列管阻力相关的动量源、湍动源、耗散源本构关系;二是采用气泡群的径向升力和湍流扩散力平衡方程确定气含率径向分布。新模型中引入的阻力系数由流体力学文献给出,只有两个径向力和耗散参数需实验确定。模型计算的气含率和液速分布在宽泛的条件下与实验测量值符合良好,能够定量描述“烟囱效应”以及内构件参数对流动的影响。     

Rückvermischung in Blasensäulen mit Einbauten

Back-mixing in Bubble Columns Fitted with Internals. Interals installed in bubble column reactors serve mainly for heat transfer and for influencing (suppressing) liquid circulation. Reinforcement of mixing is observed for experimentally for internals subjected to longitudinal flow, which is attributable in limitation of transverse exchange and the resulting increase of axial eddy dimensions. The experimental findings can be readily described by the axial dispersion model for uniform cross sections and equations are given for estimating the dispersion coefficients of the gaseous and liquid phases as a function of the central liquid circulation velocity. Internals subjected to transverse flow hinder the establishment of a large scale circulatory motion and therefore suppress mixing on the bubble column. Two calculation procedures of differing model depth are presented which permit determination of concentration and temperature profiles in bubble column reactor cascades. Moreover, equations are given for estimating reflux conditions on sieve plates and bundled tube heat exchangers in cross flow which are based on experimental investigations.     

CFD modeling of slurry bubble column reactors for Fisher-Tropsch synthesis

Industrial bubble column reactors for Fischer-Tropsch (FT) synthesis include complex hydrodynamic, chemical and thermal interaction of three material phases: a population of gas bubbles of different sizes, a liquid phase and solid catalyst particles suspended in the liquid. In this paper, a CFD model of FT reactors has been developed, including variable gas bubble size, effects of the catalyst present in the liquid phase and chemical reactions, with the objective of predicting quantitative reactor performance information useful for design purposes. The model is based on a Eulerian multifluid formulation and includes two phases: liquid-catalyst slurry and syngas bubbles. The bubble size distribution is predicted using a Population Balance (PB) model. Experimentally observed strong influence of the catalyst particles concentration on the bubble size distribution is taken into account by including a catalyst particle induced modification of the turbulent dissipation rate in the liquid. A simple scaling modification to the dissipation rate is proposed to model this influence in the PB model. Additional mass conservation equations are introduced for chemical species associated with the gas and liquid phases. Heterogeneous and homogeneous reaction rates representing simplified FT synthesis are taken from the literature and incorporated in the model.Hydrodynamic effects have been validated against experimental results for laboratory scale bubble columns, including the influence of catalyst particles. Good agreement was observed on bubble size distribution and gas holdup for bubble columns operating in the bubble and churn turbulence regimes. Finally, the complete model including chemical species transport was applied to an industrial scale bubble column. Resulting hydrocarbon production rates were compared to predictions made by previously published one-dimensional semi-empirical models. As confirmed by the comparisons with available data, the modeling methodology proposed in this work represents the physics of FT reactors consistently, since the influence of chemical reactions, catalyst particles, bubble coalescence and breakup on the key bubble-fluid drag force and interfacial area effects are accounted for. However, heat transfer effects have not yet been considered. Inclusion of heat transfer should be the final step in the creation of a comprehensive FT CFD simulation methodology. A significant conclusion from the modeling results is that a highly localized FT reaction rate appears next to the gas injection region when the syngas flow rate is low. As the FT reaction is exothermal, it may lead to a highly concentrated heat release in the liquid. From the design perspective, the introduction of appropriate heat removal devices may be required.     

GAS MIXING IN SLUGGING AND TURBULENT FLUIDIZED BEDS

The gas phase mixing in a fluidized bed of glass beads (d_p = 0.362 mm) in the slugging and turbulent flow regimes has been studied in a 0.1 m-ID × 3.0 m high Plexiglas column.

The gas dispersion in the downstream of the bed has been described by a diffusion process with the axial and radial dispersion coefficients. The radial dispersion coefficient of the gas phase is nearly constant with the variation of gas velocity in the slugging flow regime, but it increases with an increase in gas velocity in the turbulent flow regime.

Appreciable backmixing of the gas phase is pronounced in the slugging flow regime whereas the lower gas backmixing is produced in the turbulent flow regime. The gas backmixing coefficient increases with an increase in gas velocity in the slugging flow regime, but it decreases slightly with an increase in gas velocity in the turbulent flow regime.

The radial mixing and backmixing coefficients of the gas in terms of Peclet numbers have been correlated with the relevant dimensionless parameters (U_g/U_mf, p_s/p_g, d_p/D_t).

The gas flow pattern in the bed has been well represented by a simplified model based on the two gas phases in the dilute and dense phases which are percolating through the bed in plug flow. The present model can predict the gas exchange coefficient between the phases, the fractions of the dilute phase, the interstitial gas in the dense phase, and the interstitial gas velocity in the bed.     

Ammonia absorption from a bubble expanding at a submerged orifice into water

To investigate the mechanism of gas absorption from a bubble containing soluble and insoluble components, a gaseous mixture of ammonia and nitrogen was bubbled into water. The growth curve, volume, surface area and shape of the growing bubbles were measured with parameters such as inlet gas composition, gas flow rate and gas chamber volume. The bubble volume decreased with the increasing composition of ammonia in a bubble, decreasing gas chamber volume and decreasing gas flow rate.To reasonably express the mass transfer from the bulk of a gas in a bubble to the bulk of a liquid, the overall mass transfer resistance was evaluated by the mass transfers in the gas phase, interface and liquid phase.The non-spherical bubble formation model combined with the overall mass transfer resistance estimated well experimental bubble shape, bubble volume at its detachment from an orifice, growth rate and mass transfer rate.Moreover, the change of concentration with bubble growth time and the fractional absorption during bubble formation were simulated.     

Transient gas–liquid mass transfer model for thin liquid films on structured solid packings

This paper describes a model for gas–liquid mass transfer through thin liquid films present on structured packings for gas–liquid operations under dispersed gas flow regime. The model has been derived for two cases: the absorption (or desorption) of a gaseous component into the liquid film and the transfer of the gaseous component through the liquid film to the packing surface where an infinitely fast reaction takes place. These cases have been solved for three bubble geometries: rectangular, cylindrical, and spherical. For Fourier numbers below 0.3, the model corresponds to Higbie’s penetration theory for both cases. The Sherwood numbers for cylindrical and spherical bubbles are 20% and 35% higher, respectively, than for rectangular bubbles. In case of absorption and Fourier numbers exceeding 3, the effect of bubble geometry becomes more pronounced. The Sherwood numbers for cylindrical and spherical bubbles now are 55% and 100% higher, respectively, than for rectangular bubbles. In case of an infinitely fast reaction at the packing surface, the Sherwood number corresponds to Whitman’s film theory (Sh=1$Sh=1$) for all bubble geometries. In this paper also practical approximations to the derived Sherwood numbers are presented. The approximations for both cases and all bubble geometries describe all the model data within an error of 4%. The application of the model has been demonstrated for three examples: (1) gas–liquid mass transfer for a structured packing; (2) gas–liquid mass transfer in a microchannel operated with annular flow; (3) gas–liquid mass transfer in a microchannel with Taylor flow.     

基于气泡群相间作用力模型的加压鼓泡塔流体力学模拟

目前,多数文献报道了冷态加压湍动鼓泡塔内流动特征,并且通过实验数据回归相关经验关联式。然而,此类关联式适用范围有限,难以直接外推到工业鼓泡塔反应器条件。因此,在FLUENT平台上建立了基于气泡群相间作用力的、动态二维加压鼓泡塔计算流体力学模型。通过数值模拟考察了操作压力为0.5~2.0 MPa,表观气速为0.20~0.31 m·s^-1,内径0.3 m鼓泡塔内流场特性参数分布,并且与冷态实验数据进行比较。结果表明,采用修正后的气泡群曳力模型、径向力平衡模型以及壁面润滑力模型描述气泡群相间作用力,能够较为准确地反映平均气含率和气含率径向分布随操作压力和表观气速变化的规律。     

Gas hold-up and liquid mixing at low and intermediate gas velocities I. Air-water system

Gas hold-up and liquid phase dispersion experiments have been carried out in a 0.06 m bubble column at varying liquid and gas velocities. The results obtained show that the coefficient of liquid mixing varies with the flow regime. The isotropic turbulence theory of Baird and Rice (Chem. Eng. J., 9 (1975) 171) was used to provide dimensionally consistent correlations for the chain bubbling, bubbly and churn turbulent flow regimes. The gas hold-up was determined to increase with gas velocity in the chain bubbling and bubbly flow regimes. The results obtained from this study also show that the Froude number represents a useful criterion for mapping flow regimes in vertical bubble columns.     

Quantifying sub-grid scale (SGS) turbulent dispersion force and its effect using one-equation SGS large eddy simulation (LES) model in a gas–liquid and a liquid–liquid system

The one-equation SGS LES model has shown promise in revealing flow details as compared to the Dynamic model, with the additional benefit of providing information on the modelled SGS-turbulent kinetic energy (Niceno et al., 2008). This information on SGS-turbulent kinetic energy (SGS-TKE) offers the possibility to more accurately model the physical phenomena at the sub-grid level, especially the modelling of the SGS-turbulent dispersion force (SGS-TDF). The use of SGS-TDF force has the potential to account for the dispersion of particles by sub-grid scale eddies in an LES framework, and through its use, one expects to overcome the conceptual drawback faced by Eulerian–Eulerian LES models. But, no work has ever been carried out to study this aspect. Niceno et al. (2008) could not study the impact of SGS-TDF effect as their grid size was comparable to the dispersed bubble diameter. A proper extension of research ahead would be to quantify the effect of sub-grid scale turbulent dispersion force for different particle systems, where the particle sizes would be smaller than filter-size. This work attempts to apply the concept developed by Lopez de Bertodano (1991) to approximate the turbulent diffusion of the particles by the sub-grid scale liquid eddies. This numerical experimentation has been done for a gas–liquid bubble column system (Tabib et al., 2008) and a liquid–liquid solvent extraction pump-mixer system ( [Tabib et al., 2010] and [28] ). In liquid–liquid extraction system, the organic droplet size is around 0.5 mm, and in bubble columns, the bubble size is around 3–5 mm. The simulations were run with mesh size coarser than droplet size in pump-mixer, and for bubble column, two simulations were run with mesh size finer and coarser than bubble diameter. The magnitude of SGS-TDF values in all the cases were compared with magnitude of other interfacial forces (like drag force, lift force, resolved turbulent dispersion force, force due to momentum advection and pressure). The results show that the relative magnitude of SGS-TDF as compared to other forces were higher for the pump-mixer than for the coarser and finer mesh bubble column simulations. This was because in the pump-mixer, the ratio of “dispersed phase particle diameter to the grid-size” was smaller than that for the bubble column runs. Also, the inclusion of SGS-TDF affected the radial hold-up, even though the magnitudes of these SGS-TDF forces appeared to be small. These results confirms that (a) the inclusion of SGS-TDF will have more pronounced effect for those Eulerian–Eulerian LES simulation where grid-size happens to be more than the particle size, and (b) that the SGS-TDF in combination with one-equation-SGS-TKE LES model serves as a tool to overcome a conceptual drawback of Eulerian–Eulerian LES model.     

垂直风冷翅片管中氨水鼓泡吸收特性

详细描述了垂直风冷翅片管吸收器中氨水鼓泡吸收的传热和传质过程。管外侧套用翅片,管内侧中氨水吸收溶液和氨气都从吸收器的底部流入、顶部流出。根据质量守恒方程和能量守恒方程建立了热质传递的微分数学模型。该模型分析了吸收器中两相流(即波动流、弹状流、泡状流)的变化,同时考虑了不同的两相流中气液相之间的热质传递以及两相流与管外空气之间的热量传递。通过解模型的微分方程,得到了一些重要参数(温度、摩尔分数)的局部值以及这些参数在吸收高度方向上的变化趋势。     

填料塔传质模型的研究——二维混合池随机模型

本文推导和提出了一个新的数学模型——二维混合池随机模型.它能用来模拟填料塔的液体流动和传质特性,以及计算塔中液、气两相浓度分布.该模型的主要特点是:(1)它通过调整混合池间轴向和径向的流动和混合,能很好地模拟填料塔复杂的液体流动状态;(2)模拟计算考虑了液体流动分布的随机性质.研究结果表明,填料塔塔径增大或填料层增高而产生的传质效率下降的原因主要是液体的非均匀流动、轴向混合的加剧和不完全的径向混合.     

Axial thrust of axial flow impellers

This paper presents an analysis of the axial thrust of axial flow high-speed impellers under a turbulent regime of flow of an agitated liquid. The axial thrust is calculated from the measured total axial force affecting the cylindrical fully baffled mixing vessel and from the radial profile of the axial component of the ensemble-averaged mean velocity in the impeller discharge stream. The results of experimentally determined values of the dimensionless criteria (thrust number and momentum number) are successfully compared with the axial thrust of the pitched blade impellers calculated from the theoretically predicted simplified radial profiles of the axial component of the mean velocity in the impeller discharge stream.