Modeling of turbulent gas–liquid bubbly flows using stochastic Lagrangian model and lattice-Boltzmann scheme

In this paper we present detailed, three-dimensional and time-resolved simulations of turbulent gas–liquid bubbly flows. The continuous phase is modeled using a lattice-Boltzmann (LB) scheme. The scheme solves the large-scale motions of the turbulent flow using the filtered conservation equations, where the Smagorinsky model has been used to account for the effects of the sub-filter scales. A Lagrangian approach has been used for the dispersed, bubbly phase. That is we update the equations of motion of individual bubbles. It is shown that the incorporation of the sub-filter scale fluid fluctuations along the bubble trajectory improves the predictions. Collisions between bubbles are described by the stochastic inter-particle collision model based on kinetic theory developed by Sommerfeld (2001). It has been found that the collision model not only dramatically decreases computing time compared to the direct collision method, but also provides an excellent computational efficiency on parallel platforms. Furthermore, it was found that the presented modeling technique provides very good agreement with experimental data for mean and fluctuating velocity components.     

Euler–Lagrange modeling of a gas–liquid stirred reactor with consideration of bubble breakage and coalescence

Simulations of a gas–liquid stirred reactor including bubble breakage and coalescence were performed. The filtered conservation equations for the liquid phase were discretized using a lattice‐Boltzmann scheme. A Lagrangian approach with a bubble parcel concept was used for the dispersed gas phase. Bubble breakage and coalescence were modeled as stochastic events. Additional assumptions for bubble breakup modeling in an Euler–Lagrange framework were proposed. The action of the reactor components on the liquid flow field was described using an immersed boundary condition. The predicted number‐based mean diameter and long‐term averaged liquid velocity components agree qualitatively and quantitatively well with experimental data for a laboratory‐scale gas–liquid stirred reactor with dilute dispersion. Effects of the presence of bubbles, as well as the increase in the gas flow rate, on the hydrodynamics were numerically studied. The modeling technique offers an alternative engineering tool to gain detailed insights into complex industrial‐scale gas–liquid stirred reactors. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Predicting the diameters of droplets produced in turbulent liquid–liquid dispersion

The droplet size distribution in liquid–liquid dispersions is a complex convolution of impeller speed, impeller type, fluid properties, and flow conditions. In this work, we present three a priori modeling approaches for predicting the droplet diameter distributions as a function of system operating conditions. In the first approach, called the two-fluid approach, we use high-resolution solutions to the Navier–Stokes equations to directly model the flow of each phase and the corresponding droplet breakup/coalescence events. In the second approach, based on an Eulerian–Lagrangian model, we describe the dispersed fluid as individual spheres undergoing ongoing breakup and coalescence events per user-defined interaction kernels. In the third approach, called the Eulerian–Parcel model, we model a sub-set of the droplets in the Eulerian–Lagrangian model to estimate the overall behavior of the entire droplet population. We discuss output from each model within the context of predictions from first principles turbulence theory and measured data.     

A model for the consolidation of warp‐knitted reinforced laminates

A model for the consolidation of thermoplastic composites reinforced with a warp‐knitted fabric was developed. The evolution of void content during composite consolidation achieved via film stacking was related to the processing parameters and the material properties. Since the knitting process results in local variations of fiber volume fractions even within a tow, the flow mechanisms are not identical to those occurring in homogeneously dispersed fibers. Two different types of micro‐scale porosities were determined and a unit cell geometry was proposed for modeling. The reduction of the effective pressure due to the gas entrapment was also accounted for. Predictions of the variation of the void content as a function of time, pressure and temperature were compared to experimental data. As a good correlation was found between experiments and predictions, this approach can thus be applied to the consolidation of textile reinforcements in which the tows are locally compressed.     

The experimental observation and modelling of microdroplet formation within a plastic microcapillary array

This paper reports an experimental study of the formation of a two-phase liquid mixture in a circular capillary tube of 0.74 mm diameter. Organic liquid, the continuous phase, flowed through the capillary. Aqueous liquid, the dispersed phase, was injected through a hypodermic entering the side of the capillary and a stream of aqueous droplets was formed in the flowing organic liquid. The observed droplet diameters depended strongly on the ratio of the flow-rates between the dispersed and continuous phases: droplet diameters ranged between 480 and 64 μm. A simple model gave good predictions, matching the data and showing how the droplet diameter is dependant on the flow rates of the two phases. The flow geometry was similar to the T-junction configuration used for emulsion formation in microfluidic devices and was fabricated from an extruded plastic capillary array termed a microcapillary film (MCF).     

湿法脱硫系统弧形板带钩除雾器流场数值模拟与分析

采用计算流体力学方法对除雾器内流场进行数值模拟.除雾器内气液两相流动的数值计算主要用基于欧拉-拉格朗日方法的离散相模型.流体被当做连续相,其流场可通过时均N-S方程求得,而离散相液滴的轨迹则可通过已经计算的流场追踪得到.通过计算不同工作参数下除雾器的除雾效率和压降,分析并总结了不同参数对除雾效率和压降的影响规律,对除雾...     

Liquid flow and phase holdup—measurement and CFD modeling for two-and three-phase bubble columns

Bubble columns are an important class of contacting devices in chemical industry and biotechnology. Their simple setup makes them ideal reactors for two- and three-phase operations such as fermentations or heterogeneous catalysis. Still, design and operation of these reactors is subject to widely empirical scale-up strategies. With recent advances in the development of measurement techniques, a more detailed approach to the development of optimized reactors for specific operations should become possible. This report is based on detailed measurements of local dispersed phase holdups in a pilot plant-sized bubble column operated at high superficial gas velocities and solid holdups. It deals with the influence of superficial gas velocity, solid loading and sparger geometry on measured and computed liquid flow velocities and holdup distributions. Liquid velocity measurements have been performed using the electrodiffusion method, modeling calculations have been carried out using the computational fluid dynamics (CFD) code CFX-4.3. Measurement results presented here give an insight into the development of liquid circulation and fluctuating velocity distribution depending on superficial gas velocity, solid loading and sparger geometry. CFD results implementing a multi-fluid model with k-ε turbulence and special momentum exchange terms for direct gas-solid interactions show that, even on standard PC workstations, this kind of computations can deliver qualitatively reasonable agreement with measurements.     

Numerical modelling and simulation of pulverized solid‐fuel combustion in swirl burners

A finite‐volume numerical model for computer simulation of pulverized solid‐fuel combustion in furnaces with axisymmetric‐geometry swirl burner is presented. The simulation model is based on the k ? ε single phase turbulence model, considering the presence of the dispersed solid phase via additional source terms in the gas phase equations. The dispersed phase is treated by the particle source in cell (PSIC) method. Solid fuel particle devolatilization, homogenous and heterogeneous chemical reaction processes are modelled via a global combustion model. The radiative heat transfer equation is also resolved using the finite volume method. The numerical simulation code is validated by comparing computational and experimental results of pulverized coal in an experimental furnace equipped with a swirl burner. It is shown that the developed numerical code can successfully predict the flow field and flame structure including swirl effects and can therefore be used for the design and optimization of pulverized solid‐fuel swirl burners.     

Numerical and experimental study on the effect of solid particle sphericity on cyclone pressure drop

The continuous flow inside cyclone separator is usually simulated by solving the Reynolds averaged Navier–Stokes equations in Eulerian reference frame whereas the dispersed phase is modeled using Lagrangian approach. Although these methods have had a remarkable success, more advanced ideas are needed to model particulate phase in cyclones, especially the non-spherical shaped particles. Numerical simulation is verified with experimental results for the gas-solid flow in a cyclone separator. Reynolds Averaged Navier–Stokes equations (RANS) employing the RNG-based k–ε turbulence model are used to simulate the gas phase. 3-D particle tracking procedure is used for the solid phase. Three different equations for the drag coefficient are utilized in the numerical modeling to acquire more understanding of the behavior of non-spherical particles in cyclones. Computations resulted in the difference of pressure between the inlet and exit of the cyclone, and results are compared with experimental data. Experiments included measuring the separation efficiency of different shapes and sizes of particles. The results indicate that the CFD simulation can effectively reveal the pressure drop behavior as well as separation efficiency of gas-non-spherical particle flow in cyclone.     

Acceleration of CFD simulation of gas-solid flow by coupling macro-/meso-scale EMMS model

Gas-solid flow features significant dynamic multi-scale structure; multi-scale modeling is therefore in order. In this article, the macro-scale EMMS model was coupled with a two-fluid method (TFM) elaborated by the meso-scale EMMS model resolving sub-grid scale heterogeneity to simulate the hydrodynamics of circulating fluidized bed (CFB) risers. The overall flow distribution under the steady state was approximately predicted by the macro-scale EMMS model, which serves as the initial condition for meso-scale TFM simulations reproducing the dynamic behavior of heterogeneous gas-solid flows. Using the solid circulation flux as criterion, it was shown that this coupling approach can significantly reduce the time required to reach the statistically steady state, as compared to the packed bed or homogeneously dispersed initial condition. It also suggests a general approach to speedup dynamic simulation in the multi-scale paradigm of computation.     

流体-固体两相流的数值模拟

鉴于流体 -固体两相流及其数值模拟在化学工程中愈来愈广泛的应用 ,本文综述了Euler坐标系下流体相湍流模型、颗粒轨道模型以及流体 -颗粒双流体模型的基本原理和数值模拟方法 ;对相间耦合和颗粒间的相互作用也进行了介绍 ,特别是对能详细描述多颗粒间相互作用的颗粒离散单元法在流体 -固体两相流中的应用进行了详细描述 ;在评述各模型的优缺点和分析目前存在的问题的基础上 ,提出了今后的发展方向     

Sequential and iterative architectures for distributed model predictive control of nonlinear process systems

In this work, we focus on distributed model predictive control of large scale nonlinear process systems in which several distinct sets of manipulated inputs are used to regulate the process. For each set of manipulated inputs, a different model predictive controller is used to compute the control actions, which is able to communicate with the rest of the controllers in making its decisions. Under the assumption that feedback of the state of the process is available to all the distributed controllers at each sampling time and a model of the plant is available, we propose two different distributed model predictive control architectures. In the first architecture, the distributed controllers use a one‐directional communication strategy, are evaluated in sequence and each controller is evaluated only once at each sampling time; in the second architecture, the distributed controllers utilize a bi‐directional communication strategy, are evaluated in parallel and iterate to improve closed‐loop performance. In the design of the distributed model predictive controllers, Lyapunov‐based model predictive control techniques are used. To ensure the stability of the closed‐loop system, each model predictive controller in both architectures incorporates a stability constraint which is based on a suitable Lyapunov‐based controller. We prove that the proposed distributed model predictive control architectures enforce practical stability in the closed‐loop system and optimal performance. The theoretical results are illustrated through a catalytic alkylation of benzene process example. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

CFD simulation of the hydrodynamics in an internal air-lift reactor with two different configurations

Computational fluid dynamics (CFD) was used to investigate the hydrodynamic parameters of two internal airlift bioreactors with different configurations. Both had a riser diameter of 0.1 m. The model was used to predict the effect of the reactor geometry on the reactor hydrodynamics. Water was utilized as the continuous phase and air in the form of bubbles was applied as the dispersed phase. A two-phase flow model provided by the bubbly flow application mode was employed in this project. In the liquid phase, the turbulence can be described using the k-? model. Simulated gas holdup and liquid circulation velocity results were compared with experimental data. The predictions of the simulation are in good agreement with the experimental data.     

Modeling fluid behavior and droplet interactions during liquid-liquid separation in hydrocyclones

A mechanical separation process in a hydrocyclone is described in which disperse water droplets are separated from a continuous diesel fuel phase. This separation process is influenced by droplet-droplet interaction effects like droplet breakup and coalescence resulting in a change of droplet size distribution. A simulation model is developed coupling the numerical solution of the flow field in the hydrocyclone based on computational fluid dynamics with population balances. The droplet size distribution is discretized and each discrete droplet size fraction is assumed to be an individual phase within a multiphase-mixture model. The droplet breakup and coalescence rates are defined as mass transfer rates between the discrete phases by the aid of user-defined functions. All model equations are solved with the CFD software package FLUENT™. The investigations show the impact of the cyclone geometry on the coupled population and separation dynamics. Cyclone separators with an optimized geometry show less steep velocity gradients increasing the coalescence rates and improving the separation efficiency. The calculated droplet size distributions at the cyclone overflow and at the underflow show good accordance with experimental data. The basic modeling approach can be extended and adapted to other disperse multiphase flow systems.     

Micromechanic modeling and analysis of the flow regimes in horizontal pneumatic conveying

Pneumatic conveying is an important technology for industries to transport bulk materials from one location to another. Different flow regimes have been observed in such transportation processes, but the underlying fundamentals are not clear. This article presents a three‐dimensional (3‐D) numerical study of horizontal pneumatic conveying by a combined approach of discrete element model for particles and computational fluid dynamics for gas. This particle scale, micromechanic approach is verified by comparing the calculated and measured results in terms of particle flow pattern and gas pressure drop. It is shown that flow regimes usually encountered in horizontal pneumatic conveying, including slug flow, stratified flow, dispersed flow and transition flow between slug flow and stratified flow, and the corresponding phase diagram can be reproduced. The forces governing the behavior of particles, such as the particle–particle, particle‐fluid and particle‐wall forces, are then analyzed in detail. It is shown that the roles of these forces vary with flow regimes. A general phase diagram in terms of these forces is proposed to describe the flow regimes in horizontal pneumatic conveying. © 2011 American Institute of Chemical Engineers AIChE J, 2011     

Analysis of Particle Transport and Deposition of Micron-Sized Particles in a 90° Bend Using a Two-Fluid Eulerian–Eulerian Approach

Two-phase flows involving dispersed particle and droplet phases are common in a variety of natural and industrial processes, such as aerosols, blood flow, emulsions, and gas-catalyst systems. For sufficiently dilute particle/aerosol phases, a simplified one-way coupling is often assumed, in which the continuous primary phase is unaffected by the presence of the dispersed secondary phase and standard CFD methods can be applied. To predict the transport and deposition of the particle phase, typically a Lagrangian particle-tracking or Eulerian one-fluid/two-phase drift-flux approach is used. Here, a full two-fluid Eulerian modeling approach is presented for coarse particles (>1 μm), in which transport equations are numerically solved for both particle-phase continuity and particle-phase momentum. Simulation results were obtained for a laminar flow regime (Re 100 and 1000) in a 90° elbow, and the effects of grid topology and resolution were investigated. Additionally, gravity effects were considered for both Re cases. Results using this full two-fluid Eulerian approach were validated against experimental data and other computational studies. One key novel contribution of this work is presentation of a simple algorithm for stabilizing the Eulerian particle-phase equation. To the authors' knowledge, this is the first study documenting a full two-fluid Eulerian approach for dilute particle phases in laminar flow on unstructured (prism/tetrahedral) meshes. The results show the potential of the two-fluid approach for providing a useful alternative to the more typical Lagrangian approach for prediction of coarse-particle transport and wall deposition.

Copyright 2015 American Association for Aerosol Research     

Multi‐Phase‐Multi‐Size‐Group Model for the Inclusion of Population Balances into the CFD Simulation of Gas‐Liquid Bubbly Flows

A CFD model for the simulation of gas‐liquid bubbly flow is developed. In the model, the multi‐phase flow is simulated by an Eulerian‐Eulerian approach using several phase definitions (from 3 to 10). The bubble size distribution is simulated by a solution of the discretized population balance equation with coalescence and break‐up of bubbles. The number of the discretized population balance equations in the model is larger than the number of the phases used in the flow field simulation. A desired accuracy in the simulation can be achieved by choosing a suitable number of phases as a compromise between accuracy and computational cost. With this model, more detailed flow hydrodynamics and bubble size distribution can be obtained. The model was tested with different operating conditions and for different numbers of dispersed phases in a bubble column, and was verified with a bubble size distribution obtained experimentally.     

Scale-up of Microfiltration Processes

A flow rate and resistance-based approach for upscaling of microfiltration processes from lab scale to process scale is presented, in correlation with biopharmaceutical processes. Basic element is the modeling of filtration curves using a resistance-in-series model based on the Darcy equation. The influences of the filtration setup and the fouling layer are described as additional resistances that change in course of filtration. The necessary parameters, such as setup resistances and filtration areas, are determined by water flow rate measurements. The model is validated by filtration of a particulate test solution. The presented approach can be used for constant flow and constant pressure driven filtration processes.     

Deacidification of corn oil by solvent extraction in a perforated rotating disc column

The deacidification of corn oil by continuous liquid-liquid extraction was investigated in a rotating disc column. The solvent was ethanol containing approximately 6% water. The influence of rotor speed, oil phase flow, and column geometry upon the dispersed phase holdup and the mass transfer efficiency was studied. The dispersed phase holdup increased with the increase of rotor speed and oil phase flow. Pratt's equation was used for calculating the characteristic velocity. An inverse relation was observed between the characteristic velocity and rotor speed, which is different from data previously reported in the literature. The estimated volumetric mass transfer coefficients increased as rotor speed and oil phase flow increased. The experimental results proved that it is feasible to obtain a refined oil with an oleic acid content less than 0.3 wt% by continuous solvent extraction. They also indicated that the corresponding loss of neutral oil was less than 5 wt%. Such value for the loss of neutral oil is significantly lower than the results reported in the literature for alkali or physical refining of corn oil.