CFD simulation of particle suspension in a stirred tank

Particle suspension characteristics are predicted computationally in a stirred tank driven by a Smith turbine. In order to verify the hydrodynamic model and numerical method, the predicted power number and flow pattern are compared with designed values and simulated results from the literature, respectively. The effects of particle density, particle diameter, liquid viscosity and initial solid loading on particle suspension behavior are investigated by using the Eulerian–Eulerian two-fluid model and the standard k–? turbulence model. The results indicate that solid concentration distribution depends on the flow field in the stirred tank. Higher particle density or larger particle size results in less homogenous distribution of solid particles in the tank. Increasing initial solid loading has an adverse impact on the homogeneous suspension of solid particles in a low-viscosity liquid, whilst more uniform particle distribution is found in a high-viscosity liquid.     

Development and elaboration of numerical method for simulating gas–liquid–solid three-phase flows based on particle method

A numerical method for simulating gas–liquid–solid three-phase flows based on the moving particle semi-implicit (MPS) approach was developed in this study. Computational instability often occurs in multiphase flow simulations if the deformations of the free surfaces between different phases are large, among other reasons. To avoid this instability, this paper proposes an improved coupling procedure between different phases in which the physical quantities of particles in different phases are calculated independently. We performed numerical tests on two illustrative problems: a dam-break problem and a solid-sphere impingement problem. The former problem is a gas–liquid two-phase problem, and the latter is a gas–liquid–solid three-phase problem. The computational results agree reasonably well with the experimental results. Thus, we confirmed that the proposed MPS method reproduces the interaction between different phases without inducing numerical instability.     

Numerical study of elbow erosion due to sand particles under annular flow considering liquid entrainment

Sand particle erosion is always a challenge in natural gas production. In particular, the erosion in gas–liquid–solid annular flow is more complicated. In this study, a three-phase flow numerical model that couples the volume of fluid multiphase flow model and the discrete phase model was developed for prediction of erosion in annular flow. The ability of the numerical model to simulate the gas–liquid annular flow is validated through comparison with the experimental data. On the basis of the above numerical model, the phase distribution in the pipe was analyzed. The liquid entrainment behavior was reasonably simulated through the numerical model, which guaranteed the accuracy of predicting the particle erosion. Additionally, four erosion prediction models were used for the erosion calculation, among them, the Zhang et al. erosion model predicted the realistic results. Through the analysis of the particle trajectory and the particle impact behavior on the elbow, the cushion effect of the liquid film on the particles and the erosion morphology generation at the elbow were revealed.     

Simulating gas–liquid multiphase flow using meshless Lagrangian method

A multiphase flow model has been established based on a moving particle semi‐implicit method. A surface tension model is introduced to the particle method to improve the numerical accuracy and stability. Several computational techniques are employed to simplify the numerical procedure and further improve the accuracy. A particle fraction multiphase flow model is developed and verified by a two‐phase Poiseuille flow. The multiphase surface tension model is discussed in detail, and an ethanol drop case is introduced to verify the surface tension model. A simple dam break is simulated to demonstrate the improvements with various modifications in particle method along with a new boundary condition. Finally, we simulate several bubble rising cases to show the capacity of this new model in simulating gas–liquid multiphase flow with large density ratio difference between phases. The comparisons among numerical results of mesh‐based model, experimental data, and the present model, indicate that the new multiphase particle method is acceptable in gas–liquid multiphase fluids simulation. Copyright © 2014 John Wiley & Sons, Ltd.     

Semi-automatic image analysis methodology for the segmentation of bubbles and drops in complex dispersions occurring in bioreactors

Characterization of multiphase systems occurring in fermentation processes is a time-consuming and tedious process when manual methods are used. This work describes a new semi-automatic methodology for the on-line assessment of diameters of oil drops and air bubbles occurring in a complex simulated fermentation broth. High-quality digital images were obtained from the interior of a mechanically stirred tank. These images were pre-processed to find segments of edges belonging to the objects of interest. The contours of air bubbles and oil drops were then reconstructed using an improved Hough transform algorithm which was tested in two, three and four-phase simulated fermentation model systems. The results were compared against those obtained manually by a trained observer, showing no significant statistical differences. The method was able to reduce the total processing time for the measurements of bubbles and drops in different systems by 21–50% and the manual intervention time for the segmentation procedure by 80–100%.     

固体火箭燃气射流驱动液柱过程的CFD分析

固体火箭燃气射流驱动液柱过程会产生一个复杂的非稳态多相流场,为了研究液柱对固体火箭发动机工作过程中射流流场的降温效果,并揭示燃气冲击液柱的流动演化和气水之间的相互作用,利用FLUENT软件中耦合了液态水汽化方程的VOF多相流计算模型对燃气与液柱之间的耦合流动及相变过程进行了数值模拟,并与无液柱情况下射流流场的计算结果进行了对比分析。计算结果表明,当有液柱平衡体时射流流场中的压力、温度、速度波动幅度均减小,减弱了射流流场中的湍流脉动强度;液柱与燃气之间的汽化以及液柱的阻碍作用减小了射流流场的轴向发展位移,尾管后的完全发展射流流场核心区域内的压力峰值降低了0.9 MPa,温度峰值降低了503 K,速度峰值降低了291 m/s,验证了实验中液柱对燃气射流流场的降温效果。     

Estimation of solid concentration in solid–liquid two-phase flow in horizontal pipeline using inverse-problem approach

In this study, an inverse-problem method was applied to estimate the solid concentration in a solid–liquid two-phase flow. An algebraic slip mixture model was introduced to solve the forward problem of solid–liquid convective heat transfer. The time-average conservation equations of mass, momentum, energy, as well as the volume fraction equation were computed in a computational fluid dynamics (CFD) simulation. The solid concentration in the CFD model was controlled using an external program that included the inversion iteration, and an optimal estimation was performed via experimental measurements. Experiments using a fly-ash–water mixture and sand–water mixture with different solid concentrations in a horizontal pipeline were conducted to verify the accuracy of the inverse-problem method. The estimated results were rectified using a method based on the relationship between the estimated results and estimation error; consequently, the accuracy of the corrected inversion results improved significantly. After a verification through experiments, the inverse-problem method was concluded to be feasible for predicting the solid concentration, as the estimation error of the corrected results was within 7% for all experimental samples for a solid concentration of less than 50%. The inverse-problem method is expected to provide accurate predictions of the solid concentration in solid–liquid two-phase flow systems.     

Research on multiphase flows in Thermo-Energy Engineering Institute of Southeast University

Multiphase flows have received increasing attention over the past decades. This paper describes the research carried out in Thermo-Energy Engineering Institute of Southeast University in recent years, focusing on several common issues associated with multiphase flows in industry, such as: boiling of falling film and complex structure of gas–liquid flow under large difference in temperature, free surface flows involving liquid jets and drop formation, mixing behaviors of gas–liquid–solid three-phase flow, and fluidization characteristics of cylindrical particles. Numerical methods ranging from empirical to CFD models were developed for predictions, and experimental works were essentially conducted for validation and modification. For all cases, simulated results were validated with experiments and good agreements were obtained. Based on the combined modeling and experimental approach, fundamental understanding of multiphase processes in a specific circumstance is achieved under conditions relevant to the actual industrial-scale, such as transport phenomena, flow patterns, fluid dynamics and interactions between phases.     

Effects of particle size and concentration on bubble coalescence and froth formation in a slurry bubble column

A new approach for simulating the formation of a froth layer in a slurry bubble column is proposed. Froth is considered a separate phase, comprised of a mixture of gas, liquid, and solid. The simulation was carried out using commercial flow simulation software (FIRE v2014) for particle sizes of 60–150 μm at solid concentrations of 0–40 vol%, and superficial gas velocities of 0.02–0.034 m/s in a slurry bubble column with a hydraulic diameter of 0.2 m and height of 1.2 m. Modelling calculations were conducted using a Eulerian–Eulerian multiphase approach with k–ε turbulence. The population balance equations for bubble breakup, bubble coalescence rate, and the interfacial exchange of mass and momentum were included in the computational fluid dynamics code by writing subroutines in Fortran to track the number density of different bubble sizes. Flow structure, radial gas holdup, and Sauter mean bubble diameter distributions at different column heights were predicted in the pulp zone, while froth volume fraction and density were predicted in the froth zone. The model was validated using available experimental data, and the predicted and experimental results showed reasonable agreement. To demonstrate the effect of increasing solid concentration on the coalescence rate, a solid-effect multiplier in the coalescence efficiency equation was used. The solid-effect multiplier decreased with increasing slurry concentration, causing an increase in bubble coalescence efficiency. A slight decrease in the coalescence efficiency was also observed owing to increasing particle size, which led to a decrease in Sauter mean bubble diameter. The froth volume fraction increased with solid concentration. These results provide an improved understanding of the dynamics of slurry bubble reactors in the presence of hydrophilic particles.     

一种基于黎曼解处理大密度比多相流SPH的改进算法

多相流界面存在密度、黏性等物理场间断,直接采用传统光滑粒子水动力学(smoothedparticle hydrodynamics,SPH)方法进行数值模拟,界面附近的压力和速度存在震荡.一套基于黎曼解能够处理大密度比的多相流SPH计算模型被提出,该模型利用黎曼解在处理接触间断问题方面的优势,将黎曼解引入到SPH多相流计算模型中,为了能够准确求解多相流体物理黏性、减小黎曼耗散,对黎曼形式的SPH动量方程进行了改进,又将Adami固壁边界与黎曼单侧问题相结合来施加多相流SPH固壁边界,同时模型中考虑了表面张力对小尺度异相界面的影响,该模型没有添加任何人工黏性、人工耗散和非物理人工处理技术,能够反应多相流真实物理黏性和物理演变状态.采用该模型首先对三种不同粒子间距离散下方形液滴震荡问题进行了数值模拟,验证了该模型在处理异相界面的正确性和模型本身的收敛性;后又通过对Rayleigh--Taylor不稳定、单气泡上浮、双气泡上浮问题进行了模拟计算,结果与文献对比吻合度高,异相界面捕捉清晰,结果表明,本文改进的多相流SPH模型能够稳定、有效的模拟大密度比和黏性比的多相流问题.      

An impedance probe for the measurements of liquid hold-up and mixing time in two/three-phase stirred tank reactors

A new probe based on the measurement of the electrical impedance has been developed to measure liquid hold-up in gas/liquid, solid/liquid and gas/solid/liquid stirred tank reactors. It allows measurements of liquid hold-up and mixing time to be made in stirred tanks. The main advantage of the new probe is that it is absolutely non-intrusive, because it uses the shaft and the baffles' support as electrodes, and that it can be used both for laboratory scale reactors as well as for industrial stirred tank reactors. The relation between impedance and liquid hold-up under loading conditions closely follows the predictions made by means of the Bruggeman model. Therefore, the new probe does not need any calibration, in that the liquid hold-up can be theoretically computed by the measurement of impedance. Received: 1 January 2000/Accepted: 8 March 2001     

Venturi-type fluidic sampler for liquid–solid mixtures

Static-type samplers are required for sampling corrosive, toxic, high-temperature, or radioactive liquid–solid fluids. We have designed a compact reverse flow diverter pumping system for transferring liquid–solid mixtures. In accordance with the Venturi principle, an acceptable volume of liquid–solid fluid is automatically collected into a sampling bottle. The effects of sampling needle sizes, sectional area of the T-section, solid concentration, and liquid viscosity on the performance of fluidic samplers were experimentally investigated. The sample volume increased upon the reduction of the sampling needle length and the increase of the sectional area of the T-section, but decreased with the increase of solid concentration and liquid viscosity. Unbiased samples of acceptable volume were produced by the proposed fluidic sampler, even at 10.21 mPa s liquid viscosity, 35 wt% solid concentration, and 6.74 m sampling height.     

On the stability of Taylor bubbles inside a confined highly porous medium

This work focuses on the local hydrodynamics of a multiphase gas–liquid flow forced into an innovative medium of high porosity (96%): an open cell solid foam. The gas (nitrogen) and liquid (ethanol) phases are injected at constant flow-rates in a millichannel to form a well-controlled Taylor flow which enters the porous medium. Based on a fluorescence technique, the apparent liquid holdup in the porous medium is quantified, and its evolution in time and along the porous medium extracted from spatiotemporal diagrams. The analysis of the main frequency, when varying the gas–liquid flow-rate ratio, leads to the identification of two hydrodynamic regimes. A model based on a scaling analysis is proposed to quantify the dimensionless numbers describing the transition between both regimes. It points out that the bubble length fixed by the Taylor flow is the control parameter. The model prediction of the critical bubble length at which the transition occurs is in good agreement with the experimental observations.     

Fundamental validation of the finite volume particle method for 3D sloshing dynamics

The use of the finite volume particle (FVP) method is validated for three‐dimensional sloshing dynamics with a free surface by comparing with results from experiments. In the first part, two typical sloshing experiments for a single liquid phase are simulated, and slosh characteristics that include the free surface behavior and hydrodynamic pressure are reported. Moreover, the influences of the circular wall geometry and spatial resolution in the simulation are studied in a sensitivity analysis. In the second part, two sloshing problems with solid bodies are simulated to preliminarily verify the applicability of the FVP method to three‐dimensional solid bodies' motion in liquid flow. Good agreement between simulations and corresponding experiments indicates that the present FVP method well reproduces three‐dimensional sloshing behavior. Copyright © 2010 John Wiley & Sons, Ltd.     

Direct simulation of multiphase flows with modeling of dynamic interface contact angle

We describe a modeling technique for dynamic contact angle between a phase interface and a solid wall using a generalized Navier boundary condition in the context of a front-tracking-based multiphase method. The contact line motion is determined by the generalized Navier slip boundary condition in order to eliminate the infinite shear stress at the contact line. Applying this slip boundary condition only to the interface movement with various slip ratios shows good agreement with experimental results compared to allowing full fluid slip along the solid surface. The interface slip model performs well on grid convergence tests using both the slip ratio and slip length models. A detailed energy analysis was performed to identify changes in kinetic, surface, and potential energies as well as viscous and contact line dissipation with time. A friction coefficient for contact line dissipation was obtained based on the other computed energy terms. Each energy term and the friction coefficient were compared for different grid resolutions. The effect of varying the slip ratio as well as the contact angle distribution versus contact line speed was analyzed. The behavior of drop impact on a solid wall with different advancing and receding angles was investigated. Finally, the proposed dynamic contact model was extended to three dimensions for large-scale parallel calculations. The impact of a droplet on a solid cylinder was simulated to demonstrate the capabilities of the proposing formulation on general solid structures. Widely different contact angles were tested and showed distinctive characteristic behavior clearly.     

湍流横掠固定颗粒的全尺度直接数值模拟

气固两相流模拟中,当固相尺度接近或大于Kolmogorov尺度时,普通的点源模型将不再适用,固体相的体积效应和表面效应将对流体相产生显著的影响。通过采用直接数值模拟方法,结合内嵌边界方法对湍流中不同湍流强度流体横掠大于Kolmogorov尺度的固相颗粒进行了全尺度模拟,讨论分析了在两种湍流度下方形颗粒对湍流的调制影响以及颗粒的受力情况。     

Direct numerical simulations of gas–solid–liquid interactions in dilute fluids

The dynamic interactions between gas bubbles, rigid particles and liquid can lead to profound nonlinearities in the aggregate behavior of a multiphase fluid. Predicting the nonlinear dynamics of the multiphase mixture hence requires understanding how the phases interact at the scale of individual interfaces, but these interactions are notoriously difficult to resolve in models. The goal of this paper is to develop and validate a computational method capable of capturing the complex flow interactions between gas bubbles and rigid particles immersed in a Newtonian liquid. We focus on multiphase systems that are dilute enough for the solid and gas components to move through and be moved by the ambient liquid. We use level sets with a topology-preserving advection scheme to track the gas interfaces. To include the motion of the rigid particles, we couple distributed Lagrange multipliers to an immersed-boundary method. The high viscosity contrast between the liquid and the gas requires both time splitting and approximate factorization to efficiently solve the governing equations consisting of the conservation of mass, momentum and energy. To resolve interactions between interfaces that vary drastically in size, we refine our mesh adaptively in the vicinity of the boundary.     

Three-dimensional multi-relaxation time lattice-Boltzmann model for the drop impact on a dry surface at large density ratio

Extensive application of the multiphase lattice Boltzmann model to realistic fluid flows is often restricted by the numerical instabilities induced at high liquid-to-gas density ratios, and at low viscosities. In this paper, a three-dimensional multi-relaxation time (MRT) lattice Boltzmann model with an improved forcing scheme is reported for simulating multiphase flows at high liquid-to-gas density ratios and relatively high Reynolds numbers. The model is based on a recently presented model in the literature. Firstly, the MRT multiphase model is evaluated by verifying Laplace’s law and achieving thermodynamic consistency for a static droplet. Then, a relationship between the fluid–solid interaction potential parameter and contact angle is investigated. Finally, the improved three-dimensional MRT Lattice Boltzmann model is employed in the simulation of the impingement of a liquid droplet onto a flat surface for a range of Weber and Reynolds numbers. The dynamics of the droplet spreading is reproduced and the predicted maximum spread factor is in good agreement with experimental data published in the literature.     

Flow visualization of shock/water column interactions

The breakup of a liquid droplet induced by a high speed gas stream is a typical multiphase flow problem. The shock/droplet interaction is the beginning stage of the droplet breakup. Therefore, investigation of the shock/droplet interactions would be a milestone for interpreting the mechanism of the droplet breakup. In this study, a compressible multiphase solver with a five-equation model is successfully developed to study shock/water column interactions. For code validation, interface-only, gas–gas shock tube, and gas–liquid shock tube problems are first computed. Subsequently, a planar shock wave interacting with a water column is simulated. The transmitted wave and the alternative appearances of local high- and low-pressure regions inside the water column are observed clearly. Finally, a planar shock wave interacting with two water columns is investigated. In this work, both horizontal and vertical arrangements of two water columns are studied. It is found that different arrangements can result in the diversity of the interacting process. The complex flow structures generated by shock/water column interactions are presented by flow-visualization techniques.      

COMPARISON OF ANALYTICAL SOLUTIONS FOR CMSMPR CRYSTALLIZER WITH QMOM POPULATION BALANCE MODELING IN FLUENT

Fluent version 6.2 computational fluid dynamics environment has been enhanced with a population balance capability that operates in conjunction with its multiphase calculations to predict the particle size distribution within the flow field. The population balance is solved by the quadrature method of moments （QMOM）. Fluent＇s prediction capabilities are tested by using a 2-dimensional analogy of a constantly stirred tank reactor with a fluid flow compartment that mixes the fluid quickly and efficiently using wall movement and has a feed stream and a product stream. The results of these Fluent simulations using QMOM population balance solver are compared to steady state analytical solutions for the population balance in a stirred tank where 1） growth, 2） aggregation, and 3） breakage, take place separately and 4） combined nucleation and growth and 5） combined nucleation, growth and aggregation take place. The results of these comparisons show that the moments of the population balance are accurately predicted for nucleation, growth, aggregation and breakage when the flow field is turbulent. With laminar flow the mixing is not ideal and as a result the steady state well mixed solutions are not accurately simulated.