Eulerian-Lagrangian Numerical Scheme for Simulating Advection, Dispersion, and Transient Storage in Streams and a Comparison of Numerical Methods

Past applications of one-dimensional advection, dispersion, and transient storage zone models have almost exclusively relied on a central differencing, Eulerian numerical approximation to the nonconservative form of the fundamental equation. However, there are scenarios where this approach generates unacceptable error. A new numerical scheme for this type of modeling is presented here that is based on tracking Lagrangian control volumes across a fixed (Eulerian) grid. Numerical tests are used to provide a direct comparison of the new scheme versus nonconservative Eulerian numerical methods, in terms of both accuracy and mass conservation. Key characteristics of systems for which the Lagrangian scheme performs better than the Eulerian scheme include: nonuniform flow fields, steep gradient plume fronts, and pulse and steady point source loadings in advection-dominated systems. A new analytical derivation is presented that provides insight into the loss of mass conservation in the nonconservative Eulerian scheme. This derivation shows that loss of mass conservation in the vicinity of spatial flow changes is directly proportional to the lateral inflow rate and the change in stream concentration due to the inflow. While the nonconservative Eulerian scheme has clearly worked well for past published applications, it is important for users to be aware of the scheme’s limitations.     

Alternative Approaches to Modeling Fluence Distribution and Microbial Inactivation in Ultraviolet Reactors: Lagrangian versus Eulerian

A study was performed to evaluate alternative methods for predicting the ultraviolet (UV) reactor performance using computational fluid dynamics. The study consists of modeling the UV fluence distribution and microbial inactivation using either Lagrangian or Eulerian methods for both low- and medium-pressure UV reactors. In the Eulerian method, fluence distributions were calculated using a flow-weighted and a mass-weighted fraction technique. The results show that the Eulerian flow-weighted fraction fluence distribution agreed well with the Lagrangian particle tracking fluence distribution when applied to the UV reactor outlet plane. However, when applied to planes downstream from effluent hydraulic structures, the Eulerian fluence distribution method was influenced by the additional convective mixing from these hydraulic structures and predicts a tighter fluence distribution range than the Lagrangian method. The Eulerian approach to modeling microbial inactivation seems comparable to the Lagrangian particle tracking approach and can be viewed as a suitable alternative to the Lagrangian approach. The results also show that the Eulerian mass-weighted fraction distribution is comparable to the microbial kinetic weighted Lagrangian particle tracking approach, which can provide greater sensitivity to the low fluence regions in the UV reactor.     

A Comprehensive Analysis of Macrosegregation Formation During Twin-Roll Casting

Metallurgical and Materials Transactions B - A two-phase Eulerian–Eulerian volume-averaged model is used to predict the formation of macrosegregation during the twin-roll casting of...     

Flow and Heat Transfer Performance of Slag and Matte in the Settler of a Copper Flash Smelting Furnace

Simulation of two‐phase flow in a copper flash smelting settler with simultaneous tapping of slag and matte is carried out using Eulerian‐Eulerian two‐fluid model and the flow and heat transfer performance of slag and matte is examined. Detailed velocity vectors, temperature and volume fraction distributions are obtained. The results show that the small copper droplets will be suspended in the slag. When the droplet diameter is large enough, the slag and matte layer are clearly formed and the dispersion layer between the slag and matte layers becomes thinner at larger droplet sizes and its thickness remains nearly unchanged when the copper droplet diameter is larger than about 500 μm.     

一种新的静态轧制过程有限元模拟方法

提出了一种将欧拉法与拉格朗日法结合起来的静态轧制过程有限元模拟新方法.其主要内容包括:在轧制件纵向上用欧拉坐标, 厚度和宽度方向上用拉格朗日坐标,时间变量是独立的,计算轧制件厚度和宽度方向上的实际位移时采用的流线形积分改用沿纵向的欧拉坐标一元积分.     

An eulerian finite-element model for determination of deformation state of a copper subjected to orthogonal cutting

An Eulerian finite-element (FE) model was developed to predict the stress and strain distributions in the material subjected to the orthogonal machining process. Metallographic sections taken from commercially pure copper samples and subjected to orthogonal cutting were examined to determine the local strain gradients generated in the material ahead of the cutting tool tip. Local flow stress values were estimated from the microhardness measurements. Experimental flow stress and equivalent plastic strain values were found to obey a Voce-type exponential relationship, which was used in the development of the material model for the numerical simulations. The sizes of both the primary deformation zone (350 μm) and the secondary deformation zone (50 μm) predicted by the numerical model were in agreement with the experimental observations. The experimental results showed that the equivalent strain was 3.65 in the material 50 μm directly ahead of the tool tip, which compared well with the numerically observed strain (3.50). According to the numerical observations, along the primary shear plane, the high tool tip stress of 410 MPa decreased to 260 MPa near the chip root. Numerical and experimental stress and strain distributions correlated well in terms of both magnitudes and distributions, indicating that the application of an Eulerian FE approach served to predict the deformation state of the material ahead of the tool tip successfully.     

Modeling of Quasi-Four-Phase Flow in Continuous Casting Mold Using Hybrid Eulerian and Lagrangian Approach

Metallurgical and Materials Transactions B - Lagrangian tracking model combined with Eulerian multi-phase model is employed to predict the time-dependent argon–steel–slag–air...     

六流小方坯中间包气幕挡墙的数学模拟

根据6流200 mm×200 mm方坯30 t中间包的结构操作工艺参数,采用欧拉两流体模型、多孔介质模型、欧拉-拉格朗日随机轨道模型及Monte-Carlo法,并引入气泡吸附模型,用数学模拟法对比研究了采用气幕挡墙技术对6流中间包内钢液流动特性及夹杂物去除的影响。结果表明,采用气幕挡墙技术优化后,可以有效改善钢液的流动状态,均衡各出口停留时间,有效延长钢液的平均停留时间,降低死区体积,提高夹杂物去除率,适应多流中间包超纯净钢冶炼的需求。     

Fluid Flow,Dissolution, and Mixing Phenomena in Argon-Stirred Steel Ladles

Metallurgical and Materials Transactions B - In the current study, the multiphase fluid flow in argon-stirred steel ladles is simulated using an Eulerian–Lagrangian two-phase approach. The...     

Fluid flow behaviour of liquid in cylindrical vessels stirred by one or two air jets

In the present paper, based on the two‐phase model (Eulerian‐Eulerian model), the three‐dimensional fluid flow in water system and liquid steel system stirred by one or two gas jets is simulated. A new modified k‐? turbulence model is introduced to consider the bubbles movement contribution to k and ?. The mathematical simulation agrees well with the experimental results. Calculation indicates that the distance of the two jet nozzles has a big effect on the fluid flow behaviour. Placing two gas injection nozzles at the half radii of one diameter of the bottom generates a much better mixing than that injected by only one nozzle with the same total gas flow rate.     

喷粉透气砖狭缝内气——固两相流动数值模拟

狭缝型喷粉透气砖是铁水底喷粉脱硫预处理工艺重要功能性元件,对底喷粉脱硫工艺的顺利实施影响重大.结合实际应用情况,基于欧拉-欧拉双流体和颗粒动力学理论,对喷粉透气砖狭缝内气-固两相流进行了三维数值模拟,得到狭缝内的流场、压力场和颗粒相体积分数场分布.喷粉透气砖狭缝内颗粒相体积分数非均匀段长度一般为250 mm,加速段长度一般小于250 mm,在颗粒直径为20μm时单缝内的压降最大,为2350 Pa.工业试验结果表明,底喷粉工艺脱硫效率比同类型顶喷粉工艺提高15%以上.      

Study on Desulphurization in Molten Iron Pretreatment Process Based on a New Stirring Method

In this work, numerical simulations for the flow characteristics in a tank of KR mechanical stirring or/and gas injection are performed using the Fluent software. The Eulerian multi-fluid model is employed along with the standard k-ε turbulence model to simulate the gas-liquid flow in the stirring tank. A multiple reference frame approach is used to model the impeller rotation. Combined the KR mechanical stirring method and gas injection method, a new gas injection plus mechanical stirring method is proposed. The present results show that the gas phase distributes widely in the eccentric gas injection plus mechanical stirring tank. Therefore, the gas holdup would be increased and the better gas-liquid mixing effect can be obtained in the gas injection plus mechanical stirring case.     

Mass Conservative Transport Scheme for the Application of the ELCIRC Model to Water Quality Computation

An attempt was made to couple the water quality model of Danshuei River to the three-dimensional unstructured-grid hydrodynamic model [Eulerian–Lagrangian circulation model (ELCIRC)]. The Eulerian–Lagrangian scheme for the solution of the transport equations of salt in ELCIRC was demonstrated to be not mass conservative. The scheme was replaced with a finite-volume/finite-difference upwind scheme to ensure mass conservation both locally and globally. The same scheme was also used for the scalar transport equation in the water quality model. The representation of mass flux in the scalar transport equation is carefully formulated to be consistent with that of volume flux used in the continuity equations of ELCIRC. It was demonstrated that the newly revised scheme (1) conserved mass locally and globally; (2) conserved mass for both conservative and nonconservative substances subjected to biogeochemical transformation; and (3) preserved the integrity of the wetting-and-drying scheme. Further, the baroclinic simulation using the newly revised scheme showed a better result in terms of salt intrusion and salinity distribution in the Danshuei River estuary.     

Transient Flow and Inclusion Removal in Gas Stirred Ladle during Teeming Process

A water model of a typical 150t ladle was designed and constructed to determine the flow characteristics. A kind of organic emulsion was selected to model nonmetallic inclusion particles with the purpose of studying the inclusion removal effect under gas blowing in a teeming ladle. The presented modeling method for inclusion particles in the teeming process is different from those under steady condition. The numerical simulation was performed by using commercial software with the Eulerian‐Eulerian multiphase model applied to a model gas blown through a ladle. The numerical component of this study was conducted aiming at exploring the transient flow characteristics in teeming ladle corresponding to the physical experimental condition. Under the present conditions the authors came to the conclusion that soft gas blowing (2.7～4.0 × 10^?6 m³/s) was favourable to float inclusion particles into the slag layer. It is suggested to end the gas blowing when the drainage percentage reaches 50%.     

Modeling of the Twin-Roll Casting Process: Transition from Casting to Rolling

During twin-roll casting, an alloy melt is passing the gap between two counter-rotating rolls, where cooling and solidification leads to the continuous formation of a solid strand. In order to describe this process, a two-phase Eulerian–Eulerian volume-averaging model is presented that accounts for (1) transport and growth of spherical grains within a flowing melt, (2) the formation of a coherent solid network above a specific solid fraction and (3) the viscoplastic flow of the solid network with the interstitial melt during casting and compression. For the considered case of an inoculated Al–4wt%Cu alloy, the process conditions are chosen such that two relatively thick viscoplastic semi-solid shells meet between the rolls, and thus, the material is pressed together and squeezed against the casting direction. The squeezed out material consists of segregated melt and some solid that quickly disappears after melting. It is observed during this study that macrosegregation distributions are inherently connected to the mush deformation that is enforced during the hot rolling process.     

Study of Flow in a Blanket Clarifier Using Computational Fluid Dynamics

This work simulated the flow pattern of the sludge blanket clarifier at the Bansin Water Treatment Plant, Taiwan by multiphase flow, three-dimensional analysis. The following three models were developed individually: One-phase flow (water) in the clarifier—this model acquires the basic water-flow pattern; a homogeneous porous medium at the bottom of the clarifier—this porous medium represents the sludge blanket; and, the Eulerian granular multiphase model, which was utilized to obtain solid effluent flux and to determine the effects of particle size and density on sludge blanket stability. Analytical results indicated that the clarifier has two principal circulations inside and outside the reaction well. A plentiful, dense and thick sludge blanket should exist at the clarifier bottom; otherwise particles could flow out through the gap between bottom of the reaction well and top of blanket surface, resulting in poor water quality. In the multiphase flow model, large particles and a high particle density are positively correlated with sludge blanket stability.     

Mathematical Modeling of Fluid Flow in Bath during Combined Side and Top Blowing AOD Refining Process of Stainless Steel: Mathematical Model of the Fluid Flow

Considering that the liquid flow field under the conditions of the combined side and top blowing would be a combined result from the common action of the side blowing gas streams and a gas top blowing jet, as the first attempt, the three‐dimensional mathematical models for the flows of molten steel in an AOD converter bath during the simple side and top blowing processes have been proposed and developed, respectively. And the mathematical model of the flow in the bath during the combined blowing AOD refining process of stainless steel has been given by the composition and superposition of the two models. In the composed model, the gas‐liquid two‐phase flow is described and treated in terms of the two‐fluid (Eulerian‐Eulerian) model. The especially modified two‐equation k?ε model for the turbulence in the liquid phase is employed. And, the surface of the sunken pit formed by impact of the gas jet blown from a top lance at the central location of the bath liquid surface is regarded as a revolution paraboloid. The related details of the composed model are shown.     

Numerical computations of fluid flow and heat transfer in a gas-stirred liquid bath

The flow and temperature fields due to bottom air injection in a cylindrical vessel containing water were numerically analyzed. The Eulerian approach was used for the formulation of both the continuous and the dispersed phases. The computational domain was extended beyond the undisturbed height of the liquid in the bath to accommodate practical gas injection systems. Turbulence in the liquid phase was modeled using a two-equationk- ε model. Interphase friction and heat transfer coefficients were calculated by using correlations available in the literature. The general-purpose computer program PHOENICS was employed to predict the velocity, vol-ume fraction, and the temperature fields of each phase. Turbulent dispersion of the phases was modeled by introducing a “dispersion Prandtl number.” The predicted flow fields were com-pared with experimental measurements available in the literature. The results are of interest in the design and operation of a wide variety of material processing operations.     

Numerical Computational Fluid Dynamics-Based Models of Ultraviolet Disinfection Channels

Various numerical modeling approaches, all based on computational fluid dynamics (CFD) solutions for the flow field, are studied for an ultraviolet disinfection system in which the lamps are oriented perpendicular to the flow direction. A two-dimensional model assumption is made in all simulations, for which turbulent flow solutions were obtained with commercial CFD software (FIDAP). Two modeling approaches were studied. A continuum Eulerian approach was taken in formulating an appropriate advection–diffusion equation which is solved for the viable micro-organism concentration. Alternatively, a Lagrangian approach, in which particles are numerically introduced into the flow and their trajectories through a spatially varying field of ultraviolet intensities were computed, was also investigated. The effect of modeling unsteady-flow features associated with vortex shedding and motion on the extent of disinfection was examined by comparing time-averaged results based on an unsteady-flow continuum model with the results from an analogous simulation assuming a steady flow. Under the steady-flow assumption, differences between predictions of the Eulerian continuum approach and the Lagrangian particle-trajectory approach were also considered. Both modeling approaches yielded similar predictions over a range of loadings, and tended to underestimate the extent of disinfection when compared to measurements at the pilot scale.     

浮选三相流中气泡运动特性的数值模拟

为获取浮选气泡在矿浆中的运动规律及三相流中浮选气泡的最佳尺寸,运用欧拉模型模拟不同初始直径的气泡在不同密度矿浆中的运动过程.结果表明:在给定的初始条件下,同一浓度的矿浆中,单个浮选气泡所能捕获的矿物量以直径4mm的气泡最多,气泡尺寸增大或减小后,其矿物捕获量都有所减少.当矿浆中固相质量分数在20%~40%之间变化时,矿物捕获量最多的气泡尺寸变化不大,并且随着矿浆中固相质量分数的增大,单个气泡的捕获量增大,矿物粒子回收率增加.在实际生产中,直径为3.5~4 mm的中等大小气泡在运动过程中变形程度小,气泡水平偏移及浮升速度适中,对矿物粒子的捕获率及运载能力和浮升能力较强,有利于提高浮选产量和质量.