Microstructures of Polymer Solutions of Flow Past a Confined Cylinder

Numerical simulation is used to investigate the flow of polymer solutions past a symmetrically/asymmetrically confined cylinder by using FENE-P model and PTT model. A collocated finite volume method on unstructured triangular meshes is presented and its validity is proved by comparing the predicted velocity and stress point-wise with experimental data and numerical results in corresponding references. Microstructures of polymer solutions, including molecular orientation, extension, deformation, entanglement, are investigated through analyzing the information of conformation tensor in FENE-P model. Present results are hoping to give more insight into microscopic of complex flows and be more helpful to the industrial application.     

射流流化床中锥形分布板对流动的影响

给出了具有锥形分布板的射流流化床中浓密气固两相流动的多相流体力学基本方程组. 采用二维正交曲线坐标并生成了数值网格,用改进的IPSA方法求解二维正交曲线坐标中的多相流基本方程组,并编制了大型通用程序,流场可视化使用Tecplot软件. 对于给定的模拟计算,计算结果与实验值吻合. 模拟计算中改变了锥形筛板的角度、射流管的直径、床层高度、分布板开孔率的分布、射流气速、床层表观气速等,通过模拟得到床内的流动图像,考察了射流高度及颗粒循环的影响.     

The hydrodynamics of a hydrocyclone based on a three-dimensional multi-continuum model

The concept and principles of applying a multi-continuum model for calculating a hydrocyclone performance is presented. In this model the carrying liquid is described as one continuum, and each particle fraction, with its characteristic size is described as a separate continuum. Particle–particle and particle–fluid interactions derived from a lubrication theory and a collision theory are discussed. A set of governing partial differential equations consisting of mass and momentum conservation equations together with constitutive expressions is discussed. These equations were discretized by applying an unstructured grid consisting of tetrahedral elements. A numerical solver based on a finite element method combined with a segregated approach is described. The numerical approach is subject to ongoing research.     

Accurate void fraction calculation for three-dimensional discrete particle model on unstructured mesh

An accurate and efficient analytical method for computing the three-dimensional local void fraction is proposed in the context of discrete particle modeling. It is developed for the general case of unstructured meshes whose use is unavoidable to efficiently simulate modern gas-solid fluidized bed reactors characterized by complex geometries. The method relates the three-dimensional void fraction to several geometrical parameters. This allows the exact voidage evaluation for the frequently occurring case of having particles not wholly contained within one grid cell regardless its shape. Failing to accurately account for these common particle configurations in dense gas-particle systems has proven detrimental to the accuracy of their simulations.     

Modeling heterogeneous downward dense gas‐particle flows

A novel approach is proposed to model heterogeneous downward dense gas‐particle flows. The homogeneous behavior of the flow is described by the mass and momentum transport equations of the gas and particulate phases solved using a mono‐dimension finite volume method on staggered grids. The heterogeneous features of the flow are predicted simultaneously using the bubble‐emulsion formalism. The gas compressibility is taken into consideration. The model is supplemented with a new correlation to account for the wall‐particle frictional effects. The predictions are compared with the vertical profiles of pressure and the amount of gas that flows up and down two standpipes and a cyclone dipleg of an industrial fluid catalytic cracking unit and of a cold small‐scale circulating fluidized bed. The trends are well predicted. The model gives further information and is thus an innovative starting point for downward dense gas‐particle flow hydrodynamics investigation. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Numerical simulation of three‐dimensional gas‐solid particle flow in a horizontal pipe

A three‐dimensional model of particulate flows using the Reynolds Averaged Navier‐Stokes method is presented. The governing equations of the gas–solids flow are supplemented with appropriate closure equations to take into account all the relevant forces exerted on the solid particles, such as particle‐turbulence interactions, turbulence modulation, particle–particle interactions, particle–wall interactions, as well as gravitational, viscous drag, and lift forces. A finite volume numerical technique was implemented for the numerical solution of the problem. The method has been validated by comparing its results with the limited number of available experimental data for the velocity and turbulence intensity of the gas–particle flow. The results show that the presence of particles in the flow has a significant effect on all the flow variables. Most notably, the distribution of all the parameters becomes asymmetric, because of the gravitational effect on the particles and particle sedimentation. © 2011 American Institute of Chemical Engineers AIChE J, 2011     

Investigation on Separation Efficiency in Supersonic Separator with Gas-Droplet Flow Based on DPM Approach

Supersonic separator is a new technology based on the adiabatic expansion of swirling gas flow, and at present it has demonstrated great application potential in separating and processing droplet liquid contained in natural gas. However, its coefficient of performance is still low and there seems to be a large gap in the method that evaluates the separation efficiency in a satisfactory manner. In order to promote the wide application of this technology in the dehydration field, it is necessary to find a new and feasible approach that can be used to predict the flow characteristic and separation performance inside a supersonic separator. In this paper, a comprehensive three-dimensional fluid numerical model to study the flow behavior and separation efficiency in a supersonic separator was established coupled with the discrete particle model (DPM). The mixture of air and water droplets was chosen as working fluid. The gas phase was modeled with compressible Navier–Stokes equations for two-phase flow and the RSM turbulence model was taken into account. The droplet phase was modeled with the discrete particle model (DPM), in which the droplets are assumed to have the same sphere shape and ignore the phase transition and nucleation process. A pilot test facility was carried out to validate the numerical model. The experimental results not only indicate that the new dehydration device can efficiently separate the liquid droplets from wet gas, but also prove that the numerical results were great agreements with the experimental results. Furthermore, based on the proposed numerical approach, the gas-droplet turbulent flow structures were predicted, the effects of different structure parameters and operation conditions on the separation efficiency were also investigated. The current works settle a foundation for further explorations on the supersonic gas–liquid separation flows inside a supersonic separator as well as the possible new applications.     

负氧平衡发射药膛口燃烧流场的数值模拟

采用多组分ALE( Arbitrary Lagrangian-Eulerian)方程组对含有高速运动弹丸的负氧平衡发射药膛口射流燃烧流场进行了数值模拟.分别用HLLC格式和基元反应模型处理对流项和化学反应项,用网格局部重构的动网格技术处理因弹丸大位移动边界造成的网格变形,并基于非结构动网格和分区算法开发了并行程序,对膛...     

基于双流体模型的流化床模拟

从单相流体力学中描述气体流动的Navier-Stokes方程和单颗粒运动的Newton方程出发,使用比较严格的体积平均法推导出描述气固两相宏观流动的模型方程组并设法确定了模型参数,把该方程组加以简化,能得到Gidaspow、Blake和Davidson等人的模型方程,初步证明了模型的正确性,求解使用了经本文改进的基于控制容积有限差分的IPSA方法,编制了通用程序,模拟了二维射流流化床中浓密气固两相的流动,并计算出射流的穿透深度。     

稀疏两相射流中颗粒碰撞的数值研究

为了研究稀疏气固两相流动中颗粒间的碰撞行为及其对颗粒扩散的影响,对三维两相湍流射流进行了直接数值模拟。其中对流场控制方程的求解采用有限容积法和分步投影算法,对颗粒的跟踪采用拉格朗日方法,对颗粒间的碰撞采用硬球模型模拟。结果发现,在流场中局部浓度较高的区域颗粒碰撞频繁发生;受局部富集效应和湍流输运作用两方面的影响,颗粒的平均碰撞次数并不是随着Stokes数的增加呈现简单的线性增加,而是在Stokes数为0.1附近存在一个极值;考虑颗粒间的碰撞作用以后,颗粒的分布更加均匀,沿横向和展向的扩散也都有所增加。     

Computational fluid dynamics for dense gas–solid fluidized beds: a multi-scale modeling strategy

Dense gas–particle flows are encountered in a variety of industrially important processes for large scale production of fuels, fertilizers and base chemicals. The scale-up of these processes is often problematic, which can be related to the intrinsic complexities of these flows which are unfortunately not yet fully understood despite significant efforts made in both academic and industrial research laboratories. In dense gas–particle flows both (effective) fluid–particle and (dissipative) particle–particle interactions need to be accounted for because these phenomena, to a large extent, govern the prevailing flow phenomena, i.e. the formation and evolution of heterogeneous structures. These structures have significant impact on the quality of the gas–solid contact and as a direct consequence thereof strongly affect the performance of the process.Due to the inherent complexity of dense gas-particles flows, we have adopted a multi-scale modeling approach in which both fluid–particle and particle–particle interactions can be properly accounted for. The idea is essentially that fundamental models, taking into account the relevant details of fluid–particle (lattice Boltzmann model (LBM)) and particle–particle (discrete particle model (DPM)) interactions, are used to develop closure laws to feed continuum models which can be used to compute the flow structures on a much larger (industrial) scale. Our multi-scale approach (see Fig. 1) involves the LBM, the DPM, the continuum model based on the kinetic theory of granular flow, and the discrete bubble model. In this paper we give an overview of the multi-scale modeling strategy, accompanied by illustrative computational results for bubble formation. In addition, areas which need substantial further attention will be highlighted.     

镜像流体法模拟单颗粒沉降和绕凸起物流动

提出一种新的计算流体力学方法,即镜像流体法,通过指定固体区域内的流场参数,使相界面边界条件隐含满足,使得固液两相运动可以在固定的欧拉坐标系中求解。采用SIMPLE算法和控制容积法离散控制微分方程组。利用镜像流体方法数值模拟了单个球形颗粒的自由沉降过程,以及幂律流体、Carreau-Bird流体和粘弹性的Oldroyd-B流体绕半圆环形、三角形和梯形凸起物的二维圆管流动问题,模拟结果与报道的实验数据及计算结果很接近,初步验证了本算法的可靠性。     

A numerical study of fluidization behavior of Geldart A particles using a discrete particle model

This paper reports on a numerical study of fluidization behavior of Geldart A particles by use of a 2D soft-sphere discrete particle model (DPM). Some typical features, including the homogeneous expansion, gross particle circulation in the absence of bubbles, and fast bubbles, can be clearly displayed if the interparticle van der Waals forces are relatively weak. An anisotropy of the velocity fluctuation of particles is found in both the homogeneous fluidization regime and the bubbling regime. The homogeneous fluidization is shown to represent a transition phase resulting from the competition of three kinds of basic interactions: the fluid-particle interaction, the particle-particle collisions (and particle-wall collisions) and the interparticle van der Waals forces. In the bubbling regime, however, the effect of the interparticle van der Waals forces vanishes and the fluid-particle interaction becomes the dominant factor determining the fluidization behavior of Geldart A particles. This is also evidenced by the comparisons of the particulate pressure with other theoretical and experimental results.     

Verification of filtered two‐fluid models for gas‐particle flows in risers

The effect of solid boundaries on the closure relationships for filtered two‐fluid models for riser flows was probed by filtering the results obtained through highly resolved kinetic theory‐based two‐fluid model simulations. The closures for the filtered drag coefficient and particle phase stress depended not only on particle volume fraction and the filter length but also on the distance from the wall. The wall corrections to the filtered closures are nearly independent of the filter length and particle volume fraction. Simulations of filtered model equations yielded grid length independent solutions when the grid length is ～half the filter length or smaller. Coarse statistical results obtained by solving the filtered models with different filter lengths were the same and corresponded to those from highly resolved simulations of the kinetic theory model, which was used to construct the filtered models, thus verifying the fidelity of the filtered modeling approach. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

A FINITE VOLUME ANALYSIS OF VACUUM FREEZE DRYING PROCESSES OF SKIM MILK SOLUTION IN TRAYS AND VIALS

A numerical code that can predict vacuum freeze drying processes in trays and vials was developed using a finite volume method to discretize the governing partial differential equations. Along with the finite volume method, a moving grid system was adopted to handle irregular and continuously changing physical domains encountered during the primary drying stage. To show the validity of the present calculation scheme, freeze drying in a tray was simulated and the results were compared with available experimental data. After successful validation, freeze drying processes in vials with different operation policies were simulated to show the capability of the present calculation tool in handling multi-dimensional freeze drying problems.     

Eulerian–Lagrangian method for three-dimensional thermal reacting flow with application to coal gasifiers

Energy transport and chemistry are modeled in an extension of the Eulerian–Lagrangian computational particle fluid dynamics (CPFD) methodology. The CPFD methodology is based on the MP-PIC method, which uses a stochastic particle method for the particle phase and an Eulerian method for the fluid phase, to solve equations for dense particle flow. In our extension of CPFD, an enthalpy equation describes energy transport for fluid, and provides for transfer of sensible and chemical energy between phases and within the fluid mixture. Homogenous and heterogeneous chemistry are described by reduced-chemistry, and the reaction rates are implicitly solved numerically on the Eulerian grid. Inter-phase momentum and energy transfer are also implicitly calculated, giving a robust numerical solution from the dilute flow to close-pack limits. A three-dimensional example of a hot fluidized bed coal gasifier is presented with homogeneous and heterogeneous chemistry. The inter-dependencies of fluidization, thermal, and chemistry behaviors in this complex three-dimensional calculation are described.     

The finite differences method for solving systems on irregular shapes

A relatively simple and efficient symbolic-numerical procedure based on the finite differences method for solving partial differential equations on systems of irregular shapes is presented. The new concept is based on the spline parameterization of the irregular domain. The curvilinear domain of the real system is transformed to the rectangular domain by spline functions where the finite differences method is used to solve the transformed system of depended variables. The numerical results are then transported back to the original irregular shape of the system. In order to present the symbolic-numerical technique effectively, the Laplace's equation of heat transfer with the Dirichlet and the Neumann boundary conditions in different 2D curvilinear domains is considered. The proposed technique is applied for the non-steady-state heat transfer by conduction as well. Numerical experiments were performed to justify the proposed method.     

Arbitrary shaped ice particle melting under the influence of natural convection

This work is devoted to numerical simulations of an arbitrary shaped ice particle melting inside water under the influence of natural convection. Specifically, four different shapes of the ice particle have been studied: sphere, cylinder, cross shaped cylinder, and irregular sphere with radial bumps on its surface. A 2D axisymmetric particle‐resolved numerical model has been employed on a fixed grid to study the detailed melting dynamics of an ice particle. The solid‐liquid interface is treated as a porous medium characterized by the permeability coefficient which is used to damp the velocity values inside the interface. The model results have been compared with an existing experimental results produced by A. Shukla et al. (Metal Mater Trans B. 2011; 42(1):224–235). Very good agreement between our predictions and experimental data have been achieved. Based on the analysis of numerical simulation results, melting process is found to advance through two distinct regimes, namely, establishment of the natural convection and active melting of ice particle exhibiting substantial amount of fluid‐particle interactions. A set of dimensionless parameters have been identified to distinguish between regimes. Finally, we developed a semi‐empirical to predict the melting of any arbitrary shaped ice particle and validated it against the particle‐resolved numerical simulation and experimental results. The comparison showed good agreement. Finally, the presented semi‐empirical model can be used as sub‐grid model in Euler‐Lagrange based numerical models to study the phase change phenomena in particulate flow systems. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3158–3176, 2017     

Discrete element simulation of particle flow in arbitrarily complex geometries

Conventional simulations of dense particle flows in complex geometries usually involve the use of glued particles to approximate geometric surface. This study is concerned with the development of a robust and accurate algorithm for detecting the interaction between a spherical particle and an arbitrarily complex geometric surface in the framework of soft-sphere discrete element model (DEM) without introducing any assumptions. Numerical experiments specially designed to validate the algorithm shows that the new algorithm can accurately predict the contact state of a particle with a complex geometric surface. Based on the proposed algorithm, a new solver for simulation of dense particle flows is developed and implemented into an open source computational fluid dynamics (CFD) software package OpenFOAM. The solver is firstly employed to simulate hydrodynamics in a bubble fluidized bed. Numerical results show that a 3D simulation can predict the bubble size better than a 2D simulation. Subsequently, gas–solid hydrodynamics in an immersed tube fluidized bed is simulated. Results show that bubble coalescence and breakup behavior around the immersed tubes are well captured by the numerical model. In addition, seven different particle flow patterns around the immersed tubes are identified based on the numerical results obtained.