Influence of drag laws on pressure and bed material recirculation rate in a cold flow model of an 8 MW dual fluidized bed system by means of CPFD

A cold flow model of an 8 MW dual fluidized bed (DFB) system is simulated using the commercial computational particle fluid dynamics (CPFD) software package Barracuda. The DFB system comprises a bubbling bed connected to a fast fluidized bed with the bed material circulating between them. As the hydrodynamics in hot DFB plants are complex because of high temperatures and many chemical reaction processes, cold flow models are used. Performing numerical simulations of cold flows enables a focus on the hydrodynamics as the chemistry and heat and mass transfer processes can be put aside. The drag law has a major influence on the hydrodynamics, and therefore its influence on pressure, particle distribution, and bed material recirculation rate is calculated using Barracuda and its results are compared with experimental results. The drag laws used were energy-minimization multiscale (EMMS), Ganser, Turton–Levenspiel, and a combination of Wen–Yu/Ergun. Eleven operating points were chosen for that study and each was calculated with the aforementioned drag laws. The EMMS drag law best predicted the pressure and distribution of the bed material in the different parts of the DFB system. For predicting the bed material recirculation rate, the Ganser drag law showed the best results. However, the drag laws often were not able to predict the experimentally found trends of the bed material recirculation rate. Indeed, the drag law significantly influences the hydrodynamic outcomes in a DFB system and must be chosen carefully to obtain meaningful simulation results. More research may enable recommendations as to which drag law is useful in simulations of a DFB system with CPFD.     

Drag models for simulating gas–solid flow in the turbulent fluidization of FCC particles

This paper examines the suitability of various drag models for predicting the hydrodynamics of the turbulent fluidization of FCC particles on the Fluent V6.2 platform. The drag models included those of Syamlal–O’Brien, Gidaspow, modified Syamlal–O’Brien, and McKeen. Comparison between experimental data and simulated results showed that the Syamlal–O’Brien, Gidaspow, and modified Syamlal–O’Brien drag models highly overestimated gas–solid momentum exchange and could not predict the formation of dense phase in the fluidized bed, while the McKeen drag model could not capture the dilute characteristics due to underestimation of drag force. The standard Gidaspow drag model was then modified by adopting the effective particle cluster diameter to account for particle clusters, which was, however, proved inapplicable for FCC particle turbulent fluidization. A four-zone drag model (dense phase, sub-dense phase, sub-dilute phase and dilute phase) was finally proposed to calculate the gas–solid exchange coefficient in the turbulent fluidization of FCC particles, and was validated by satisfactory agreement between prediction and experiment.     

Study of fluid cell coarsening for CFD-DEM simulations of polydisperse gas–solid flows

Particle polydispersity is ubiquitous in industrial fluidized beds, which possesses a significant impact on hydrodynamics of gas–solid flow. Computational fluid dynamics-discrete element method (CFD-DEM) is promising to adequately simulate gas–solid flows with continuous particle size distribution (PSD) while it still suffers from high computational cost. Corresponding coarsening models are thereby desired. This work extends the coarse-grid model to polydisperse systems. Well-resolved simulations with different PSDs are processed through a filtering procedure to modify the gas–particle drag force in coarse-grid simulations. We reveal that the drag correction of individual particle exhibits a dependence on filtered solid volume fraction and filtered slip velocity for both monodisperse and polydisperse systems. Subsequently, the effect of particle size and surrounding PSD is quantified by the ratio of particle size to Sauter mean diameter. Drag correction models for systems with monodisperse and continuous PSD are developed. A priori analysis demonstrates that the developed models exhibit reliable prediction accuracy.     

气固两相流介尺度LBM-DEM模型

LBM-DEM耦合方法通常是指一种颗粒流体系统直接数值模拟算法,即是一种不引入经验曳力模型的计算方法,颗粒尺寸通常比计算网格的长度大一个量级,颗粒的受力通过表面的粘性力与压力积分获得,其优点是能描述每个颗粒周围的详细流场,产生详细的颗粒-流体相互作用的动力学信息,可以探索颗粒流体界面的流动、传递和反应的详细信息及两相相互作用的本构关系,但其缺点是计算量巨大,无法应用于真实流化床过程模拟。本文针对气固流化床中的流体以及固体颗粒间的多相流体力学行为,建立了一种稠密气固两相流的介尺度LBMDEM模型,即LBM-DEM耦合的离散颗粒模型,实现在颗粒尺度上流化床的快速离散模拟。该耦合模型采用格子玻尔兹曼方法(LBM)描述气相的流动和传递行为,离散单元法(DEM)用于描述颗粒相的运动,并利用能量最小多尺度(EMMS)曳力解决气固耦合不成熟问题,以提高其模拟精度。通过经典快速流态化的模拟,验证了介尺度LBM-DEM耦合模型的有效性。模拟结果表明介尺度LBM-DEM模型是一种探索实验室规模气固系统的有力手段。     

CFD modeling of liquid–solid fluidization: Effect of drag correlation and added mass force

Computational fluid dynamics (CFD) has been widely used to study the hydrodynamics of gas–solid fluidization; however, its applications in liquid–solid fluidization are relatively rare. In this study, CFD simulations of a liquid–solid fluidized bed are carried out, focusing on the effect of drag correlation and added mass force on the hydrodynamics of liquid–solid fluidization. It is shown that drag correlation has a significant effect on the simulation results and the correlation proposed by Beetstra et al. (2007) gives the best agreement with experimental data. We further show that the added mass force does play an important role in CFD simulation of liquid–solid fluidization, and therefore should not be ignored in CFD simulations.     

New formula for drag coefficient of cylindrical particles

The drag force on a cylindrical particle is calculated using lattice Boltzmann method.The results show that the drag coefficient of a particle with different orientation angles decreases with increasing Reynolds number.When the principal axis of the particle is parallel to flow,the drag coefficient is much larger than that of others and decreases fastest with increasing Reynolds number,which becomes more obvious with increasing particle aspect ratio.When the principal axis of the particle is inclined to flo...     

Numerical investigations on gas–solid flow in circulating fluidized bed risers using a new cluster-based drag model

A cluster-based drag model is proposed for the gas–solid circulating fluidized bed (CFB) riser by including the cluster information collected from image processing and wavelet analysis into the calculation of system drag. The performance of the proposed drag model is compared with some commonly used drag models. A good agreement with the experimental data is achieved by the proposed cluster-based drag model. Error analysis of the proposed cluster-based drag model based on the local distributions of solids holdup and particle velocity is conducted. The clustering phenomenon in the low-density and high-density CFB risers and the effect of the cluster size on the simulation accuracy are also numerically studied by the proposed drag model.     

Slow gas motions and the negative drag of a strongly heated spherical particle

In the slow flows of a strongly and nonuniformly heated gas, in the continuum regime (Kn → 0) thermal stresses may be present. The theory of slow nonisothermal continuum gas flows with account for thermal stresses was developed in 1969–1974. The action of the thermal stresses on the gas results in certain paradoxical effects, including the reversal of the direction of the force exerted on a spherical particle in Stokes flow. The propulsion force effect is manifested at large but finite temperature differences between the particle and the gas. This study is devoted to the thermal-stress effect on the drag of a strongly heated spherical particle traveling slowly in a gas for small Knudsen numbers (M ～ Kn → 0), small but finite Reynolds numbers (Re ≤ 1), a linear temperature dependence of the transport coefficients µ ∝ T, and large but finite temperature differences ((T _w ? T _∞ )/T _M8 ～ 1). Two different systems of equations are solved numerically: the simplified Navier-Stokes equations and the modified Navier-Stokes equations with account for the thermal stresses.     

Slow motions of a circular cylinder experiencing slip near a plane wall

A theoretical study is presented for the two-dimensional creeping flow caused by a long circular cylindrical particle translating and rotating in a viscous fluid near a large plane wall parallel to its axis. The fluid is allowed to slip at the surface of the particle. The Stokes equations for the fluid velocity field are solved in the quasi-steady limit using cylindrical bipolar coordinates. Semi-analytical solutions for the drag force and torque acting on the particle by the fluid are obtained for various values of the slip coefficient associated with the particle surface and of the relative separation distance between the particle and the wall. The results indicate that the translation and rotation of the confined cylinder are not coupled with each other. For the motion of a no-slip cylinder near a plane wall, our hydrodynamic drag force and torque results reduce to the closed-form solutions available in the literature. The boundary-corrected drag force and torque acting on the particle decrease with an increase in the slip coefficient for an otherwise specified condition. The plane wall exerts the greatest drag on the particle when its migration occurs normal to it, and the least in the case of motion parallel to it. The enhancement in the hydrodynamic drag force and torque on a translating and rotating particle caused by a nearby plane wall is much more significant for a cylinder than for a sphere.     

DEM simulation of polydisperse systems of particles in a fluidized bed

Numerical simulations based on three-dimensional discrete element model (DEM) are conducted for mono-disperse, binary and ternary systems of particles in a fluidized bed. Fluid drag force acting on each particle depending on its size and relative velocity is assigned. The drag coefficient corresponding to Ergun’s correlation is applied to the system of fluidized bed with particle size ratios of 1:1 for the mono-disperse system, 1:1.2, 1:1.4 and 1:2 for the binary system and 1:1.33:2 for the ternary system b...     

Fundamental solutions for axi-symmetric translational motion of a microstretch fluid

The fundamental solution for the axi-symmetrictranslational motion of a microstretch fluid due to a concentrated point body force is obtained.A general formula for thedrag force exerted by the fluid on an axi-symmetric rigid particle translating in it is then deduced.As an application to theobtained drag formula,this paper has discussed the problemof creeping translational motion of a rigid sphere in a microstretch fluid.The slip boundary condition on the surfaceof the spherical particle is applied.The drag force and theother physical quantities are obtained and represented graphically for various values of the micropolarity and slip parameters.     

Constitutive relations for the interaction force in multicomponent particulate flows

In the mechanics of multiphase (or multicomponent) mixtures, one of the outstanding issues is the formulation of constitutive relations for the interaction force. In this paper, we give a brief review of the various relations proposed for this interaction force. The review is tilted toward presenting the works of those who have used the mixture theory (or the theory of interacting continua) to derive or to propose a relationship for the interaction (or diffusive) force. We propose a constitutive relation which is general and frame-indifferent and thus suitable for use in many flow conditions. At the end, we provide an alternative approach for finding the drag force on a particle in a particulate mixture. This approach has been used in the non-Newtonian fluid mechanics to find the drag force on surfaces.     

Validation of EMMS-based drag model using lattice Boltzmann simulations on GPUs

Interphase momentum transport in heterogeneous gas–solid systems with multi-scale structure is of great importance in process engineering. In this article, lattice Boltzmann simulations are performed on graphics processing units (GPUs), the computational power of which exceeds that of CPUs by more than one order of magnitude, to investigate incompressible Newtonian flow in idealized multi-scale particle–fluid systems. The structure consists of a periodic array of clusters, each constructed by a bundle of cylinders. Fixed pressure boundary condition is implemented by applying a constant body force to the flow through the medium. The bounce-back scheme is adopted on the fluid–solid interfaces, which ensures the no-slip boundary condition. The structure is studied under a wide range of particle diameters and packing fractions, and the drag coefficient of the structure is found to be a function of voidages and fractions of the clusters, besides the traditional Reynolds number and the solid volume fractions. Parameters reflecting multi-scale characters are, therefore, demonstrated to be necessary in quantifying the drag force of heterogeneous gas–solid system. The numerical results in the range 0.1 ≤ Re ≤ 10 and 0 < ? < 0.25 are compared with Wen and Yu's correlation, Gibilaro equation, EMMS-based drag model, the Beetstra correlation and the Benyahia correlation, and good agreement is found between the simulations and the EMMS-based drag model for heterogeneous systems.     

Axisymmetric creeping motion of a slip spherical particle in a nonconcentric spherical cavity

A semianalytical study of the creeping flow caused by a spherical fluid or solid particle with a slip surface translating in a viscous fluid within a spherical cavity along the line connecting their centers is presented in the quasisteady limit of small Reynolds number. In order to solve the Stokes equations for the flow field, a general solution is constructed from the superposition of the fundamental solutions in the two spherical coordinate systems based on both the particle and cavity. The boundary conditions on the particle surface and cavity wall are satisfied by a collocation technique. Numerical results for the hydrodynamic drag force exerted on the particle are obtained with good convergence for various values of the ratio of particle-to-cavity radii, the relative distance between the centers of the particle and cavity, the relative viscosity or slip coefficient of the particle, and the slip coefficient of the cavity wall. In the limits of the motions of a spherical particle in a concentric cavity and near a cavity wall with a small curvature, our drag results are in good agreement with the available solutions in the literature. As expected, the boundary-corrected drag force exerted on the particle for all cases is a monotonic increasing function of the ratio of particle-to-cavity radii, and becomes infinite in the touching limit. For a specified ratio of particle-to-cavity radii, the drag force is minimal when the particle is situated at the cavity center and increases monotonically with its relative distance from the cavity center to infinity in the limit as it is located extremely away from the cavity center. The drag force acting on the particle, in general, increases with an increase in its relative viscosity or with a decrease in its slip coefficient for a given configuration, but surprisingly, there are exceptions when the ratio of particle-to-cavity radii is large.     

Temperature force of interaction between spherical particles

The force of interaction between small particles in a gas induced by a temperature difference between the particle surface and the gas far away from the particle is considered. The particle dimensions correspond to the free-molecular, transitional, and continuum heat transfer regimes. A Monte-Carlo numerical method of direct statistical simulation of the solution of the nonlinear Boltzmann equation and the results of asymptotic solutions are used. The force of interaction between two hot or cold spherical particles is investigated. The dependence of the temperature force on the particle size, i.e. on the flow regime (Knudsen number), and the distance between the particles is examined. Approximations for these dependences are constructed.     

Two-fluid smoothed particle hydrodynamics simulation of submerged granular column collapse

In this paper, a two-fluid smoothed particle hydrodynamics (SPH) model, based on the mixture theory, is employed to investigate the complex interactions between the solid particles and the ambient water during the process of submerged granular column collapse. From the simulation, two regimes of the collapse, one being quick and the other being slow, are identified and the reasons of formation are analyzed. It is found that, a large internal friction angle of the granular phase, representing large drag force between solid particles, helps form the slow regime. Small hydraulic conductivity, representing large inter-phase drag force, also retards the collapse dramatically. Good agreements between our numerical results and other researchers’ numerical and experimental results are observed, which demonstrates the capability of the proposed two-fluid SPH approach in dealing with saturated water–soil mixture flows.     

Drag reduction by reconfiguration of a poroelastic system

Because of their flexibility, trees and other plants deform with great amplitude (reconfigure) when subjected to fluid flow. Hence the drag they encounter does not grow with the square of the flow velocity as it would on a classical bluff body, but rather in a less pronounced way. The reconfiguration of actual plants has been studied abundantly in wind tunnels and hydraulic canals, and recently a theoretical understanding of reconfiguration has been brought by combining modelling and experimentation on simple systems such as filaments and flat plates. These simple systems have a significant difference with actual plants in the fact that they are not porous: fluid only flows around them, not through them. We present experimentation and modelling of the reconfiguration of a poroelastic system. Proper scaling of the drag and the fluid loading allows comparing the reconfiguration regimes of porous systems to those of geometrically simple systems. Through theoretical modelling, it is found that porosity affects the scaling of the drag with flow velocity. For high porosity systems, the scaling is the same as for isolated filaments while at low porosity, the scaling is constant for a large range of porosity values. The scalings for the extreme values of porosity are also obtained through dimensional analysis.     

Experiments and simulations of gas-solid flow in an airlift loop reactor

The hydrodynamics in a gas-solid airlift loop reactor was investigated systematically using experimental measurements and CFD simulation.In the experiments,the time averaged parameters,such as solid fraction and particle velocity,were measured by optical fiber probe.In the simulation,the modified Gidaspow drag model accounting for the interparticles clustering was incorporated into the Eulerian-Eulerian CFD model with particulate-phase kinetic theory.Predicted values of solid fraction and particle velocity ...     

Particle-scale and sub-grid drag models coupled CFD for simulating the CO methanation in a CFB riser

The diffusion and chemical reactions inside the catalyst particles and the heterogeneous flow structure in the computational cells are key factors to affect the accuracy of the coarse-grid simulation in circulating fluidized bed (CFB) methanation reactors. In this work, a particle-scale model is developed to calculate the effective reaction rate considering the transient diffusion and chemical reactions in the particle scale, i.e., the scale of the single catalyst particle. A modified sub-grid drag model is proposed to consider the effects of the meso-scale and chemical reactions on the heterogeneous gas-solid interaction, where the meso-scale is between the single particle and the whole reactor and featured with the particle cluster. Subsequently, a coupled model is developed by integrating the particle-scale and modified sub-grid drag models into CFD. Moreover, the coupled model is validated to achieve accurate predictions on the CO methanation process in a CFB riser. Notably, the coupled model can be performed with a coarse grid (∼58 times particle diameter) and a large time step (0.005 s) to accelerate the simulation. By simply changing the reaction kinetics, different gas-solid catalytic reaction systems can be simulated by using the coupled model.     

Stratified flow under an ice keel—a numerical approach

A numerical investigation of the flow of two immiscible stratified fluids under an isolated keel has been undertaken. The investigation utilized the two-dimensional Euler equations for incompressible flow, and the solution of these equations has been obtained by using the well-known finite volume marker and cell approach. Experimental drag-force measurements are also presented for a family of two-dimensional topographic models of fixed height with increasing surface slopes in a two-layer density system. The range of flow speeds explored covers the Froude number range from subcritical to fully supercritical. The drag force measurements are augmented by detailed observations of the interface distortion. The results clearly show large drag increases arising from the internal wave systems generated in the stratified flow. Very good agreement has been found between the experimental and numerical results for both the interface shape between the two fluids and the drag force on a variety of keels.