Particle size distribution in CPFD modeling of gas–solid flows in a CFB riser

A computational particle fluid dynamics (CPFD) numerical method to model gas–solid flows in a circulating fluidized bed (CFB) riser was used to assess the effects of particle size distribution (PSD) on solids distribution and flow. We investigated a binary PSD and a polydisperse PSD case. Our simulations were compared with measured solids concentrations and velocity profiles from experiments, as well as with a published Eulerian-Eulerian simulation. Overall flow patterns were similar for both simulation cases, as confirmed by experimental measurements. However, our fine-mesh CPFD simulations failed to predict a dense bottom region in the riser, as seen in other numerical studies. Above this bottom region, distributions of particle volume fraction and particle vertical velocity were consistent with our experiments, and the simulated average particle diameter decreased as a power function with riser height. Interactions between particles and walls also were successfully modeled, with accurate predictions for the lateral profiles of particle vertical velocity. It was easy to implement PSD into the CPFD numerical model, and it required fewer computational resources compared with other models, especially when particles with a polydisperse PSD were present in the heterogeneous flow.     

Particle size distribution in CPFD modeling of gas-solid flows in a CFB riser

A computational particle fluid dynamics(CPFD) numerical method to model gas-solid flows in a circulating fluidized bed(CFB) riser was used to assess the effects of particle size distribution(PSD) on solids distribution and flow.We investigated a binary PSD and a polydisperse PSD case.Our simulations were compared with measured solids concentrations and velocity profiles from experiments,as well as with a published Eulerian-Eulerian simulation.Overall flow patterns were similar for both simulation cases,as confirmed by experimental measurements.However,our fine-mesh CPFD simulations failed to predict a dense bottom region in the riser,as seen in other numerical studies.Above this bottom region,distributions of particle volume fraction and particle vertical velocity were consistent with our experiments,and the simulated average particle diameter decreased as a power function with riser height.Interactions between particles and walls also were successfully modeled,with accurate predictions for the lateral profiles of particle vertical velocity.It was easy to implement PSD into the CPFD numerical model,and it required fewer computational resources compared with other models,especially when particles with a polydisperse PSD were present in the heterogeneous flow.     

Evaluation of the effect of wall boundary conditions on numerical simulations of circulating fluidized beds

A computational fluid dynamics (CFD) modeling of the gas–solids two-phase flow in a circulating fluidized bed (CFB) riser is carried out. The Eularian–Eularian method with the kinetic theory of granular flow is used to solve the gas–solids two-phase flow in the CFB riser. The wall boundary condition of the riser is defined based on the Johnson and Jackson wall boundary theory (Johnson & Jackson, 1987) with specularity coefficient and particle–wall restitution coefficient. The numerical results show that these two coefficients in the wall boundary condition play a major role in the predicted solids lateral velocity, which affects the solid particle distribution in the CFB riser. And the effect of each of the two coefficients on the solids distribution also depends on the other one. The generality of the CFD model is further validated under different operating conditions of the CFB riser.     

Transport modeling of sedimenting particles in a turbulent pipe flow using Euler–Lagrange large eddy simulation

A volume-filtered Euler–Lagrange large eddy simulation methodology is used to predict the physics of turbulent liquid–solid slurry flow through a horizontal periodic pipe. A dynamic Smagorinsky model based on Lagrangian averaging is employed to account for the sub-filter scale effects in the liquid phase. A fully conservative immersed boundary method is used to account for the pipe geometry on a uniform cartesian grid. The liquid and solid phases are coupled through volume fraction and momentum exchange terms. Particle–particle and particle–wall collisions are modeled using a soft-sphere approach. Three simulations are performed by varying the superficial liquid velocity to be consistent with the experimental data by Dahl et al. (2003). Depending on the liquid flow rate, a particle bed can form and develop different patterns, which are discussed in light of regime diagrams proposed in the literature. The fluctuation in the height of the liquid-bed interface is characterized to understand the space and time evolution of these patterns. Statistics of engineering interest such as mean velocity, mean concentration, and mean streamwise pressure gradient driving the flow are extracted from the numerical simulations and presented. Sand hold-up calculated from the simulation results suggest that this computational strategy is capable of predicting critical deposition velocity.     

Effect of viscoelasticity on the rotation of a sphere in shear flow

When particles are dispersed in viscoelastic rather than Newtonian media, the hydrodynamics will be changed entailing differences in suspension rheology. The disturbance velocity profiles and stress distributions around the particle will depend on the viscoelastic material functions. Even in inertialess flows, changes in particle rotation and migration will occur. The problem of the rotation of a single spherical particle in simple shear flow in viscoelastic fluids was recently studied to understand the effects of changes in the rheological properties with both numerical simulations [D’Avino et al., J. Rheol. 52 (2008) 1331–1346] and experiments [Snijkers et al., J. Rheol. 53 (2009) 459–480]. In the simulations, different constitutive models were used to demonstrate the effects of different rheological behavior. In the experiments, fluids with different constitutive properties were chosen. In both studies a slowing down of the rotation speed of the particles was found, when compared to the Newtonian case, as elasticity increases. Surprisingly, the extent of the slowing down of the rotation rate did not depend strongly on the details of the fluid rheology, but primarily on the Weissenberg number defined as the ratio between the first normal stress difference and the shear stress.In the present work, a quantitative comparison between the experimental measurements and novel simulation results is made by considering more realistic constitutive equations as compared to the model fluids used in previous numerical simulations [D’Avino et al., J. Rheol. 52 (2008) 1331–1346]. A multimode Giesekus model with Newtonian solvent as constitutive equation is fitted to the experimentally obtained linear and nonlinear fluid properties and used to simulate the rotation of a torque-free sphere in a range of Weissenberg numbers similar to those in the experiments. A good agreement between the experimental and numerical results is obtained. The local torque and pressure distributions on the particle surface calculated by simulations are shown.     

3D full-loop simulation and experimental verification of gas-solid flow hydrodynamics in a dense circulating fluidized bed

Because of their advantages of high efficiency and low cost, numerical research methods for large-scale circulating fluidized bed （CFB） apparatus are gaining ever more importance. This article presents a numer- ical study of gas-solid flow dynamics using the Eulerian granular multiphase model with a drag coefficient correction based on the energy-minimization multi-scale （EMMS） model. A three-dimensional, full-loop, time-dependent simulation of the hydrodynamics of a dense CFB apparatus is performed. The process parameters （e.g., operating and initial conditions） are provided in accordance with the real experiment to enhance the accuracy of the simulation. The axial profiles of the averaged solid volume fractions and the solids flux at the outlet of the cyclone are in reasonable agreement with experimental data, thereby verifying the applicability of the mathematical and physical models. As a result, the streamline in the riser and standpipe as well as the solids distribution contours at the cross sections is analyzed. Computational fluid dynamics （CFD） serves as a basis for CFB modeling to help resolve certain issues long in dispute but difficult to address experimentally. The results of this study provide the basis of a general approach to describing dynamic simulations of gas-solid flows.     

CFD–DEM study of effect of bed thickness for bubbling fluidized beds

The effect of bed thickness in rectangular fluidized beds is investigated through the CFD–DEM simulations of small-scale systems. Numerical results are compared for bubbling fluidized beds of various bed thicknesses with respect to particle packing, bed expansion, bubble behavior, solids velocities, and particle kinetic energy. Good two-dimensional (2D) flow behavior is observed in the bed having a thickness of up to 20 particle diameters. However, a strong three-dimensional (3D) flow behavior is observed in beds with a thickness of 40 particle diameters, indicating the transition from 2D flow to 3D flow within the range of 20–40 particle diameters. Comparison of velocity profiles near the walls and at the center of the bed shows significant impact of the front and back walls on the flow hydrodynamics of pseudo-2D fluidized beds. Hence, for quantitative comparison with experiments in pseudo-2D columns, the effect of walls has to be accounted for in numerical simulations.     

Numerical simulation of a dense solid particle flow inside a cyclone separator using the hybrid Euler–Lagrange approach

This paper presents a numerical simulation of the flow inside a cyclone separator at high particle loads. The gas and gas–particle flows were analyzed using a commercial computational fluid dynamics code. The turbulence effects inside the separator were modeled using the Reynolds stress model. The two phase gas–solid particles flow was modeled using a hybrid Euler–Lagrange approach, which accounts for the four-way coupling between phases. The simulations were performed for three inlet velocities of the gaseous phase and several cyclone mass particle loadings. Moreover, the influences of several submodel parameters on the calculated results were investigated. The obtained results were compared against experimental data collected at the in-house experimental rig. The cyclone pressure drop evaluated numerically underpredicts the measured values. The possible reason of this discrepancies was disused.     

Effects of grid size on predictions of bed expansion in bubbling fluidized beds of Geldart B particles: A generalized rule for a grid-independent solution of TFM simulations

Numerical simulations of gas–solid fluidized beds based on the kinetic theory of granular flow exhibit a significant dependence on domain discretization. Bubble formation, bubble size and shape all vary greatly with the discretization, and the use of an inappropriate scale resolution leads to inaccurate predictions of fluidization hydrodynamics. In this study, grid-independent solutions of the two fluid model were examined by comparing the bed expansions obtained from numerical simulations with experimental results and empirical predictions, based on bubbling fluidized beds of Geldart B particles. Grid independence was achieved with a grid resolution equal to 18 times the particle diameter. The simulation results were compared with previously published data for verification purposes. The results of this work should provide a guideline for choosing the appropriate grid size and thereby minimize the time and expense associated with large simulations.     

Euler–Lagrange simulation of high pressure shock waves

This paper presents the numerical simulation of overdriven detonation (or O.D.D.) that occurs when a high velocity object impacts an explosive. The pressure and the velocity at this state are higher than those of the Chapman–Jouguet (C–J) state. First, before the simulation of this event, a study of PBX air blast by using multi-material Eulerian method is presented. Pressure peaks are computed for several distances from the explosive. Second, the O.D.D. phenomenon is modeled by the Euler–Lagrange penalty coupling, which permits to couple a Lagrangian mesh of the flyer plate to multi-material Eulerian mesh of explosives and air. This coupling gives us the high detonation velocities in the acceptor explosive and demonstrates that it is able to handle shock–structure interaction problems.     

Investigation on effect of drag models on flow behavior of power-law fluid–solid two-phase flow in fluidized bed

In this study, a Eulerian-Eulerian two-fluid model combined with the kinetic theory of granular flow is adopted to simulate power-law fluid–solid two-phase flow in the fluidized bed. Two new power-law liquid–solid drag models are proposed based on the rheological equation of power-law fluid and pressure drop. One called model A is a modified drag model considering tortuosity of flow channel and ratio of the throat to pore, and the other called model B is a blending drag model combining drag coefficients of high and low particle concentrations. Predictions are compared with experimental data measured by Lali et al., where the computed porosities from model B are closer to the measured data than other models. Furthermore, the predicted pressure drop rises as liquid velocity increases, while it decreases with the increase of particle size. Simulation results indicate that the increases of consistency coefficient and flow behavior index lead to the decrease of drag coefficient, and particle concentration, granular temperature, granular pressure, and granular viscosity go down accordingly.     

Assessment of the kinetic-frictional model for dense granular flow

This paper aims to quantitatively assess the application of kinetic-frictional model to simulate the motion of dry granular materials in dense condition, in particular, the annular shearing in Couette configuration. The weight of frictional stress was varied to study the contribution of the frictional stress in dense granular flows. The results show that the pure kinetic-theory-based computational fluid dynamics （CFD） model （without frictional stress） over-predicts the dominant solids motion of dense granular flow while adding frictional stress [Schaeffer, D. G. （1987）. Instability in the evolution equations describing incompressible granular flow. Journal of Differential Equations, 66（1）, 19-50] with the solids pressure of [Lun, C. NTK., Savage, S. B., Jeffrey, D. J., ＆ Chepurniy, N. （1984）. Kinetic theories for granular flow： Inelastic particles in Couette flow and slightly inelastic particles in a general flow field. Journal of Fluid Mechanics, 140, 223-256] in the CFD model improves the simulation to better conform available experimental results. The results also suggest that frictional stress transmission plays an important role in dense granular flow and should not be neglected in granular flow simulations. Compatible simulation results to the experimental data are seen by increasing the weight of frictional stress to a factor of 1.25-1.5. These improved simulation results suggest the current constitutive relations （kinetic-frictional model） need to be improved in order to better reflect the real dense granular flow.     

A new flux-limiting approach–based kinetic scheme for the Euler equations of gas dynamics

This paper proposes a new kinetic-theory-based high-resolution scheme for the Euler equations of gas dynamics. The scheme uses the well-known connection that the Euler equations are suitable moments of the collisionless Boltzmann equation of kinetic theory. The collisionless Boltzmann equation is discretized using Sweby's flux-limited method and the moment of this Boltzmann level formulation gives a Euler level scheme. It is demonstrated how conventional limiters and an extremum-preserving limiter can be adapted for use in the scheme to achieve a desired effect. A simple total variation diminishing criteria relaxing parameter results in improving the resolution of the discontinuities in a significant way. A 1D scheme is formulated first and an extension to 2D on Cartesian meshes is carried out next. Accuracy analysis suggests that the scheme achieves between first- and second-order accuracy as is expected for any second-order flux-limited method. The simplicity and the explicit form of the conservative numerical fluxes add to the efficiency of the scheme. Several standard 1D and 2D test problems are solved to demonstrate the robustness and accuracy.     

稠密气固两相湍流流动的实验和数值模拟

基于气固两相流动模型计算循环流化床内稠密气固两相流湍流动,颗粒动理学方法模拟颗粒相湍动能,ＳＧＳ模型模拟气相湍流,采用γ－射线密度计和非等速取样管测量局部颗粒浓度和流率,利用ＦＦＴ方法计算颗粒浓度功率谱密度。模拟计算得到上升管内气相和固相速度和浓度分布等。同时数值模拟与Ｔｓｕｊｉ等和Ｋｎｏｗｌｔｏｎ等试验结果进行了比较,结果表明数值模拟计算与实验结果相吻合。     

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.     

用拟压缩性方法求解不可压Euler方程

用拟压缩性方法和Ｊａｍｅｓｏｎ的有限体积算法求解了二维和三维定常可可压Ｅｕｌｅｒ方程。分别采用显、隐式时间离散推进求解;分析了人工粘性的阶数对定常解收敛性的影响,应用该方法计算了单个翼型和翼身组合体的低速绕流,结果与实验吻合较好。     

Eulerian–Lagrangian simulation of distinct clustering phenomena and RTDs in riser and downer

Numerical simulation of fully developed hydrodynamics of a riser and a downer was carried out using an Eulerian–Lagrangian model, where the particles are modeled by the discrete element method (DEM) and the gas by the Navier–Stokes equations. Periodic flow domain with two side walls was adopted to simulate the fully developed dynamics in a 2D channel of 10 cm in width. All the simulations were carried out under the same superficial gas velocity and solids holdup in the domain, starting with a homogenous state for both gas and solids, and followed by the evolution of the dynamics to the heterogeneous state with distinct clustering in the riser and the downer. In the riser, particle clusters move slowly, tending to suspend along the wall or to flow downwards, which causes wide residence time distribution of the particles. In the downer, clusters still exist, but they have faster velocities than the discrete particles. Loosely collected particles in the clusters move in the same direction as the bulk flow, resulting in plug flow in the downer. The residence time distribution (RTD) of solids was computed by tracking the displacements of all particles in the flow direction. The results show a rather wide RTD for the solids in the riser but a sharp peak RTD in the downer, much in agreement with the experimental findings in the literature. The ensemble average of transient dynamics also shows reasonable profiles of solids volume fraction and solids velocity, and their dependence on particle density.     

Sloshing simulation of standing wave with time-independent finite difference method for Euler equations

The numerical solutions of standing waves for Euler equations with the nonlinear free surface boundary condition in a two-dimensional(2D) tank are studied.The irregular tank is mapped onto a fixed square domain through proper mapping functions. A staggered mesh system is employed in a 2D tank to calculate the elevation of the transient fluid.A time-independent finite difference method,which is developed by Bang-fuh Chen,is used to solve the Euler equations for incompressible and inviscid fluids.The numer...     

高超声速再入体表面热流计算

运用非结构网格计算外部无粘流场,并结合边界层内粘性主导区域的工程算法,计算高超声速飞行器的气动加热。通过求解三维Euler方程确定复杂外形飞行器的边界层外缘参数,在理论与经验公式的基础上,利用局部相似性解的方法计算了钝锥和钝双锥外形有攻角再入的表面热流,并与国内外文献的NS方程数值计算结果和风洞试验结果进行了对比,三者的结果吻合较好。     

Evaluation of the effect of wall boundary conditions on numerical simulations of circulating fluidized beds

A computational fluid dynamics （CFD） modeling of the gas-solids two-phase flow in a circulating fluidized bed （CFB） riser is carried out. The Eularian-Eularian method with the kinetic theory of granular flow is used to solve the gas-solids two-phase flow in the CFB riser. The wall boundary condition of the riser is defined based on the Johnson and Jackson wall boundary theory （Johnson ＆ Jackson, 1987） with specularity coefficient and particle-wall restitution coefficient.The numerical results show that these two coefficients in the wall boundary condition play a major role in the predicted solids lateral velocity, which affects the solid particle distribution in the CFB riser. And the effect of each of the two coefficients on the solids distribution also depends on the other one. The generality of the CFD model is further validated under different operatin~ conditions of the CFB riser.