Evaluation of wall boundary condition parameters for gas–solids fluidized bed simulations

Wall boundary conditions for the solids phase have significant effects on numerical predictions of various gas–solids fluidized beds. Several models for the granular flow wall boundary condition are available in the open literature for numerical modeling of gas–solids flow. A model for specularity coefficient used in Johnson and Jackson boundary conditions by Li and Benyahia (Li and Benyahia, AIChE J. 2012;58:2058–2068) is implemented in the open‐source CFD code‐MFIX. The variable specularity coefficient model provides a physical way to calculate the specularity coefficient needed by the partial‐slip boundary conditions for the solids phase. Through a series of two‐dimensional numerical simulations of bubbling fluidized bed and circulating fluidized bed riser, the model predicts qualitatively consistent trends to the previous studies. Furthermore, a quantitative comparison is conducted between numerical results of variable and constant specularity coefficients to investigate the effect of spatial and temporal variations in specularity coefficient. Published 2013 American Institute of Chemical Engineers AIChE J, 59: 3624–3632, 2013     

Assessment of gas-particle flow models for pseudo-2D fluidized bed applications

The aim of this work is to provide more insight into the general modeling criteria for simulating pseudo-2D bubbling fluidized beds. For this purpose, two experimental-based problems are studied. First, a fluidized bed with a high-speed central jet problem is analyzed. A qualitative study of the first bubble indicates that the bubble shape prediction is highly sensitive to the frictional model adopted. The most accurate results in terms of bubble shape and detachment time are given by a frictional model that relates the strain-rate fluctuations with the granular temperature. Second, a uniformly fluidized bed problem in bubbling regime is considered. For this case, the drag models and boundary conditions for the particulate phase are investigated. Time-averaged solid phase velocity profiles are compared with the results of the literature where it is found that no-slip conditions (or partial slip with a high specularity coefficient) are more appropriate than slip conditions at the walls for these regimes. Regarding the drag force, although none of the models presented could match the experimental velocity predictions for low gas velocities at the lower region of the bed, the Di Felice model produces the most accurate results for the whole range of regimes considered.     

Influence of solid-phase wall boundary condition on CFD simulation of spouted beds

The influence of solid-phase wall boundary condition in terms of specularity coefficient and particle–wall restitution coefficient on the flow behavior of spouted beds was investigated using two-fluid model approach in the computational fluid dynamics software FLUENT 6.3. Parametric studies of specularity coefficient and particle–wall restitution coefficient were performed to evaluate their effects on the flow hydrodynamics in terms of fountain height, spout diameter, pressure drop, local voidage and particles velocity. The numerical predictions were compared with available experimental data in the literatures to obtain the suitable values of specularity coefficient and particle–wall restitution coefficient for spouted beds. The simulated results show that the solid-phase wall boundary condition plays an important role in CFD modeling of spouted beds. The specularity coefficient has a pronounced effect on the spouting behavior and a small specularity coefficient (0.05) can give good predictions, while the particle–wall restitution coefficient is not critical for the holistic flow characteristics.     

Numerical investigation of gas mixing in gas‐solid fluidized beds

Gas mixing in a tall narrow fluidized bed operated in the slugging fluidization regime is simulated with the aid of computational fluid dynamics. In the first part, a parametric study is conducted to investigate the influence of various parameters on the gas mixing. Among the parameters studied, the specularity coefficient for the partial‐slip solid‐phase wall boundary condition had the most significant effect on gas mixing. It was found that the solid‐phase wall boundary condition needs to be specified with great care when gas mixing is modeled, with free slip, partial slip and no‐slip wall boundary conditions giving substantial differences in the extent of gas back mixing. Axial and radial tracer concentration profiles for different operating conditions are generally in good agreement with experimental data from the literature. Detailed analyses of tracer back mixing are carried out in the second part. Two parameters, the tracer backflow fraction and overall gas backflow fraction, in addition to axial profiles of cross‐sectional averaged tracer concentrations, are evaluated for different flow conditions. Qualitative trends are consistent with reported experimental findings. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

Experimental and Numerical Study of Grinding Media Flow in a Ball Mill

An experimental and numerical study on the grinding media dynamics inside a baffled ball mill under different solid‐flow regimes, namely, cascading, cataracting, and centrifuging, is described. The Eulerian approach was used for all simulations and the boundary condition at the drum wall was investigated by means of the specularity coefficient parameter. This effort is an important approach in representing the particle‐wall interaction in a ball mill. The restitution coefficient of the balls was experimentally measured using a video camera, and its influence was evaluated by comparing the numerical and experimental outcome of flow patterns. The simulations results proved that the specularity and restitution coefficients effects at the drum wall were more evident at high rotational speeds.     

Partial slip boundary conditions for collisional granular flows at flat frictional walls

We derive new boundary conditions (BCs) for collisional granular flows of spheres at flat frictional walls. A new theory is proposed for the solids stress tensor, translational and rotational energy dissipation rate per unit area and fluxes of translational and rotational fluctuation energy. In the theory we distinguish between sliding and sticking collisions and include particle rotation. The predictions are compared with literature results obtained from a discrete particle model evaluated at a given ratio of rotational to translational granular temperature. We find that the new theory is in better agreement with the observed stress ratios and heat fluxes than previous kinetic theory predictions. Finally, we carry out two fluid model simulations of a bubbling fluidized bed with the new BCs, and compare the simulation results with those obtained from discrete particle simulations. The comparison reveals that the new BCs are better capable of predicting solids axial velocity profiles, solids distribution near the walls and granular temperatures. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1853–1871, 2017     

Boundary conditions for collisional granular flows of frictional and rotational particles at flat walls

Collisions between frictional particles and flat walls are determined using Coulomb friction and both tangential and normal restitution, and pseudothermal states of particles are described by both the translational and rotational granular temperatures. Then, new models for the stresses and the fluxes of fluctuation energy for the collisional granular flows at the walls are derived. These new models are tested and compared with the literature data and models. The ratio of rotational to translational granular temperatures is shown to be crucial on accurately predicting the shear stress and energy flux and is dependent on the normalized slip velocity as well as the collisional parameters. Using a theoretical but constant value for this ratio, predictions by the new models could still agree better with the literature data than those by the previous models. Finally, boundary conditions are developed to be used within the framework of kinetic theory of granular flow. © 2014 American Institute of Chemical Engineers AIChE J 60: 4065–4075, 2014     

CFD simulation of the high shear mixing process using kinetic theory of granular flow and frictional stress models

In order to enhance process understanding and to develop predictive process models in high shear granulation, there is an ongoing search for simulation tools and experimental methods to model and measure the velocity and shear fields in the mixer. In this study, the Eulerian-Eulerian approach to model multiphase flows has been used to simulate the mixer flow. Experimental velocity profiles for the solid phase at the wall in the mixer have been obtained using a high speed camera following the experimental procedure as described by Darelius et al. [2007a. Measurement of the velocity field and frictional properties of wet masses in a high shear mixer. Chemical Engineering Science, 62, 2366-2374]. The governing equations for modelling the dense mixer flow have been closed by using closure relations from the kinetic theory of granular flow (KTGF) combined with frictional stress models. The free slip and partial slip boundary conditions for the solid phase velocity at the vessel wall have been utilized. The partial slip model originally developed for dilute flows by Tu and Fletcher [1995. Numerical computation of turbulent gas-solid particle flow in a 90^° bend. A.I.Ch.E. Journal, 41, 2187-2197] has been employed. It was found that the bed height could be well predicted by implementing the partial slip model, whereas the free slip model could not capture the experimentally found bed height satisfactorily. In the simulation, the swirling motion of the rotating torus formed was over-predicted and the tangential wall velocity was under-predicted, probably due to the fact that the frictional stress model needs to be further developed, e.g. to tackle cohesive particles in dense flow. The advantage of using the Eulerian-Eulerian approach compared to discrete element methods is that there is no computational limitation on the number of particles being modelled, and thus manufacturing scale granulators can be modelled as well.     

Modeling dilute gas-particle flows in horizontal channels with different wall roughness

The dilute turbulent steady-state gas-particle flows in flat horizontal channels with different wall surface roughness are considered. The kinetic theory of granular flows has been employed for modeling. The new approach to defining boundary conditions for a solid phase, which is based on the tangential restitution coefficient, has been applied. The model has been validated by comparison of the computed data with the experimental results.     

颗粒相壁面条件对提升管内气固流动模拟的影响

引言提升管是非均匀结构显著的气固两相流动体系,其流动特性主要表现为轴向空隙率的"S"形分布、径向的"环-核"结构以及团聚物的生成和破碎等。近年来,国内外学者致力于数值计算方法的研究增多,其中双流体模型的应用最为广泛;颗     

Flow Channel Boundaries in Silos

The critical slip planes at the silo filling state are compared with the flow channel boundary during silo discharge for semi‐mass flows. The static critical slip planes are determined by using the dynamic programming method based on the stress field of granular solids stored in silos at the filling state. The flow channel boundary is estimated through the finite element analysis of the silo discharge. The results indicate that the critical slip line lies above the flow channel boundary. This characteristic can be attributed to the changeover of major principal stress directions of granular solids from the silo filling to the silo discharge. The analysis demonstrates that the silo wall friction tends to lift up the critical slip plane and flow boundary. A simple correlation is developed between the positions of critical slip planes and flow boundaries and is experimentally verified.     

A second‐order moment method applied to gas–solid risers

Second‐order moment method of particles is proposed on the basis of the kinetic theory of granular flow. Closure equations for the third‐order velocity moments are presented to account for the increase of the probability of collisions of particles on the basis of the elementary kinetic theory and order of magnitude analysis. The boundary conditions for the set of equations describing flow of particles are proposed with the consideration of the momentum exchange by collisions between the wall and the particles. The distributions of velocity, concentration and moments of particles are predicted. Simulated results are compared with experimental data measured by Tartan and Gidaspow and Bhusarapu et al. in risers, and Tsuji et al. in a vertical pipe. The effects of the closure equations for the third‐order velocity moments and the fluid‐particle velocity correlation tensor on flow behavior of particles are analyzed. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

The effect of mixer properties and fill level on granular flow in a bladed mixer

The discrete element method was used to study the effect of mixer properties and fill level on the granular flow of monodisperse, cohesionless spheres in a bladed mixer. For fill levels just covering the span of the blades, a three‐dimensional (3‐D) recirculation zone develops in front of the blades, which promotes vertical and radial mixing. Increasing fill level reduces the size of the recirculation zone, decreases bed dilation and hinders particle diffusivities. However, above a critical fill level, the behavior of the particles within the span of the blade is found to be invariant of fill level. At low‐fill levels, the pressure within the particle bed varies linearly with bed height and can be approximated by hydrostatics. At higher fill levels, a constant pressure region develops within the span of the blades due to the angled pitch of the blades. Cylinder wall friction is shown to significantly influence granular behavior in bladed mixers. At low‐wall friction, the 3‐D recirculation zone observed for high‐wall friction conditions does not develop. High‐wall friction leads to an increase in convective and diffusive particle mixing. Shear stresses are shown to be a function of wall friction. Blade position along the vertical axis is shown to influence flow patterns, granular temperature and stress. The effect of increasing the mixer diameter at a constant particle diameter was also studied. When the mixer diameter is larger than a critical size such that wall effects are minimized, the observed granular behavior follows simple scaling relations. Particle velocities and diffusivities scale linearly with mixer size and blade speed. Normal and shear stress profiles are found to scale linearly with the total weight of the particle bed. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Thermophoresis of axisymmetric aerosol particles along their axes of revolution

The axisymmetric thermophoretic motion of an aerosol particle of revolution in a uniformly prescribed temperature gradient is studied theoretically. The Knudsen number is assumed to be small so that the fluid flow is described by a continuum model. A method of distribution of a set of spherical singularities along the axis of revolution within a prolate particle or on the fundamental plane within an oblate particle is used to find the general solutions for the temperature distribution and fluid velocity field. The jump/slip conditions on the particle surface are satisfied by applying a boundary‐collocation technique to these general solutions. Numerical results for the thermophoretic velocity of the particle are obtained with good convergence behavior for various cases. For the axisymmetric thermophoresis of an aerosol spheroid with no temperature jump and frictional slip at its surface, the agreement between our results and the available analytical solutions is very good. The thermophoretic velocity of a spheroid along its axis of revolution in general increases with an increase in its axial‐to‐radial aspect ratio, but there are exceptions. For most practical cases of a spheroid with a specified aspect ratio, its thermophoretic mobility is not a monotonic function of its relative jump/slip coefficients and thermal conductivity. © 2008 American Institute of Chemical Engineers AIChE J, 2009     

壁面滑移对两种聚合物熔体共挤出影响的数值研究

在壁面滑移的边界条件下,利用聚合物流体计算软件包POLYFLOW对两种熔体的二维等温共挤出进行了数值模拟.在两侧壁面滑移系数相同和两侧壁面滑移系数不同这两种情形下分别计算了共挤出流动的速度场、压力场、黏度场及剪切速率场,讨论了壁面滑移对共挤出流场、界面形状和挤出胀大的影响.模拟结果表明：当两侧壁面滑移情况相同时,滑移系数越大,界面偏移越大,熔体胀大率增大;当两侧壁面滑移情况不同时,滑移系数相差越大,界面偏移越大,滑移系数小的一侧熔体挤出胀大显著.     

Catalytic Ozone Decomposition in a Gas‐Solids Circulating Fluidized‐Bed Riser

Computational fluid dynamics (CFD) modeling of the catalytic ozone decomposition reaction in a circulating fluidized‐bed (CFB) riser, using iron‐impregnated fluid catalytic cracking particles as catalyst, is carried out. The catalytic reaction is defined as a one‐step reaction, and the reaction equation is modified by with respect to the particle surface area, A_p, and an empirical coefficient. 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 simulation results are compared with experimental data, and the reaction rate is modified by using an empirical coefficient, to provide better simulation results than the original reaction rate. Moreover, the particle size has great effects on the reaction rate. The generality of the CFD model is further validated under different operating conditions of the riser.     

Hydrodynamic modeling of particle rotation for segregation in bubbling gas-fluidized beds

A multi-fluid Eulerian model has been improved by incorporating particle rotation using kinetic theory for rapid granular flow of slightly frictional spheres. A simplified model was implemented without changing the current kinetic theory framework by introducing an effective coefficient of restitution to account for additional energy dissipation due to frictional collisions. Simulations without and with particle rotation were performed to study the bubble dynamics and bed expansion in a monodispersed bubbling gas-fluidized bed and the segregation phenomena in a bidispersed bubbling gas-fluidized bed. Results were compared between simulations without and with particle rotation and with corresponding experimental results. It was found that the multi-fluid model with particle rotation better captures the bubble dynamics and time-averaged bed behavior. The model predictions of segregation percentages agreed with experimental data in the fluidization regime where kinetic theory is valid to describe segregation and mixing.     

Numerical Simulation of Tube Erosion in a Bubbling Fluidized Bed with a Dense Tube Bundle

Tube erosion in a bubbling fluidized bed is numerically studied using the Eulerian‐Eulerian method coupled with a monolayer kinetic energy dissipation model. The hydrodynamical simulations are performed under conditions with three different superficial gas velocities. The time‐averaged bubble frequency and bubble rise velocity are calculated to characterize the bed hydrodynamics. The erosion rates of two target tubes are simulated and the influence of the bubble behaviors on erosion rates is evaluated. Compared with the experimental data in the literature, the bubble behaviors are well captured by the simulations. Good agreement between the calculated and measured erosion rates is also obtained for the two target tubes. The bubble behaviors around the tubes have direct impact on the tube erosion. Only small discrepancies in the calculated erosion rates are found when using different particle‐wall restitution coefficients and specularity coefficients.     

Measurements of slip velocity and frictional heating in the capillary extrusion of linear‐low‐density polyethylene with a fluoropolymer processing aid

The slip velocity and frictional or slip heating of linear‐low density polyethylene with a fluoropolymer processing aid in capillary flow were measured by rheo‐particle image velocimetry and thermal imaging. The pure polymer did not show slip before the stick‐slip regime but exhibited strong slip when blended with the processing additive. However, for shear stresses beyond the stick‐slip regime, the pure polymer and the blend exhibited the same flow behavior with slip. The slip velocity increased with the shear stress at two different rates before and after the stick‐slip and the contribution of slip to the total flow rate exhibited a minimum. Significant rises in temperature were measured under slip and no slip conditions, being these much higher than the values predicted by the adiabatic flow assumption. Clear difference was made between viscous and frictional heating before the stick‐slip regime, even though they could not be distinguished from one another at higher stresses. Overall, in the presence of slip, frictional and viscous heating act synergistically producing higher temperature rises in the melt. Finally, in contrast to predictions by numerical simulations of viscous heating, measured velocity profiles did not evidence the heating effects in the shear stress range analyzed in this work. POLYM. ENG. SCI., 56:837–845, 2016. © 2016 Society of Plastics Engineers