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.     

Effect of coefficient of restitution in Euler-Euler CFD simulation of fluidized-bed hydrodynamics

Collision between particles plays an important role in determining the hydrodynamic characteristics of gas-solid flow in a fluidized bed.In the present work,earlier work(Loha,Chattopadhyay. Chatterjee,2013) was extended to study the effect of the elasticity of particle collision on the hydrodynamic behavior of a bubbling fluidized bed filled with 530-μm particles.The Eulerian-Eulerian two-fluid model was used to simulate the hydrodynamics of the bubbling fluidized bed.where the solid-phase properties were calculated by applying the kinetic theory of granular flow.To investigate the effect of the elasticity of particle collision,different values of the coefficient of restitution were applied in the simulation and their effects were studied in detail.Simulations were performed for two different solid-phase wall boundary conditions.No bubble formation was observed for perfectly elastic collision.The bubble formation started as soon as the coefficient of restitution was set below 1.0,and the space occupied by bubbles in the bed increased with a decrease in the coefficient of restitution.Simulation results were also compared with experimental data available in the literature,and good agreement was found for coefficients of restitution of 0.95 and 0.99.     

Effect of wall boundary condition on CFD simulation of CFB risers

The effect of solid-phase wall boundary condition on the numerical simulation of gas-solid flow in CFB risers containing FCC particles was investigated using the two-fluid model incorporating the kinetic theory of granular flow.Both the Gidaspow drag model and the EMMS-based drag model were used.The Johnson and Jackson(1987) wall boundary condition was applied to describe the interaction between particles and wall.Based on the experimental system of Li and Kwauk(1994),parametric studies of specularity coefficient(φ=1.0,0.6,0.0005,0.00005,0) and particle-wall restitution coefficient(e_w=0.6,0.9,0.95,0.99,0.999) were performed to evaluate their effects on axial voidage profile,solids flux,meso-scale and heterogeneous structures.Simulation results showed that solid-phase wall boundary condition had little effect on axial voidage profile when the Gidaspow drag model was used.However,the specularity coefficient φ had a pronounced influence on flow behavior when the EMMS-based drag model was used,and a small specularity coefficient(φ=0.00005,0) could result in better agreement with experimental data.The particle-wall restitution coefficient e_w plays but a minor role in the holistic flow characteristics.     

A new model for dissipative particle dynamics boundary condition of walls with different wettabilities

The implementation of solid-fluid boundary condition has been a major challenge for dissipative particle dynamics(DPD)method.Current implementations of boundary conditions usually try to approach a uniform density distribution and a velocity profile close to analytical solution.The density oscillations and slip velocity are intentionally eliminated,and different wall properties disappear in the same analytical solution.This paper develops a new wall model that combines image and frozen particles and a new strategy to emphasize different wall properties especially wettabilities.The strategy first studies the realistic wall-fluid system by molecular dynamics(MD)simulation depending on physical parameters.Then,a DPD simulation is used to match the density and velocity profiles with the new wall model.The obtained DPD parameters can simulate the systems with the same wall and fluid materials.With this method,a simulation of the Poiseuille flow of liquid argon with copper walls is presented.Other walls with super-hydrophilic,hydrophilic,and hydrophobic wettabilities are also simulated.The limitations of the analytical solution and the effect of the wall-fluid interaction are discussed.The results show that the method suggested in this paper can simulate the mesoscale behavior of the microchannel flow related to realistic systems.     

Segregation behavior of a ternary mixture of titanium dioxide particles in a pseudo two-dimensional fluidized bed

The segregation behavior of a mixture of silica-coated titanium dioxide(TiO2)particles of three different sizes in a pseudo two-dimensional fluidized bed was studied experimentally by the freeze-sieving method and numerically by the multi-fluid model(MFM).Three-dimensional computational fluid dynamics(CFD)simulations were carried out to evaluate the effects of the solid wall boundary conditions on particle segregation in terms of specularity and particle-wall restitution coefficients.The quantitative indexes of segregation tendency and segregation degree were used to determine the axial segregation of the mixture in triangular coordinates.The simulation results revealed that the axial segregation increased with the specularity coefficient,whereas the particle-wall restitution coefficient had a minor effect on axial segregation.Comparison of the simulation results with experimental data showed that the appropriate value of the specularity coefficient used in the CFD model depended on superficial gas velocity.The study of the effects of superficial gas velocity on segregation behavior demonstrated that the greatest segregation was obtained at minimum fluidization velocity and the segregation decreased as the gas velocity gradually increased.     

Experimental and computational studies on flow behavior of gas–solid fluidized bed with disparately sized binary particles

This paper presents experimental and computational studies on the flow behavior of a gas-solid fluidized bed with disparately sized binary particle mixtures. The mixing/segregation behavior and segregation efficiency of the small and large particles are investigated experimentally. Particle composition and operating conditions that influence the fluidization behavior of mixing/segregation are examined. Based on the granular kinetics theory, a multi-fluid CFD model has been developed and verified against the experimental results. The simulation results are in reasonable agreement with experimental data. The results showed that the smaller particles are found near the bed surface while the larger particles tend to settle down to the bed bottom in turbulent fluidized bed. However, complete segregation of the binary particles does not occur in the gas velocity range of 0.695-0.904 m/s. Segregation efficiency increases with increasing gas velocity and mean residence time of the binary particles, but decreases with increasing the small particle concentration. The calculated results also show that the small particles move downward in the wall region and upward in the core. Due to the effect of large particles on the movement of small particles, the small particles present a more turbulent velocity profile in the dense phase than that in the dilute phase.     

Lie group analysis for thermophoretic and radiative augmentation of heat and mass transfer in a Brinkman-Darcy flow over a flat surface with heat generation

A boundary layer analysis is presented to investigate numerically the effects of radiation,thermophoresis and the dimensionless heat generation or absorption on hydromagnetic flow with heat and mass transfer over a flat surface in a porous medium.The boundary layer equations are transformed to non-linear ordinary differential equations using scaling group of transformations and they are solved numerically by using the fourth order Runge-Kutta method with shooting technique for some values of physical parameters.Comparisons with previously published work are performed and the results are found to be in very good agreement.Many results are obtained and a representative set is displayed graphically to illustrate the influence of the various parameters on the dimensionless velocity,temperature and concentration profiles as well as the local skin-friction coefficient,wall heat transfer,particle deposition rate and wall thermophoretic deposition velocity.The results show that the magnetic field induces acceleration of the flow,rather than deceleration(as in classical magnetohydrodynamics(MHD) boundary layer flow) but to reduce temperature and increase concentration of particles in boundary layer.Also,there is a strong dependency of the concentration in the boundary layer on both the Schmidt number and mass transfer parameter.     

Numerical simulation of gas-solid flow with two fluid model in a spouted-fluid bed

The flow characteristics in a spouted-fluid bed differ from those in spouted or fluidized beds because of the injection of the spouting gas and the introduction of a fluidizing gas. The flow behavior of gas-solid phases was predicted using the Eulerian-Eulerian two-fluid model （TFM） approach with kinetic theory for granular flow to obtain the flow patterns in spouted-fluid beds. The gas flux and gas incident angle have a significant influence on the porosity and particle concentration in gas-solid spouted-fluid beds. The fluidizing gas flux affects the flow behavior of particles in the fountain. In the spouted-fluid bed, the solids volume fraction is low in the spout and high in the annulus. However, the solids volume fraction is reduced near the wall.     

Filtration characteristics of granular bed with layered drawers for removing dust from gas streams

Filtration tests were conducted on a granular bed filter with layered drawers filled with corundum particles with sizes between either 1 mm and 1.5 mm or 2 mm and 3 mm or with quartz sand particles with sizes between 0.125 mm and 1.5 mm.Filtration velocity,filter particle thickness,and filter particle size were all found to influence the filtration efficiency and the pressure drop of both the fixed granular bed and the layered-drawer granular bed.Granular strata with different thickness ratios also strongly influenced the filtration efficiency and pressure drop.For a granular bed with two sizes of filter particles,the coarse granules in the upper layer capture dust with large particle sizes,while the fine granules in the lower layer capture dust with smaller particle sizes that passes through the filter cake and upper layer.Optimal operating conditions were determined at which the filtration efficiency was found to be 99.42%with a bed pressure drop of 320 Pa.     

Generation of linear and nonlinear waves in numerical wave tank using clustering technique-volume of fluid method

A two-dimensional(2D) numerical model is developed for the wave simulation and propagation in a wave flume.The fluid flow is assumed to be viscous and incompressible,and the Navier-Stokes and continuity equations are used as the governing equations.The standard k-ε model is used to model the turbulent flow.The NavierStokes equations are discretized using the staggered grid finite difference method and solved by the simplified marker and cell(SMAC) method.Waves are generated and propagated using a piston type wave maker.An open boundary condition is used at the end of the numerical flume.Some standard tests,such as the lid-driven cavity,the constant unidirectional velocity field,the shearing flow,and the dam-break on the dry bed,are performed to valid the model.To demonstrate the capability and accuracy of the present method,the results of generated waves are compared with available wave theories.Finally,the clustering technique(CT) is used for the mesh generation,and the best condition is suggested.     

Prediction of hypersonic boundary layer transition on sharp wedge flow considering variable specific heat

When the air temperature reaches 600 K or higher, vibration is excited. The specific heat is not a constant but a function of temperature. Under this condition, the transition position of hypersonic sharp wedge boundary layer is predicted by using the improved eN method considering variable specific heat. The transition positions with different Mach numbers of oncoming flow, half wedge angles, and wall conditions are computed condition, the nearer to the Mach number The results show that for the same oncoming flow condition and wall transition positions of hypersonic sharp wedge boundary layer move much leading edge than those of the flat plate. The greater the oncoming flow the closer the transition position to the leading edge.     

CFD-DEM simulation of Small-Scale Challenge Problem 1 with EMMS bubble-based structure-dependent drag coefficient

In this study,the energy minimization multi-scale(EMMS)/Bubbling model is coupled with the computational fluid dynamics/discrete element method(CFD-DEM)model via a structure-dependent drag coefficient to simulate the National Energy Technology Laboratory(NETL)small-scale challenge problem using the open-source multiphase flow code MFIX.The numerical predictions are compared against particle velocity measurements obtained from high-speed particle image velocimetry(HSPIV)and differential pressure measurements.The drag-reduction effect of the EMMS bubble-based drag coefficient is observed to significantly improve predictions of the horizontal particle velocity and granular temperature when compared to several other drag coefficients tested;however,the vertical particle velocity and pressure fluctuation characteristic predictions are degraded.The drag-reduction effect is characterized by a reduction in the sizes of slugs or voids,as identified through spectral decomposition of the pressure fluctuations.Overall,this study shows great promise in employing drag coefficients,developed via multi-scale approaches(such as the EMMS paradigm),in CFD-DEM models.     

DEM Modeling of Particle Breakage in Silica Sands under One-Dimensional Compression

A Discrete Element Method(DEM) model is developed to study the particle breakage effect on the one-dimensional compression behavior of silica sands. The ‘maximum tensile stress' breakage criterion considering multiple contacts is adopted to simulate the crushing of circular particles in the DEM. The model is compared with published experimental results. Comparison between the compression curves obtained from the numerical and experimental results shows that the proposed method is very effective in studying the compression behavior of silica sands considering particle breakage. The evolution of compression curves at different stress levels is extensively studied using contact force distribution, variation of contact number and particle size distribution curve with loading. It is found that particle breakage has great impact on compression behavior of sand, particularly after the yield stress is reached and particle breakage starts.The crushing probability of particles is found to be macroscopically affected by stress level and particle size distribution curve, and microscopically related to the evolutions of contact force and coordination number. Once the soil becomes well-graded and the average coordination number is greater than 4 in two-dimension, the crushing probability of parent particles can reduce by up to5/6. It is found that the average contact force does not always increase with loading, but increases to a peak value then decreases once the soil becomes more well-graded. It is found through the loading rate sensitivity analysis that the compression behavior of sand samples in the DEM is also affected by the loading rate. Higher yield stresses are obtained at higher loading rates.     

Numerical simulations of gas-particle flow behavior created by low-level rotary-winged aircraft flight over particle bed

The aerodynamics of gas-particle suspensions is simulated as an Euler-Euler two-fluid model in a revolving rotor over a particle bed. The interactions of collisions between the blade and particles and particle-particle interactions are modeled using the kinetic theory of granular flow(KTGF). The gas turbulence induced by the rotation of the rotor is modeled using the kg-εg model. The flow field of a revolving rotor is simulated using the multiple reference frame(MRF) method. The distributions of velocities, volume fractions, and gas pressure are predicted while the aircraft hovers at different altitudes.The gas pressure decreases from the hub to the tip of the blade, and it is higher at the pressure side than that at the suction side of the rotor. The turbulent kinetic energy of the gas increases toward the blade tip. The volume fraction of particles decreases as the hovering altitude increases. The simulated pressure coefficient is compared with that in experimental measurements.     

Segregation of particulate solids＂ Experiments and DEM simulations

Segregation of granular materials is a complex phenomenon, difficult to measure quantitatively and to predict. Discrete element method （DEM） can be a useful tool to predict segregation effects and to support the industrial design. In this context, a very challenging idea is the characterization of the granular solids to provide the key parameters needed for a successful DEM simulation of segregation processes. Rolling friction, sliding friction and the coefficient of restitution are the critical parameters to be studied. These microscopic simulation parameters are calibrated by comparing the macroscopic behavior of granular matter in standard bulk experiments, which have the advantage of being highly repeatable and reliable. An experimental method is presented to characterize free surface segregation. The effects of different particle properties, particularly, shape and size, on segregation of cohesionless materials were investi- gated. From the experiments, particle size demonstrated a stronger effect on segregation than particle shape. Finally, the corresponding DEM simulations of the segregation experiments were presented. The parameters obtained by calibration were validated by the comparison of the modeled segregation behav- ior with the experimental results. Thus, calibrated DEM simulations are capable of predicting segregation effects.     

Micromechanics of breakage in sharp-edge particles using combined DEM and FEM

By combining DEM （Discrete Element Method） and FEM （Finite Element Method）, a model is established to simulate the breakage of twodimensional sharp-edge particles, in which the simulated particles are assumed to have no cracks. Particles can, however, crush during different stages of the numerical analysis, if stress-based breakage criteria are fulfilled inside the particles. With this model, it is possible to study the influence of particle breakage on macro- and micro-mechanical behavior of simulated angular materials. Two series of tests, with and without breakable particles, are simulated under different confining pressures based on conditions of biaxial tests. The results, presented in terms of micromechanical behavior for different confining pressures, are compared with macroparameters. The influence of particle breakage on microstructure of sharp-edge materials is discussed and the related confining pressure effects are investigated. Breakage of particles in rockfill materials are shown to reduce the anisotropy coefficients of the samples and therefore their strength and dilation behaviors.     

Non-Newtonian effect on natural convection flow over cylinder of elliptic cross section

The non-Newtonian effect in the boundary layer flow over a horizontal elliptical cylinder is investigated numerically. A modified power-law viscosity model is used to correlate the non-Newtonian characteristics of the fluid flow. For natural convectionflows, the surface of the cylinder is maintained by the uniform surface temperature(UST)or the uniform heat flux(UHF) condition. The governing equations corresponding to theflow are first transformed into a dimensionless non-similar form using suitable transformations. The resulting equations are solved numerically by an efficient finite difference scheme. The numerical results are presented for the skin friction coefficient and the local Nusselt number with the eccentric angle for different values of the power-law index n. The local skin friction coefficient and the local Nusselt number are found to be higher and lower, respectively, for the shear thickening fluids(n > 1) than the other fluids(n≤1).The effects of different elliptical configurations on the average Nusselt number are also presented and discussed for both conditions of the surface temperature.     

An improved correlation of the pressure drop in stenotic vessels using Lorentz’s reciprocal theorem

A mathematical model of the human cardiovascular system in conjunction with an accurate lumped model for a stenosis can provide better insights into the pressure wave propagation at pathological conditions. In this study, a theoretical relation between pressure drop and flow rate based on Lorentz’s reciprocal theorem is derived, which offers an identity to describe the relevance of the geometry and the convective momentum transport to the drag force. A voxelbased simulator V-FLOW VOF3 D, where the vessel geometry is expressed by using volume of fluid(VOF) functions, is employed to find the flow distribution in an idealized stenosis vessel and the identity was validated numerically. It is revealed from the correlation that the pressure drop of NS flow in a stenosis vessel can be decomposed into a linear term caused by Stokes flow with the same boundary conditions, and two nonlinear terms. Furthermore, the linear term for the pressure drop of Stokes flow can be summarized as a correlation by using a modified equation of lubrication theory, which gives favorable results compared to the numerical ones. The contribution of the nonlinear terms to the pressure drop was analyzed numerically, and it is found that geometric shape and momentum transport are the primary factors for the enhancement of drag force. This work paves a way to simulate the blood flow and pressure propagation under different stenosis conditions by using 1D mathematical model.     

Dual solutions in MHD stagnation-point flow of Prandtl fluid impinging on shrinking sheet

The present article investigates the dual nature of the solution of the magneto- hydrodynamic （MHD） stagnation-point flow of a Prandtl fluid model towards a shrinking surface. The self-similar nonlinear ordinary differential equations are solved numerically by the shooting： method. It is found that the dual solutions of the flow exist for cer- tain values of tile velocity ratio parameter. The special case of the first branch solutions （the classical Newtonian fluid model） is compared with the present numerical results of stretching flow. The results are found to be in good agreement. It is also shown that the boundary layer thickness for the second solution is thicker than that for the first solution.     

A CLOSED SYSTEM OF EQUATIONS FOR DENSE TWO-PHASE FLOW AND EXPRESSIONS OF SHEARING STRESS OF DISPERSED PHA’E AT A WALL

In this paper.each of the two phases in dense two-phase flow is considered ascontinuous medium and the fimdamental equations for two-phase flow are described inEulerian form.The generalized constitutive relation of the Bingham fluid is applied to thedispersed phase with the analysis of physical mechanism of of dense two-phase flow.Theshearing stress of dispersed phase at a wall is used to give a boundary condition.Then amathematical model for dense two-phase flow is obtained.In addition.the expressions ofshearing stress of dispersed phase at a wall is derived according to the fundamental,model ofthe frictional collision between dispersed-phase particles and the wall.