CFD simulation of internal-loop airlift reactor using EMMS drag model

The simulation of internal-loop airlift reactors is challenging because complex meso-scale structures exist in different sections of the reactor,separated by the draft tube.This paper reports on the computational fluid dynamics(CFD) simulation of internal-loop airlift reactors using a new drag model derived from the dual-bubble-size(DBS) model,an extended energy-minimization multi-scale(EMMS) approach for gas-liquid flows.Compared with the traditional Schiller-Naumann(S-N) correlation,the new model improves the simulation of gas holdup in the riser and downcomer significantly.In particular,gas holdup and circulation of two-phase flow can be modeled successfully using the new model,whereas traditional drag models such as the S-N correlation show an absence of gas in the downcomer.The simulation demonstrates the advantage and potential of this new model for internal-loop airlift reactors.     

二维喷动床CFD-DEM模拟中曳力模型的影响

CFD-DEM已经广泛应用到喷动床的研究中,其模拟的准确性与用于处理颗粒-流体相互作用的曳力模型密切相关。为了探究不同曳力模型对喷动床CFD-DEM模拟结果的影响,基于非结构化网格的喷动床仿真,使用7个曳力模型分别对锥底喷动床内气固两相运动进行了数值模拟。综合床层压降、喷动高度和颗粒速度特性三个方面,Wen-Yu模型和Gibilaro模型预测的气固两相运动最剧烈,其次是Di Felice模型、Syamlal-O’Brien模型、Gidaspow模型和Huilin-Gidaspow模型,BVK模型预测的气固两相运动最平缓。由于模拟的气固两相体系属于密相体系,Huilin-Gidaspow模型的光滑过渡函数没有产生效果,所以Gidaspow模型和Huilin-Gidaspow模型在各个方面的预测结果基本一致。     

EMMS mixture model with size distribution for two-fluid simulation of riser flows

Further development of an energy-minimization multiscale modeling approach to simulating two-phase flow under turbulent conditions that considers the size distribution of mesoscale structures, i.e. bubbles and clusters, is presented. User-defined values of minimum and maximum cluster or bubble diameters were specified. A uniform size distribution was first considered as a test case, in which the drag force comprised contributions from each size group. The mathematical form of the objective function describing the energy for suspension and transport was not altered. The heterogeneity index of this new drag modification was then used to simulate pilot-scale circulating fluidized-bed risers involving Geldart group A particles. The results were validated against available experimental data. The model is capable of capturing both axial and radial profiles of flow-field variables.     

CFD-DEM simulation of spouting of corn-shaped particles

Three dimensionally coupled computational fluid dynamics (CFD) and discrete element method (DEM) were used to investigate the flow of corn-shaped particles in a cylindrical spouted bed with a conical base. The particle motion was modeled by the DEM, and the gas motion by the k-? two-equation turbulent model. A two-way coupling numerical iterative scheme was used to incorporate the effects of gas–particle interactions in terms of momentum exchange. The corn-shaped particles were constructed by a multi-sphere method. Drag force, contact force, Saffman lift force, Magnus lift force, and gravitational force acting on each individual particle were considered in establishing the mathematical modeling. Calculations were carried out in a cylindrical spouted bed with an inside diameter of 200 mm, a height of 700 mm, and a conical base of 60°. Comparison of simulations with experiments showed the availability of the multi-sphere method in simulating spouting action with corn-shaped particles, but it depended strongly on the number and the arrangement of the spherical elements. Gas–solid flow patterns, pressure drop, particle velocity and particle concentration at various spouting gas velocity were discussed. The results showed that particle velocity reaches a maximum at the axis and then decreases gradually along the radial direction in the whole bed. Particle concentration increases along the radial direction in the spout region but decreases in the fountain region, while it is nearly constant in the annulus region. Increasing spouting gas velocity leads to larger pressure drop, remarkably increased speed of particle moving upward or downward, but decreased particle concentration.     

Accelerating CFD–DEM simulation of processes with wide particle size distributions

Size-reduction systems have been extensively used in industry for many years. Nevertheless, reliable engineering tools to be used to predict the comminution of particles are scarce. Computational fluid dynamics(CFD)–discrete element model(DEM) numerical simulation may be used to predict such a complex phenomenon and therefore establish a proper design and optimization model for comminution systems.They may also be used to predict attrition in systems where particle attrition is significant. Therefore,empirical comminution functions(which are applicable for any attrition/comminution process), such as:strength distribution, selection, equivalence, breakage, and fatigue, have been integrated into the threedimensional CFD–DEM simulation tool. The main drawback of such a design tool is the long computational time required owing to the large number of particles and the minute time-step required to maintain a steady solution while simulating the flow of particulate materials with very fine particles.The present study developed several methods to accelerate CFD–DEM simulations: reducing the number of operations carried out at the single-particle level, constructing a DEM grid detached from the CFD grid enabling a no binary search, generating a sub-grid within the DEM grid to enable a no binary search for fine particles, and increasing the computational time-step and eliminating the finest particles in the simulation while still tracking their contribution to the process.The total speedup of the simulation process without the elimination of the finest particles was a factor of about 17. The elimination of the finest particles gave additional speedup of a factor of at least 18.Therefore, the simulation of a grinding process can run at least 300 times faster than the conventional method in which a standard no binary search is employed and the smallest particles are tracked.     

Coupled CFD-DEM simulation of hydrodynamic bridging at constrictions

This paper presents a coupled CFD-DEM approach to simulate the flow of particulate suspensions in the intermediate concentration regime where solid volume concentration is 1% < ϕ < 50%. In particular, hydrodynamic multi-particle bridging during flow through a single constriction in a rectangular channel is studied. It is shown that for neutrally buoyant, monodispersed particulate suspensions, the probability of jamming increases with the particle concentration. There also exists a critical particle concentration (ϕ*) for spontaneous bridging, which depends on the ratio of pore size to particle size, the flow velocity, the particle-fluid density contrast, and the flow geometry leading to the constriction. The ϕ* has a strong dependence on the outlet-to-particle relative size (R_o). For 1.5 ≤ R_o ≤ 2.5, a direct transition from a flowing state to a jammed state was observed. For R_o ≥ 3, the flowing state typically transitioned to a dense state characterized by the accumulation of particles near the constriction before jamming. Increasing the inlet-to-particle relative size (R_ip) lowers ϕ* by increasing the number of particles arriving at the constriction simultaneously. The effect of changing R_ip is more pronounced at high R_o when the probability of bridging is lower. A high fluid velocity increases particle interactions near the constriction and accelerates the onset of bridging. However, no distinct effect of velocity on ϕ* was observed in this study. A higher particle-to-fluid density ratio (ρ_p/ρ_f) increases the probability of bridging and leads to a lower ϕ* in a given constriction geometry. The effect saturates at higher ρ_p/ρ_fwhen gravitational forces completely dominate over viscous drag forces. ϕ* is also found to decrease with increasing angle of constriction convergence (θ) for θ < 30°, but increases beyond that at $\theta ={60}^{\circ }$.     

On the drag coefficient of triangular profiles

Summary Results of a laboratory study on the determination of the drag coefficient of triangular profiles simulating a train of sedimentary dunes are here presented. The study is carried out in a low speed wind tunnel by performing a direct measurement of the total drag force acting on one of the profiles and then subtracting the skin shear force to obtain the net pressure drag force. Drag coefficient behavior is studied as a function of the profile Reynolds number. Results are then discussed using some recent criteria available in literature.

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Sommario Si espongono i risultati di un lavoro sperimentale volto allo studio del coefficiente di resistenza di un profilo triangulare con geometria analoga a quella delle dune fluviali. Gli esperimenti sono condotti in una galleria del vento a bassa velocità, misurando direttamente la forza totale esercitata dalla corrente su uno dei profili e provvedendo poi a sottrarre la forza di attrito superficiale stimata. L'andamento del coefficiente di attrito è studiato in funzione del numero di Reynolds. I risultati sono po discussi alla luce di alcuni recenti contributi bibliografici.

     

带自由表面水流与离散颗粒耦合模型研究

基于考察泥沙运动的细观行为特征,采用离散单元法(DEM)模拟泥沙颗粒运动,结合带自由表面的水动力学计算模型,建立了CFD-DEM耦合数值模型。计算程序开发基于Fortran语言来实现。耦合模型中实现了硬球模型和软球模型两种颗粒碰撞模型,应用范围较广。作为自由表面水流与泥沙颗粒流数值模型的初步研究,在模型建立的基础上,对模型做了基本的验证。分别通过单颗粒静水沉降和混合颗粒群分选两个计算工况,验证了模型的正确性及模拟精度。该耦合模型可进一步丰富带自由表面水流条件下泥沙运动的研究手段。     

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 prediction of particle slip velocity in turbulence by CFD-DEM simulation

Turbulent environment improves the flotation recovery of fine particles by promoting the particle–bubble collision rate, which directly depends on the particle slip velocity. However, the existing slip velocity models are not applicable to fine particles in turbulence. The mechanism of turbulence characteristics and particle properties on the slip velocity of fine particles in turbulence was unclear. In this study, a coupled ANSYS FLUENT and EDEM based on computational fluid dynamics (CFD) and discrete element method (DEM) were used to simulate the slip velocity of fine particles in the approximately homogenous isotropic turbulence, which was excited by the grid. The reliability of the used CFD-DEM simulation method was validated against the slip velocity measured by the particle image velocimetry (PIV) experiments. In particular, the effects of the particle shapes, particle densities, and turbulence intensities on the slip velocity have been investigated with this numerical method. Numerical results show that particle shapes have no significant effect on fine particles between 37 and 225 μm. The slip velocity of the spherical particles increases with the turbulence intensity and particle density. Based on the simulated data, a model which has a correlation coefficient of 0.95 is built by using nonlinear fitting.     

CFD-DEM simulation of the pneumatic conveying of fine particles through a horizontal slit

Fine particles play a significant role in many industrial processes.To study the dynamic behavior of fine particle and their deposition in rock fractures,the pneumatic conveying of fine particles(approximately100 μm in diameter) through a small-scale horizontal slit(0.41 m × 0.025 m) was studied,which is useful for the sealing technology of underground gas drainage in coal mining production.The CFD-DEM method was adopted to model the gas-particle two-phase flow;the gas phase was treated as a continuum and modeled using computational fluid dynamics(CFD),particle motion and collisions were simulated using the DEM code.Then,the bulk movement of fine particles through a small-scale horizontal slit was explored numerically,and the flow patterns were further investigated by visual inspection.The simulation results indicated that stratified flow or dune flow can be observed at low gas velocities.For intermediate gas velocities,the flow patterns showed pulsation phenomena,and dune flow reappeared in the tail section.Moreover,periodic flow regimes with alternating thick and sparse stream structures were observed at a high gas velocity.The simulation results of the bulk movement of fine particles were in good agreement with the experimental findings,which were obtained by video-imaging experiments.Furthermore,the calculated pressure drop versus gas velocity profile was investigated and compared with relative experimental findings,and the results showed good agreement.Furthermore,the particle velocity vectors and voidage distribution were numerically simulated.Selected stimulation results are presented and provide a reference for the further study of fine particles.     

Bodies of revolution with minimal drag coefficient and low heat transfer at high supersonic speeds

On the basis of modified Newtonian theory and the theory of selfsimilar hypersonic flows we study the form of the optimal contour of a body of revolution with minimal drag coefficient at hypersonic speeds. It is shown that bodies of optimal form also have a small heat transfer coefficient, much smaller than for a conical body. It is established experimentally that the optimal properties of these bodies of revolution are also retained for moderate supersonic flight speeds.In concluslion the author wishes to thank V. V. Sychev for valuable discussions of this problem.     

An extended unresolved CFD-DEM coupling method for simulation of fluid and non-spherical particles

This study develops an extended unresolved CFD-DEM coupling method for simulation of the fluid–solid flow with non-spherical particles. The limitation of fluid grid size is discussed, by simulating the settling of a cylinder in a Newtonian fluid based on the resolved and unresolved CFD-DEM coupling method. Then, the calculation of porosity and the fluid–particle relative velocity based on the particle shape enlargement method for simulation of non-spherical particles is proposed. The availability of the particle shape enlargement method for the simulation of non-spherical particles with different sphericity is discussed in this work, by comparing it with the results from the equivalent diameter enlargement method. The limitation of the equivalent diameter enlargement method for non-spherical particles is revealed from the simulation results. Several typical cases are employed to elaborate and verify the extended unresolved CFD-DEM method based on particle shape enlargement method, by presenting a good consistency with the experimental results. It proves that the extended unresolved CFD-DEM method is suitable for different CFD grid size ratios, and consolidates that it is a universal calculation method for CFD-DEM coupling simulation.     

The importance of turbulence macroscale in determining the drag coefficient of spheres

Turbulence macroscale, from evidence provided, is at least as important as its intensity in determining the drag coefficient of spheres, particularly when macroscale and sphere diameter are comparable. Particular combinations of scale, intensity and Reynolds number can produce sudden and repeatable marked changes in flow conditions which are as important as the well known change in boundary layer conditions at critical Reynolds number. More detailed analysis suggests that other researchers' results appear sometimes to be mutually incompatible simply because they were dealing with differnt areas of the complicated relationship between drag coefficient. Reynolds number, turbulence intensity and macroscale.     

The effects of freestream turbulence on the drag coefficient of a sphere

The effects of freestream turbulence intensity and integral length scale as freestream turbulent parameters on the drag coefficient of a sphere were experimentally investigated in a closed circuit wind tunnel. The Reynolds number, Re = Ud/ν, was varied from 2.2 × 10⁴ to 8 × 10⁴ by using spheres with diameter d of 20, 51 and 102 mm in addition to altering the freestream velocity, U. The freestream turbulence intensity Tu and flow integral length scale Λ were manipulated by the utilization of orifice perforated plates. The proper combination of orifice perforated plate hole diameter, sphere size, and sphere location along the center line of the wind tunnel enabled the independent alterations of turbulence intensity and relative integral length scale (Λ/d) from 1.8% to 10.7% and from 0.1 to 2.6, respectively, at each studied Reynolds number. Results show that over the range of conditions studied, the drag always decreases with increasing Tu and, the critical Reynolds number at which the drag coefficient is dramatically reduced is decreased by increasing Tu. Most interestingly, the drag at any particular Re and Tu may be significantly lowered by reducing Λ/d; this is particularly the case at high Re and Tu.     

Numerical simulation of vortex-induced drag of elastic swimmer models

We present numerical simulations of simplified models for swimming organisms or robots, using chordwise flexible elastic plates. We focus on the tip vortices originating from three-dimensional effects due to the finite span of the plate. These effects play an important role when predicting the swimmer's cruising velocity, since they contribute significantly to the drag force. First we simulate swimmers with rectangular plates of different aspect ratios and compare the results with a recent experimental study. Then we consider plates with expanding and contracting shapes. We find the cruising velocity of the contracting swimmer to be higher than the rectangular one, which in turn is higher than the expanding one. We provide some evidence that this result is due to the tip vortices interacting differently with the swimmer.     

Approximate solutions for drag coefficient of bubbles moving in shear-thinning elastic fluids

The drag coefficient for bubbles with mobile or immobile interface rising in shear-thinning elastic fluids described by an Ellis or a Carreau model is discussed. Approximate solutions based on linearization of the equations of motion are presented for the highly elastic region of flow. These solutions are in reasonably good agreement with the theoretical predictions based on variational principles and with published experimental data. C _D Drag coefficient - E ^* Differential operator [E ^{* 2} = ²/² + (sin/ ²)/(1/sin /)] - El Ellis number - F _D Drag force - K Consistency index in the power-law model for non-Newtonian fluid - n Flow behaviour index in the Carreau and power-law models - P Dimensionless pressure [=(p – p ₀)/₀ (U /R)] - p Pressure - R Bubble radius - Re ₀ Reynolds number [= 2R U /₀] - Re Reynolds number defined for the power-law fluid [= (2R) ⁿ U ^2–n /K] - r Spherical coordinate - t Time - U Terminal velocity of a bubble - u Velocity - Wi Weissenberg number - Ellis model parameter - Rate of deformation - Apparent viscosity - ₀ Zero shear rate viscosity - Infinite shear rate viscosity - Spherical coordinate - Parameter in the Carreau model - ^* Dimensionless time [=/(U /R)] - Dimensionless length [=r/R] - Second invariant of rate of deformation tensors - ^* Dimensionless second invariant of rate of deformation tensors [=/(U /R)²] - Second invariant of stress tensors - ^* Dimensionless second invariant of second invariant of stress tensor [= / ₀ ² (U /R)²] - Fluid density - Shear stress - ^* Dimensionless shear stress [=/ ₀ (U /R)] - _1/2 Ellis model parameter - ₁ ^2/* Dimensionless Ellis model parameter [= _1/2/ ₀(U /R)] - Stream function - ^* Dimensionless stream function [=/U R ²]     

Optical measurement of velocity and drag coefficient of droplets accelerated by shock waves

The drag coefficient of micron-sized droplets accelerated by a shock wave has been investigated. The motion of the droplets was studied by an optical measurement system, and an inertial relaxation in the mist flow is discussed in detail. An expansion-shock tube was employed in the present experiment, in which water droplets were produced by a homogeneous condensation when humid nitrogen gas expanded adiabatically in the test section. The local mean diameter and local number density of the droplet cloud were 1.0 m and on the order of 10¹² particles/m³, respectively, as estimated using a light scattering measurement in a preliminary experiment. The droplet cloud accelerated behind a shock wave was observed using a direct shadowgraph method with a spatial filter. Since the intensity of transmitted light through the mist flow is a function of the radius and number density of droplets, we can obtain the locally averaged number density distribution under an adequate approximation. The transmitted light intensity was related to the velocity distribution of droplets under the adequate assumption. So, the acceleration of droplets was estimated from the velocity ratio between the droplets and gas flow. Then, the drag coefficient was calculated for the particle Reynolds number. The experimental result was also compared to a numerical prediction.