Comparative analysis on gas–solid drag models in MFIX-DEM simulations of bubbling fluidized bed

In this study,the open-source software MFIX-DEM simulations of a bubbling fluidized bed(BFB)are applied to assess nine drag models according to experimental and direct numerical simulation(DNS)results.The influence of superficial gas velocity on gas–solid flow is also examined.The results show that according to the distribution of time-averaged particle axial velocity in y direction,except for Wen–Yu and Tenneti–Garg–Subramaniam(TGS),other drag models are consistent with the experimental and DNS results.For the TGS drag model,the layer-by-layer movement of particles is observed,which indicates the particle velocity is not correctly predicted.The time domain and frequency domain analysis results of pressure drop of each drag model are similar.It is recommended to use the drag model derived from DNS or fine grid computational fluid dynamics–discrete element method(CFD-DEM)data first for CFD-DEM simulations.For the investigated BFB,the superficial gas velocity less than 0.9 m·s^(-1) should be adopted to obtain normal hydrodynamics.

CFD Simulation of Particles Mixing and Segregation in a Rotary Coating Disk: Influence of Drag Models and Restitution Coefficient

In this paper, the dynamics of a transverse plane of a rotary coating disk of a binary mixture system comprising sand and urea particles were simulated using the two-fluid model along with the kinetic theory of granular flow in Fluent 19.1. Although some parameters relating to the material properties and size of the rotary coating disk have been researched, the effects of both drag force and restitution coefficient on the flow characteristics have yet to be examined. Thus, this paper numerically examines the effect of the inclusion of drag models and particle-particle restitution coefficients on particle dynamics in a rotary disk operating in the rolling regime of the granular bed. Three particle-particle drag models were considered: the Schiller-Naumann, Syamlal-O’Brien, and Gidaspow. The Syamlal-O’Brien and Gidaspow models were both able to successfully simulate particle segregation in a perfect rolling regime, whereas the Schiller-Naumann drag model appeared to be unable to predict the segregation of the particles and the rolling flow regime under the assumed conditions. Four different values of the restitution coefficient were also investigated: 0.7, 0.8, 0.9, and 0.95. The higher restitution values of 0.9 and 0.95 were found to substantially affect flow characteristics, ensuring suitable rolling regime behaviour for the bed during the rotational movement. The lower restitution coefficients of 0.7 and 0.8, on the other hand, indicated that irregular velocity vectors could be obtained in the active region of the granular bed.

Improvements of evaporation drag model

A special visible experiment facility has been designed and built, and an observable experiment is per- formed by pouring one or several high-temperature particles into a water pool in the facility. The experiment result has verified Yang’s evaporation drag model, which holds that the non-symmetric profile of the local evaporation rate and the local density of vapor would bring about a resultant force on the hot particle so as to resist its motion. How- ever, in Yang’s evaporation drag model, radiation heat transfer is taken as the only way to transfer heat from hot par- ticle to the vapor-liquid interface, and all of the radiation energy is deposited on the vapor-liquid interface and con- tributed to the vaporization rate and mass balance of the vapor film. In improved model heat conduction and heat convection are taken into account. This paper presents calculations of the improved model, putting emphasis on the effect of hot particle’s temperature on the radiation absorption behavior of water.

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.

Fluid-solid drag models selection for simulating wheat straw particle movement in anaerobic digester

Computational fluid dynamics(CFD)has been utilized to simulate the movements of wheat straw particles for agitator speed selection in full-scale wet digestion.Previous research has found that the current drag model generally used for depicting the motion of spherical particles cannot match the movement behavior of wheat straw particles with their non-spherical shape.In this study,the sedimentation experiment and horizontal flow experiment of straw particles were determined using a V20-3D camera and a micro Particle Image Velocimetry(PIV)system.With analyses of the experimental data and CFD simulation results,the prediction accuracies of the non-spherical drag models of Hölzer and Sommerfeld(HS),Kishore and Gu(KG),Haider and Levenspiel(HL),Richter and Nikrityuk(RN),and Fabio Dioguardi(FD)were evaluated by the motion of individual straw particles.The results showed that the KG model has a significant advantage over the other drag models,both simulating the particle settling velocities in a one dimensional settling experiment and simulating the predictable trajectory in a two-dimensional horizontal flow experiment.Therefore,the KG drag model was selected to simulate with CFD the wheat straw particle movement to select agitator speeds.Additionally,the realizable k-turbulence model was proven to be superior to the other turbulence models for simulating the continuous phase flow with CFD.

Estimation of Displacement and Extension due to Reverse Drag of Normal Faults: Forward Method

In the case of reverse drag of normal faulting, the displacement and horizontal extension are determined based on the established equations for the three mechanisms: rigid body, vertical shear and inclined shear. There are three sub-cases of basal detachment for the rigid body model: horizontal detachment, antithetic detachment and synthetic detachment. For the rigid body model, the established equations indicate that the total displacement on the synthetic base (Dt2) is the largest, that on the horizontal base (Dt1) is moderate, and that on the antithetic base (Dt3) is the smallest. On the other hand, the value of (Dt1) is larger than the displacement for the vertical shear (Dt4). The value of (Dt1) is larger than or less than the displacement for the inclined shear (Dt5) depending on the original fault dip δ0, bedding angle θ, and the angle of shear direction β. For all original parameters, the value of Dt5 is less than the value of Dt4. Also, by comparing three rotation mechanisms, we find that the inclined shear produces largest extension, the rigid body model with horizontal detachment produces the smallest extension, and the vertical shear model produces moderate extension.

Multi-fluid Eulerian simulation of mixing of binary particles in a gas-solid fluidized bed with a cohesive particle-particle drag model

A particle-particle(p-p)drag model is extended to cohesive particle flow by introducing solid surface energy to characterize cohesive collision energy loss.The effects of the proportion of cohesive particles on the mixing of binary particles were numerically investigated with the use of a Eulerian multiphase flow model incorporating the p-p drag model.The bed expansion,mixing,and segregation of Geldart-A and C particles were simulated with varying superficial velocities and Geldart-C particle proportions,from which we found that the p-p drag model can reasonably predict bed expansion of binary particles.Two segregation types of jetsam-mixture-flotsam and mixture-flotsam processes were observed during the fluidization processes for the Geldart-A and C binary particle system.The mixing processes of the binary particle system can be divided into three scales:macro-scale mixing,meso-scale mixing,and micro-scale mixing.At a constant superficial velocity the optimal mixing was observed for a certain cohesive particle proportion.

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.

Effect of adjusted mesoscale drag model on flue gas desulfurization in powder-particle spouted beds

An energy minimum multiscale model was adjusted to simulate the mesoscale structure of the flue gas desulfurization process in a powder-particle spouted bed and verified experimentally.The obtained results revealed that the spout morphology simulated by the adjusted mesoscale drag model was unstable and discontinuous bubbling spout unlike the stable continuous spout obtained using the Gidaspow model.In addition,more thorough gas radial mixing was achieved using the adjusted mesoscale drag model.The mass fraction of water in the gas mixture at the outlet determined by the heterogeneous drag model was 1.5 times higher than that obtained by the homogeneous drag model during the simulation of water vaporization.For the desulfurization reaction,the experimental desulfurization efficiency was 75.03%,while the desulfurization efficiencies obtained by the Gidaspow and adjusted mesoscale drag models were 47.63%and 75.08%,respectively,indicating much higher accuracy of the latter technique.

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.

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 charac- teristics 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,subdense 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.

A new drag model for TFM simulation of gas-solid bubbling fluidized beds with Geldart-B particles

In this work,a new drag model for TFM simulation in gas-solid bubbling fluidized beds was proposed,and a set of equations was derived to determine the meso-scale structural parameters to calculate the drag characteristics of Geldart-B particles under low gas velocities.In the new model,the meso-scale structure was characterized while accounting for the bubble and meso-scale structure effects on the drag coefficient.The Fluent software,incorporating the new drag model,was used to simulate the fluidization behavior.Experiments were performed in a Plexiglas cylindrical fluidized bed consisting of quartz sand as the solid phase and ambient air as the gas phase.Comparisons based on the solids hold-up inside the fluidized bed at different superficial gas velocities,were made between the 2D Cartesian simulations,and the experimental data,showing that the results of the new drag model reached much better agreement with experimental data than those of the Gidaspow drag model did.

Drag Torque Prediction Model for the Wet Clutches

Reduction of drag torque in disengaged wet clutch is one of important potentials for vehicle transmission improvement. The flow of the oil film in clutch clearance is investigated. A three-dimension Navier-Stokes(N-S) equation based on laminar flow is presented to model the drag torque. Pressure and speed distribution in radial and circumferential directions are deduced. The theoretical analysis reveals that oil flow acceleration in radial direction caused by centrifugal force is the key reason for the shrinking of oil film as constant feeding flow rate. The peak drag torque occurs at the beginning of oil film shrinking. A variable is introduced to describe effective oil film area and drag torque after oil film shrinking is well evaluated with the variable. Under the working condition, tests were made to obtain drag torque curves at different clutch speed and oil viscosity. The tests confirm that simulation results agree with test data. The model performs well in the prediction of drag torque and lays a theoretical foundation to reduce it.

Experimental Research and Mathematical Model of Drag Torque in Single-plate Wet Clutch

Reduction of drag torque is one of important potentials to improve transmission efficiency.Existing mathematical model of drag torque was not accurate to predict the decrease after oil film shrinking because of the difficulty in modeling the flow pattern between two plates.Flow pattern was considered as laminar flow and full oil film in the gap between two plates in traditional model.Subsequent equivalent circumferential degree model presented an improvement in oil film shrinking due to centrifugal force,but was also based on full oil film in the gap,which resulted difference between model prediction and experimental data.The objective of this paper is to develop an accurate mathematical model for the above problem by using experimental verification.An experimental apparatus was set up to test drag torque of disengaged wet clutch consisting of single friction and separate plate.A high speed camera was used to record the flow pattern through transparent quartz disk plate.The visualization of flow pattern in the clearance was investigated to evaluate the characteristics of oil film shrinking.Visual test results reveal that the oil film begins to shrink from outer radius to inner radius at the stationary plate and only flows along the rotating plate after shrinking.Meanwhile,drag torque decreases sharply due to little contact area between the stationary plate and the oil.A three-dimensional Navier-Stokes (N-S) equation based on laminar flow is presented to model the drag torque.Pressure distributions in radial and circumferential directions as well as speed distributions are deduced.The model analysis reveals that the acceleration of flow in radial direction caused by centrifugal force is the key reason for the shrinking at the constant feeding flow rate.An approach to descript flow pattern was presented on the basis of visual observation.The drag torque predicted by the model agrees well with test data for non-grooved wet clutch.The proposed model enhances the precision for predicting drag torque,and lays down a framework on which some subsequent models are developed.

CFD simulations of gas-solid flow in an industrial-scale circulating fluidized bed furnace using subgrid-scale drag models

Mesoscale flow structures such as clusters and streamers of particles are characteristic features of gas-solid flow in fluidized beds.Numerical simulations of gas-solid flows for industrial-scale fluidized beds are often performed using the Eulerian description of phases.An accurate prediction of this type of flow structure using the Eulerian modeling approach requires a sufficiently fine mesh resolution.Because of the long computational time required when using fine meshes,simulations of industrial-sized units are usually conducted using coarse meshes,which cannot resolve the mesoscale flow structures.This leads to an overestimation of the gas-solid drag force and a false prediction of the flow field.For these cases,a correction must be formulated for the gas-solid drag.We have simulated a large-scale circulating fluidized bed furnace using different gas-solid drag models and compared the model results with measurements.

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 coefflcient 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. Parame- ters 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.

Research on Drag Torque Prediction Model for the Wet Clutches

Considering the surface tension effect and centrifugal effect,a mathematical model based on Reynolds equation for predicting the drag torque of disengage wet clutches is presented. The model indicates that the equivalent radius is a function of clutch speed and flow rate. The drag torque achieves its peak at a critical speed. Above this speed,drag torque drops due to the shrinking of the oil film. The model also points out that viscosity and flow rate effects on drag torque. Experimental results indicate that the model is reasonable and it performs well for predicting the drag torque peak.

Micro-bubble Drag Reduction on a High Speed Vessel Model

轮船壳形式在水下区域强烈影响轮船的抵抗。在轮船抵抗的主要因素是皮肤磨擦抵抗。球状的弓，聚合物油漆，水驱虫剂油漆(高度防水的墙) ，空气注射，和特定的粗糙被研究人员用作一次尝试获得抵抗减小和轮船的操作效率。微水泡的注射是为阴沉的摩擦抵抗的一种有希望的技术。注射空气水泡应当以某种方式在狂暴的边界层内修改精力并且从而降低皮肤磨擦。这研究的目的是在一支海军上识别注射微水泡的效果快的巡逻队船(FPB ) 有下列主要尺寸的 57 m 类型模型：L=2 450 公里， B=400 公里，和 T=190 公里。微水泡注射和水泡速度的地点的影响也被调查。轮船模型被其速度能被改变并且调整的一台电动机拉。轮船模型抵抗被一个负担房间变换器精确测量。有或没有微水泡的注射的轮船抵抗的比较作为 drag 系数和弗鲁德数字的功能在一张图上被显示出。在船体中央部后面的微水泡注射是最好的地点完成，这被显示出最有效拖减小，和微水泡的罐头活动范围 6%9% 引起的 drag 减小。

Assessment of surface drag coefficient parametrizations based on observations and simulations using the Weather Research and Forecasting model

海气界面动量交换对台风发展起着重要作用,其估算公式依赖于拖曳系数。本文利用观测和台风模拟试验对八种拖曳系数参数化方案进行系统的评估。结果表明,相对于早期的参数化方案,近些年提出的参数化方案对拖曳系数的描述有了显著的改进,主要体现在高风速条件下。不同的拖曳系数参数化方案对超强台风"海燕"的模拟路径几乎没有影响,但是对其强度、尺寸和结构的模拟结果有显著影响。