Numerical simulations of dense granular flow in a two-dimensional channel:The role of exit position

Molecular dynamics simulations have been performed to elucidate the influence of exit position on a dense granular flow in a two-dimensional channel. The results show that the dense flow rate remains constant when the exit is far from the channel wall and increases exponentially when the exit moves close to the lateral position. Beverloo’s law proves to be successful in describing the relation between the dense flow rate and the exit size for both the center and the lateral exits.Further simulated results confirm the existence of arch-like structure of contact force above the exit. The effective exit size is enlarged when the exit moves from the center to the lateral position. As compared with the granular flow of the center exit, both the vertical velocities of the grains and the flow rate increase for the lateral exit.

AN ANALYTIC SOLUTION OF DENSE TWO-PHASE FLOW IN A VERTICAL PIPELINE

According to a mathematical model for dense two-phase flows presented in the previous pape[1],a dense two-phase flow in a vertical pipeline is analytically solved, and the analytic expressions of velocity of each continuous phase and dispersed phase are respectively derived. The results show that when the drag force between twophasesdepends linearly on their relative velocity, the relative velocity profile in the pipeline coincides with Darcy's law except for the thin layer region near the pipeline wall, and that the theoretical assumptions in the dense two-phase flow theory mentioned are reasonable.

Numerical simulation of dense particle-gas two-phase flow using the minimal potential energy principle

A simulation method of dense particle-gas two-phase flow has been developed. The binding force is introduced to present the impact of particle clustering and its expression is deduced according to the principle of minimal potential energy. The cluster collision, break-up and coalescence models are proposed based on the assumption that the particle cluster are treated as one discrete phase. These models are used to numerically study the two-phase flow field in a circulating fluidized bed （CFB）. Detailed results of the cluster structure, cluster size, particle volume fraction, gas velocity, and particle velocity are obtained. The correlation between the simulation results and experimental data justifies that these models and algorithm are reasonable, and can be used to efficiently study the dense particle-gas two-phase flow.

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

Inthis paper, each of the two phases in dense two-phase flow is considered as continuous medium and the fundamental equations for two-phase flow arc described in Eulerian form. The generalized constitutive relation of the Bingham fluid is applied to the dispersed phase with the analysis oj physical mechanism of dense two-phase flow. The shearing stress of dispersed phase at a wall is used to give a boundary condition. Then a mathematical model for dense two-phase flow is obtained. In addition, the expressions of shearing stress of dispersed phase at a wall is derived according to the fundamental model of the friclional collision between dispersed-plutse particles and the wall.

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.

Obstacle Avoidance of Flapping⁃Wing Air Vehicles Based on Optical Flow and Fuzzy Control

The flapping-wing air vehicle(FWAV)is a kind of bio-inspired robot whose wings can flap up and down like bird and insect wings.A vision-based obstacle avoidance method for FWAVs is proposed in this paper.First,the Farneback algorithm is used to calculate the optical flow field of the first-view video frames taken by the on-board image transmission camera.Based on the optical flow information,a fuzzy obstacle avoidance controller is then designed to generate the FWAV steering commands.Experimental results show that the proposed obstacle avoidance method can accurately identify obstacles and achieve obstacle avoidance for FWAVs.

Two-phase turbulence models for simulating dense gas-particle flows

The two-fluid model is widely adopted in simulations of dense gas-particle flows in engineering facili- ties. Present two-phase turbulence models for two-fluid modeling are isotropic. However, turbulence in actual gas-particle flows is not isotropic. Moreover, in these models the two-phase velocity correlation is closed using dimensional analysis, leading to discrepancies between the numerical results, theoretical analysis and experiments. To rectify this problem, some two-phase turbulence models were proposed by the authors and are applied to simulate dense gas-particle flows in downers, risers, and horizontal channels; Experimental results validate the simulation results. Among these models the USM-O and the two-scale USM models are shown to give a better account of both anisotropic particle turbulence and particle-particle collision using the transport equation model for the two-phase velocity correlation.

MATHEMATICAL MODELS AND NUMERICAL SIMULATION FOR DENSE PARTICULATE FLOWS

Sedimentation of particles in inclined and vertical vessels is numerically simulated by the Eulerian two-fluid model. The numerical results show an interesting phenomenon with two circulation vortexes in a vertical vessel but one in the inclined vessel. Sensitivity tests indicate that the boundary layer effect is the key to induce this phenomenon. A numerical method based on 2D unstructured meshes is presented to solve the hard-sphere discrete particle model. Several applications show the numerical method has a good performance to simulate dense particulate flows in irregular domains without regard to element types of the mesh.

Fully automatic DOM generation method based on optical flow field dense image matching

Automatic Digital Orthophoto Map(DOM)generation plays an important role in many downstream works such as land use and cover detection,urban planning,and disaster assessment.Existing DOM generation methods can generate promising results but always need ground object filtered DEM generation before otho-rectification;this can consume much time and produce building facade contained results.To address this problem,a pixel-by-pixel digital differential rectification-based automatic DOM generation method is proposed in this paper.Firstly,3D point clouds with texture are generated by dense image matching based on an optical flow field for a stereo pair of images,respectively.Then,the grayscale of the digital differential rectification image is extracted directly from the point clouds element by element according to the nearest neighbor method for matched points.Subsequently,the elevation is repaired grid-by-grid using the multi-layer Locally Refined B-spline(LR-B)interpolation method with triangular mesh constraint for the point clouds void area,and the grayscale is obtained by the indirect scheme of digital differential rectification to generate the pixel-by-pixel digital differentially rectified image of a single image slice.Finally,a seamline network is automatically searched using a disparity map optimization algorithm,and DOM is smartly mosaicked.The qualitative and quantitative experimental results on three datasets were produced and evaluated,which confirmed the feasibility of the proposed method,and the DOM accuracy can reach 1 Ground Sample Distance(GSD)level.The comparison experiment with the state-of-the-art commercial softwares showed that the proposed method generated DOM has a better visual effect on building boundaries and roof completeness with comparable accuracy and computational efficiency.

CFD investigation of structural effects of internal gas intake on powder conveying performance in fuel supply systems for aerospace engines

Optimal design of gas intake in powder fuel supply systems is crucial for performance of aerospace engines.There is little research on the impact of intake structure on powder conveying performance.Three novel internal intakes were proposed,which are spherical,cube-shaped,and dome-shaped.After validation,CFD simulations demonstrate that fluctuation of mass flow rate of powders in the dome-shaped intake is reduced by about 73.3%compared with the annular external one.Variation trends of phase velocities are similar for the spherical and cube-shaped intakes,while those are similar for the annular external and dome-shaped internal intakes.Fluctuation of area of gas zone for the annular external and spherical internal intakes is larger than that for the cube-shaped and dome-shaped internal intakes.Pressure and relative pressure drop in the fluidization chamber have a stable stage,and fluctuation of relative pressure drop is small when dome-shaped internal intake is used.

New concept for ADS spallation target: Gravity-driven dense granular flow target

For the Chinese-ADS project, to provide enough neutrons to drive the subcritical system, tens of MW spallation targets for the C-ADS are necessary. This is not an easy task. Here we propose a new concept for a gravity-driven dense granular flow target, in which heavy metal grains are chosen as the spallation target material. Compared with currently widely used targets, this conceptual design has advantages with regard to heat removal, thermal shock protection, neutron yield, radiotoxicity reduction, and convenient operation. The gravity-driven dense granular flow target has the potential to easily deal with these issues and to form a foundation for tens of MW spallation targets for cost-effective facilities. Preliminary simulations and experiments have been completed to support this conceptual design.

COMPUTATIONAL FLUID DYNAMICS FOR DENSE GAS-SOLID FLUIDIZED BEDS: A MULTI-SCALE MODELING STRATEGY

Dense gas-particle flows are encountered in a variety of industrially important processes for large scale production of fuels, fertilizers and base chemicals. The scale-up of these processes is often problematic and is related to the intrinsic complexities of these flows which are unfortunately not yet fully understood despite significant efforts made in both academic and industrial research laboratories. In dense gas-particle flows both (effective) fluid-particle and (dissi-pative) particle-particle interactions need to be accounted for because these phenomena to a large extent govern the prevailing flow phenomena, i.e. the formation and evolution of heterogeneous structures. These structures have significant impact on the quality of the gas-solid contact and as a direct consequence thereof strongly affect the performance of the process. Due to the inherent complexity of dense gas-particles flows, we have adopted a multi-scale modeling approach in which both fluid-particle and particle-particle interactions can be properly accounted for. The idea is essentially that fundamental models, taking into account the relevant details of fluid-particle (lattice Boltzmann model) and particle-particle (discrete particle model) interactions, are used to develop closure laws to feed continuum models which can be used to compute the flow structures on a much larger (industrial) scale. Our multi-scale approach (see Fig. 1) involves the lattice Boltzmann model, the discrete particle model, the continuum model based on the kinetic theory of granular flow, and the discrete bubble model. In this paper we give an overview of the multi-scale modeling strategy, accompanied by illustrative computational results for bubble formation. In addition, areas which need substantial further attention will be highlighted.

Mixed Model for Silt-Laden Solid-Liquid Two-Phase Flows

The kinetic theory of molecular gases was used to derive the governing equations for dense solid-liquid two-phase flows from a microscopic flow characteristics viewpoint by multiplying the Boltzmann equation for each phase by property parameters and integrating over the velocity space. The particle collision term was derived from microscopic terms by comparison with dilute two-phase flow but with consideration of the collisions between particles for dense two-phase flow conditions and by assuming that the particle-phase velocity distribution obeys the Maxwell equations. Appropriate terms from the dilute two-phase governing equations were combined with the dense particle collision term to develop the governing equations for dense solid-liquid turbulent flows. The SIMPLEC algorithm and a staggered grid system were used to solve the discretized two-phase governing equations with a Reynolds averaged turbulence model. Dense solid-liquid turbulent two-phase flows were simulated for flow in a duct. The simulation results agree well with experimental data.

Material removal model of magnetorheological finishing based on dense granular flow theory

Magnetorheological finishing(MRF)technology is widely used in the fabrication of high-precision optical elements.The material removal mechanism of MRF has not been fully understood because MRF technology involves the integration of electromagnetics,contact mechanics,and materials science.In this study,the rheological properties of the MR polishing fluid in oscillation model have been investigated.We propose that the shear-thinned MR polishing fluid over the polishing area should be considered a dense granular flow,based on which a new contact model of MRF over the polishing area has been constructed.Removal function and processing force test experiments were conducted under different working gaps.The normal pressure and effective friction equations over the polishing area were built based on the continuous medium and dense granular flow theories.Then,a novel MRF material removal model was established.A comparison of the results of the theoretical model with actual polishing results demonstrated the accuracy of the established model.The novel model proposed herein reveals the generation mechanism of shear force over a polished workpiece and realizes effective decoupling of the main processing parameters that influence the material removal of MRF.The results of this study will provide new and effective theoretical guidance for the process optimization and technology improvement of MRF.

Experimental and numerical investigation of liquid-solid binary fluidized beds： Radioactive particle tracking technique and dense discrete phase model simulations

Liquid-solid binary fluidized beds are widely used in many industries. However, the flow behavior of such beds is not well understood due to the lack of accurate experimental and numerical data. In the current study, the behavior of monodisperse and binary liquid-solid fluidized beds of the same density but dif- ferent sizes is investigated using radioactive particle tracking （RPT） technique and a dense discrete phase model （DDPM）. Experiments and simulations are performed in monodisperse fluidized beds containing two different sizes of glass beads （0.6 and I mm） and a binary fluidized bed of the same particles for vari- ous bed compositions. The results show that both RPT and DDPM can predict the mixing and segregation pattern in liquid-solid binary fluidized beds. The mean velocity predictions of DDPM are in good agree- ment with the experimental findings for both monodisperse and binary fluidized beds. However, the axial root mean square velocity predictions are only reasonable for bigger particles. Particle-particle interac- tions are found to be critical for predicting the flow behavior of solids in liquid-solid binary fluidized beds.

Dense gas-particle flow in vertical channel by multi-lattice trajectory model

A multi-lattice deterministic trajectory(MLDT) model is developed to simulate dense gas-particle flow in a vertical channel.The actual inter-particle collision and particle motion are treated by a Lagrangian model with three sets of lattices to reduce computational time.Cluster formation and motion near the wall are successfully predicted with mean particle volume fraction and velocity,showing quantitatively agreement with experimental results.The mechanism of particles concentrated near the wall is investigated by considering effects of gravity,particle-wall collisions,inter-particle collisions and velocity profiles of the gas phase.It is shown that the inter-particle collision and gas-phase velocity distribution are the essential factors for cluster formation near the wall,while gravity and particle-wall collision only have minor effects on particle concentration near the wall.Particles are unable to remain in the high velocity region due to the strong inter-particle collisions,while they tend to stay in the low velocity region for weak inter-particle collisions.In addition,the effects of channel width and particle sizes on cluster formation are also investigated and it is found that particle concentration near the wall reduces with the decrease of channel width and increase of particle size.

Velocity profiles and energy fluctuations in simple shear granular flows

Rheology analysis of granular flows is important for predicting geophysical hazards and designing industrial processes. Using a discrete element method, we simulate simple shear flows in 3D under a constant confining pressure of 10 kPa. The inertial number proposed by the GDR MiDi group in France is adopted to distinguish rheology regimes, Both translational and angular velocity profiles are investigated, and both fluid-like and solid-like behavior modes are observed in the flows. The maximum angular velocity occurs near the localized deformation area. We also investigate the energy characteristics of the flows and find that at very small shearing speed, the mean kinetic energy density ek is close to zero, while the mean elastic energy density ec is much greater. At large shearing speed, ek increases. The fluctuating parts of the two types of energy increase with increasing shear speed. Thus, the mean energy density ratio ek/ec can be used in addition to the inertial number to distinguish flow regimes. These results provide insights from energetics into the rheological properties of granular flows.

Multi-scale numerical simulation of fluidized beds: Model applicability assessment

In the past few decades,multi-scale numerical methods have been developed to model dense gas-solidflow in fluidized beds with different resolutions,accuracies,and efficiencies.However,ambiguity needsto be clarified in the multi-scale numerical simulation of fluidized beds:(i)the selection of the submodels,parameters,and numerical resolution;(ii)the multivariate coupling of operating conditions,bed configurations,polydispersity,and additional forces.Accordingly,a state-of-the-art review is performed to assess the applicability of multi-scale numerical methods in predicting dense gas-solid flow influidized beds at specific fluidization regimes(e.g.,bubbling fluidization region,fast fluidization regime),with a focus on the inter-particle collision models,inter-phase interaction models,collision parameters,and polydispersity effect.A mutual restriction exists between resolution and efficiency.Higherresolution methods need more computational resources and thus are suitable for smaller-scale simulations to provide a database for closure development.Lower-resolution methods require fewercomputational resources and thus underpin large-scale simulations to explore macro-scale phenomena.Model validations need to be further conducted under multiple flow conditions and comprehensivemetrics(e.g.,velocity profiles at different heights,bubbles,or cluster characteristics)for furtherimprovement of the applicability of each numerical method.

Trace Projection Transformation： a new method for measurement of debris flow surface velocity fields

Spatiotemporal variation of velocity is impor- tant for debris flow dynamics. This paper presents a new method, the trace projection transformation, for accurate, non-contact measurement of a debris-flow surface velocity field based on a combination of dense optical flow and perspective projection transformation. The algorithm for interpreting and processing is implemented in C ＋＋ and realized in Visual Studio 2012. The method allows quantitative analysis of flow motion through videos from various angles （camera positioned at the opposite direction of fluid motion）. It yields the spatiotemporal distribution of surface velocity field at pixel level and thus provides a quantitative description of the surface processes. The trace projection transformation is superior to conventional measurement methods in that it obtains the full surface velocity field by computing the optical flow of all pixels. The result achieves a 90% accuracy of when comparing with the observed values. As a case study, the method is applied to the quantitative analysis of surface velocity field of a specific debris flow.

Second-order moment modeling of dispersed two-phase turbulence-Part 2-USM-Θ two-phase turbulence model and USM-SGS two-phase stress model

Dense gas-particle flows are frequently encountered in fluidized beds,riser and downer reactors,pneumatic transport and the near-wall zone of dilute gas-particle flows.Particle-particle collision plays an important role in the behavior of two-phase flows.In this paper a USM-Q two-phase turbulence model for dense gas-particle flows is proposed to account for both two-phase turbulence and inter-particle collision.For two-fluid large-eddy simulation of gas-particle flows,the author proposed a unified second-order moment(USM) two-phase SGS stress model and a two-phase k-kp SGS energy-equation stress model.The proposed models can fully account for the interaction between the gas and particle SGS stresses.