Kinematics and dynamics of a particle on a non-simple harmonic vibrating screen

The motion of a particle on a screen is directly affected by the motion of the screen if airflow and intergranular friction are ignored. To study this effect, a mathematical model was established to analyze the motion of a planar reciprocating vibrating screen, and a matrix method was employed to derive its equation of motion. The motion of the screen was simulated numerically and analyzed using MATLAB. The results show that the screen undergoes non-simple harmonic motion and the law of motion of each point in the screen is different. The tilt angle of the screen during screening is not constant but varies according to a specific periodic function. The results of numerical simulations were verified through experiments. A high-speed camera was used to track the motion of three points in the longitudinal direction of the screen. The balance equation for forces acting on a single particle on the screen was derived based on the non-simple harmonic motion of the screen. These forces were simulated using MATLAB. Different types of particle motion like slipping forward, moving backward, and being tossed to different parts of the screen were analyzed. A vibro-impact motion model for a particle on the non-simple harmonic vibrating screen was established based on the nonlinear law of motion of the particle. The stability of fixed points of the map is discussed. Regimes of different particle behaviors such as stable periodic motion, period-doubling bifurcation motion, Hopf bifurcation motion, and chaotic motion were obtained. With the actual law of motion of the screen and the behavior of a particle on the screen, a theoretical basis for design optimization of the screen is provided.     

DEM simulation of particle mixing in a sheared granular flow

Mixing behaviors of particles are simulated in a sheared granular flow using differently colored but otherwise identical glass spheres, with five different bottom wall velocities. By DEM simulation, the solid fractions, velocities, velocity fluctuations and granular temperatures are measured.The mixing layer thicknesses are compared with the calculations from a simple diffusion equation using the data of apparent self-diffusion coefficients obtained from the current simulation measurements. The calculations and simulation results showed good agreements, demonstrating that the mixing process of granular materials occurred through the diffusion mechanism.     

DEM simulation of particle mixing in a sheared granular flow

Mixing behaviors of particles are simulated in a sheared granular flow using differently colored but otherwise identical glass spheres, with five different bottom wall velocities. By DEM simulation, the solid fractions, velocities, velocity fluctuations and granular temperatures are measured. The mixing layer thicknesses are compared with the calculations from a simple diffusion equation using the data of apparent self-diffusion coefficients obtained from the current simulation measurements. The calculations and simulation results showed good agreements, demonstrating that the mixing process of granular materials occurred through the diffusion mechanism.     

DEM simulation of particle percolation in a packed bed

The phenomenon of spontaneous particle percolation under gravity is investigated by means of the discrete element method. Percolation behaviors such as percolation velocity, residence time distribution and radial dispersion are examined under various conditions. It is shown that the vertical velocity of a percolating particle moving down through a packing of larger particles decreases with increasing the restitution coefficient between particles and diameter ratio of the percolating to packing particles. With the increase of the restitution coefficient, the residence time and radial dispersion of the percolating particles increase. The packing height affects the residence time and radial dispersion. But, the effect can be eliminated in the analysis of the residence time and radial dispersion when they are normalized by the average residence time and the product of the packing height and packing particle diameter, respectively. In addition, the percolation velocity is shown to be related to the vertical acceleration of the percolating particle when an extra constant vertical force is applied. Increasing the feeding rate of percolating particles decreases the dispersion coefficient.     

DEM simulation of particle percolation in a packed bed

The phenomenon of spontaneous particle percolation under gravity is investigated by means of the discrete element method. Percolation behaviors such as percolation velocity,residence time distribution and radial dispersion are examined under various conditions. It is shown that the vertical velocity of a percolating particle moving down through a packing of larger particles decreases with increasing the restitution coefficient between particles and diameter ratio of the percolating to packing particles. With the increase of the restitution coefficient,the residence time and radial dispersion of the percolating particles increase. The packing height affects the residence time and radial dispersion. But,the effect can be eliminated in the analysis of the residence time and radial dispersion when they are normalized by the average residence time and the product of the packing height and packing particle diameter,respectively.In addition,the percolation velocity is shown to be related to the vertical acceleration of the percolating particle when an extra constant vertical force is applied. Increasing the feeding rate of percolating particles decreases the dispersion coefficient.     

Control of separation phenomena in a high-speed flow by means of the surface electric discharge

The results of an experimental and theoretical investigation of the interaction between a surface electric discharge and a supersonic air flow in a constant cross-section channel are given. The features of the generation of the surface discharge in the flow are described. A model of the interaction is proposed. The regime of gasdynamic screening of a mechanical obstacle on the channel wall is investigated. Data on the change in the main flow parameters as a result of the generation of a surface discharge are given. The experimental results are compared with the results of calculations based on a simplified model of the interaction.     

Numerical study of magnetohydrodynamic laminar flow separation in a channel with smooth expansion

The flow of an electrically conducting incompressible viscous fluid in a plane channel with smooth expansion in the presence of a uniform transverse magnetic field has been analysed. A solution technique for the governing magnetohydrodynamic equations in primitive variable formulation has been developed. A co‐ordinate transformation has been employed to map the infinite irregular domain into a finite regular computational domain. The governing equations are discretized using finite‐difference approximations in staggered grid. Pressure Poisson equation and pressure correction formulae are derived and solved numerically. It is found that with increase in the magnetic field, the size of the flow separation zone diminishes and for sufficiently large magnetic field, the separation zone disappears completely. The peak u‐velocity decreases with increase in the magnetic field. It is also found that the asymmetric flow in a symmetric geometry, which occurs at moderate Reynolds numbers, becomes symmetric with sufficient increase in the transverse magnetic field. Thus, a transverse magnetic field of suitable strength has a stabilizing effect in controlling flow separation, as also in delaying the transition to turbulence. Copyright © 2008 John Wiley & Sons, Ltd.     

Large eddy simulation of separation control over a backward-facing step flow by suction

Separation control over a backward-facing step (BFS) flow by continuous suction was numerically investigated using the turbulence model of large eddy simulation (LES). The effect of suction control on the flow fields was scrutinised by altering the suction flow coefficient, and the results indicate that suction is not only very effective in shortening the reattachment length but also very influential in reducing the tangential velocity gradient and turbulence fluctuations of the reattached flows. With increasing increments of the absolute suction flow coefficient, the effect of suction control is more significant. Furthermore, the detailed flow fields (including the time-averaged stream and velocity fields) and turbulence characteristics (including the time-averaged resolved kinetic energy and RMS velocity) for the BFS models with or without suction are presented to discuss the mechanism of suction control. Comparisons of the time-averaged statistics between the numerical simulations and corresponding experiments are conducted, and it shows that the LES based on the dynamic kinetic energy subgrid-scale model (DKEM) can acquire exact results. Therefore, feasibility of the numerical methods to simulate suction-controlled models is validated.     

High-fidelity numerical simulation of the flow field around a NACA-0012 aerofoil from the laminar separation bubble to a full stall

In the present work, large eddy simulations of the flow field around a NACA-0012 aerofoil near stall conditions are performed at a Reynolds number of 5 × 10⁴, Mach number of 0.4, and at various angles of attack. The results show the following: at relatively low angles of attack, the bubble is present and intact; at moderate angles of attack, the laminar separation bubble bursts and generates a global low-frequency flow oscillation; and at relatively high angles of attack, the laminar separation bubble becomes an open bubble that leads the aerofoil into a full stall. Time histories of the aerodynamic coefficients showed that the low-frequency oscillation phenomenon and its associated physics are indeed captured in the simulations. The aerodynamic coefficients compared to previous and recent experimental data with acceptable accuracy. Spectral analysis identified a dominant low-frequency mode featuring the periodic separation and reattachment of the flow field. At angles of attack α ≤ 9.3°, the low-frequency mode featured bubble shedding rather than bubble bursting and reformation. The underlying mechanism behind the quasi-periodic self-sustained low-frequency flow oscillation is discussed in detail.     

Averaging of particle data from phase Doppler anemometry in unsteady two-phase flow: Validation by numerical simulation

A novel post-processing algorithm is proposed to correct statistical bias observed in the treatment of time series obtained by a phase Doppler anemometer (PDA) at flow locations with variable particle velocity and concentration. Extensive properties of each validated particle are weighted with their inverse measuring (validation) volume to account for the procedure of particle sampling and fluctuations in the particle concentration. To compensate for the short characteristic length of the validation volume, the properties of particles are expressed by properties of fields of particle groups, using a local averaging time. A window shift and a decorrelation scheme are applied on the fields to increase their frequency resolution. This algorithm has been tested on numerical time series, provided by an Eulerian/Lagrangian code representing a gas/solids flow past a bluff body. Moments and spectral estimates of concentration and velocity of particle groups were successfully validated by the numerical simulation using the PDA data algorithm and control volume averaging. The control volume was much larger than the PDA validation volume, but the centre positions of the two volumes were identical.     

Wake response of a stationary finite-sized particle in a turbulent channel flow

Here we consider the effect of a finite-sized stationary particle in a channel flow of modest turbulence at _Reτ=178.12${\mathit{Re}}_{\tau }=178.12$. The size of particle is varied such that the particle Reynolds number ranges from about 40 to 450. The location of the particle is chosen to be either in the buffer layer (_yp+=17.81)$(y_{p+}=17.81)$ or at the channel center. Fully resolved direct numerical simulations of the turbulent channel flow around the particles is performed. Here the ambient turbulence intensity relative to the mean velocity seen by the particle is large (I=23.16%)$(I=23.16\%)$ in the buffer region, while it is substantially lower (I=4.09%)$(I=4.09\%)$ at the channel center. We present results on turbulence modulation due to the particle in terms of wake dynamics and vortex shedding.     

On identification of flow separation and vortices in internal periodic flows

To permit simplified analysis of complex time-dependent flows, possible relationship between the near-wall flow, flow separation and vortices are studied numerically for a flow in a constricted two-dimensional channel. The pulsating incoming wave-form consists of a steady flow, followed by a half-sinus flow superimposed on the steady component. One pair of vortices is created in each cycle, one vortex near each wall. The vortices propagate downstream in the next cycles, promoting flow separation as they move. Existing flow separation criteria were not found to be uniformly valid. A relation between the near-wall flow and the vortical system exists only during the steady incoming flow phase of the cycle. It seems that local criteria of flow separation cannot be found for complex internal pulsating flow fields. However, the vorticity field can be utilized, even in complex time-periodic flows, for identifying vortices that have been formed by the roll-up of shear layers.     

Influence of gravity and lift on particle velocity statistics and transfer rates in turbulent vertical channel flow

The present study reports detailed statistics for velocity and transfer rates of heavy particles dispersed in turbulent boundary layers. Statistics have been extracted from a homogeneous source of data covering a large target parameter space and are used here to analyze the effects of gravity and lift on particle dispersion and deposition in a systematic way. Datasets were obtained performing Direct Numerical Simulation (DNS) of particle-laden turbulent upward/downward flow in a vertical channel. Six values for the particle timescale (the particle Stokes number, St) ranging three orders of magnitude were considered to analyze the deposition process as the controlling mechanism was shifting from turbulent diffusion to inertia-moderated crossing trajectories. For the particle timescales examined, gravity and lift do not influence the qualitative behavior of particles even though velocity profiles and deposition coefficients are modified in a non-monotonic fashion, reaching an optimum for St ? 15. Physical mechanisms for the different behavior are discussed. Raw data and statistics obtained from the present DNS are made available at http://cfd.cineca.it (mirror site: http://158.110.32.35/download/database) and can be used to test simple models and closure equations for multiphase RANS and Large Eddy simulations.     

跨超声速风洞扩散段流动分离控制设计参数研究

为抑制跨超声速风洞扩散段的分离,提出了一种较为完备的设计方法。由于影响扩散段性能的参数较多,完全通过试验方法进行设计的成本过高,该方法通过数值模拟,结合适当的边界条件,详细描述了扩散段角度、分流锥角度与长度、孔板开孔率对扩散段性能的影响;从数值模拟的结果可以看出,孔板开孔率和扩开角对扩散段性能有显著影响,通过比较得出较为合理的参数匹配,提高了扩散段的防分离性能,并改善了出口气流质量。数值结果与试验结果结论一致,表明本文所用的方法用于扩散段气动设计是可行的,为数值模拟方法应用于风洞部段气动设计创造了一定的条件。     

Dynamic coupling of fluid and structural mechanics for simulating particle motion and interaction in high speed compressible gas particle laden flow

In this work, structural finite element analyses of particles moving and interacting within high speed compressible flow are directly coupled to computational fluid dynamics and heat transfer analyses to provide more detailed and improved simulations of particle laden flow under these operating conditions. For a given solid material model, stresses and displacements throughout the solid body are determined with the particle–particle contact following an element to element local spring force model and local fluid induced forces directly calculated from the finite volume flow solution. Plasticity and particle deformation common in such a flow regime can be incorporated in a more rigorous manner than typical discrete element models where structural conditions are not directly modeled. Using the developed techniques, simulations of normal collisions between two 1 mm radius particles with initial particle velocities of 50–150 m/s are conducted with different levels of pressure driven gas flow moving normal to the initial particle motion for elastic and elastic–plastic with strain hardening based solid material models. In this manner, the relationships between the collision velocity, the material behavior models, and the fluid flow and the particle motion and deformation can be investigated. The elastic–plastic material behavior results in post collision velocities 16–50% of their pre-collision values while the elastic-based particle collisions nearly regained their initial velocity upon rebound. The elastic–plastic material models produce contact forces less than half of those for elastic collisions, longer contact times, and greater particle deformation. Fluid flow forces affect the particle motion even at high collision speeds regardless of the solid material behavior model. With the elastic models, the collision force varied little with the strength of the gas flow driver. For the elastic–plastic models, the larger particle deformation and the resulting increasingly asymmetric loading lead to growing differences in the collision force magnitudes and directions as the gas flow strength increased. The coupled finite volume flow and finite element structural analyses provide a capability to capture the interdependencies between the interaction of the particles, the particle deformation, the fluid flow and the particle motion.     

微喷管流动粒子仿真与Navier-Stokes数值模拟比较研究

运用DSMC（Direct Simulation Monte—Carlo）方法从分子运动论层次对大膨胀比、喉部转角为尖角的微喷管流动现象进行模拟,考察来流总压对喷管性能的影响,并与Navier—Stokes方程运算结果、实验结果进行比较。研究表明：在模拟微型喷管的流动现象时,DSMC方法比N—S方程更加适用。     

Finite‐element simulation of incompressible fluid flow in an elastic vessel

Finite‐element simulation was performed to predict the incompressible Navier–Stokes flow in a domain, partly bounded by an elastic vessel, which is allowed to vary with time. Besides satisfying the physical conservation laws, both surface and the volume conservation laws are satisfied at the discrete level for ensuring the balance between physical and geometrical variables. Several problems which are amenable to analytical solutions were tested for validating the method. The simulated results are observed to agree favourably with analytical solutions. Having verified the applicability of the finite‐element code to problems involving moving grids, we consider an incompressible fluid flow bounded by rigid and elastic vessel walls. Our emphasis was placed on the validation of the formulation developed within the moving‐grid framework. Copyright © 2003 John Wiley & Sons, Ltd.     

Measurements and simulations of particle dispersion in a turbulent flow

A particle imaging technique has been used to collect droplet displacement statistics in a round turbulent jet of air. Droplets are injected on the jet axis, and a laser sheet and position-sensitive photomultiplier tube are used to track their radial displacement and time-of-flight. Dispersion statistics can be computed which are Lagrangian or Eulerian in nature. The experiments have been simulated numerically using a second-order closure scheme for the jet and a stochastic simulation for the particle trajectories. Results are presented for non-vaporizing droplets of sizes from 35 to 160 μm. The simulations have underscored the importance of initial conditions and early droplet displacement history on the droplet trajectory for droplets with large inertia relative to the turbulence. Estimates of initial conditions have been made and their effect on dispersion is quantified.     

In-line imaging measurements of particle size,velocity and concentration in a particulate two-phase flow

A novel method is developed for in-line measurements of particle size, velocity and concentration in a dilute, particulate two-phase flow based on trajectory image processing. The measurement system consists of a common industrial CCD camera, an inexpensive LED light and a telecentric lens. In this work, the image pre-processing steps include stitching, illumination correction, binarization, denoising, and the elimination of unreal and defocused particles. A top-hat transformation is found to be very effective for the binarization of images with non-uniform background illumination. Particle trajectories measured within a certain exposure time are used to directly obtain particle size and velocity. The particle concentration is calculated by using the statistics of recognized particles within the field of view. We validate our method by analyzing experiments in a gas-droplet cyclone separator. This in-line image processing method can significantly reduce the measurement cost and avoid the data inversion process involved in the light scattering method.     

A numerical exploration of secondary separation in starting flow around a flat plate by the discrete vortex model

In the present work, a further numerical simulation of the starting flow around a flat plate normal to the direction of motion in a uniform fluid has been made by means of the discrete vortex method. The secondary separation occurring at rear surface of the plate is explored, and predicted approximately using Thwait's method. The calculated results show that in the early stages of the flow secondary separation does occur. The evolution of flow field, the vortex growing process and the characteristics of secondary vortices have been described. The time dependent drag coefficients, the vorticity shed from the edges and rear surface, and the separation positions are calculated as well as the distributions of velocity and pressure on the plate. In the case of flow normal to the plate, the calculated secondary vortices are weak. Their existence will change the local velocity distributions and affect pressure distributions. However, the effect on drag coefficient is negligible.