The evolution of the cellular structure of the two-dimensional creeping flow induced by a rotating circular cylinder set in the centre of a rectangular channel is studied numerically and experimentally when the aspect ratio A increases from 1 to 7. In the calculations, depending on the value of A, either only series in terms of polar coordinates, or both matched polar and Cartesian coordinates series are employed to represent the stream function and an efficient least-squares method, very easy to program, is selected to satisfy some of the boundary conditions. For the experiments, a special technique which visualizes intermittently the paths of solid tracers during long times of exposure permits us to observe the fluid motion in the whole domain, even in the regions where the velocities are very small. An excellent measure of agreement between the numerical and experimental results is found. Thus it is clearly shown how, in the region beyond the rotating flow directly driven by the cylinder, the two main corner cells visualized at A = 1, develop with increasing A and then coalesce, to finally merge and give rise to a single central cell. This central cell develops in its turn, tending finally to the unbounded channel reference cell, after passing through a maximum length however. Owing to the very high precision of the calculations, many details of the flow development have been clearly shown, in particular the periodicity, with increasing A, of all the different phases, progressively inducing a succession of cells. The prediction that the angle of separation of the fluid boundaries of the cells tends towards the theoretical limit of 58.61° when the aspect ratio becomes large is also confirmed.
Complex matter may take various forms from granular matter, soft matter, fluid-fluid, or solid-fluid mixtures to compact heterogeneous material. Cellular automata models make a suitable and powerful tool for catching the influence of the microscopic scale in the macroscopic behavior of these complex systems. Rather than a survey, this paper attempts to bring out the main concepts underlying these models. A taxonomy is presented with four general types proposed: sandpile, latticegas, lattice-grain, and hybrid models. A discussion follows with general questions; namely, grain-size, synchronization, topology and scalability, and consistency of the models.
In this work, Discrete Element Method (DEM) is used in order to calculate the motion of granular material in rotating dryers. We are particularly interested in analysing the effect of flight shape on the behaviour of spherical particles in the cross section of the dryer. We will be using two segments flights and three different profiles : a straight flight (180 • between both segments), an angled flight (with an angle of 120 •) and a rightangled flight (90 •). The results show that the profile of the flight affects significantly the motion of the particles in the cross section of the dryer. Changing the angle between the segment's flight, changes the flight loading and thus the material holdup which leads to different discharging profiles of the flight. For a right angled flight, the range of the discharge angle increases leading to a more uniformized cascade pattern in time and an enlarging of the area occupied by the curtains of particles. The specific durations (discharging time, falling time) are also determined and studied as a function of the flight shape.
We present some experiments and calculations that illustrate the establishment of a cellular Stokes flow between two parallel plates. The structure of this flow is composed of successive closed eddies. The study of the influence of an additional plate mounted midway between the channel walls shows the sensitivity of these eddies to the variation of the geometry. We suggest that this flow might be introduced in the specialized teaching of fluid mechanics, to show examples of transfer by cellular motion.
This paper presents a theoretical description of a particle motion in a rotary dryer equipped with straight lifters distributed on its periphery. In this configuration, the transport of granular materials occurs with cyclic cascades that can be decomposed into three phases: lifting, discharging, and falling into the air stream. In order to describe each of these phases, we have focused on the motion of a single particle in a rotating drum. In this condition, the analytical solution of the motion equation of each phase is found. With these solutions, the position and the velocity of the particle at any time are thus expressed as a function of physical parameters of the particle, physical parameters of the drum, and physical parameters of air in the drum, called operating parameters in practice. With these equations, we are able to calculate the behaviour of the particle as a function of the operating parameters. The transposition to the industrial context is made with an application. We show how these equations particularly permit the estimation of the Mean Residence Time (MRT) of material during the drying process as a function of operating parameters. Such estimations have been validated by comparison with experimental data of MRT found in the literature. The work presented in this paper gives some useful mathematical relations for whose who are interested in drum design optimization (lifter length, drum radius, drum length, etc.). More specifically, they can be used to help with the choice of operational parameters values that would achieve a given value of MRT for particular product.
Motion and deposition of solid particles in fibrous filter with circular, diamond, and square fibers are numerically investigated. A coupled Lattice Boltzmann (LB) and discrete element (DE) method is presented and applied to simulate the filtration process in particulate flow, taking into account the mutual interaction between fluid and particle. The influence of pertinent parameters such as the Reynolds number, the particle-to-fiber diameter ratio, and the particle-to-fluid density ratio on filtration performance (pressure drop and capture efficiency) is analyzed for fibrous filter with different fiber cross-sectional shapes. The simulation results indicate that both the pressure drop and the capture efficiency of filter are considerably affected by the fiber’s shape. Dimensionless drag force increases with the Reynolds number when Re > 1. The filter with diamond fiber has a lower pressure drop than that of the circular and square cases. Meanwhile, the deposition of particles on the surface of square fiber is more favorable. From the filter quality factor standpoint, filter with diamond fiber exhibits a better filtration performance.
The transport and deposition of particles over a fixed obstacle set in a fluid flow is investigated numerically. A two-dimensional model, based on lattice Boltzmann (LB) method and discrete element (DE) method, is used to simulate particle deposition. The corresponding method is two-way coupling in the sense that particle motion affects the fluid flow and reciprocally. The particle capture efficiency, as a function of particle size and Stokes number, is investigated using one-way (effect of the particle on the fluid is not considered) and two-way coupling respectively. The numerical simulations presented in this work are useful to understand the transport and deposition of particles and to predict the single fiber collection efficiency. The effect of obstruction shape on single fiber collection efficiency is investigated with LB-DE methods. Results show that the influence of particle on the flow field cannot be neglected for particles with large size. Numerical results for circular fiber collection efficiency are in good agreement with theoretical prediction and existing correlations. Enhanced collection efficiency is achieved by changing the fiber shape.
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