SIMULATION OF SEDIMENTATION OF TWO CIRCULAR PARTICLES WITH COLLISION CONSIDERED IN VERTICAL CHANNEL

D2Q9 model of lattice Boltzmann equation method was used to simulate the sedimentation of two circular particles in a bounded two dimension channel. The characteristics of the sedimentation shows some periodicity for the Reynolds number Re chosen, 0.1-20. The larger the Reynolds number, the stronger the interaction between the two particles and the larger the transversal displacements. For large Re, the two particles leading alternately; for small Re, the initially leading particle will keep its leading position and for moderate Re, the initially upper particle will get leading position and keep it. The influence of the initially relative position of the two particles on sedimentation is small. The width of the channel won＇t change the characteristics of the sedimentation as a whole, but will change the period of the sedimentation. The wider the channel, the longer the period will be.

SEDIMENTATION OF CIRCULAR PARTICLES IN OLDROYDB FLUID

The sedimentation of circular particles in a vertical channel filled withOldroyd ― B fluid was studied by an improved Distributed Lagrange Multiplier/fictitious domain(DLM) method. The sedimenting behaviors of two particles are presented firstly, which shows that,when the particles are dropped in a viscoealstic fluid, the stable configuration is the one wherethe particles are aligned parallel to the flow direction when the Mach number Mis less than 1 andthe elasticity number E is greater than 1. This agrees well with the known experimental in Ref. [1]and simulation results in Ref. [2]. Our simulations also show that, as in Newtonian fluid, thesedimentation of the particles will be accelerated due to the .interaction between particles in aviscoealstic fluid.

Direct numerical simulation of the motion of circular pollutant particles in Newtonian fluid

An improved implementation of distributed multiplier/fictitious domain method is presented for the direct numerical simulation of particulate flow. The key improvement is to replace a finite element triangulation for the velocity and a “twice coarser' triangulation for the pressure with a rectangular discretization for the velocity and pressure. For code validation, the sedimentation of a single particle in a two dimensional channel was simulated. The results showed that the simulation is independent of the mesh size as well as the time step. The comparison between experimental data and this simulation showed that our code can give a more accurate simulation on the motion of particles than previous DLM code. The code was then applied to simulate the sedimentation of 600 particles in a rectangular box. The falling course is presented and discussed. At the same time, this simulation also demonstrates that the method presented in this paper can be used for solving the initial problems involving a lager number of particles exactly with computing durations kept at acceptable levels.

THE MOTION OF A SPHERICAL PARTICLE IN THE STOKES FLOW OUTSIDE A CIRCULAR ORIFICE

For any study ofa suspension entering a pore, the knowledge of the force and moment exerted on a solute particle in an arbitrary position outside the pore is essential, 'This paper for the first lime presents approximate analytical expressions (in closed form) of all the twelve force and moment coefficienis for a sphere outsied a circular orifice, on the basis of a number of discrete data computed by Yan et al(1987).These coefficients are then applied to calculate the trajectory and angular velocity of a spherical particle approaching the pore at zero Reynolds number. The trajectory is in excellent agreement with the available experimental results. An analysis of the relative importance of the coefficients shows that the rotation effect cannot be neglected near the pore opening or near the wall, and that the lateral force effect must be taken into account in the neighborhood of the edge of the pore opening. It is due to neglecting these factors that previous theoretical results deviate from the experimental ones near the pore opening. The effects of the ratio of the particle to pore radii as well as the influences of the graritytbuoyance on the particle trajectory, velocity distribution and rotation are discnssed in detail. It is pointed out that in the experiments of neutrally-buoyant suspensions, the restriction on the density of the particle is most demanding for a large particle size.The expressions of forces and moments presenled herein are complete, relatively accurate and convenient, thus providing a good prerequisite for further studies of any problems involving the entrance of particles to a pare.

Sedimentation of a single particle between two parallel walls

The sedimentation of a single circular particle between two parallel walls was studied by means of direct numerical simulation (DNS) and experiment. The improved implementation of distributed Lagrange multiplier/fictitious domain method used in our DNS is a promising new way for simulation of particulate flows. The settling behaviors of the particle are presented ranging in Reynolds number from 0 to about 700, which showed that our results for low Reynolds numbers agreed well with that reported before. Nevertheless, for higher Reynolds numbers our results were different from theirs. The long-term mean equilibrium positions in our results were all on the centerline, but not at off-center position as reported before. In order to validate our simulation, experiments were also conducted. The results showed that the sedimenting behavior simulated in this paper agreed well with our experiment result.

INTERACTIONS BETWEEN TWO SEDIMENTING PARTICLES WITH DIFFERENT SIZES

An improved implementation of Distributed Lagrange multiplier/fictitious domain method was presented and used to simulate the interactions between two circular particles sedimenting in a two_dimensional channel. The simulation results were verified by comparison with experiments. The results show that the interactions between two particles with different sizes can be described as drafting, kissing, tumbling and separating. Only for small diameter ratio, the two particles will interact undergoing repeated DKT (Drafting, Kissing and Tumbling) process. Otherwise, the two particles will separate after their tumbling. The results also show that, during the interaction process, the motion of the small particle is strongly affected while the large particle is affected slightly.

DIRECT NUMERICAL SIMULATION OF PARTICULATE FLOWS

In this paper, a new method-Distributed La-grange Multiplier/fictitiousdomain (DLM) method for partic-ulate flows was improved. A rectangular mesh was introduced todiscretize the domain, and the buoyant force was considered for predicting the positions ofparticles. In order to validate the presented algorithm, the sedimentation of a single circularparticle was simulated using different mesh sizes and time steps firstly. The results show that thesimulation is independent of the mesh size as well as the time step. And then, the interactionsbetween two falling particles, including drafting, kissing and tumbling, and the sedimentation of 18particles also have been simulated with the code.