Simulating the Particle Flow

We have presented some of the latest CFD simulations of cyclone gas flow, both from the reviewed and the nom-eviewed literature. Many questions remain, and swirling flow remains very difficult to simulate correctly in all respects. 

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Due to the very low volumetric concentration of the dispersed particles involved in the fluid flow for most cyclones, the presence of the particles does not have a significant effect on the fluid flow itself. In these circumstances, the fluid and the particle flows may be considered separately in the numerical simulation. A common approach is to first solve the fluid flow equations without considering the presence of particles, and then simulate the particle flow based on the solution of the fluid flow to compute the drag and other interactive forces that act on the particles. 

In computation using the stochastic trajectory model, the Monte Carlo approach is commonly employed. It is necessary to calculate several thousands, or even tens of thousands, of trajectories to simulate the particle flow field. The central issue in developing the stochastic trajectory model is how to model the instantaneous turbulent gas flow field. The method... 

An appropriate model of the Reynolds stress tensor is vital for an accurate prediction of the fluid flow in cyclones, and this also affects the particle flow simulations. This is because the highly rotating fluid flow produces a. strong nonisotropy in the turbulent structure that causes some of the most popular turbulence models, such as the standard k-e turbulence model, to produce inaccurate predictions of the fluid flow. The Reynolds stress models (RSMs) perform much better, but one of the major drawbacks of these methods is their very complex formulation, which often makes it difficult to both implement the method and obtain convergence. The renormalization group (RNG) turbulence model has been employed by some researchers for the fluid flow in cyclones, and some reasonably good predictions have been obtained for the fluid flow. 

Cate etal. (2001) propose a method for the calculation of crystal-crystal collisions in the turbulent flow field of an industrial crystallizer. It consists of simulating the internal flow of the crystallizer as a whole and of simulating the motion of individual particles suspended in the turbulent flow in a small subdomain (box) of the crystallizer. 

Thus far, these models cannot really be used, because no theory is able to yield the reaction rate in terms of physically measurable quantities. Because of this, the reaction term currently accounts for all interactions and effects that are not explicitly known. These more recent theories should therefore be viewed as an attempt to give understand the phenomena rather than predict or simulate it. However, it is evident from these studies that more physical information is needed before these models can realistically simulate the complete range of complicated behavior exhibited by real deposition systems. For instance, not only the average value of the zeta-potential of the interacting surfaces will have to be measured but also the distribution of the zeta-potential around the mean value. Particles approaching the collector surface or already on it, also interact specifically or hydrodynamically with the particles flowing in their vicinity [100, 101], In this case a many-body problem arises, whose numerical... 

Understanding the dependence of film structure and morphology on system layout and process parameters is a core topic for the further development of ZnO technology. Work is being performed on in situ characterization of deposition processes. Growth processes are simulated using Direct Simulation Monte-Carlo (DSMC) techniques to simulate the gas flow and sputter kinetics simulation and Particle-ln-Cell Monte-Carlo (PICMC) techniques for the plasma simulation [132]. 

Another objective in the study of the application of CFD in crystallization is to simulate the particle size distribution in crystallization. In order to solve this problem, the simulation should take into account the population balance. The internal coordinates of the population balance make it difficult to utilize it in the CFD environment. In addition, different-sized particles have different hydrodynamics, which causes further complications. Wei and Garside [42] used the assumption of MSMPR and the moments of population balance to avoid the above difficulties in the simulation of precipitation. In the CFX commercial application, the MUSIC model offers a method for solving the population balance equation in CFD and defines the flow velocity of different-sized particles... 

At the most fundamental level (corresponding to direct numerical simulations), the gas flow field is modeled at scales smaller than the size of the particles. The interaction of the gas phase with the particles is considered by imposing suitable boundary conditions at the surface of the solids. 

Particle trajectory is the result of the interaction of the particle with the electric field and the flow field. To simulate the particle trajectories, there are two approaches. The first approach is the Lagrangian tracking method, which neglects the finite size of the particles and treats them as point particles and solves the field variables without the presence of the particles [8]. In this case, only the effect of the field variables on the particle is considered. The second approach is the stress tensor approach, which includes the size effect of the particle. In this approach, the field variables are solved with the presence of the finitesized particle, and the particle translates as a result of the interaction of the particle with the electric and flow field [8]. In each incremental movement of the particle, the field variables need to be resolved. The former approach is very simple and works good to some extent, and the latter approach is accurate yet computationally expensive. 

The examples of non-Newtonian microchannel flows cited in the present article so far inherently assume that the continuum hypothesis is not disobeyed, so far as the description of the basic governing equations is concerned. This, however, ceases to be a valid consideration in certain fluidic devices, in which the characteristic system length scales are of the same order as that of the size of the macromolecules being transported. Fan et al. [10], in a related study, used the concept of finitely extended nonlinear elastic (FENE) chains to model the DNA molecules and employed the dissipative particle dynamics (DPD) approach to simulate the underlying flow behavior in some such representative cases. From their results, it was revealed that simple DPD fluids essentially behave as Newtonian fluids in Poiseuille flows. However, the velocity profiles of FENE... 

FIGURE 7.30 (See color insert.) DEM simulation of particle flow pattern (left) and force network (right) in a horizontal section of a bladed mixer. (Reprinted from Chem. Eng. ScL, 59, Zhou, Y.C., Yu, A.B., Stewart, R.L., and Bridgwater, J., Microdynamic analysis of the particle flow in a cylindrical bladed mixer, 1343-1364, Copyright 2004, with permission from Elsevier.)... 

In most microfluidics and nanofluidics, the atomistic effects on electroosmotic flows are neghgible. But when the characteristic length is comparable with the molecular size of fluid, it should be considered. Molecular dynamics methods have been used to simulate the particle effects in nanoscale electroosmotic flows [23, 24]. However, it is too time-consuming to simulate a real electroosmotic micro- and nanofluidics by molecular dynamics. The multiscale modeling and analysis would be a possible research direction. 

It is not easy to study the particle flow pattern experimentally. In order to give an impression of the flow of a particle through a cyclone, we can resort to CFD simulations. Figure 3.1.4 shows a series of particle trajectories. The particles are injected at different radial positions along the inlet in a precalculated gas flow field. The swirling motion is not shown. 

Dissipative particle dynamics (DPD) is a technique for simulating the motion of mesoscale beads. The technique is superficially similar to a Brownian dynamics simulation in that it incorporates equations of motion, a dissipative (random) force, and a viscous drag between moving beads. However, the simulation uses a modified velocity Verlet algorithm to ensure that total momentum and force symmetries are conserved. This results in a simulation that obeys the Navier-Stokes equations and can thus predict flow. In order to set up these equations, there must be parameters to describe the interaction between beads, dissipative force, and drag. 

Guichardon etal. (1994) studied the energy dissipation in liquid-solid suspensions and did not observe any effect of the particles on micromixing for solids concentrations up to 5 per cent. Precipitation experiments in research are often carried out at solids concentrations in the range from 0.1 to 5 per cent. Therefore, the stirred tank can then be modelled as a single-phase isothermal system, i.e. only the hydrodynamics of the reactor are simulated. At higher slurry densities, however, the interaction of the solids with the flow must be taken into account. 

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