Flow modeling, computational fluid dynamics

Many attempts have been made to obtain (semi-)analytical descriptions for non-Newtonian coating flows. These are necessarily approximate and the approximations made to obtain tractable mathematics are sometimes non-physical [58]. These models do not predict the coating behaviour very well from the rheological parameters. The thickness is usually considerably overestimated. It seems more advantageous to simulate non-Newtonian coating flows by computational fluid dynamic methods (see also Ref. [58]). 

The simplest case of fluid modeling is the technique known as computational fluid dynamics. These calculations model the fluid as a continuum that has various properties of viscosity, Reynolds number, and so on. The flow of that fluid is then modeled by using numerical techniques, such as a finite element calculation, to determine the properties of the system as predicted by the Navier-Stokes equation. These techniques are generally the realm of the engineering community and will not be discussed further here. 

Computer Models, The actual residence time for waste destmction can be quite different from the superficial value calculated by dividing the chamber volume by the volumetric flow rate. The large activation energies for chemical reaction, and the sensitivity of reaction rates to oxidant concentration, mean that the presence of cold spots or oxidant deficient zones render such subvolumes ineffective. Poor flow patterns, ie, dead zones and bypassing, can also contribute to loss of effective volume. The tools of computational fluid dynamics (qv) are useful in assessing the extent to which the actual profiles of velocity, temperature, and oxidant concentration deviate from the ideal (40). 

The Prandtl mixing length concept is useful for shear flows parallel to walls, but is inadequate for more general three-dimensional flows. A more complicated semiempirical model commonly used in numerical computations, and found in most commercial software for computational fluid dynamics (CFD see the following subsection), is the A — model described by Launder and Spaulding (Lectures in Mathematical Models of Turbulence, Academic, London, 1972). In this model the eddy viscosity is assumed proportional to the ratio /cVe. 

Particle trajectories can be calculated by utilizing the modern CFD (computational fluid dynamics) methods. In these calculations, the flow field is determined with numerical means, and particle motion is modeled by combining a deterministic component with a stochastic component caused by the air turbulence. This technique is probably an effective means for solving particle collection in complicated cleaning systems. Computers and computational techniques are being developed at a fast pace, and one can expect that practical computer programs for solving particle collection in electrostatic precipitators will become available in the future. 

Computational fluid dynamics (CFD) is the numerical analysis of systems involving transport processes and solution by computer simulation. An early application of CFD (FLUENT) to predict flow within cooling crystallizers was made by Brown and Boysan (1987). Elementary equations that describe the conservation of mass, momentum and energy for fluid flow or heat transfer are solved for a number of sub regions of the flow field (Versteeg and Malalase-kera, 1995). Various commercial concerns provide ready-to-use CFD codes to perform this task and usually offer a choice of solution methods, model equations (for example turbulence models of turbulent flow) and visualization tools, as reviewed by Zauner (1999) below. 

W. Shyy, H. S. Udaykumar, M. M. Rao, R. W. Smith. Computational Fluid Dynamics with Moving Boundaries in Series in Computational and Physical Processes in Mechanics and Thermal Sciences. Washington, DC Taylor Francis, 1995 W. Shyy. Computational Modeling for Fluid Flow and Interfacial Transport. Amsterdam Elsevier, 1994. 

In this chapter, a number of transport phenomena with entirely different natures are compared for liquids filling porous systems. Here transport can refer to flow, diffusion, electric current or heat transport. Corresponding NMR measuring techniques will be described. Applications to porous model objects will be juxtaposed to computational fluid dynamics simulations. 

If one wants to model a process unit that has significant flow variation, and possibly some concentration distributions as well, one can consider using computational fluid dynamics (CFD) to do so. These calculations are very time-consuming, though, so that they are often left until the mechanical design of the unit. The exception would occur when the flow variation and concentration distribution had a significant effect on the output of the unit so that mass and energy balances couldn t be made without it. 

There have been several studies in which the flow patterns within the body of the cyclone separator have been modelled using a Computational Fluid Dynamics (CFD) technique. A recent example is that of Slack et a/. 54 in which the computed three-dimensional flow fields have been plotted and compared with the results of experimental studies in which a backscatter laser Doppler anemometry system was used to measure flowfields. Agreement between the computed and experimental results was very good. When using very fine grid meshes, the existence of time-dependent vortices was identified. These had the potentiality of adversely affecting the separation efficiency, as well as leading to increased erosion at the walls. 

As computers become faster, the complexity of problem that can be usefully simulated increases. Areas of interest include combining computational fluid dynamics (CFD) modelling with chemical kinetics to investigate (and hence reduce) the effect of flow maldistributions on aftertreatment system efficiency, and simulating catalyst deactivation over the lifetime of the catalyst. 

Figure 12.4 Mastering column distribution design. On the left-hand side are shown computational fluid dynamic modeling results, and on the right-hand side are displayed pictures of the stationary phase cross section after an experiment with a dye (flow goes from the bottom to the top) (a) without a distributor, and (b) with a correctly designed distributor.

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