Computational fluid dynamics techniques

Computation fluid mixing and computational fluid dynamic techniques have increasingly been used to elucidate solids distribution in agitated vessels [44],... 

In contrast to the pseudo 3-D models, tmly multi-dimensional models use, in general, finite element or finite volume CFD (Computational Fluid Dynamics) techniques to solve full 3-D Navier-Stokes equations with appropriate modifications to account for electrochemistry and current distribution. The details of electrochemistry may vary from code to code, but the current density is calculated almost exclusively from Laplace equation for the electric potential (see Equation (5.24)). Inside the electrolyte, the same equation represents the migration of ions (e g. 0= in SOFC), elsewhere it represents the electron/charge transfer. In what follows, we briefly summarize a commonly used multi-dimensional model for PEM fuel cells because of its completeness and of the fact that it also addresses most essential features of SOFC modeling. 

Grochowicz et al. modeled the secondary flow in serpentine and coiled tubes as the measure of the radial mixing using computational fluid dynamics techniques. They showed that flow characteristics in serpentine tubes result in considerably less band broadening per unit length than in linear tubes of the same inner... 

A single set of conservation eqnations valid for both porous electrodes and the free electrolyte region is derived and nnmerically solved using a computational fluid dynamics technique. This numerical methodology is capable of simulating a two-dimensional cell with the fluid flow taken into consideration. The motion of the liquid electrolyte is governed by the Navier-Stokes equation with the Boussinesq approximation and the continuity equation as follows ... 

In addition, just as employee participation is the key element of process SMSs, worker involvement is crucial to the effective application of safety cases. Unfortunately, the perception among many that a safety case is a lengthy highly technical document that can only be understood by specialists mitigates effective employee participation. For example, the Computational Fluid Dynamics technique used to model explosion overpressure uses very sophisticated mathematics. This sophistication makes communication with nonspecialists a challenge. In addition, the sheer size and complexity of a safety case may serve as a barrier to the involvement of nontechnical personnel. 

Hontanon E, Escudero M J, Bautista C, Garcia-Ybarra P L and Daza L (20(X)) Optimisation of flow-field in polymer electrolyte membrane fuel cells using computational fluid dynamics techniques, J. Power Sources, 86, pp. 363-368. 

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. 

Computational fluid dynamics (CFD) is the analysis of systems involving fluid flow, energy transfer, and associated phenomena such as combustion and chemical reactions by means of computer-based simulation. CFD codes numerically solve the mass-continuity equation over a specific domain set by the user. The technique is very powerful and covers a wide range of industrial applications. Examples in the field of chemical engineering are ... 

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) The technique of using computers to provide an assessment of the flow of air and other fluids. 

This study investigates the hydrodynamic behaviour of an aimular bubble column reactor with continuous liquid and gas flow using an Eulerian-Eulerian computational fluid dynamics approach. The residence time distribution is completed using a numerical scalar technique which compares favourably to the corresponding experimental data. It is shown that liquid mixing performance and residence time are strong functions of flowrate and direction. 

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. 

Chemical engineers, however, have to find practical ways for dealing with turbulent flows in flow devices of complex geometry. It is their job to exploit practical tools and find practical solutions, as spatial variations in turbulence properties usually are highly relevant to the operations carried out in their process equipment. Very often, the effects of turbulent fluctuations and their spatial variations on these operations are even crucial. The classical toolbox of chemical engineers falls short in dealing with these fluctuations and its effects. Computational Fluid Dynamics (CFD) techniques offer a promising alternative approach. 

Figure 10 Rotational (tangential) flow (UA) as a function of stirring rate (co) for paddle (filled circles) and basket (open circles) Mean SD position S2 approximately 1 cm above the paddle and midway between the paddle shaft and the wall of the dissolution vessel. (Please note that, in contrast to simulation techniques such as, for instance, computational fluid dynamics, these data are based on dissolution experiments.) Source Data from Ref. 10, UPE method.

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. 

The computational fluid dynamics investigations listed here are all based on the so-called volume-of-fluid method (VOF) used to follow the dynamics of the disperse/ continuous phase interface. The VOF method is a technique that represents the interface between two fluids defining an F function. This function is chosen with a value of unity at any cell occupied by disperse phase and zero elsewhere. A unit value of F corresponds to a cell full of disperse phase, whereas a zero value indicates that the cell contains only continuous phase. Cells with F values between zero and one contain the liquid/liquid interface. In addition to the above continuity and Navier-Stokes equation solved by the finite-volume method, an equation governing the time dependence of the F function therefore has to be solved. A constant value of the interfacial tension is implemented in the summarized algorithm, however, the diffusion of emulsifier from continuous phase toward the droplet interface and its adsorption remains still an important issue and challenge in the computational fluid-dynamic framework. 

The data presented in Fig. 77 deal with flow states, these being far more complicated than those encountered in the ventilation technique. It would certainly be of interest to examine which tips and statements can be delivered here by the Computational Fluid Dynamics (CFD) ... 

Simulation techniques suitable for the description of phenomena at each length-scale are now relatively well established Monte Carlo (MC) and Molecular Dynamics (MD) methods at the molecular length-scale, various mesoscopic simulation methods such as Dissipative Particle Dynamics (Groot and Warren, 1997), Brownian Dynamics, or Lattice Boltzmann in the colloidal domain, Computational Fluid Dynamics at the continuum length-scale, and sequential-modular or equation-based methods at the unit operation/process-systems level. 

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