Computational methods fluid dynamics

Another detailed method of determining pressures is computational fluid dynamics (CFD), which uses a numerical solution of simplified equations of motion over a dense grid of points around the building. Murakami et al. and Zhoy and Stathopoulos found less agreement with computational fluid dynamics methods using the k-e turbulence model typically used in current commercial codes. More advanced turbulence models such as large eddy simulation were more successful but much more costly. ... 

Computational fluid dynamics methods may allow for more accurate predictions. These models account for turbulence and other parameters such as thermal effects. A description of these methods is included in Chapter 11. 

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. 

Industrial use of hydrogen has experienced a few accidents, which subsequently have been useful in defining norms and procedures. One occurred in a narrow Stockholm street in 1983, where 13.5 kg of H2 escaped from a set of 20-MPa pressure tanks with defect cormections and exploded (Fig. 5.4a) 16 people were injured, and 10 cars and the adjacent building were heavily damaged. This accident has recently been modelled by computational fluid dynamics methods, giving the distribution of H2 velocities and concentra-... 

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]). 

Computational fluid dynamics methods, which typically calculate flow field variables at himdreds of thousands of points inside the reactor to come up with overall reaction rates, are far better suited for the analysis of such systems. Another difference between CFD and traditional design methods is the minimal reliance of CFD on experimental data and extrapolation of that data to different scales, a process known as scale-up. Computational fluid dynamics relies on solving the fundamental equations of motion and conservation. These equations are scale independent and can be solved directly for the full-scale equipment. 

At present, computational fluid dynamics methods are finding many new and diverse applications in bioengineering and biomimetics. For example, CFD techniques can be used to predict (1) velocity and stress distribution maps in complex reactor performance studies as well as in vascular and bronchial models (2) strength of adhesion and dynamics of detachment for mammalian cells (3) transport properties for nonhomogeneous materials and nonideal interfaces (4) multicomponent diffusion rates using the Maxwell-Stefan transport model, as opposed to the limited traditional Fickian approach. 

Ma, Z., Venkataraman, R. and Farooque, M. Study of the Gas Flow Distribution and Heat Transfer for Externally Manifolded Fuel Cell Stack Using Computational Fluid Dynamics Method , Journal of Fuel Cell Science and Technology, 1, No. 1, 2004, 49-55. 

This method has been devised as an effective numerical teclmique of computational fluid dynamics. The basic variables are the time-dependent probability distributions f x, f) of a velocity class a on a lattice site x. This probability distribution is then updated in discrete time steps using a detenninistic local rule. A carefiil choice of the lattice and the set of velocity vectors minimizes the effects of lattice anisotropy. This scheme has recently been applied to study the fomiation of lamellar phases in amphiphilic systems [92, 93]. 

Hughes, T. J. R., Franca, L. P. and Balestra, M., 1986. A new finite-element formulation for computational fluid dynamics. 5. Circumventing the Babuska-Brezzi condition - a stable Petrov-Galerkin formulation of the Stokes problem accommodating equal order interpolations. Cornput. Methods Appl. Meek Eng. 59, 85-99. 

Versteeg, H. K. and Malalasekera, W., An Introduction to Computational Fluid Dynamics—The Finite Volume Method, Addison Wesley Longman Ltd., 1995. 

Four methods for industrial air technology design are presented computational fluid dynamics (CFD), thermal building dynamics simulation, multizone... 

Four methods for industrial air technology design are presented in this chapter computational fluid dynamics (CFD), thermal building-dynamics simulation, multizone airflow models, and integrated airflow and thermal modeling. In addition to the basic physics of the problem, the methods, purpose, recommended applications, limitations, cost and effort, and examples are pro vided. 

I FIGURE II.I Trade-off between the complexity of the method and information content of resuits, Simpie methods are at the lower left complex methods, such as computational fluid dynamics, are near the upper right corner of the graph. 

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. 

A drawback of the Lagrangean artificial-viscosity method is that, if sufficient artificial viscosity is added to produce an oscillation-free distribution, the solution becomes fairly inaccurate because wave amplitudes are damped, and sharp discontinuities are smeared over an increasing number of grid points during computation. To overcome these deficiencies a variety of new methods have been developed since 1970. Flux-corrected transport (FCT) is a popular exponent in this area of development in computational fluid dynamics. FCT is generally applicable to finite difference schemes to solve continuity equations, and, according to Boris and Book (1976), its principles may be represented as follows. 

Correspondingly all calculations are finite element method (FEM)-based. Furthermore, the flow channel calculations are based on computer fluid dynamics (CFD) research test for the optimization of the mbber flow. 

There are many nonintrusive experimental tools available that can help scientists to develop a good picture of fluid dynamics and transport in chemical reactors. Laser Doppler velocimetry (LDV), particle image velocimetry (PIV) and sonar Doppler for velocity measurement, planar laser induced fluorescence (PLIF) for mixing studies, and high-speed cameras and tomography are very useful for multiphase studies. These experimental methods combined with computational fluid dynamics (CFDs) provide very good tools to understand what is happening in chemical reactors. 

So far, some researchers have analyzed particle fluidization behaviors in a RFB, however, they have not well studied yet, since particle fluidization behaviors are very complicated. In this study, fundamental particle fluidization behaviors of Geldart s group B particle in a RFB were numerically analyzed by using a Discrete Element Method (DEM)- Computational Fluid Dynamics (CFD) coupling model [3]. First of all, visualization of particle fluidization behaviors in a RFB was conducted. Relationship between bed pressure drop and gas velocity was also investigated by the numerical simulation. In addition, fluctuations of bed pressure drop and particle mixing behaviors of radial direction were numerically analyzed. 

In practice, the process regime will often be less transparent than suggested by Table 1.4. As an example, a process may neither be diffusion nor reaction-rate limited, rather some intermediate regime may prevail. In addition, solid heat transfer, entrance flow or axial dispersion effects, which were neglected in the present study, may be superposed. In the analysis presented here only the leading-order effects were taken into account. As a result, the dependence of the characteristic quantities listed in Table 1.5 on the channel diameter will be more complex. For a detailed study of such more complex scenarios, computational fluid dynamics, to be discussed in Section 2.3, offers powerful tools and methods. However, the present analysis serves the purpose to differentiate the potential inherent in decreasing the characteristic dimensions of process equipment and to identify some cornerstones to be considered when attempting process intensification via size reduction. 

In computational fluid dynamics only the last two methods have been extensively implemented into commercial flow solvers. Especially for CFD problems the FVM has proven robust and stable, and as a conservative discretization scheme it has some built-in mechanism of error avoidance. For this reason, many of the leading commercially available CFD tools, such as CFX4/5, Fluent and Star-CD, are based on the FVM. The oufline on CFD given in this book wiU be based on this method however, certain parts of the discussion also apply to the other two methods. 

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