Fluid dynamics, computational

CFD codes are structured aroimd the numerical algorithms that can help tackle fluid problems. To provide easy access to their solving power, all commercial CFD packages include sophisticated user interfaces to input problem parameters and to examine the results. Hence, all codes contain three main elements  

This is the first step in building and analysing a flow model. 

A pre-processor consists of the input of a flow problem by means of an operator-friendly interface and subsequent transformation of this input into a form suitable for use by the solver. The pre-processing stage involves  

Two solvers FLUENT and CFX were developed independently by ANSYS and have a number of things in common, but they also have some significant differences. Both are control-volume based for high accuracy and rely heavily on a pressure-based solution technique for broad applicability. They differ mainly in the way they integrate the fluid flow equations and in their equation solution strategies. 

The CFX solver uses finite elements (cell vertex numerics), similar to those used in mechanical analysis, to discretise the domain. In contrast, the FLUENT solver uses finite volumes (cell-centred numerics). 

We have examined some of the most widely acclaimed and cited cyclone models. There is one more way of predicting the flow pattern, pressure drop and the separation efficiency in cyclones and swirl tubes, however by Computational Fluid Dynamics, or CFD for short. 

In CFD, the equations governing the flow of the gas the Navier-Stokes equations, are written in a finite difference form, and solved with the aid of a computer on a grid of points spanning the body of the separator. The particles can either be treated as a sort of second fluid in the cyclone, or as individual particles, which can be tracked in the precalculated gas flow field. 

For this reason turbulence models are required. These are meant to mimic the influence on the turbulence on the mean gas flow pattern. Correctly mimicking the effect of the turbulence is especially difficult in swirling flows, and we will, among other things, look more closely at this issue in this chapter. 

This book has emphasized simple solution techniques that are easy to understand and implement. Simple solutions are a luxury for the engineer, saving personal time at the expense of computer time and memory, which are comparatively cheap. They also allow direct and first-hand knowledge of exactly what the computer is doing. Unfortunately, some problems are too big for simple and easily understood methods to work. Most detailed modeling of turbulence falls into this category and is the domain of CFD. 

Computational fluid mechanics has had some notable successes in duplicating experimental results for turbulent reactors, both tubes and tanks. As one example, one simulation closely agreed with experiments for the yield of a Bourne reaction in a fed-batch laboratory reactor that was stirred by a half-moon agitator  

Large computer models becoming de facto black boxes is an emerging problem that is not confined to CFD. Within chemical reaction engineering, mistakes can be minimized by always comparing the results to those of simple models and by remembering that experiments are the final proof. 

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Computational Fluid Dynamics Applied to Process Engineering. 

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. 

Although the Arrhenius equation does not predict rate constants without parameters obtained from another source, it does predict the temperature dependence of reaction rates. The Arrhenius parameters are often obtained from experimental kinetics results since these are an easy way to compare reaction kinetics. The Arrhenius equation is also often used to describe chemical kinetics in computational fluid dynamics programs for the purposes of designing chemical manufacturing equipment, such as flow reactors. Many computational predictions are based on computing the Arrhenius parameters. 

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. 

P. J. Roache, Computational Fluid Dynamics, Hermosa Pubhshers, Albuquerque, N.M., 1982. 

It has become quite popular to optimize the manifold design using computational fluid dynamic codes, ie, FID AP, Phoenix, Fluent, etc, which solve the full Navier-Stokes equations for Newtonian fluids. The effect of the area ratio, on the flow distribution has been studied numerically and the flow distribution was reported to improve with decreasing yiR. 

A numerical study of the effect of area ratio on the flow distribution in parallel flow manifolds used in a Hquid cooling module for electronic packaging demonstrate the useflilness of such a computational fluid dynamic code. The manifolds have rectangular headers and channels divided with thin baffles, as shown in Figure 12. Because the flow is laminar in small heat exchangers designed for electronic packaging or biochemical process, the inlet Reynolds numbers of 5, 50, and 250 were used for three different area ratio cases, ie, AR = 4, 8, and 16. 

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. 

Computational fluid dynamics (CFD) emerged in the 1980s as a significant tool for fluid dynamics both in research and in practice, enabled by rapid development in computer hardware and software. Commercial CFD software is widely available. Computational fluid dynamics is the numerical solution of the equations or continuity and momentum (Navier-Stokes equations for incompressible Newtonian fluids) along with additional conseiwation equations for energy and material species in order to solve problems of nonisothermal flow, mixing, and chemical reaction. 

FIG. 6-56 Computational fluid dynamic simulation of flow over a square cylinder, showing one vortex shedding period. (From Choudliuty, et al., Trans. ASME Fluids Div, TN-076[1994].)... 

Relatively uncomphcated transparent tank studies with tracer fluids or particles can give a similar feel for the overall flow pattern. It is important that a careful balance be made between the time and expense of calculating these flow patterns with computational flirid dynamics compared to their apphcabihty to an actual industrial process. The future of computational fluid dynamics appears very encouraging and a reasonable amount of time and effort put forth in this regard can yield immediate results as well as potential (or future process evaluation. 

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

Application of Computational Fluid Dynamics and Computational Fluid Mixing in Reactors... 

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 ... 

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

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