Fluid dynamics, description

In macroscopic reactors, knowledge of the velocity profile in the channel cross-section is a necessary and sufficient prerequisite to describe the material transport. In microscopic dimensions down to a few micrometers, diffusion also has to be considered. In fact, without the influence of diffusion, extremely broad residence time distributions would be found because of the laminar flow conditions. Superposition of convection and diffusion is called dispersion. Taylor [91] was among the first to notice this strong dominating effect in laminar flow. It is possible to transfer his deduction to rectangular channels. A complete fluid dynamic description has been given of the flow, including effects such as the influence of the wall, the aspect ratio and a chemical wall reaction on the concentration field in the cross-section [37]. 

The criterion of Eq. (202) is a simplified fluid dynamic description of three-phase fluidized beds capable of application over a wide range of conditions. They have also compared the predictions of Eq. (202) with their experimental data, showing a good agreement. 

An idealized fluid-dynamic description of slugging behaviour... 

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. 

A mathematical description of continuum fluid dynamics can proceed from two fundamentally different points of view (1) A macroscopic, or top-down ([hass87], [hass88]), approach, in which the equations of motions are derived as the most... 

Virtual prototyping will be the future method to develop new reactors and chemical processes. With a good description of the fluid dynamics, and mass and heat transfer in the reactor, the specific chemical reactions and physical properties of the fluid can be changed and a process optimization can be performed in virtual... 

The present book is devoted to both the experimentally tested micro reactors and micro reaction systems described in current scientific literature as well as the corresponding processes. It will become apparent that many micro reactors at first sight simply consist of a multitude of parallel channels. However, a closer look reveals that the details of fluid dynamics or heat and mass transfer often determine their performance. For this reason, besides the description of the equipment and processes referred to above, this book contains a separate chapter on modeling and simulation of transport phenomena in micro reactors. 

Boiling at a heated surface, as has been shown, is a very complicated process, and it is consequently not possible to write and solve the usual differential equations of motion and energy with their appropriate boundary conditions. No adequate description of the fluid dynamics and thermal processes that occur during such a process is available, and more than two mechanisms are responsible for the high... 

Another Lagrangian-based description of micromixing is provided by multienvironment models. In these models, the well macromixed reactor is broken up into sub-grid-scale environments with uniform concentrations. A four-environment model is shown in Fig. 5.16. In this model, environment 1 contains unmixed fluid from feed stream 1 environments 2 and 3 contain partially mixed fluid and environment 4 contains unmixed fluid from feed stream 2. The user must specify the relative volume of each environment (possibly as a function of age), and the exchange rates between environments. While some qualitative arguments have been put forward to fit these parameters based on fluid dynamics and/or flow visualization, one has little confidence in the general applicability of these rules when applied to scale up or scale down, or to complex reactor geometries. 

Not surprisingly, the Bernardi and Verbrugge model forms the basis for many other models that came after it. most notably the computational-fluid-dynamics (CFD) models, as discussed in the next section. In terms of direct descendants of this model, the model of Chan et al. " takes the Bernard and Verbrugge model and incorporates carbon monoxide effects at the anode as per the Springer et al. ° description. The models of Li and co-workers - " " ... 

It is common within the industry to characterize chemical processes in terms of one or a few global reaction steps, assigning an Arrhenius rate expression to describe the rate of each reaction. If knowledge of the detailed chemistry is inadequate or the chemical scheme is to be combined with computational fluid dynamics for a complex flow description, a simplified chemistry may be necessary. It is important, however, to realize that such a chemical description can only be used for the narrow range of conditions (temperature, composition, etc.) for which it is developed. Any extrapolation outside these conditions may be erroneous or even disastrous. 

Analytically Reduced Mechanisms Some problems can be described by models that involve a full reaction mechanism in combination with simplied fluid dynamics. Other applications may involve laminar or turbulent multidimensional reactive flows. For problems that require a complex mathematical flow description (possibly CFD), the computational cost of using a full mechanism may be prohibitive. An alternative is to describe... 

When motion of the fluid consists of only small fluctuations about a state of near-rest, Lhe continuum equations are linearized by neglecting nonlinear terms and they become lhe equalions of acoustics. A large variety of fluid motions are described as sound waves when the small-motion or acoustic description can be used, the principle of superposition is valid. This powerful principle allows addition of simple simultaneous motions to represent a more complex motion, such as the sound reaching lhe audience from the instruments of a symphony orchestra. The superposition principle does not apply to large-scale (nonacoustical) motions, and the subject of fluid dynamics (in distinction from acoustics) treats nonlinear flows. i.e.. those that cannot be described as superpositions of other flows. 

When Bernie Shizgal arrived at UBC in 1970, his research interests were in applications of kinetic theory to nonequilibrium effects in reactive systems. He subsequently applied kinetic theory methods to the study of electron relaxation in atomic and molecular moderators,46 hot atom chemistry, nucleation,47 rarefied gas dynamics,48 gaseous electronics, and other physical systems. An important area of research has been the kinetic theory description of the high altitude portion of planetary atmospheres, and the escape of atmospheric species.49 An outgrowth of these kinetic theory applications was the development of a spectral method for the solution of differential and integral equations referred to as the quadrature discretization method (QDM), which has been used with considerable success in statistical, quantum, and fluid dynamics.50... 

Computational fluid dynamics enables us to investigate the time-dependent behavior of what happens inside a reactor with spatial resolution from the micro to the reactor scale. That is to say, CFD in itself allows a multi-scale description of chemical reactors. To this end, for single-phase flow, the space resolution of the CFD model should go down to the scales of the smallest dissipative eddies (Kolmogorov scales) (Pope, 2000), which is inversely proportional to Re-3/4 and of the orders of magnitude of microns to millimeters for typical reactors. On such scales, the Navier-Stokes (NS) equations can be expected to apply directly to predict the hydrodynamics of well-defined system, resolving all the meso-scale structures. That is the merit of the so-called DNS. 

Then, a survey of micro reactors for heterogeneous catalyst screening introduces the technological methods used for screening. The description of microstructured reactors will be supplemented by other, conventional small-scale equipment such as mini-batch and fixed-bed reactors and small monoliths. For each of these reactors, exemplary applications will be given in order to demonstrate the properties of small-scale operation. Among a number of examples, methane oxidation as a sample reaction will be considered in detail. In a detailed case study, some intrinsic theoretical aspects of micro devices are discussed with respect to reactor design and experimental evaluation under the transient mode of reactor operation. It will be shown that, as soon as fluid dynamic information is added to the pure experimental data, more complex aspects of catalysis are derivable from overall conversion data, such as the intrinsic reaction kinetics. 

The description of small scale turbulent fields in confined spaces by fundamental approaches, based on statistical methods or on the concept of deterministic chaos, is a very promising and interesting research task nevertheless, at the authors knowledge, no fundamental approach is at the moment available for the modeling of large-scale confined systems, so that it is necessary to introduce semi-empirical models to express the tensor of turbulent stresses as a function of measurable quantities, such as geometry and velocity. Therefore, even in this case, a few parameters must be adjusted on the basis of independent measures of the fluid dynamic behavior. In any case, it must be underlined that these models are very complex and, therefore, well suited for simulation of complex systems but neither for identification of chemical parameters nor for online control and diagnosis [5, 6],... 

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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