Computational fluid dynamics calculations

In most, but not all circumstances, the core gas temperature, T, is the natural reference temperature for the compressed gas because the highest temperature at the end of compression is responsible for the development of spontaneous ignition in the shortest time [88, 95]. Exceptionally, when the compression heats the reactants to temperatures that correspond to the region of ntc for that particular mixture, combustion may be initiated in the cooler boundary layer region. That is, gases which, at the end of compression, are colder than those in the adiabatic core control the duration of the ignition delay. This was demonstrated by Schreiber and coworkers by the simulation of alkane combustion, using various reduced kinetic schemes, in computational fluid dynamic calculations [102-104]. 

With pervaporation membranes the water can be removed during the condensation reaction. In this case, a tubular microporous ceramic membrane supplied by ECN [124] was used. The separating layer of this membrane consists of a less than 0.5 mm film of microporous amorphous silica on the outside of a multilayer alumina support. The average pore size of this layer is 0.3-0.4 nm. After addition of the reactants, the reactor is heated to the desired temperature, the recyde of the mixture over the outside of the membrane tubes is started and a vacuum is apphed at the permeate side. In some cases a sweep gas can also be used. The pressure inside the reactor is a function of the partial vapor pressures and the reaction mixture is non-boiling. Although it can be anticipated that concentration polarization will play an important role in these systems, computational fluid dynamics calculations have shown that the membrane surface is effectively refreshed as a result of buoyancy effects [125]. 

The comparison of the experimental results with computational fluid dynamics calculations of the gas flow indicates a clear correlation of the flow model behavior with the appearance of recirculation loops in the reaction chamber and the effect of the gas jet at the entrance of the gas-liquid contact zone (Figure 14.4). The latter considerably increases the mixing in the gas phase and prevents the development of plug-flow behavior in the gas phase. 

In the cases the port operations intensity is on nearly equal level, the identification of seabed degradation can be assessed on the basis of prediction methods developed on the basis of real observations, physical model tests and CFD (Computational Fluid Dynamics) calculations (Kraskowski, 2009). If the port operations are carried out near the... 

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). 

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. 

In theory it should be possible to calculate the capture efficiency without measurements. Some attempts have used computational fluid dynamics (CFD) models, but difficulty modeling air movement and source characteristics have shown that it will be a long time before it will be possible to calculate the capture efficiency in advance. ... 

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. 

Harlow, F. H., and A. A. Amsden. 1971. A numerical fluid dynamics calculation method for all flow speeds. J. of Computational Physics. 8(2) 197-213. 

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. 

As the large-scale computational fluid dynamics (CFD) simulations often invoke simplifying the kinetics as one-step overall reaction, the extraction of such bulk flame parameter as overall activation energy is especially useful when the CFD calculation with detailed chemistry is not feasible. Based on the experimental results, the deduced overall achvation energies of the three equivalence ratios are shown in Figure 4.1.10a. It can be observed that the variation of with is nonmonotonic and peaks near the stoichiometric condition. 

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. 

Two numerical methods have been used for the solution of the spray equation. In the first method, i.e., the full spray equation method 543 544 the full distribution function / is found approximately by subdividing the domain of coordinates accessible to the droplets, including their physical positions, velocities, sizes, and temperatures, into computational cells and keeping a value of / in each cell. The computational cells are fixed in time as in an Eulerian fluid dynamics calculation, and derivatives off are approximated by taking finite differences of the cell values. This approach suffersfrom two principal drawbacks (a) large numerical diffusion and dispersion... 

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. 

To simulate the thermally induced stresses in a cell, temperature distribution data in the cell must first be known. The cell performance and related temperature distribution in a cell during these operations are calculated using a computational fluid dynamics code. 

Another important modeling aspect is the simulation of catalytic process parameters and reactor configurations. Such models are typically associated with process engineering, and involve computational fluid dynamics and heat- and mass-transfer calculations. They are essential in the process planning and scale-up. However, as this book deals primarily with the chemical aspects of catalysis, the reader is referred to the literature on industrial catalysis and process simulations for further information [49,56]. 

In the microfluid dynamics approaches the continuity and Navier-Stokes equation coupled with methodologies for tracking the disperse/continuous interface are used to describe the droplet formation in quiescent and crossflow continuous conditions. Ohta et al. [54] used a computational fluid dynamics (CFD) approach to analyze the single-droplet-formation process at an orifice under pressure pulse conditions (pulsed sieve-plate column). Abrahamse et al. [55] simulated the process of the droplet break-up in crossflow membrane emulsification using an equal computational fluid dynamics procedure. They calculated the minimum distance between two membrane pores as a function of crossflow velocity and pore size. This minimum distance is important to optimize the space between two pores on the membrane... 

Computational fluid dynamic (CFD) calculations were performed to give the Pd concentration profile in a nanopore of the oxide catalyst carrier layer [283]. For wet chemical deposition most of the catalyst was deposited in the pore mouth, in the first 4 pm of the pore. Thus, most of the hydrogenation reaction is expected to occur in this location. For electrochemical deposition, large fractions of the catalyst are located... 

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