Fluid Dynamic Modeling

Unfortunately, the present models are still on a level aiming at reasonable solutions with several model parameters tuned to known flow fields. For predictive purposes, these models are hardly able to predict unknown flow fields with reasonable degree of accuracy. It appears that the CFD evaluations of bubble columns by use of multidimensional multi-fluid models still have very limited inherent capabilities to fully replace the empirical based analysis (i.e., in the framework of axial dispersion models) in use today [68]. After two decades performing fluid dynamic modeling of bubble columns, it has been realized that there is a limit for how accurate one will be able to formulate closure laws adopting the Eulerian framework. In the subsequent sections a survay of the present stams on bubble column modeling is given. 

It has been shown by Svendsen et al. [161], among others, that the time averaged experimental data on the flow pattern in cylindrical bubble columns is close to axi-symmetric. Fair agreement between experimental- and simulated results are generally obtained for the steady velocity fields in both phases, whereas the steady phase distribution is still aproblem. Therefore, it was anticipated that the 2D axi-symmetric simulations capture the pertinent time-averaged flow pattern that is needed for the analysis of many (not aU) mechanisms of interest for chemical engineers. Sanyal et al. [137] and Krishna and van Baten [81] for example stated that the 2D models 

8 Lateral movement of the bubble hose in a flat bubble column [9]. Reprinted with permission from Elsevier 

Considering the interfacial- and turbulent closures for vertical bubble driven flows, no extensive progress has been observed in the later publications. However, two 

1 Steady-State or Dynamic Simulations, Closures, and Numerical Grid Arrangements 

Implementing the added mass force has barely any influence on the steady state solution [30, 66]. Been et al [30] explained this to some extent surprising result by the fact that the simulations soon reach a quasi-stationary state where there is only minor acceleration. The bubble jets observed close to the distributor plate are then disregarded. However, the convergence rate and thus the computational costs are often significantly improved implementing this force. 

Effects similar to those of the lift force are observed when implementing the turbulent dispersion force using the gradient diffusion model. This dispersion force closure smoothes out sharp velocity gradients in the domain. If the model overestimates the diffusive effect, the velocity profiles may become completely flat over the column cross section. 

The radial wall lift force proposed by Antal et al [2] requires a certain minimum resolution of the grid close to the wall. The values of the model coefficients are crucial for the development of the profiles since these parameters determine the magnitude of the force as well as the operative distance from the wall. The magnitude of the force is highest for larger bubbles, and the force is very sensitive to the bubble size. However, the force does not alter the flow development significantly except very close to the wall. 

In several reports on bubble column modeling a constant gas density is employed. This assumption is not consistent for tall columns that are operated 

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Computational Fluid Dynamics modelling predictions (Al-Rashed etal., 1996) indicate that such velocity gradients can vary considerably throughout a vessel, as illustrated in Figure 8.28. 

The point of this terse introduction is that cellular automata represent not just a formalism for describing a certain particular class of behaviors (lattice gas simulations of fluid dynamics, models of chemical reactions and diffusion processes, etc.), but a much more general template for original and heretofore untapped ways of looking at a large class of unsolved or only poorly understood fundamental problems. 

The presence of a lithosphere with a thickness up to 100 km above the plume head obscures observations that could be made in terms of heat flow, gravity field or seismic structure. Establishing the temperature and flow fields beneath a hotspot thus becomes a difficult exercise. Several key parameters (Fig. 2) are poorly constrained and mostly result from theoretical fluid dynamics model, which underlines their large uncertainty. The temperature anomaly within the hotspot region is generally estimated to be approximately 200 100°C with large uncertainties (Shilling 1991 Sleep 1990). These temperature anomalies will induce smaller densities in the plume and the flux of the density anomalies is called buoyancy flux as defined in (Sleep 1990) ... 

Kelly, A. A., Examination of smoke movement in a two-story compartment using salt water and computational fluid dynamics modeling, MS Thesis, Department of Fire Protection Engineering, University of Maryland, College Park, Maryland, 2001. 

As mentioned earlier, reformate from a fuel processor often needs addition processing to reduce the carbon monoxide levels. Researchers at the Stevens Institute of Technology are developing a microscale preferential oxidation (FrOx) reactor to decrease the carbon monoxide level in the reformate stream to below 100 ppm. As part of their research, they used advanced computational fluid dynamic modeling. 

Other fluid dynamic models of slurry flow have also been developed by other workers [57]. Coppeta, Rodgers, Radzak, and coworkers examined slurry flow, both from a simulation point of view, and from an experimental angle [6,10,11]. A special test apparatus is used consisting of flourescent injections of die that is entrained beneath a glass wafer enabling observation of slurry flow patterns and residence time. Such studies are instrumental... 

Until very recently fluid dynamical models of multiphase reactors were considered intractable. This situation is rapidly changing with the development of high performance computers. Today s workstations allow new approaches to. .. modeling. 

McCarthy LG, Kosiol C, Healy AM, Bradley G, Sexton JC, Corrigan OI. Simulating the hydrodynamic conditions in the United States Pharmacopeia paddle dissolution apparatus. AAPS Pharm Sci Tech 2003 4(2) Article 22. McCarthy LG, Bradley G, Sexton JC, Corrigan OI, Healy AM. Computational fluid dynamics modeling of the paddle dissolution apparatus agitation rate, mixing patterns, and fluid velocities. AAPS Pharm Sci Tech 2004 5(2) Article 31. 

The success of the ID fluid dynamic model to describe the flow field in the DPF channel (Konstandopoulos and Johnson, 1989 Konstandopoulos et al., 1999, 2003) is an indication for the existence of a (nearly) self-similar flow field. A necessary condition for the application of the ID model for the heat transfer problem as well, is that the wall velocity ww variation must be small along the characteristic channel length required for establishment of a steady heat transfer pattern (i.e. a length of a2ftz/y.lh). In transferring the above to the case of flow and heat transfer in a DPF channel we may formally write the heat balance as... 

Figure 12.4 Mastering column distribution design. On the left-hand side are shown computational fluid dynamic modeling results, and on the right-hand side are displayed pictures of the stationary phase cross section after an experiment with a dye (flow goes from the bottom to the top) (a) without a distributor, and (b) with a correctly designed distributor.

Known scale-up correlations thus may allow scale-up when laboratory or pilot plant experience is minimal. The fundamental approach to process scaling involves mathematical modeling of the manufacturing process and experimental validation of the model at different scale-up ratios. In a paper on fluid dynamics in bubble column reactors, Lubbert and coworkers [52] noted Until very recently fluid dynamical models of multiphase reactors were considered intractable. This situation is rapidly changing with the development of high-perfonnance computers. Today s workstations allow new approaches to. .. modeling. ... 

Table 7.3 Boundary conditions used in the fluid-dynamic model of the air channel of Figure 7.11.

Sciacovelli A. (2006) Thermo-fluid dynamic model of a planar solid oxide fuel cell, Graduation Thesis, Politecnico di Torino [in Italian]. 

The effects deriving from both nonideal mixing and the presence of multiphase systems are considered, in order to develop an adequate mathematical modeling. Computational fluid dynamics models and zone models are briefly discussed and compared to simpler approaches, based on physical models made out of a few ideal reactors conveniently connected. 

Index Entries Screw reactor computational fluid dynamics modeling backflow hydrolysis. 

As yet there is no fluid dynamic model that describes in quantitative detail the bubble formation process but it is barely necessary for a reaction engineering model. It is adequate to assume that entering reactant gas passes in plug flow through the bottom layer of particles, say, one initial bubble diameter deep and thereafter forms bubbles. Initial bubble diameter is readily estimated from the known flow through the orifice and the fact that frequency is about 8/s. Above this distributor layer the two-phase bubble model can be applied. 

Many current models treat ventilation loss based on the assumption of a well-mixed space. Furtaw et al. (1996) conducted experiments with pre-set ventilation rates and constant source strengths. These authors showed that rooms with high ventilation rates behave as well-mixed spaces, and that the ventilation rate accurately accounts for steady-state levels and ventilation loss when the source is turned off. At lower ventilation rates, mixing is not uniform and concentrations near the source deviate from those further away. However, once the source is turned off, the ventilation rate accurately accounts for the observed decrease in air concentration. The assumption of a well-mixed room is questionable in the case in which there are few activities and no mixing of air currents. In such cases, diffusion and multiple-zone models can be used to more realistically capture spatial heterogeneity (Furtaw et al., 1996 Nicas, 1996, 1998). Another approach for estimation is a fluid dynamics model utilizing a supercomputer (Matoba et al., 1994a). 

Figure 3.21 shows an example of the air velocity field in an SOFC of the shape given in Fig. 3.20. The segment shown goes from the centre of the air inlet to the wall of the second tube used for return air (vertical axis) and horizontally covers the innermost part of the tube, where the air (with its oxygen) is forced to deflect back into the outer of the two tubes. This is evidently the most difficult part to model, and most fluid dynamics models allow the number of computation elements to be increased in such regions.

Figure 3.21. Velocity field calculated by a fluid dynamics model for the turning area of the air/oxygen flow in a solid oxide fuel cell at operating temperature. (Reprinted from S. Campanari and P. lora (2004). Definition and sensitivity analysis of a finite volume SOFC model for a tubular cell geometry. /. Power Sources 132,113-126. Used by permission from Elsevier.)...

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