Flow field types

An alternative and complementary use of CFD in fixed bed simulation has been to solve the actual flow field between the particles (Fig. lb). This approach does not simplify the geometrical complexities of the packing, or replace them by the pseudo-continuum that is used in the first approach. The governing equations for the interstitial fluid flow itself are solved directly. The contrast is thus between the interstitial flow field type of simulation and the superficial flow... 

The microrheology makes it possible to expect that (i) The drop size is influenced by the following variables viscosity and elasticity ratios, dynamic interfacial tension coefficient, critical capillarity number, composition, flow field type, and flow field intensity (ii) In Newtonian liquid systems subjected to a simple shear field, the drop breaks the easiest when the viscosity ratio falls within the range 0.3 < A- < 1.5, while drops having A- > 3.8 can not be broken in shear (iii) The droplet breakup is easier in elongational flow fields than in shear flow fields the relative efficiency of the elongational field dramatically increases for large values of A, > 1 (iv) Drop deformation and breakup in viscoelastic systems seems to be more difficult than that observed for Newtonian systems (v) When the concentration of the minor phase exceeds a critical value, ( ) >( ) = 0.005, the effect of coalescence must be taken into account (vi) Even when the theoretical predictions of droplet deformation and breakup... 

Based on microrheology, it is possible to expect that (i) the drop size is influenced by the following variables viscosity and elasticity ratios, dynamic interfacial tension coefficient, critical capillary number, composition, flow field type, and flow field intensity (ii) in Newtonian liquid systems subjected to a simple shear field, the drop breaks most easily when the viscosity ratio falls within the... 

Fig. 17.17 Selected points of polarization curves as function of contact pressure for MEAs from different suppliers and measured with different flow field types, (a) Celtec -P2100 MEA with grid flow fields, (b) Celtec -P2100 MEA with fivefold serpentine flow fields and (c) Dapozol -G55 MEA with grid flow fields (ini/ Air = 1.2/2 ). (d) EuMA-Tech MEA with fivefold...

In Chapter 4 the development of axisymmetric models in which the radial and axial components of flow field variables remain constant in the circumferential direction is discussed. In situations where deviation from such a perfect symmetry is small it may still be possible to decouple components of the equation of motion and analyse the flow regime as a combination of one- and two-dimensional systems. To provide an illustrative example for this type of approximation, in this section we consider the modelling of the flow field inside a cone-and-plate viscometer. 

Systems with extraction only The most common of this type use slot exhaust devices that are more or less uniformly distributed across the exhaust wall of the booth (e.g., the back Wall). Some attention has to be paid to maintaining a uniform distribution of the exhaust volume flow across the slit openings. Rows of bellmouth inlets or even vortex hoods are more advantageous because they provide a more uniform flow field. 

The draft tubes of the reaetor are hollow in order to allow eooling or heating fluid to eireulate. The 300-ml laboratory-seale reaetor (1) is geometrieally similar to the larger reaetors. A marine-type impeller (propeller) provides a smooth and even flow field throughout the reaetor. 

The numerical solution of these equations is not trivial, since for reasonably low viscosities the flow becomes turbulent. A popular method of treating these equations (together with the equations of energy and mass conservation) is the MAC method [156,157]. For the case of immiscible fluids or moving internal interface a phase-field-type approach seems to be successful [78,158,159]. Because of the enormous requirements of computing ressources the development in this field is still relatively slow. We expect, however, an impact from the more widespread availability of massively parallel computers in the near future. 

There is considerable experimental evidence indicating loss of biological activity of macromolecules such as globular proteins and enzymes at gas-Hquid [57], liquid-solid (Fig. 26) [107] and liquid-liquid [108] interfaces. The extent of inactivation has been shown to be strongly influenced by the prevailing flow field and by, many other factors including the presence and/or absence of additives and contaminants and the type of solid surfaces (Figs. 27 and 28) [107]. 

In shear studies, the most commonly used type of device for the generation of well-defined flow fields is the rotational viscometer. The use of these devices for the rheological characterization of liquids is well established [137]. Compared with the capillary and jet devices (Sects. 5.1 and 5.2), rotational viscometers allow the investigation of the effects of continuous rather than intermittent shearing. 

In real life, the parcels or blobs are also subjected to the turbulent fluctuations not resolved in the simulation. Depending on the type of simulation (DNS, LES, or RANS), the wide range of eddies of the turbulent-fluid-flow field is not necessarily calculated completely. Parcels released in a LES flow field feel both the resolved part of the fluid motion and the unresolved SGS part that, at best, is known in statistical terms only. It is desirable that the forces exerted by the fluid flow on the particles are dominated by the known, resolved part of the flow field. This issue is discussed in greater detail in the next section in the context of tracking real particles. With a RANS simulation, the turbulent velocity fluctuations remaining unresolved completely, the effect of the turbulence on the tracks is to be mimicked by some stochastic model. As a result, particle tracking in a RANS context produces less realistic results than in an LES-based flow field. 

It makes sense to compare the implications (in terms of simulation times) of using FV vs. LB in simulating turbulent-flow fields in process devices. Hoekstra (2000) demonstrated the numerical implications of applying different numerical schemes in an industrial application. He compared the outcome of his RANS simulation for a gas cyclone with that of a LES carried out by Derksen and Van den Akker (2000). Table I presents a number of numerical features of the two types of simulations. 

A second choice to be made relates to the size of the flow domain. It may be worthwhile to limit the calculational job by reducing the size of the flow domain, e.g., by identifying an axis or plane of symmetry, or, in a cylindrical vessel with baffles mounted on the wall, due to periodicity in the azimuthal direction. Commercial software accomplishes these choices by means of symmetry cells and cyclic cells, respectively although such choices reduce the size of the simulation, they may eliminate the possibility of finding the real (asymmetric, unstable, or transient) 3-D flow field. The presence of feed pipes or drain or withdrawal pipes may also make the use of symmetry or cyclic cells impossible. Again, this issue only plays a role in RANS-type simulations. 

All measurements, of course, have to be made at a finite concentration. This implies that interparticle interactions cannot be fully neglected. However, in very dilute solutions we can safely assume that more than two particles have only an extremely small chance to meet [72]. Thus only the interaction between two particles has to be considered. There are two types of interaction between particles in solution. One results from thermodynamic interactions (repulsion or attraction), and the other is caused by the distortion of the laminar fiow due to the presence of the macromolecules. If the particles are isolated only the laminar flow field is perturbed, and this determines the intrinsic viscosity but when the particles come closer together the distorted flow fields start to overlap and cause a further increase of the viscosity. The latter is called the hydrodynamic interaction and was calculated by Oseen to various approximations [3,73]. Figure 7 elucidates the effect. 

In addition to the three basic FF designs mentioned, various new FF channel concepts (e.g., biomimetic or fractal flow fields, improved mass transfer channels with variable channel cross section, etc.) have been proposed recently [275]. In all cases, the DL requirements and design will depend on the type of FF design. Therefore, it is critical to understand the relationship between any flow field design and the corresponding DL. 

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