Vorticity region

The mixing and transport of fluids in a microchannel is a slow process due to the absence of recirculation regions (vortices), and to overcome this absence it is essential to assure the automation of the devices. The transport and mixing of fluids can be improved through passive or active techniques, using, for instance, mechanical actuators or tridimensional microstructures, fuUy integrated in the microdevices (Suh and Kang, 2010 Lee et al., 2011). 

Here (0 is the magnitude of the vorticity vector, which is directed along the z axis. An irrotational flow is one with zero vorticity. Irro-tational flows have been widely studied because of their useful mathematical properties and applicability to flow regions where viscous effects m be neglected. Such flows without viscous effec ts are called in viscid flows. 

For most applications, the engineer must instead resort to turbulence models along with time-averaged Navier-Stokes equations. Unformnately, most available turbulence models obscure physical phenomena that are present, such as eddies and high-vorticity regions. In some cases, this deficiency may partially offset the inherent attractiveness of CFD noted earlier. 

In a vortex (rigid-body rotation), Ljungqvist has shown that the mean value of the concentration over the entire region inside the streamline where the point of emission is situated is considerably higher than that of the outside. This allows us to use the concept of contamination accumulation in the context of vortices. 

It has also been shown, using visual illustrative methods, that accumulation can occur in the wake of people or objects, provided that the contaminants are emitted in the vortex region. Special consideration must be taken with instabilities and vortices generated by the working person. Vortices can also occur in empty open unidirectional airflow benches. 

The flow pattern in Fig. 10.55 has a violent turbulent region, characterized by a vortex street and two free vortices rotating in opposite directions... 

A little bit of physical intuition as to how the vortices form in the first place may help in explaining the behavior as TZ is increased still further. We know that u = 0 at the cylinder s surface. We also know that the velocity increases rapidly as we get further from that surface. Therefore vortices are due to this rapid local velocity variation. If the variation is small enough, there is enough time for the vorticity to diffuse out of the region just outside the cylinder s surface and create a large von Karman vortex street of vorticity down stream [feyn64]. 

The region of stable trailing vortices was sustained to Reynolds numbers up to 5000 ( ). Other flow regimes were observed at higher Reynolds numbers but are probably not achieved in polystyrene reactors. 

In a stirred tank reactor, these low-pressure regions are behind the impeller blades, in the trailing vortices leaving the impeller blades, behind the baffles, and at the center of the large turbulent eddies. 

Fluid particles that are heavier than the continuous phase tend to move away from the low-pressure regions. They are thrown out of the turbulent eddies and the trailing vortices, and will thus collide more randomly. 

The low density of gases makes it more difficult to keep the bubbles dispersed. The bubbles will move to the low-pressure areas, that is, behind the impellers, in the trailing vortices close to the impeller, behind the baffles, and at the inner side after a bend. The bubbles will coalesce in these areas with high gas holdup. It is very difficult to design reactors without low-pressure regions where the low-density fluid will accumulate. One such reactor is the monolith reactor for multiphase flow [32, 33]. 

The (isotropic) eddy viscosity concept and the use of a k i model are known to be inappropriate in rotating and/or strongly 3-D flows (see, e.g., Wilcox, 1993). This issue will be addressed in more detail in Section IV. Some researchers prefer different models for the eddy viscosity, such as the k o> model (where o> denotes vorticity) that performs better in regions closer to walls. For this latter reason, the k-e model and the k-co model are often blended into the so-called Shear-Stress-Transport (SST) model (Menter, 1994) with the view of using these two models in those regions of the flow domain where they perform best. In spite of these objections, however, RANS simulations mostly exploit the eddy viscosity concept rather than the more delicate and time-consuming RSM turbulence model. They deliver simulation results of in many cases reasonable or sufficient accuracy in a cost-effective way. 

This formulation results very insightful according to Equation 8.30, particles move under the action of an effective force — We , i.e., the nonlocal action of the quantum potential here is seen as the effect of a (nonlocal) quantum force. From a computational viewpoint, these formulation results are very interesting in connection to quantum hydrodynamics [21,27]. Thus, Equations 8.27 can be reexpressed in terms of a continuity equation and a generalized Euler equation. As happens with classical fluids, here also two important concepts that come into play the quantum pressure and the quantum vortices [28], which occur at nodal regions where the velocity field is rotational. 

Eddies are turbulent instabilities within a flow region (Fig. 2). These vortices might already be present in a turbulent stream or can be generated downstream by an object presenting an obstacle to the flow. The latter turbulence is known as Karman vortex streets. Eddies can contribute a considerable increase of mass transfer in the dissolution process under turbulent conditions and may occur in the GI tract as a result of short bursts of intense propagated motor activity and flow gushes. ... 

Additionally, macroscopic flow structure of 3-D bubble columns were studied [10]. The results reported can be resumed as follows (a) In disperse regime, the bubbles rise linearly and the liquid flow falls downward between the bubble stream, (b) If gas velocity increases, the gas-liquid flow presents a vortical-spiral flow regime. Then, cluster of bubbles (coalesced bubbles) forms the central bubble stream moving in a spiral manner and 4-flow region can be identified (descending, vortical-spiral, fast bubble and central flow region). Figure 10 shows an illustrative schemes of the results found in [10]. 

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