Vortex field

High turbulence is required for efficient mixing this is created by the vortex field which forms behind the blades. For all the gas to flow through this region it must enter the vessel close to and preferably underneath the disk hence it is recommended that spargers should always be nearer, about a distance of DJ2 below the agitator, where D( is the impeller diameter. 

Motion in Rotational (Centrifugal or Vortex) Fields. In a centrifugal or vortex field, the radial motion of a particle at a distance R from the center of rotation is governed by... 

Then, in accord with eq. 1.188, the vortex field inside the solenoid (r < a) is ... 

Currently the widely used turbulence models are standard K-s model, RNG K-e model and the Reynolds stress model (RSM). Standard K-s model is based on isotropic turbulence model, its simulation result error of separator flow field is large (Shan Yongbo, 2005). RNG K-s model has improved with a standard K-s model, but there are still larger defects. To improve the cyclone vortex field strength prediction results a greater extent, algebraic stress turbulence model based... 

The set of four Maxwell equations may be interpreted as follows Eq. (2.94) is called Gauss law and identifies charges as the sources of the electric field. Similarly, Ampere s law represented by Eq. (2.95) states that both a current density and a time-varying electric field give rise to a magnetic vortex field. 

MIXING, DIFFUSION AND CHEMICAL REACTION OF LIQUIDS IN A VORTEX FIELD... 

Although the model, as well as the analytical techniques, were conceived particularly for the problem of the diffusion flame, it was clear that they would encompass both the case of slow chemistry in a vortex field and the diffusive mixing problem in general. The following work uses the vortex distortion model to study in detail the mixing of two liquids, their rapid chemical reaction and their slow chemical reaction, exhibiting those fluid mechanical features that characterize laminar mixing processes,... 

Because the primary interest here is to assess the augmentation of chemical reaction by the vortex field, we shall limit the discussion to a simple bimolecular reaction. 

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. 

Temporal sequence of OH-LIF measurements captures a localized extinction event in a turbulent nonpremixed CH4/H2/N2 jet flame (Re 20,000) as a vortex perturbs the reaction zone. The time between frames is 125 ps. The velocity field from PIV measurements is superimposed on the second frame and has the mean vertical velocity of 9m/s subtracted. (From Hult, J. et al.. Paper No. 26-2, in 10th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, 2000. With permission.)... 

Figure 2. Radial-axial velocity field and temperature contours for a rotating-disk reactor at an operating condition where a buoyancy-driven recirculation vortex has developed. The disk temperature is HOOK, the Reynolds number is 1000, Gr/Re / = 6.2, fo/f = 1.28, and L/f = 2.16. The disk radius is 4.9 cm, the spin rate is 495 rpm. The maximum axial velocity is 55.3 cm/sec. The gas is helium.

Figure 2.46 Section of a micro channel with electrodes embedded in the channel walls (left). When an electric field is applied along the channel, different flow patterns may be created depending on the potential of the individual electrodes. The right side shows the time evolution of an ensemble of tracer particles initially positioned in the center of the channel for a flow field alternating between the single- and the four-vortex pattern shown on the left [144].

Reactors which generate vortex flows (VFs) are common in both planktonic cellular and biofilm reactor applications due to the mixing provided by the VF. The generation of Taylor vortices in Couette cells has been studied by MRM to characterize the dynamics of hydrodynamic instabilities [56], The presence of the coherent flow structures renders the mass transfer coefficient approaches of limited utility, as in the biofilm capillary reactor, due to the inability to incorporate microscale details of the advection field into the mass transfer coefficient model. 

In the 1990s, Bakker and Van den Akker (1994, 1996)—see also R.A. Bakker s PhD thesis (1996)—continued this mechanistic modeling approach by attempting a completely deterministic description of the 3-D small-scale flow field in which the chemical reactions take place at the pace the various species meet. Starting point is a lamellar structure of layers intermittently containing the species involved in the reaction. These authors conceived such small-scale structures as Cylindrical Stretched Vortex (CSV) tubes being strained in the direction of their axis and—as a result—shrinking in size in a plane normal to... 

Consequently, Bakker (1996) described the concentration evolution of a single layer subjected to the vorticity field of a single CSV by means of a onedimensional differential equation where both the nondimensional time and the nondimensional spatial coordinate contain the exponential shrinking rate. In this respect, the CSV approach differs from the various Bourne models in which the successive generation of several multiple-layer stacks is required and vortex age is a crucial element. 

Kleinert H.. Gauge Fields in Condensed Matter, Vol. 1 Superflow and Vortex Lines, World Scientific, Singapore,1989. 

For scalar eddies smaller than the Kolmogorov scale, the physics of scalar mixing changes. As illustrated in Fig. 3.6, vortex stretching causes the scalar field to become one-dimensional at a constant rate (Batchelor 1959). Thus, for 1 < rj, the mixing rate can be approximated by /e i/2... 

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