Vortex method

Givi, P. 1994. Spectral and random vortex methods in turbulent reacting flows. In Turbulent reacting Bows. Eds. P. A. Libby and F.A. Wilhams. London, UK Academic Press. 475-572. 

L. Greengard and V. Rokhlin, The Rapid Evaluation of Potential Fields in Three Dimensions, in Vortex Methods, C. Andersson and C. Greengard, eds., vol. 1360 of Lect. Notes Math., Springer-Verlag, 1988, 121-141. 

Vibration-induced fluidizing is accompanied, as in the vortex method, by the separation of the powder material by particle size and mass. Therefore, application of inhibited layers of the coating can be regulated using only one fluidizing bath incorporating a pol3mier powder mixture with Cl. With this aim, vibrations of different frequencies are imposed in turn on the powder and article in a bath separated into sections by, e.g., baffles. 

The molecular dynamics, Monte Carlo methods, the Lagrangian probability density function (PDF) methods, and the Lattice Boltzmann (LBM) method are among these methods. Methods such as the smoothed particle hydrodynamics (SPH) and the vortex method initially developed as probabiUstic methods, but nowadays they are most frequently used as deterministic. 

As early as 1973 Chorin (1973, 1989, 1994) introduced the two-dimensional random vortex method, a particle method for the solution of the Navier-Stokes equations. These particles can be thought of as carriers of vorticity. Weak solutions to the conservation equations are obtained as superpositions of point vertices, the evolution of which is described by deterministic ODEs. A random walk technique is used to approximate diffusion, and vorticity creation at boundaries to represent the no-slip boundary condition. The extension to three dimensions followed in 1982 (Beale and Majda 1982). An important improvement in stability and smoothness was achieved by Anderson and Greengard (1985) by removing the singularities associated with point vertices. Anderson and Greengard (1988) and Marchioro and Pulvirenti (1984) have written comprehensive reviews of the method. 

Marchioro, C. Pulvirenti, M. Vortex Methods in T wo-Dimensional Fluid Mechanics, Springer Berlin, 1984. 

Vortex method A specified amount of solution in a beaker is stirred while a specified amount of superabsorbent polymer is added. The time for the liquid surface to become flat or for the stirrer chip to hide beneath the liquid is measured. 

However, when the rate of water absorption is very fast because of a certain type and particle size, such a measurement is very difficult. Therefore, the use of a method to determine the force to eliminate fluidity (gelation force) is regarded as a reasonable approach. Due to its ease of use, the vortex method (see Table 2) is selected. 

Remarks When the amount of absorption is low or the rate of absorption is small, it is difficult to measure using this vortex method. In this case, the amoimt of the sample can be... 

In the LES, the turbulent perturbations at the inlet are being generated by the vortex method [30, 53]. The vortex method is a time-dependent inlet condition creating coherent perturbations, which are added on a specified mean velocity profile via a fluctuating vorticity field. The gas velocity fluctuations at the inlet are crucial for the formation of the droplet cluster structures detected in the experiments. The advantage of the vortex method is that the fluctuatiOTis are coherent and, in contrast to random fluctuations, allow small fluctuatiOTis in the gas to grow with time and distance from the inlet. Thus, a delay of the cluster formation can be avoided. In this context, it is also important to choose a proper value for the fluctuation intensity scale. From 20 % fluctuation intensity scale to 40 % increases the segmentation of the dispersed phase into cluster. A value of 40 % has been found to match the cluster structures and the velocity profiles of the dispersed phase in the experiments best. 

Mathey, F., Cokjlat, D., Bertoglio, J. P., Sergent, E. (2003) Specification of LES inlet boundary condition using vortex method. Turbulence of Heat and Mass Transfer, 4i... 

The vortex method is often employed in research and technical laboratories to offer a quick assessment of SAP swelling rate. Water or saline solution (50.0 g) is poured in a lOOmL beaker and its temperature is adjusted at 30°C. It is stirred at 600rpm using a magnetic stirrer. The SAP sample (mesh 50-60, Wq=0.50-2.0g) is added and a stopwatch is started. The time elapsing from the addition of the SAP into the fluid to the disappearance of vortex (tvd, s) is measured. The swelling rate (SR, g/g.s)=(50/Wo)/tvd. 

The vortex method, one existing vacuum generation technique, allows mobile robots to maintain a solid grip by means of a constant airflow that creates a suction that in turn produces negative pressure in this closed area, resulting in the necessary force of attraction between the robots and the wall. 

Thermochemical Liquefaction. Most of the research done since 1970 on the direct thermochemical Hquefaction of biomass has been concentrated on the use of various pyrolytic techniques for the production of Hquid fuels and fuel components (96,112,125,166,167). Some of the techniques investigated are entrained-flow pyrolysis, vacuum pyrolysis, rapid and flash pyrolysis, ultrafast pyrolysis in vortex reactors, fluid-bed pyrolysis, low temperature pyrolysis at long reaction times, and updraft fixed-bed pyrolysis. Other research has been done to develop low cost, upgrading methods to convert the complex mixtures formed on pyrolysis of biomass to high quaHty transportation fuels, and to study Hquefaction at high pressures via solvolysis, steam—water treatment, catalytic hydrotreatment, and noncatalytic and catalytic treatment in aqueous systems. 

Vortex formation leads to a considerable drop in mixing efficiency and should be suppressed as much as possible in practical applications to increase the homogenizing effects of mixers. The preferable method of vortex suppression is to install vertical baffles at the walls of the mixing tank. These impede rotational flow without interfering with the radial or longitudinal flow. Figure 11 illustrates such a system. 

A large variety of methods can be used for zoning, such as inclined jets, horizontal cooled jets, vertical jets, floor jets, nozzle ducts, and vortex. Examples of different methods are illustrated in Fig. 8.13. 

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. 

Liquid vortexing in suction vessel, thus creating gas enU ainment into suction piping, figure 3-43 suggests a common method to eliminate suction vor-... 

Of much greater relevance in micro reactors are rectangular channels, which were the subject of a study by Cheng et al. [110], among others. They solved the Navier-Stokes equation for channel cross-sections with an aspect ratio between 0.5 and 5 and Dean numbers between 5 and 715 using a finite-difference method. The vortex patterns obtained as a result of their computations are depicted in Figure 2.20 for two different Dean numbers. 

If final sample solutions will be stored for several days, the derivatization of the HMS metabolite may reverse. If the derivatization has reversed, the HMS method recovery would be low and an additional broad peak (underivatized HMS) would be visible after the derivatized HMS peak. In this case, add 10 qL of fresh BSTFA to the final sample solution in the GC vial, vortex the sample for several seconds and re-inject the sample solution. 

---