Vortex dynamics

Grier, D.G. 2003. Fluid dynamics Vortex rings in a constant electric field. Nature 424 267—268. 

FIG. 6-56 Computational fluid dynamic simulation of flow over a square cylinder, showing one vortex shedding period. (From Choudliuty, et al., Trans. ASME Fluids Div, TN-076[1994].)... 

Cyclone Separators Finer feed sohds, from 0.04 to 0.0005 m (1.5 in to 28 mesh), may be treated in dynamic separators of the Dutch State Mines cyclone type (Fig. 19-36). In cyclone separators, the medium and the feed enter the separator together tangentially at the feed inlet (1) the short cyhndiical section (2) carries the central vortex finder (3), which prevents short circuiting within the cyclone. Separation is made in the cone-shaped part of the cyclone (4) by the action of centrifugal and centripetal forces. The heavier portion of the feed leaves the cyclone at the apex opening (5), and the hghter portion leaves at the overflow top orifice (6). 

Computational accuracy can be dramatically improved by dynamically adding elements where they minimize the error. For example, more elements ean be added in the neighborhood of a strong gradient in the velocity to help resolve shocks and vortex sheets. Elements may be removed from regions of smooth flow to minimize the computational cost without degrading the overall accuracy. The concept is shown in Fig. 9.6 where a finer mesh overlays the original mesh. This mesh refinement can be carried out to as many levels as necessary [15], [16], [17]. 

A much more pronounced vortex formation in expanding combustion products was found by Rosenblatt and Hassig (1986), who employed the DICE code to simulate deflagrative combustion of a large, cylindrical, natural gas-air cloud. DICE is a Eulerian code which solves the dynamic equations of motion using an implicit difference scheme. Its principles are analogous to the ICE code described by Harlow and Amsden (1971). 

In fluid dynamics the behavior in this system is described by the full set of hydrodynamic equations. This behavior can be characterized by the Reynolds number. Re, which is the ratio of characteristic flow scales to viscosity scales. We recall that the Reynolds number is a measure of the dominating terms in the Navier-Stokes equation and, if the Reynolds number is small, linear terms will dominate if it is large, nonlinear terms will dominate. In this system, the nonlinear term, (u V)u, serves to convert linear momentum into angular momentum. This phenomena is evidenced by the appearance of two counter-rotating vortices or eddies immediately behind the obstacle. Experiments and numerical integration of the Navier-Stokes equations predict the formation of these vortices at the length scale of the obstacle. Further, they predict that the distance between the vortex center and the obstacle is proportional to the Reynolds number. All these have been observed in our 2-dimensional flow system obstructed by a thermal plate at microscopic scales. ... 

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. 

M.R. Jumaev Evolution of random pulses at nonlinear systems with fluctuating parameters -Dissertation for Doctor in Science in Theoretical Physics (2002) M.R. Jumaev NATO Advanced Research Workshop, Vortex dynamics and high temperature superconductors , Tashkent, Uzbekistan, 16-23 May 2002 (2002). M.R. Jumaev Evolution of random and regular pulses at nonlinear systems with constant and fluctuating parameters , Bukhara, Universitet (2004). 

Karl Fischer titrators, 23 477 Karmen-vortex street, 11 668 Karr RPC plate, 10 779-780 Karstedt s catalyst, in silicone network preparation, 22 563 Karstenite, 5 785t Karyoplasts, 12 451, 458 Kashin-Beck disease, selenium and, 22 101 Kaspar s dynamic filter, 11 384 Katapinands, 24 44 Kauri-butanol value, 23 89 Kazakhstan... 

J. J. Thomson, The Electron in Chemistry (London Chapham and Hall, 1923) preface. His earliest applications of physics to chemistry included Treatise on the Motion of Vortex Rings (1883) and Applications of Dynamics to Physics and Chemistry (1888). 

As discussed earlier, the particle/droplet dynamics can be significantly modified by timing the fuel injection to be in- or out-of-phase with the large-scale vortex structures. To explore if timed fuel injection could alter the stability characteristics, the flow was forced at the quarter-wave mode of the inlet and droplet injection was timed to be in- or out-of-phase with the forcing. Results from these simulations show that the pressure fluctuations at the quarter-wave mode of the inlet can indeed be amplified or attenuated depending on the phasing of the droplet injection. 

VORTEX DYNAMICS, ENTRAINMENT. AND NONPREMIXED COMBUSTION IN RECTANGULAR JETS... 

The time-dependent simulations of free jets discussed here focus on the vortex dynamics and transition to turbulence downstream of the jet exit. For the sake of computational efficiency, the author concentrates on the study of jet flow initialized with laminar conditions with a thin rectangular vortex sheet having slightly rounded-off corner regions and uniform initial momentum thickness [9]. Initial conditions for the simulated jets involve top>-hat initial velocity profiles... 

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