Turbulent vortex flow

Figure 15 Photograph of flow pattern at different Reynolds number, (a) Taylor vortex flow (Re = 177), (b) wavy vortex flow (Re = 505), (c) weakly turbulent vortex flow (Re = 3027), and (d) turbulent vortex flow (Re = 8072) (Dutta and Ray, 2004).

Internal Flow. Depending on the atomizer type and operating conditions, the internal fluid flow can involve compHcated phenomena such as flow separation, boundary layer growth, cavitation, turbulence, vortex formation, and two-phase flow. The internal flow regime is often considered one of the most important stages of Hquid a tomiza tion because it determines the initial Hquid disturbances and conditions that affect the subsequent Hquid breakup and droplet dispersion. 

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. 

In their milestone work, Melander and Hussain found that the method of complex helical wave decomposition was instrumental in modeling both laminar as well as turbulent shear flows associated with coherent vortical structures, and revealed much new important data about this phenomenon than had ever been known before through standard statistical procedures. In particular, this approach plays a crucial role in the description of the resulting intermittent fine-scale structures that accompany the core vortex. Specifically, the large-scale coherent central structure is responsible for organizing nearby fine-scale turbulence into a family of highly polarized vortex threads spun azimuthally around the coherent structure. 

H. Aref. Integrable, chaotic and turbulent vortex motion in two-dimensional flows. Ann. Rev. Fluid Mech., 15 345-389, 1983. 

A second example can be generated when an intensive flow over a body produces closed field lines (called a vortex) at variable distances. This effect was observed by Strouhal (1850-1912) when some flow of air over wires produced a song. The Strouhal s singing wires give the measure of the frequency that characterizes the vortex flow. This type of flow has been used to produce the so-called grid turbulence, which has various applications in the forced cooling of electronic devices [6.29]. 

Even the turbulent vortex has finite dimensions, and it is dangerous to discount generally the possibility of diffusion effects on the basis that the reaction system has been designed to provide sufficient transport by turbulent flow. 

Whilst below the critical Reynolds number the fluid particles move along distinct stream lines and disturbances in the velocity rapidly disappear again, above this critical Reynolds number disturbances in the velocity are no longer dampened but intensified. This type of flow is called turbulent. The flow along distinct streamlines is known as laminar. Turbulent flow is always three-dimensional, unsteady and exhibits an irregular vortex pattern. The velocity at a fixed point fluctuates irregularly around a mean value. The momentary values of velocity, pressure, temperature and concentration are random quantities. 

Flow of fluid is laminar, with no vortex flow or turbulence. 

The flow is laminar there is no vortex flow or turbulence anywhere within the film. 

Saffman had interests in turbulence, viscous flows, vortex motion and water waves. He made valuable theoretical contributions to different areas of low-Reynolds-number hydrodynamics. These included the lifting force on a sphere in a shear flow at small but finite Reynolds numbers, the Brownian motion in thin liquid films, and particle motion in rapidly rotating flows. Saffinan s other contributions include dispersion in porous media, average velocity of sedimenting suspensions, and compressible low-Reynolds-number flows. 

It is practically important to consider the known criterion of large-scale turbulent vortex formation, when viscosity does not influence the mixing efficiency of the reaction mixture (automodel flow mode in relation to viscosity). The solution for achieving high turbulisation in a diffuser-confusor reactor, with local hydrodynamic resistances, is feeding the reaction mixture at lower linear flow rates enabling a substantial increase in the efficient application of tubular turbulent diffuser-confusor devices with lower reaction rate areas. 

Couette flow is a laminar circular flow occurring between a rotating (inner) cylinder and a static one, and the extension via increased speed of rotation to centrifugally-driven instabilities leads to laminar Taylor vortex flow, tending to turbulent flow as speed increases. Poiseuille flow is axial. 

Taylor vortices, amplitude modulated wavy Taylor vortex flow, and finally chaotic or turbulent flow. However, recent experimental v rk suggests that the transition process depends critically on both the annulus aspect ratio, r = 1/d, and the vortex cell axial lengtiVgap ratio, /A and that many different routes to turbulence are possible. 

At this end, to demonstrate superiority of our classical algorithms, we show some sample results of our most recent FDF simulation of the Sandia/Sydney swirl burner [35]. This configuration is selected as it is one of the most challenging turbulent flames for prediction. Figure 3 shows the contours of the azimuthal velocity field as predicted by our FDF. The simulated results agree with experimental data better than any other classical methods currently available [36]. But the computational time requirements are excessive. As another example. Fig. 4 shows the contour of filtered temperature field for the symbolic Taylor-Green vortex flow as obtained via FDF coupled with a discontinuous Galerkin flow solver [37]. Quantum computation may potentially provide a much more efficient means for such simulations. 

Fig. 4. The computation of the dimension of an attractor is illustrated using velocity data obtained fof a weakly turbulent flow in the Couette-Taylor system at R/R =16.0, where R is the Reynolds number for the onset of time-independent Taylor vortex flow. The different curves correspond to different embedding dimensions m. (a) The dependence of N(e), the average number of points within a ball of radius e, on e. (b) The slope of the curves shown in (a). Regions A,...

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