Vortex toroidal

Vortex formation on aerofoil 664,665 Vortex formation, toroidal type 297... 

Under low-frequency excitation, the flame front is wrinkled by velocity modulations (Fig. 5.2.5). The number of undulations is directly linked to frequency. This is true as far as the frequency remains low (in this experiment, between 30 and 400 Hz). The flame deformation is created by hydrodynamic perturbations initiated at the base of the flame and convected along the front. When the velocity modulation amplitude is low, the undulations are sinusoidal and weakly damped as they proceed to the top of the flame. When the modulation amplitude is augmented, a toroidal vortex is generated at the burner outlet and the flame front rolls over the vortex near the burner base. Consumption is fast enough to suppress further winding by the structure as it is convected away from the outlet. This yields a cusp formed toward burnt gases. This process requires some duration and it is obtained when the flame extends over a sufficient axial distance. If the acoustic modulation level remain low (typically v /v < 20%),... 

The study of laminar vortical structures has been well documented in the Taylor-Couette (TC) flow for an extensive range of gap sizes [33]. Of particular interest are the experimentally determined boundaries in the map of flow regimes [34], and specifically the flow regime where the propagating helical vortex and stationary toroidal vortex modes become stable simultaneously and interact in the axisym-... 

Fig. 7.11 Wake configurations for drops in water (highly purified systems), reproduced from Winnikow and Chao (W8) with permission, (a) nonoscillating nitrobenzene drop = 0.280 cm, Re = 515 steady thread-like laminar wake (b) nonoscillating m-nitrotoluene drop 4 = 0.380 cm. Re = 688 steady thread accompanied by attached toroidal vortex wake (c) oscillating nitrobenzene drop 4 = 0.380 cm. Re = 686 central thread plus axisymmetric outer vortex sheet rolled inward to give inverted bottle shape of wake (d) oscillating nitrobenzene drop = 0.454 cm. Re = 775 vortex sheet in c has broken down to form vortex rings (e) oscillating nitrobenzene drop d = 0.490 cm. Re = 804 vortex rings in d now shed asymmetrically and the drop exhibits a rocking motion.

Bhaga (B3) determined the fluid motion in wakes using hydrogen bubble tracers. Closed wakes were shown to contain a toroidal vortex with its core in the horizontal plane where the wake has its widest cross section. The core diameter is about 70% of the maximum wake diameter, similar to a Hill s spherical vortex. When the base of the fluid particle is indented, the toroidal motion extends into the indentation. Liquid within the closed wake moves considerably more slowly relative to the drop or bubble than the terminal velocity Uj, If a skirt forms, the basic toroidal motion in the wake is still present (see Fig. 8.5), but the strength of the vortex is reduced. Momentum considerations require that there be a velocity defect behind closed wakes and this accounts for the tail observed by some workers (S5). Crabtree and Bridgwater (C8) and Bhaga (B3) measured the velocity decay and drift in the far wake region. 

NOTE Do not let a cyclonic vortex develop between the solvent and sample layers. This can cause an emulsion to form. A slight dent should be visible in the surface of the solvent layer as the stirring bar sets up a toroidal current in the sample layer and this is transferred to the solvent layer. 

Figure 5. The double-spiral longitudinal vortex. A longitudinal vortex showing the development of toroidal countervortices. These occur on interaction with the pipe walls and have an effect similar to ball bearings, enhancing the forward movement. Their interior rotation follows the direction of rotation and forward motion of the central vortex, whereas the direction of their exterior rotation and translatory motion are reversed. These toroidal vortices act to transfer oxygen, bacteria, and other impurities to the periphery of the pipe, where, because of the accumulation of excessive oxygen, the inferior, pathogenic bacteria are destroyed and the water rendered bacteria-free.

With this expression for B, we find that the field fines for the solution assume a key geometric relationship in addition to the previously considered axisymmetric helicoidal solutions exemplified in the vortex filaments of the plasma focus. Several researchers [43,44] have termed P the poloidal solution and T the toroidal solution. Accordingly, if the equation for B is expressed in terms of... 

The examples presented in this chapter [308 320] are illustrations of the concepts presented in the previous chapters. They correspond to recent numerical analysis of burners which are typical of most modern high-power combustion chambers, especially of gas turbines the flame is stabilized by strongly swirled flows, the Reynolds numbers are large, the flow field sensitivity to boundary conditions is high, intense acoustic/combustion coupling can lead to self-sustained oscillations. Flames are stabilized by swirl. Swirl also creates specific flow patterns (a Central Toroidal Recirculation Zone called CTRZ) and instabilities (the Precessing Vortex Core called PVC). 

Limitations on temperatures of solid materials often cause the methods of stabilization by solid elements, discussed so far, to be impractical. In most applications of stabilization by solid elements the flame is attached in the wake behind the element, so that the solid is not fully exposed to the flame temperature. Representative examples are bluff-body flame stabilizers, such as the stabilizing rods or plates placed normal to the flow in ramjets and afterburners, which were mentioned in Sections 5.1.1 and 10.3.5. A distinctive feature of bluff-body flame stabilization is the presence of a recirculation zone behind the body. Unlike the alternate vortices shed from bluff bodies in cold flow over the Reynolds-number range of practical interest, a well-defined vortex, steady in the mean, is observed to exist just downstream from the stabilizer when combustion occurs. This is a toroidal vortex for an axisymmetric stabilizer or a pair of identical counterrotating line vortices for rodlike stabilizers. The reason for the drastic change in the... 

The study of the internal flow shows that the toroidal vortex deforms as Rei increases and separates from the boundary near the rear point at Rei = 150 (for 9S = 30°). In this case, the second vortex is formed near the internal separation point, and the velocity in the region of the second vortex is much less (approximately, 30 times) than the maximum velocity in the region of the first vortex. 

Benjamin and Ellis predicted that a ring vortex would emerge from the jet flow (a phenomenon observed by Lauterborn), which leads to the formation of a bubble ring from the toroidally deformed bubble. ... 

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