Vortex particle motion

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. 

Cyclone Separators Cyclone separators are described in Chapter 7. Typically used to remove particulate from a gas stream, the gas enters tangentially at the top of a cylinder and is forced downward into a spiral motion. The particles exit the bottom while the gas turns upward into the vortex and leaves through the top of the unit. Pressure drops through cyclones are usually from 13 to 17 mm water gauge. Although seldom adequate by themselves, cyclone separators are often an effective first step in pollution control. 

The rotational operation of a CFB leads to a vortex motion in the freeboard which tends to inhibit particle loss by elutriation. Because of the relatively compact nature of the CFB and the operating flexibility provided by the rotational motion, the CFB has been proposed for a variety of applications including coal combustion, flue gas desulfurization, gas combustion, coal liquefaction and food drying. 

Surface-active contaminants play an important role in damping out internal circulation in deformed bubbles and drops, as in spherical fluid particles (see Chapters 3 and 5). No systematic visualization of internal motion in ellipsoidal bubbles and drops has been reported. However, there are indications that deformations tend to decrease internal circulation velocities significantly (MI2), while shape oscillations tend to disrupt the internal circulation pattern of droplets and promote rapid mixing (R3). No secondary vortex of opposite sense to the prime internal vortex has been observed, even when the external boundary layer was found to separate (Sll). 

Internal circulation measurements are very difficult to obtain for gas bubbles (D8). Some results have been obtained for large liquid skirted drops using tracer particles (W2), and provide a qualitative picture of the internal motion as shown in Fig. 8.5. It is not clear whether there is a reverse vortex motion in the interior of a large fluid particle (as indicated by the dotted lines). Such a secondary vortex would appear to be necessary to satisfy velocity and stress continuity, but experimental evidence is inconclusive. 

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. 

In a refined form of the theory [37] the same quantity features as the well known quantum potential. The notion of a particle emerges in this theory in the form of a highly localized inhomogeneity that moves with the local fluid velocity, v(x, t), thus as a stable dynamic structure that exists in the fluid, for example, as a small stable vortex or a pulse-like distortion. To explain why the causal theory needs probability densities it is argued [37] that the Madelung fluid must experience more or less random fluctuations in its motion to account for irregular turbulence. The turbulence necessitates a wave theory to describe the motion of vortices embedded in the fluid. The particle velocity is therefore not exactly VS/m, nor is the density exactly... 

---