Forced vortex

Fluid Mechanics and Particle Inertia. Particles in a medium experience (1) drag, the resistive force exerted on a particle as it moves in a medium (2) inertial forces, due to the medium flow around the submerged particle or due to the particle path relative to the medium (3) centrifugal or vortex forces, due to the rotational motion of the medium (4) Coriolis forces, due to the linear and rotational motion of the medium (5) turbulent forces, due to the convective transport of the medium and (6) shear gradient, due to the relative movement of medium layers. 

The periodic shedding produces lateral forces of the same period on the cylinder. Should the cylinder be weakly supported and have a natural frequency close to the shedding frequency, it oscillates strongly in concert with the vortex street. Such behavior is responsible for the singing of power lines, the oscillation of tall smokestacks, and, most spectacularly, for the coUapse in 1940 of the newly built Tacoma Narrows suspension bridge, in Washington state, under the influence of a steady 65 km/h wind. 

For Reynolds numbers greater than 2000 baffles are commonly used with turbine impelTers and with on-centerhne axial-flow impellers. The flow patterns illustrated in Figs. 18-15 and 18-16 are quite different, but in both cases the use of Baffles results in a large top-to-bottom circulation without vortexing or severely unbalanced fluid forces on the impeller shaft. 

Vortex Depth In an unbaffled vessel with an impeller rotating in the center, centrifugal force acting on the fluid raises the fluid level at the wall and lowers the level at the shaft. The depth and shape of such a vortex (Rieger, Ditl, and Novak, Chem. Eng. ScL, 34, 397 (1978)] depend on impeller and vessel dimensions as well as rotational speed. 

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). 

Forced-vortex prewhirl. This type is shown as Vg lr = constant. This prewhirl distribution is also shown in Figure 6-14. Vg is at a maximum at the inducer inlet shroud radius, contributing to a decrease in the inlet relative Mach number. 

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. 

For Nr, > 1000, the properly baffled tank is turbulent throughout. Nq and P, are independent of Nr,. If the tank is not baffled, a forced vortex dominates the flow in the vessel. 

Figure 2.9. Forces acting on element of fluid in a vortex...

In a forced vortex the angular velocity of the liquid is maintained constant by mechanical means, such as by an agitator rotating in the liquid or by rotation in the basket of a centrifuge. 

Thus, the energy per unit mass increases with radius r and is independent of depth In the absence of an agitator or mechanical means of rotation energy transfer will take place to equalise j/ between all elements of fluid. Thus the forced vortex tends to decay into a free vortex (where energy per unit mass is independent of radius). 

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