Rotational or vortex motion in a fluid

Rotational or vortex motion in a fluid 50 Rough pipes 67, 707... 

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. 

Clearly, the helicity has a value of zero in 2D simulations. In 3D simulations, it gives an indication of how well the local rotation of a fluid element is aligned with the velocity of the element. It is useful for illustrating longitudinal vortices, or spiral motion, as is often found in vortex cores. In Figure 5-21, isosurfaces of helicity are used to depict the longitudinal vortices generated in the Kenics static mixer described in Section 5-7.10. 

Now imagine first that the swirling fluid has an infinite viscosity (behaves like a solid body). Hence, no shearing motion exists between fluid layers at different radii. In this case fluid elements at all radial positions are forced to have the same angular velocity. The angular velocity, f2, is measured in radians per unit of time, usually seconds, and therefore has units s . It equals ve/r, with v the tangential velocity, measured in m/s. Swirl with constant O is called forced vortex flow or solid-body rotation ... 

Although the vortex may attach to, and process around, the lower walls of the cyclone as in Fig. 9.2.1, vortex motion does not completely cease in the axial direction at this point or, more correctly, plane of attachment. This primary vortex induces a secondary vortex just downstream of it. This is a type of fluid coupling . The induction of the secondary vortex is probably related to the precession of the primary vortex. This precession is always in the same rotational sense as the swirl in the bulk of the vortex, as sketched in Fig. 9.2.1. 

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