Relative eddy motion

The seeond Helmholtz law states that the vortieity of a frietionless fluid does not ehange with time. Henee, if the flow at the inlet to an impeller is irrotational, the absolute flow must remain irrotational throughout the impeller. As the impeller has an angular veloeity lu, the fluid must have an angular veloeity—lu relative to the impeller. This fluid motion is ealled the relative eddy. If there were no flow through the impeller, the fluid in the... 

Though the sizes of particles which will be retained or lost by the separator can be calculated, it is found in practice that some smaller particles are retained and some larger particles are lost. The small particles which are retained have in most cases collided with other particles and adhered to form agglomerates which behave as large particles. Relatively large particles are lost because of eddy motion within the cyclone separator, and because they tend to bounce off the walls of the cylinder back into the central core... 

When the two liquid phases are in relative motion, the mass transfer coefficients in eidrer phase must be related to die dynamical properties of the liquids. The boundary layer thicknesses are related to the Reynolds number, and the diffusive Uansfer to the Schmidt number. Another complication is that such a boundaty cannot in many circumstances be regarded as a simple planar interface, but eddies of material are U ansported to the interface from the bulk of each liquid which change the concenuation profile normal to the interface. In the simple isothermal model there is no need to take account of this fact, but in most indusuial chcumstances the two liquids are not in an isothermal system, but in one in which there is a temperature gradient. The simple stationary mass U ansfer model must therefore be replaced by an eddy mass U ansfer which takes account of this surface replenishment. 

Flow in empty tubes has a relatively narrow band of velocities—or Reynolds numbers from 2000 to 10000—wherein the character changes from laminar to turbulent. In packed beds, even the laminar flow does not mean that motion is linear or parallel to the surface. Due to the many turns between particles, stable eddies develop and therefore the difference between laminar and turbulent flow is not as pronounced as in empty tubes. 

Eddy-current proximity probes are primarily used as displacement transducers. Eddy probes generate an eddy-current field, which is absorbed by a conducting material at a rate proportional to the distance between the probe and the surface. They are often used to sense shaft motion relative to a bearing (by mounting them within the bearing itself) or to measure thrust... 

The motion of particle and fluid are considered relative, and the handling of the relations are affected only by-conditions of turbulence, eddy currents, etc. 

In seawater, physical processes that transport water can also cause mass fluxes and, hence, are another means by which the salinity of seawater can be conservatively altered. The physical processes responsible for water movement within the ocean are turbulent mixing and water-mass advection. Turbulent mixing has been observed to follow Pick s first law and, hence, is also known as eddy diffusion. The rate at which solutes are transported by turbulent mixing and advection is usually much faster than that of molecular diffusion. Exceptions to this occur in locations where water motion is relatively slow, such as the pore waters of marine sediments. The effects of advection and turbulent mixing on the transport of chemicals are discussed further in Chapter 4. 

A schematic of an eddy-current damper is shown in Fig. 10.6. A copper block with resistivity p is under the influence of the magnetic field 6 of a permanent magnet. The relative motion of the magnet and the copper block in the X direction causes a force in the -x direction. By solving Maxwell s equation numerically, Nagaya (1984) calculated the force to be... 

In the zone of the MRC, the proportions of the contributions of the mean motion and of the synoptic and inertial variabilities to the total kinetic energy were 50 40 10, which is close to the estimates based on the data of moored buoy observations (see above). Thus, in the Black Sea, the relative contribution of the kinetic energy of synoptic fluctuations is sixfold lower than in the World Ocean. In the opinion of the authors of [25], this may be related to the small sizes of the sea and to the correspondingly high ratio R /L, where llL is the baroclinic Rossby radius and L is the half-width of the basin. In the Black Sea, R /L = 0.1, while in the World Ocean R /L = 0.01. At R /L > 1, no baroclinic mechanism for eddy formation cross section be implemented. 

Furthermore, the assumption is made that the motion of the centers of mass of daughter droplets to be formed (binary breakage) is similar to the relative motion of two lumps of fluid in a turbulent flow field as described by Batchelor (B6). Thus, for the inertial subrange eddies... 

Particle deposition from a moving fluid involves two aspects. First the individual particles have to be transported to the surface by one or a combination of mechanisms, including Brownian motion, turbulent diffusion, and by virtue of the momentum possessed by the particle, as it is carried in the fluid stream. It will be appreciated that the size of the particle will exert a great influence on the dominant mechanism. Larger particles would be expected to move toward a surface, as a result of the momentum they possess. Finer particles with relatively low momentum can only approach the surface across the boundary layers, by Brownian or eddy diffusion. Having reached the surface to form a part of the foulant layer, the particle has to stick , but it may be removed from the surface by the shear forces produced by the flowing fluid [see Eq. (1)]. 

---