Cyclones vortex radius

Flow Pattern In a cyclone the gas path involves a double vortex with the gas spiraling downward at the outside and upward at the inside. When the gas enters the cyclone, its velocity undergoes a redistribution so that me tangential component of velocity increases with decreasing radius as expressed by The spiral velocity in a... 

The inner vortex (often called the core of the vortex) rotates at a much higher velocity than the outer vortex. In the absence of solids, the radius of this inner vortex has been measured to be 0.4 to 0.8 r. With axial inlet cyclones, the inner core vortex is aligned with the axis of the gas outlet tube. With tangential or volute cyclone inlets, however, the vortex is not exactly aligned with the axis. The non-symmetric entry of the tangential or volute inlet causes the axis of the vortex to be slightly eccentric from the axis of the cyclone. This means that the bottom of the vortex is displaced some distance from the axis and can "pluck off and reentrain dust from the solids... 

Because the rotating motion of the gas in the cyclone separator arises from its tangential entry and no additional energy is imparted within the separator body, a free vortex is established. The energy per unit mass of gas is then independent of its radius of rotation and the velocity distribution in the gas may be calculated approximately by methods discussed in Volume 1, Chapter 2. 

For a free vortex, it is shown in Volume 1, Chapter 2, that the product of the tangential velocity and the radius of rotation is a constant. Because of fluid friction effects, this relation does not hold exactly in a cyclone separator where it is found experimentally that the tangential velocity is more nearly inversely proportional to the square root of radius,... 

Flow Pattern In a cyclone the gas path involves a double vortex with the gas spiraling downward at the outside and upward at the inside. When the gas enters the cyclone, its velocity undergoes a redistribution so that the tangential component of velocity increases with decreasing radius as expressed by V - rt". The spiral velocity in a cyclone may reach a value several times the average inlet-gas velocity. Theoretical considerations indicate that n should be equal to 1.0 in the absence of wall friction. Actual measurements [Shepherd and Lmple, Ind. Eng. Chem., 31, 972 (1939) 32, 1246 (1940)], however, indicate that n may range from 0.5 to 0.7 over a large portion of the cyclone... 

To go any further we need a relationship between U and the radius r for the vortex in a cyclone. Now for a rotating solid body, Ue = rco, where m is the angular velocity and for a free vortex Uer = constant. For the confined vortex inside the cyclone body it is has been found experimentally that the following holds approximately ... 

The rotating vortex in the main body of the cyclone below the gas outlet tube sets up a tangential velocity that varies with the radius of the cyclone. As the radius, r , decreases from the wall toward the center of the cyclone, the tangential velocity increases to a maximum that occurs at a radius slightly less than the outer radius of the gas outlet tube, r, as shown in Fig. 4. At radii much smaller than that of the gas outlet tube, the tangential gas velocity decreases to a much lower value at the center. 

Equipping a cyclone with an inlet scroll, as depicted in Fig. 15.1.4, produces an effect upon cyclone performance that is similar to that produced by increasing the body diameter, while keeping the vortex finder diameter constant. This is so because the scroll increases the inlet radius relative to a... 

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