Oscillating columns

To summarize the reactions discussed above with their models and oscillatory solutions Table IV is prepared. For each reaction (Column 1) the references of experimental motivation for studying oscillations (Column 2), and the references for mathematical models associated with each reaction (Column 3) are given. The oscillatory solutions are listed in Column 4. 

For sonic sieving, illustrated in Figure 37-32, p. 443, a flexible wall at the bottom of the column of stacked sieves is compressed providing a vertically oscillating column of air that first lifts the particles, upon release, then carries them back against mesh openings at 3600 pulses per minute. 

The Sonic Sifter has been designed to combine two motions to provide a precise particle separation. A vertical oscillating column of air and a repetitive mechanical pulse is used to move the material to be sifted through a single sieve or set of sieves. The name Sonic Sifter appears to come... 

The oscillating jet method is not suitable for the study of liquid-air interfaces whose ages are in the range of tenths of a second, and an alternative method is based on the dependence of the shape of a falling column of liquid on its surface tension. Since the hydrostatic head, and hence the linear velocity, increases with h, the distance away from the nozzle, the cross-sectional area of the column must correspondingly decrease as a material balance requirement. The effect of surface tension is to oppose this shrinkage in cross section. The method is discussed in Refs. 110 and 111. A related method makes use of a falling sheet of liquid [112]. 

Pneumatic systems use the wave motion to pressurize air in an oscillating water column (OWC). The pressurized air is then passed through an air turbine to generate electricity. In hydrauhc systems, wave motion is used to pressurize water or other fluids, which are subsequendy passed through a turbine or motor that drives a generator. Hydropower systems concentrate wave peaks and store the water dehvered in the waves in an elevated basin. The potential energy suppHed mns a low head hydro plant with seawater. 

Link-Suspended Basket Centrifuges In centrifuges with diameters larger than 762 mm (30 in), the basket, curb, curb cover, and drive form a rigid assembly flexibly suspended from three fixed posts (also known as a three-column centrifuge). The three suspension members may be either chain hnks or stiff rods in ball-and-socket joints and are spring-loaded. The suspended assembly has restrained freedom to oscillate to compensate for a normal out-of-balance condition. The drive is vertical with more efficient power transmission compared to the base-bearing type. 

Another center-fed design that nas only been usea on a preparative scale is the vertical spiral conveyor column reported by Schildknecht [Angew. Chem., 73, 612 (1961) . In this device, aversion of which is shown on Fig. 22-9, the dispersed-ciystal phase is formed in the freezing section and conveyed downward in a controlled manner by a rotating spiral with or without a vertical oscillation. 

Scale-up depends on the mechanical complexity of the crystal-transport system and techniques for removing heat. Vertical oscillating spiral columns are likely limited to about 0.2 m in diameter, whereas horizontal columns of several meters are possible. Scale-up is limited by design of melter and/or crystal-washing section. Vertical or horizontal columns of several meters in diameter are possible. 

Most of the analytical treatments of center-fed columns describe the purification mechanism in an adiabatic oscillating spiral column (Fig. 22-9). However, the analyses by Moyers (op. cit.) and Griffin (op. cit.) are for a nonadiabatic dense-bed column. Differential treatment of the horizontal-purifier (Fig. 22-8) performance has not been reported however, overall material and enthalpy balances have been described by Brodie (op. cit.) and apply equally well to other designs. 

A comparison of the axial-dispersion coefficients obtained in oscil-lating-spiral and dense-bed crystalhzers is given in Table 22-5. The dense-bed column approaches axial-dispersion coefficients similar to those of densely packed ice-washing cohimns. 

Curran R. Stewart, T. P. and Whittaker T. J. T. (1997). Design Synthesis of Oscillating Water Column Wave Energy Converters Performance Matching. Journal of Power and Energy 211 4S j-505. 

To determine the likely possibility of oscillations occurring in a new or an existing column, or even sections of a column, the original article is recommended. 

Oscillations occur because the liquid column requires more than the equilibrium quantity of air to produce the initial acceleration. It therefore becomes over-accelerated and excess of liquid enters the limb with the result that it is retarded and then subsequently has to be accelerated again. During the period of retardation some liquid may actually run backwards this can readily be prevented, however, by incorporating a non-return valve in the submergence limb. 

The symbols in the second column represent the electronic state in particular the first number is the total quantum number of the excited electron. We shall see later that in one case at least the symbol is probably incorrect. The third column gives the wave-number of the lowest oscillational-rotational level, the fourth the effective quantum number, the fifth and sixth the oscillational wave-number and the average intemuclear distance for the lowest oscillational-rotational level. The data for H2+ were obtained by extrapolation, except rQ, which is Burrau s theoretical value (Section Via). 

Each solvent passes from its reservoir directly to a pump and from the pump to a mixing manifold. After mixing, the solvents pass to the sample valve and column. The pumps control the actual program and are usually driven by stepping motors. The volume delivery of each solvent is controlled by the speed of the respective pump. In turn, the speed of each motor is precisely determined by the frequency of its power supply which can be either generated by external oscillators or, if the chromatograph is computer controlled, directly from the computer itself. 

Thus, the velocity oscillations, in the flow of an incompressible fluid, depend only on time, i.e., the liquid and vapor columns move in the capillary tube, on the whole, similar to a solid body. Bearing this in mind, we present the solution of Eq. (11.15) as follows ... 

Owing to the high computational load, it is tempting to assume rotational symmetry to reduce to 2D simulations. However, the symmetrical axis is a wall in the simulations that allows slip but no transport across it. The flow in bubble columns or bubbling fluidized beds is never steady, but instead oscillates everywhere, including across the center of the reactor. Consequently, a 2D rotational symmetry representation is never accurate for these reactors. A second problem with axis symmetry is that the bubbles formed in a bubbling fluidized bed are simulated as toroids and the mass balance for the bubble will be problematic when the bubble moves in a radial direction. It is also problematic to calculate the void fraction with these models. 

Helical strakes (strips) are fitted to the tops of tall smooth chimneys to change the pattern of vortex shedding and so prevent resonant oscillation. The same effect will be achieved on a tall column by distributing any attachments (ladders, pipes and platforms) around the column. 

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