Cluster velocity

Figure 25. Sample data on cluster velocities and length. (From Soong, Tuzla and Chen, 1995.)...

As noted, a high degree of voidage fluctuation is associated with the bursting of wavy solids layer into clusters. The intermittency of the bursting and the cluster velocity are elaborated in the following. 

We begin with an introduction to a simple model first proposed by Cavaliere and Fusco-Femiano (1976). This model assumes that the gas and galaxies are in equilibrium within the same gravitational potential. Through a measure of the X-ray surface brightness, the model relates the gas temperature to the cluster velocity dispersion, measured from the galaxies. 

The M/L ratio also puts in evidence unexpected trends. For example, using ENACS data (Adami et al. 1998b) we can show a clear dependence of M/L regarding cluster velocity dispersion (Fig. 8). It means basically that the most massive the cluster, the higher the M/L, or in other words, the most massive the cluster, the higher the value of ilm. 

Free jet expansion from the capillary produces a molecular beam in which the clusters are all traveling approximately at the sonic velocity of the gas in the capillary. Thus, cluster velocity ranges from 3 x 10 cm/s if Ar is used in the MECS to 1 X 1Q5 cm/s if He is used. 

Forty years later, measurements of masses of galaxies from rotation curves, binary pairs, cluster velocity dispersions, and other indicators had accumulated to the point where two brief 1974 reviews by an Estonian trio (3) and an American trio (4) tipped the consensus of the community in favor of... 

Figure 21.2. Schematic outline of the apparatus used for the measurement of cluster velocities (a) and typical cluster intensity profiles for different nozzle tube temperatures (b). The broken lines indicate the shift of the maxima of the intensity profiles with increasing nozzle tube temperature for the two different cluster isomers.

Griffith AF, Louge, MY. The scaling of cluster velocity at the wall of circulating fluidized bed risers. Chemical Engineering Science 1998 53 2475-2477. 

Horio et al. (1989) experimentally verified their proposed circulating fluidized bed scaling laws. The solid-to-gas density ratio was not varied in the tests thus they effectively verified the simplified set of scaling laws. Two cold scaled CFBs, fluidized using ambient air, were used in the verification. Good agreement in the axial solid fraction profiles was obtained for most of the conditions tested. An optical probe was used to verify similarity in the annular flow structures and the cluster velocities. 

A number of researchers have measured descending cluster velocities in the wall layer for a variety of flow conditions and different wall geometries, with most data between 0.5 and 2.0 m/s. The data have been well summarized by Griflith and Louge (1998) and are correlated by equation (22). 

A similar algorithm has been used to sample the equilibrium distribution [p,(r )] in the conformational optimization of a tetrapeptide[5] and atomic clusters at low temperature.[6] It was found that when g > 1 the search of conformational space was greatly enhanced over standard Metropolis Monte Carlo methods. In this form, the velocity distribution can be thought to be Maxwellian. 

Circulating fluidized beds (CFBs) are high velocity fluidized beds operating well above the terminal velocity of all the particles or clusters of particles. A very large cyclone and seal leg return system are needed to recycle sohds in order to maintain a bed inventory. There is a gradual transition from turbulent fluidization to a truly circulating, or fast-fluidized bed, as the gas velocity is increased (Fig. 6), and the exact transition point is rather arbitrary. The sohds are returned to the bed through a conduit called a standpipe. The return of the sohds can be controUed by either a mechanical or a nonmechanical valve. 

When using the clustered layout of multiple mixers, a mixer spacing of 22.5° is commonly used. It is important to position the clustered mixers opposite the cmde oudet in order to benefit from Hquid velocities during pump out. 

Radial density gradients in FCC and other large-diameter pneumatic transfer risers reflect gas—soHd maldistributions and reduce product yields. Cold-flow units are used to measure the transverse catalyst profiles as functions of gas velocity, catalyst flux, and inlet design. Impacts of measured flow distributions have been evaluated using a simple four lump kinetic model and assuming dispersed catalyst clusters where all the reactions are assumed to occur coupled with a continuous gas phase. A 3 wt % conversion advantage is determined for injection feed around the riser circumference as compared with an axial injection design (28). 

Credit for additional height of the flame center for multiple valve installations may be taken by clustering the safety valve discharge pipes to the atmosphere. The following procedure should be used for determining equivalent diameter and exit velocity to be used in the flame center calculation. Diameter and velocity are based on the total acmal area of the clustered vents. 

In this scheme, digital particles are still wandering localized clusters of informa-tionl but (conventional) variables such as space, time, velocity and so on become statistical quantities. Given that no experimental measurement to date has yet detected any statistical dispersion in the velocity of light, the sites of a hypothetical discrete underlying lattice can be no further apart than about 10 cm. 

The carbohydrate has sites for ionic interaction (clusters of sialic acid or sulphate residues) and also hydrophobic interaction (clusters of hydrophobic methyl groups offered by fucose residues). Sedimentation velocity has been a valuable tool in the selection of appropriate mucoadhesives and in the characterisation of the complexes [ 138-143]. 

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