Columns radial distribution

Figure 11.4 Radial distributions of the RMS of the fluctuating vorticity components at different times for the unheated (left column) and heated (right column) jet. The times are t = 25 (dotted curve), f = 30 (dashed curve), and f = 35 (solid curve)... 

Figure 2 Left column- NO Absorption (upper panel) and emission (lower panel) spectra at near critical conditions and room temperature for a density of 5.7 at/nm3. Right column NO-Ar radial distribution functions g(r) for the NO ground (upper panel) and excited (lower panel) states for the same state points...

As noted above, small bubbles, a uniform gas holdup radial distribution and an appropriate liquid circulating velocity can intensify mass transfer between the gas phase and the continuous phase and improve the production efficiency in EL-ALRs. In order to reduce the bubble size and obtain a more uniform radial distribution of the local gas holdup and the liquid and bubble rise velocities, and regulate the liquid circulating velocity appropriately as well, in this work, a novel internal is used and mounted in the riser column to improve hydrodynamics and mass transfer. The hydrodynamic behavior and mass transfer characteristics of an EL-ALR with the new designed internal are investigated. 

Gas absorption is a function of the gas and liquid mass transfer coefficients, the interfacial area, and the enhancement due to chemical reaction. The gas-liquid interfacial area is related to the Sauter mean bubble diameter and the gas holdup fraction. The gas holdup fraction has been reported to vary with radial position (7-11) for column internal diameters up to 0.6 m. Koide et al" Tl2), however, found that the radial distribution of gas holdup was nearly constant for a column diameter of 5.5 m. Axial distribution of average gas holdup has been reported by Ueyama et al. (10). The average gas holdup... 

Radial distributions of bubble diameters in a bubble column have been reported for column diameters up to 5.5 m (12). In all cases, the bubble size increased from the wall to the center of the column. The axial distribution of bubble diameters in bubble columns has only been reported by a few investigators ( 7, 10). Rigby et al. (7) observed that the average bubble length increased with axial position, whereas Ueyama et al. (10) did not observe a significant change in bubble diameter with axial position. 

Radial distributions of gas-phase characteristics were measured from the wall to the center of the column in 1/4-inch increments. For gas-liquid flows, steady-state operation was achieved in 10 minutes, whereas for gas-liquid-solid flows, measurements were not performed until one hour after flow conditions were established. At the end of each run, average gas holdup was measured by quick closure of the feed stream valve. The sampling rate for the conductivity probes was 0.5 millisecond per point, and the total sample time for each local measurement was 60 seconds. These sampling conditions are comparable to those of another investigator of gas-phase characteristics in bubble columns (11). 

The conductivity probe technique has been applied successfully to gas-phase measurements in a slurry bubble column. The presence of solids does not appreciably change the gas-phase characteristics for a volume fraction of solids less than 5 percent. The radial distribution functions of gas holdup and interfacial area increase significantly from the wall to the center of the column. The average Sauter mean bubble diameter is greater than the Sauter mean bubble diameter measured near the wall. 

Boundaries in fast fluidization refer mainly to the column wall as well as the inlet and outlet. Effect of the wall on pressure drop due to friction between the fluidized solids and the wall surface is minimal (Li et al, 1978), although it is the very cause of radial distribution of parameters. The configuration of the inlet and the outlet often strongly affect gas-solids flow, especially with regard to axial voidage profile. 

More detailed results take into account a wall effect to explain why elution profiles are skewed, even for nonretained solutes in modern columns. Detailed experimental results were recently presented by Farkas and Guiochon [6] on the radial distribution of flow velocity using local multichannel detection devices. On average, the flow velocity is very homogeneous in the center of the column, but, inevitably, it becomes lower near the walls. Similarly, the peak shape from a local microdetector situated near the wall is... 

Because of the cylindrical symmetry of the total electric field in the column plasma, in two-term approximation the expansion of the velocity distribution can be represented by the expression f U,v/v,r) = 2n) mg/2f [fQ(U,r)+f U,r)v /v+f.(U,r)v,/v]. This expansion includes, in addition to the isotropic distribution fo(U, r), a radial component fr(U, r) and an axial component f (U,r) of the vectorial anisotropic part of the velocity distribution. In particular, this radial distribution component allows the particle and energy current density of the electrons in the radial direction to be described and thus reveals significant aspects of the electron confinement by the radial... 

Then, following the instructions in Exercise 1.3, generate the radial distribution functions for the lithium 1 s and 2s orbitals in columns G and H. 

For each of the radial mesh points in column A calculate the Slater function equivalent of the radial distribution function in the cells of column D, with, for example,... 

At the same time, it is important to ensure that some liquid gets to the wall (220, 349). One rule of thumb (318a) recommends maintaining a set of radially distributed pour points within one packing diameter of the wall. One experience has been reported (220) where the presence of a 3-in-wide orifice pan distributor support ring in a 4-ft column caused a m or drop in column efficiency because the area under the support ring was unirrigated. 

The bar above the symbols in Equations 6.14-6.17 denotes average values. These average concentrations and the concentration in the liquid phase, C , are a function of the time t and the axial column coordinate, x. The overall balance (Equation 6.17) has to be distinguished from the balance that takes into account radial distributions within the particles ... 

Farkas, T. Guiochon, G. Contribution of the radial distribution of the flow velocity to band broadening in HPLC columns. Anal. Chem. 1997,69,4592. 

For bubble columns with height/diameter > 5, a simple open pipe at the bottom of the column is often adequate. For height/diameter < 5, a ring or finger-style perforated pipe sparger is desirable to obtain uniform radial distribution of the gas and to prevent excessive channeling of the gas up the center of the vessel. For heat transfer in bubble agitated columns, see Hart (1976) and Tamari and Nishikawa (1976). 

Abstract In this chapter, the two CMT models, i.e., c — Eci model and Reynolds mass flux model (in standard, hybrid, and algebraic forms) are used for simulating the chemical absorption of CO2 in packed column by using MEA, AMP, and NaOH separately and their simulated results are closely checked with the experimental data. It is noted that the radial distribution of Di is similar to a, but quite different from fit. It means that the conventional assumption on the analogy between the momentum transfer and the mass transfer in turbulent fluids is unjustifled, and thus, the use of CMT method for simulation is necessary. In the analysis of the simulation results, some transport phenomena are interpreted in terms of the co-action or counteraction of the turbulent mass flux diffusion. 

The radial distributions of Dt, oCf, and Vt at different height of the column are displayed in Figs. 5.19, 5.20, 5.21, and 5.22. These figures show the non-uniform distribution of dififusivity and the similarity between the shape of Dt and a,. The dissimilarity of v, with Dt and oq is seen obviously, which indicates once again the Schmidt number and Prandtl number are not a constant throughout the column. 

Fig. 5.20 Radial distribution of Dt at different column height for T12 (x is measured from column top) (Reprinted from Ref [9], Copyright 2006, with permission from American Chemical Society)...

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