Axial distributions

Todreas, N. E., and W. M. Rohsenow, 1966, The Effect of Axial Distribution on Critical Heat Flux in Annular Two Phase Flow, Proc. Third Int. Heat Transfer Conf, vol. 3, pp. 78-85, AlChE, New York. (5)... 

FIGURE 8.22 Axial distributions of relative soot yield x maximum, centerline, and soot temperatures for ethene at flow rates around soot point in coaxial diffusion flames. Row rates (ml/s) O 3.4, V 5.2, O 6.1, A 7.2, 10.9 (from Kent and Wagner [92]). 

Figure 7.4 Time averaged axial distribution of 15 /Lim particles when injected continuously and in and out of phase with the forcing frequency of 1380 Hz. 1 — continuous, 2 — in phase, and 3 — out of phase...

IfemlU. Axial distribution of pressure and porosity of an ignition-plug day measured in a CP cell, (a) Normalized pressure distribution as a"oma m d distance [( ) experimental filtration data theoretical curves (x) AP = 98kN m-2 ( ) AP = 294 kN m-2 (A)... 

Primary zone size is important with regard to efficiency and limits also. Within practical limits, a larger primary zone cross-sectional area will provide the best performance 138). Possible reasons arc lower velocities, less wall impingement by fuel, larger zone of low velocity, and less wall quenching of chemical reactions. The best axial distribution of open area of a combustor will depend on required operating conditions, the pressure loss characteristics, and the shape of the air entry ports. It will also depend on fuel-injection and fuel-volatility characteristics, as these factors will affect the amount of vapor fuel present at any location. If proper burning environment is to be obtained, these factors must be matched, and compromises in performance must be expected. 

Not surprisingly, all the data pertaining to axial distribution of contaminants in the bed were obtained for monolithic catalysts, where such determination is performed simply by successive sectioning (see Fig. 3) and analysis of each separate section. In pelleted catalysts there is considerable spatial mixing of the pellets during operation, and the sampling is also difficult. 

Radial and Axial Distributions of Heat Transfer Coefficient... 

As opposed to the relatively uniform bed structure in dense-phase fluidization, the radial and axial distributions of voidage, particle velocity, and gas velocity in the circulating fluidized bed are very nonuniform (see Chapter 10) as a result the profile for the heat transfer coefficient in the circulating fluidized bed is nonuniform. 

Third, there may be a concentration gradient of reactants and products along the length of the catalyst bed. If the structure of the catalyst depends upon the composition of the gas phase, then an average of the various structures will be measured. There is little discussion of this topic in the literature of XAFS spectroscopy of working catalysts. An extreme example of structural variations within a sample is discussed in Section 6, where there is a discussion of XAFS spatially resolved spectra recorded to allow direct observation of the axial distribution of phases present. If the XAFS data are not measured with spatial resolution, then it is recommended that XAFS data be measured under differential conversion conditions. However, if the aim of the experiment is to relate the catalyst structure directly to that in some industrial catalytic processes, then differential conversion conditions will only reflect the structure of the catalyst at the inlet of the bed. To learn about the structure of the catalyst near the outlet of the bed, the reaction has to be conducted at high conversions. If it is anticipated that this operation will lead to variations in the catalyst structure along the bed, then the feed to the micro-reactor should be one that mimics the concentration of reactants toward the downstream end of the bed (i.e., products should be added to the reactants). 

The axial distribution was measured in early experiments in the HFIR. The data were very well fit by the usual chopped cosine distribution with a small amount of reflector peaking (Fig. 4). We generally calculate the target compositions at... 

Axially distributed models of blood-tissue exchange... 

Figure 8.8 Integrated modeling of transport and metabolism. An axially distributed model of oxygen transport and metabolism [14], with parallel pathways used to simulate heterogeneity in path length and flow is used to simulate an experiment in which coronary flow is reduced and myoglobin saturation and concentrations of phosphate metabolites are measured. Data are from Zhang et al. [218],...

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. 

Inasmuch as heat transfer depends on the hydrodynamic features of fast fluidization, if the fast fluidized bed is equipped with an abrupt exit, the axial distribution of solids concentration will have a C-shaped curve (Jin et al., 1988 Bai et al., 1992 Glicksman et al., 1991. See Chapter 3, Section III.F.l). The heat transfer coefficient will consequently increase in the region near the exit, as reported by Wu et al. (1987). 

Therefore, for coal burning, neglecting radial gas dispersion and radial heterogeneity of solids concentration might be acceptable. Gas-solid flow can thus be simplified to a one-dimensional model with axial distributions only. 

Evidence of the existence of an upper dilute phase and a lower dense phase is shown by the axial distribution of bed density (Table III). 

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