Axial location

The sohds are also assumed to be in plug flow. As part of the plug flow approximation, the gas and soHds are assumed isothermal in the radial direction at a given axial location. Detailed models for kiln heat transfer are available (20,21). 

Figure 5 shows the variation of the droplet mean axial velocity at the same axial location. The primary feature of this velocity profile is that the maximum velocity peaks at the centerline. The velocity magnitude and direction in the center region tend to be related to the hquid swid strength and axial distance. A reverse (recirculation) flow with negative velocity is possible if the swid is intense. Under such conditions, the maximum velocity tends to shift away from the centerline. 

Although not universal, on most multistage compressors, the impellers are axially located by shaft sleeves. The sleeves form a part of the inter stage seal and are shrunk onto the shaft with a shrink level less than (Ik impeller. 

Between the nonbuoyant jet region and the plume region lies an intermediate region in which the flow changes from the former to the latter.The axial location of the beginning of this intermediate region depends primarily on the exit Froude number ... 

Take one step, calculating new values for B, / at the new axial location, z -I- Az. The current chapter considers only isothermal reactors, but the general case includes an ODE for temperature. The marching-ahead equations have the form... 

The solution of Equations (5.23) or (5.24) is more straightforward when temperature and the component concentrations can be used directly as the dependent variables rather than enthalpy and the component fluxes. In any case, however, the initial values, Ti , Pi , Ui , bj ,... must be known at z = 0. Reaction rates and physical properties can then be calculated at = 0 so that the right-hand side of Equations (5.23) or (5.24) can be evaluated. This gives AT, and thus T z + Az), directly in the case of Equation (5.24) and imphcitly via the enthalpy in the case of Equation (5.23). The component equations are evaluated similarly to give a(z + Az), b(z + Az),... either directly or via the concentration fluxes as described in Section 3.1. The pressure equation is evaluated to give P(z + Az). The various auxiliary equations are used as necessary to determine quantities such as u and Ac at the new axial location. Thus, T,a,b,. .. and other necessary variables are determined at the next axial position along the tubular reactor. The axial position variable z can then be incremented and the entire procedure repeated to give temperatures and compositions at yet the next point. Thus, we march down the tube. 

He — local enthalpy of liquid at given axial location... 

DNB EU — axial location at which DNB occurs for uniform heat flux (in.), starting from inception of local boiling... 

To show the power level difference between the predicted DNB heat flux and the measured local DNB heat flux, the latter was taken at the axial location to give the minimum DNB ratio (DNBR) at the actual DNB power instead of that at the actual DNB location. However, the correct ratio of measured to predicted channel powers was maintained equal to the ratio of the heat fluxes, as shown in Figure 5.71. That is,... 

The interaction of parametric effects of solid mass flux and axial location is illustrated by the data of Dou et al. (1991), shown in Fig. 19. These authors measured the heat transfer coefficient on the surface of a vertical tube suspended within the fast fluidized bed at different elevations. The data of Fig. 19 show that for a given size particle, at a given superficial gas velocity, the heat transfer coefficient consistently decreases with elevation along the bed for any given solid mass flux Gs. At a given elevation position, the heat transfer coefficient consistently increases with increasing solid mass flux at the highest elevation of 6.5 m, where hydrodynamic conditions are most likely to be fully developed, it is seen that the heat transfer coefficient increases by approximately 50% as Gv increased from 30 to 50 kg/rrfs. 

Figure 19. Interactive effects of solid flux and axial location on heat transfer in fast fluidized bed. (From Dou, Herb, Tuzla and Chen, 1991.)...

Fig. 16 2-D map of 13C DEPT-MRI spectra recorded along the length of a trickle bed. Separate acquisitions were made for each of the (a) olefinic and (b) aliphatic regions of the spectrum. The data were acquired with the bed operating at steady state for gas and 1-octene flow rates of 32 and 1.0 ml min-1, respectively. The white, horizontal lines indicate the limits of the catalyst packing. Below each 2-D map, the 1-D 13C DEPT NMR spectrum recorded at an axial location just before the reactants reach the catalyst (just above the upper white line) is shown. The peaks at 114 and 139 ppm indicate that only unreacted 1-octene exists within the bed at this location, as expected. 

The PFR model ignores mixing between fluid elements at different axial locations. It can thus be rewritten in a Lagrangian framework by substituting a = Tpfrz, where a denotes the elapsed time (or age) that the fluid element has spent in the reactor. At the end of the PFR, all fluid elements have the same age, i.e., a = rpfr. Moreover, at every point in the PFR, the species concentrations are uniquely determined by the age of the fluid particles at that point through the solution to (1.2). 

In addition, the PFR model assumes that mixing between fluid elements at the same axial location is infinitely fast. In CRE parlance, all fluid elements are said to be well micromixed. In a tubular reactor, this assumption implies that the inlet concentrations are uniform over the cross-section of the reactor. However, in real reactors, the inlet streams are often segregated (non-premixed) at the inlet, and a finite time is required as they move down the reactor before they become well micromixed. The PFR model can be easily... 

Inspection of the barrel and screw for wear can provide information on the root cause for the wear. For example, if wear occurs at an axial location on only one side of the barrei and on all sides (angular direction) of the screw, then the likely root cause is that the barrel is out of alignment at that axial location. Conversely, if the barrei is worn on all sides and the screw is worn on only one side at the same axial location, then the root cause is likely a local bend in the screw. 

I2 axial location on the screw where the melt film first forms on the screw... 

Figure 10.4 Transverse profiles of (a) mean and (6) RMS nondimensional temperature at five axial locations without (f) and with (2) radiation...

One or more 12.7-centimeter (5-inch) OD porous layers can be installed in the rig at any axial location in the three sections. Each layer could be positioned using one custom-made retaining ring behind. In all of the tests reported here the porous material was a SiC ceramic foam supplied by Hi-Tech Ceramics of Alfred, New York. All the ceramic foams were 12.7 cm (5 in.) in diameter with varying thickness from 1.3 cm (0.5 in.) to 2.5 cm (1 in.). Two different pore sizes were tested, including 8 ppcm (20 ppi) and 18 ppcm (45 ppi). According to the manufacturer the porosity of the ceramic foams was about 80%. 

Temperature profiles were measured at several axial locations to locate the peak temperatures in the combustor. The axial distance between the nozzle and the temperature-measurement cross-section is denoted by Lf With one insert in place, the peak gas temperature immediately downstream of the insert was lowered but the high-temperature region was extended radially, i.e., the pattern factor was improved, as shown in Fig. 28.2. The peak temperatures at each axial location are shown as a function of the distance from the nozzle, or Lt/D, in Fig. 28.3. For the baseline case the highest temperature of 1418 K was found at 1.8 pipe diameters downstream of the nozzle. With one porous layer present, the peak gas temperature was about 200 K lower at Lt/D = 1.8 2.2 but increased by up to 120 K and 200 K at 0.5 and 3.2 pipe diameters downstream of the nozzle, respectively. The highest flame temperature was lowered but the high-temperature region was extended to upstream and downstream. 

First, the shear layer thickness at various axial locations in the near field was quantified using time-averaged Mie-scattering images. The shear layer thickness was defined as the radial distance over which the average Mie-scattering intensity dropped from 90% to 10% of the core value. Figure 29.7 shows the results... 

It can also identify texture of the semi coke formed as illustrated in Figure 6. If a binder is used with a coal, the Plastofrost technique can determine the coal-binder interaction and the texture of coke formed from the binder phase. Although not considered in studies undertaken at Waterloo, the axial location of the thermocouples in the sample holder makes the Plastofrost procedure capable of measuring coal-coke conductivity as a function of coal, temperature and compaction pressure, with just a modest redesign of the heating slab. 

Figure 21 shows the simulated dynamic behavior of the gas temperatures at various axial locations in the bed using both the linear and nonlinear models for a step change in the inlet CO concentration from a mole fraction of 0.06 to 0.07 and in the inlet gas temperature from 573 to 593 K. Figure 22 shows the corresponding dynamic behavior of the CO and C02 concentrations at the reactor exit and at a point early in the reactor bed. The axial concentration profiles at the initial conditions and at the final steady state using both the linear and nonlinear simulations are shown in Fig. 23. The temporal behavior of the profiles shows that the discrepancies between the linear and nonlinear results increase as the final steady state is approached. Even so, there are only slight differences (less than 2% in concentrations and less than 0.5% in temperatures) in the profiles throughout the dynamic responses and at the final steady state even for this relatively major step-input change.

In a follow-up study, Koptyug et al. 115) reported images of both liquid and gas flow and mass transport phenomena in two different cylindrical monolith catalysts (one with triangular channels, the other with square channels) at various axial locations within the monolith. Heibel et al. 116,117) addressed two-phase flow in the film flow regime and reported investigations of liquid distributions in the plane perpendicular to the direction of superficial flow, in particular, addressing the accumulation of liquid in the corners of the square channels of the monolith. 

Figs. 25 to 28 show that the metal deposition in CoMo/A1203 hydrotreating catalysts is a function of the radial position within the catalyst and the axial location of the catalyst sample within the fixed-bed reactor. Nickel and vanadium both exhibit radial profiles with internal maxima, termed M-shaped profiles, at the reactor entrance. These maxima shift to the pellets edge at the reactor outlet, generating the classic U-shaped profile. 

Orgel, J. P., Wess, T. J., and Miller, A. (2000). The in situ conformation and axial location of the intermolecular cross-linked non-helical telopeptides of type I collagen. Struct. Fold. Des. 8, 137-142. 

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