Fully axial flow

B17. Bertoletti, S., Gaspari, G. P., Lombardi, C., and Zavattarelli, R., Critical heat flux data for fully developed flow of steam and water mixtures in round vertical tubes with non-uniform axial power distribution, CISE-R.74 (1963). 

Under streamline conditions, the velocity at the axis will increase from a value u at the inlet to a value 2u where fully-developed flow exists, as shown in Figure 11.9, because the mean velocity of flow u in the pipe is half of the axial velocity, from equation 336. 

The data were plotted, as shown in Fig. 11, using the effective diameter of Eq. (50) as the characteristic length. For fully turbulent flow, the liquid and gas data join, although the two types of systems differ at lower Reynolds numbers. Rough estimates of radial dispersion coefficients from a random-walk theory to be discussed later also agree with the experimental data. There is not as much scatter in the data as there was with the axial data. This is probably partly due to the fact that a steady flow of tracer is quite easy to obtain experimentally, and so there were no gross injection difficulties as were present with the inputs used for axial dispersion coefficient measurement. In addition, end-effect errors are much smaller for radial measurements (B14). Thus, more experimentation needs to be done mainly in the range of low flow rates. 

To analyze the dynamic behavior of gas-solid pipe flows, the most common and easiest system to consider is a dilute gas-solid pipe flow which is fully developed and is subject to the effects of electrostatic force and gravitational force. The fully developed flow here refers to the situation where the velocity profiles of both gas and particles are unchanged along the axial direction. The system of this nature was analyzed by Soo and Tung (1971). In this section, the analysis of Soo and Tung (1971) is presented. It is assumed that no particles are deposited on the wall surface of the pipe (or the particle deposition rate is zero). Moreover, the pipe flow is considered to be turbulent, as is true for most flow conditions. 

Attention will be restricted to fully developed flow, i.e., to flow in which all the flow variables except temperature are not changing with distance, c. along the pipe. It will also be assumed that the wall heat flux is axially constant and the wall temperature is constant around the periphery although it of course varies with axial distance. Using the coordinate system shown in Fig. 9.31, the equations governing the flow are, if the Boussinesq approximation is adopted and if viscous dissipation... 

The axial position of the transition point is highly sensitive to gas flow rates and for a 9m column will occur in only a small range of values. It is important to mention that the model used in this paper assumes fully developed flow. This might not be the case in an industrial size reactor and an entrance effect might well be observed which is not predicted here. 

The Nusselt number (Nu) for laminar, fully developed flow is eonsfanf and independenf of Re, Pr, and fhe axial loeafion. Under fhese flow eondifions Nu values for a eylindrieal ehannel wifh uniform wall heaf flux and uniform wall femperature are 4.36 and 3.66, respeefively. More Nusself number values for reefangular ehannels are available in Table 3. 

For definiteness, we consider the transfer processes between a cylindrical wall and a turbulently flowing n-component fluid mixture. For condensation of vapor mixtures flowing inside a vertical tube, for example, the wall can be considered to be the surface of the liquid condensate film. We examine the phenomena occurring at any axial position in the tube, assuming that fully developed flow conditions are attained. For steady-state conditions, the equations of continuity of mass of component i (assuming no chemical reactions), Eqs. 1.3.7 take the form... 

If it is desired to consider axial flow impellers in a gas-liquid system for any reason, it should be remembered that the upward flow of gas tends to negate the downward action ofthe pumping capacity ofthe axial flow turbine. A radial flow turbine must have three times more power than the power in the gas stream for the mixer power level to be fully effective. On the other hand, the axial flow impeller must have eight to ten times more power than in the gas stream for it to establish the axial flow pattern. 

To deal with the small UF cut, a new cascade technique was developed, the so-called helikon technique, based on the principle that an axial flow compressor can simultaneously transmit several streams of different isotopic composition without there being significant mixing between them. The UCOR process must therefore be regarded as a combination of the separation element and this technique, which makes it possible to achieve the desired enrichment with a relatively small number of large separation units by fully utilising the high separation factor available. 

Calculate the stream function for axisymmetric fully developed creeping viscous flow of an incompressible Newtonian fluid in the annular region between two concentric tubes. This problem is analogous to axial flow on the shell side of a double-pipe heat exchanger. It is not necessary to solve algebraically for all the integration constants. However, you must include all the boundary conditions that allow one to determine a unique solution for i/f. Express your answer for the stream function in terms of ... 

The sealed regions of the membrane are also included in the plot in Fig. 5.15. There, because of the fully developed flow (the radial velocity is zero, the axial velocity is constant), the pressure decreases linearly with the axial coordinate. 

The Nusselt number (Nu) for laminar, fully developed flow is constant and independent of the Re, the Prandtl number (Pr), and the axial location of the channel. 

A tubular reactor in which the fluid flow is laminar is regarded as a non-ideal reactor, as discussed in Section 3.2.2. Laminar flow is the flow pattern in which the fluid elements move in streamlines in an orderly manner and no two fluid elements moving in two different streamlines mix with each other. Thus, the fluid elements mix neither in the axial direction nor in the radial direction. This pattern of fluid flow is called fully segregafed flow. Laminar flow of fluid in a tubular vessel is depicted in Figure 3.64. 

The most notable difference in behaviour as Gj is increased beyond 200-300 kg/m s at relatively high /g is the gradual disappearance of net solids downflow at the wall (e.g., Issangya et al., 2000 Karri and Knowlton, 1998, 1999 Liu, 2001). This leads to a different flow regime (dense suspension upflow, as discussed in Sec. 3) and a more homogeneous flow structure. Typical axial solids holdup profiles appear in Fig. 19. Note that at these high values of Gj, the profiles tend to reach relatively constant holdups of the order of 15%, indicating an approach to fully developed flow. Parssinen et al. (2001) found that there were four zones in axial profiles for a much taller riser. 

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