Flow geometrical modifications

Figure 7.17 Schematics of different types of flow splitters for separation of liquid-liquid two-phase flow, (a) Geometrical modifications (e.g., Y-separator), (b) wettability based (e.g., membrane separator), and (c) gravity based separator (e.g., settler).

All the relationships presented in Chapter 6 apply directly to circular pipe. However, many of these results can also, with appropriate modification, be applied to conduits with noncircular cross sections. It should be recalled that the derivation of the momentum equation for uniform flow in a tube [e.g., Eq. (5-44)] involved no assumption about the shape of the tube cross section. The result is that the friction loss is a function of a geometric parameter called the hydraulic diameter ... 

To satisfy physical limitations, modifications to the diameters are made depending upon the magnitude of the compressible flow effects in each of the reactor sections. Lengths are geometrically scaled in the reactor throat. However, the diffuser angle is forced below a maximum angle of 6° to avoid flow separation. Residence times are controlled by appropriate variation of the length of the reactor s cylindrical section. 

The modification made was thus more than just a geometric alteration. Significant changes were made to the statics, the dynamics, and the flow in the assembly. First, due to the differences in diameter and the dogleg shape, we have a couple which loads the pipe latterly in the vertical direction. Second, we have a mass spring system with very little support... 

This suggests one use for a model such as presented here. This is to systematically investigate the sensitivity of coronary blood flow to various parameters, e.g. peripheral resistance, wall properties, geometric branching pattern, etc. Such a parametric ananalysis can be extended as the model is expanded. One possible modification to the model is to include somewhat more detail on the venous side of the coronary system. Also, as is indicated by Figure 1, it is possible to insert into the calculation multiple stenoses as well as to allow for the presence of multiple aorto-coronary bypass grafts. In the latter case, it is necessary to separately specify the wave-speed characteristics of any such grafts. 

Thus, a combination of reactor types might be used to simulate an actual reactor. In addition, the flow rates and/or volumes provide adjustable parameters which can be chosen to fit response data, i.e., modifications in the geometric model and phys-ical/chemical system can be made to better fit conversion data. Bypassing (the equivalent in some cases of dead space) can also be included in the analyses. 

The analysis of Clavin 6e Williams (1982) concerning the flame structure of wrinkled fronts in a non homogeneous flows has been extended independently by Matalon Matkowsky (1982) and by Clavin 6e Joulin (1983) to the nonlinear case of finite amplitudes of the front corrugations. As anticipated by the early phenomenological analysis of Karlowitz 6e al (1953), the modification to the normal burning velocity Uj produced by the front curvature and by the flow inhomogeneities can be expressed in terms of only one geometrical scalar i.e. the total flame stretch experienced by the front. 

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