Turbulent Flow Promoters

As discussed in Section 1.4.5, electricity costs are directly proportional to cell voltage. One way of minimizing voltage is to make the gap between anode and cathode as small as possible. This is especially important when an electrolyte with low electrical conductivity is used. Because of a very 

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It is the large scale eddies that are responsible for the very rapid transport of momentum, energy and mass across the whole flow field in turbulent flow, while the smallest eddies and their destruction by viscosity are responsible for the uniformity of properties on the fine scale. Although it is the fluctuations in the flow that promote these high transfer rates, it is... 

Considerable interest has been generated in turbulence promoters for both RO and UF. Equations 4 and 5 show considerable improvements in the mass-transfer coefficient when operating UF in turbulent flow. Of course the penalty in pressure drop incurred in a turbulent flow system is much higher than in laminar flow. Another way to increase the mass-transfer is by introducing turbulence promoters in laminar flow. This procedure is practiced extensively in enhanced heat-exchanger design and is now exploited in membrane hardware design. 

Typical flux data with two interpromoter spacings (AL) are shown in Figure 28 as a function of the cross-flow rate. The flux Increased by a factor of 3 for the best case. Though Probstein did not plot his data in this way, it is Interesting to note that the empty channel flux has a predictable 0.33 power dependence on tangential velocity. With the turbulence promoters, the slope shifts closer to the 0.7-0.8 power dependence normally observed in turbulent flow. Unfortunately, data are not available in Probstein s paper on the increased pressure drop associated with the turbulence promoters, but it would appear that the flux to power ratio is greatly improved with turbulence promoters. 

A variety of statistical models are available for predictions of multiphase turbulent flows [85]. A large number of the application oriented investigations are based on the Eulerian description utilizing turbulence closures for both the dispersed and the carrier phases. The closure schemes for the carrier phase are mostly limited to Boussinesq type approximations in conjunction with modified forms of the conventional k-e model [87]. The models for the dispersed phase are typically via the Hinze-Tchen algebraic relation [88] which relates the eddy viscosity of the dispersed phase to that of the carrier phase. While the simplicity of this model has promoted its use, its nonuniversality has been widely recognized [88]. 

Figures 13.15 and 13.16 show the findings for flow in pipes. This model represents turbulent flow, but only represents streamline flow in pipes when the pipe is long enough to achieve radial uniformity of a pulse of tracer. For liquids this may require a rather long pipe, and Fig. 13.16 shows these results. Note that molecular diffusion strongly affects the rate of dispersion in laminar flow. At low flow rate it promotes dispersion at higher flow rate it has the opposite effect.

The intense heat dissipated by viscous flow near the walls of a tubular reactor leads to an increase in local temperature and acceleration of the chemical reaction, which also promotes an increase in temperature the local situation then propagates to the axis of the tubular reactor. This effect, which was discovered theoretically, may occur in practice in the flow of a highly viscous liquid with relatively weak dependence of viscosity on degree of conversion. However, it is questionable whether this approach could be applied to the flow of ethylene in a tubular reactor as was proposed in the original publication.199 In turbulent flow of a monomer, the near-wall zone is not physically distinct in a hydrodynamic sense, while for a laminar flow the growth of viscosity leads to a directly opposite tendency - a slowing-down of the flow near the walls. In addition, the nature of the viscosity-versus-conversion dependence rj(P) also influences the results of theoretical calculations. For example, although this factor was included in the calculations in Ref.,200 it did not affect the flow patterns because of the rather weak q(P) dependence for the system that was analyzed. 

These fluctuations maybe caused by rapid variations in pressure or velocity producing random vortices and flow instabilities within the fluid. A complete mathematical analysis of turbulent flow remains elusive due to the erratic nature of the flow. Often used to promote mixing or enhance transport to surfaces, turbulent flow has been studied using electrochemical techniques [i]. 

In turbulent flow, momentum is constantly fed into the layer adjacent to the wall because of the momentum transfer between layers at different velocities. The kinetic energy of the fluid elements close to the wall does not decrease as rapidly as in laminar flow. This means that turbulent boundary layers do not become detached as quickly as laminar boundary layers. Heat and mass transfer close to the wall is not only promoted by turbulence, the fluid also flows over a larger surface area without detachment. At the same time the pressure resistance is lower because the fluid flow does not separate from the surface for a longer flow path. 

Figure 5. Gelman pleated crossflow filter cartridge. Cartridge components (A) a porous pleated support screen to provide mechanical support under applied pressure (B) the pleated microporous filtration element (C) the pleated spacer which creates the thin flow channel and promotes turbulent flow (D) the impermeable film which creates the flow channel (E) a porous support tube to provide an exit for permeate (F) open-end cap which provides for exit of product flow (G) closed-end cap completely which seals one end of module (H) outer seal ring which creates the seal between the impermeable film in the module and the interior of the housing. The back pressure support tube is not pictured. The ends of the cartridge are potted and sealed. A space between the ends of Film D and the end seals is provided to allow the entrance and exit of the flow-channel fluid.

The radial dispersion can be promoted by introducing turbulent flow or secondary flow, by diffusion alone, or by a combination of these effects. 

Pratt, H.R.C. Trans. Inst. Chem. Eng. 28 (1950) 77. The application of turbulent flow theory to transfer processes in tubes containing turbulence promoters and packings. 

The sizes of single microbial cells are very small (in the range of a few microns) compared to chemical catalyst particles coupled with the above constraints it is generally difficult to promote high velocities and turbulent-flows conditions... 

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