Efficiency velocity profile

The flow pattern efficiency depends solely upon the shape of the velocity profile in the circulating gas. In terms of the integrals appearing in the gradient equation, the flow pattern efficiency is given by equation 86. 

To evaluate the flow pattern efficiency, a knowledge of the actual hydrodynamic behavior of the process gas circulating in the centrifuge is necessary. Primarily because of the lack of such knowledge, the flow pattern efficiency has been evaluated for a number of different assumed isothermal centrifuge velocity profiles. 

The Optimum Velocity Profile. The optimum velocity profile (41), that is the velocity profile that yields the maximum value for the flow pattern efficiency, is one in which the mass velocitypv is constant over the radius of the centrifuge except for a discontinuity at the wall of the centrifuge (r = rP). This optimum velocity profile is shown in Figure 14a. For this case the following values for the separation parameters of the centrifuge are obtained... 

These simple velocity profiles do not indicate directly any dependence of the flow pattern efficiency upon the rotational speed of the centrifuge. A dependence on speed is to be expected on the basis of the argument that at high speeds the gas in the centrifuge is crowded toward the periphery of the rotor and that the effective distance between the countercurrent streams is thereby reduced. It can be seen from the two-sheU model that, as the position of upflowing stream approaches the periphery, the flow pattern efficiency drops off from its maximum value. 

The time-dependent simulations of free jets discussed here focus on the vortex dynamics and transition to turbulence downstream of the jet exit. For the sake of computational efficiency, the author concentrates on the study of jet flow initialized with laminar conditions with a thin rectangular vortex sheet having slightly rounded-off corner regions and uniform initial momentum thickness [9]. Initial conditions for the simulated jets involve top>-hat initial velocity profiles... 

Two-roll mills have been analyzed in terms of the pressure distribution and velocity profiles created between the rolls [95], the shear imposed on fluid elements exposed to these conditions in the nip region [129] and their resulting efficiency as dispersive mixing devices [130,131]. An earlier mathematical model was proposed to describe the dispersive mixing process of carbon black in rubber on roll mills, through consideration of agglomerate size distribution and... 

When the concentration boundary layer is sufficiently thin the mass transport problem can be solved under the approximation that the solution velocity within the concentration boundary layer varies linearly with distance away from the surface. This is called the L6v que approximation (8, 9] and is satisfactory under conditions where convection is efficient compared with diffusion. More accurate treatments of mass transfer taking account of the full velocity profile can be obtained numerically [10, 11] but the Ldveque approximation has been shown to be valid for most practical electrodes and solution velocities. Using the L vSque approximation, the local value of the concentration boundary layer thickness, 8k, (determined by equating the calculated flux to the flux that would be obtained according to a Nernstian diffusion layer approximation that is with a linear variation of concentration across the boundary layer) is given by equation (10.6) [12]. 

Luo and Andrade have reexamined [66] the potential of CEC by comparing the effect of the conclusions of the Rice-Whitehead theory [35] of doublelayer overlap on the determination of minimum dp with those which result from more recent treatments of the velocity profile in electroosmotic flow. They concluded that, for ionic strength <10 mM, the particle size can again be less than 1 pm, and that plate numbers up to 1 x 106 should be theoretically possible. An obstacle to the realization of such efficiencies in CEC is, however, the consequence of the recognition [6] by Giddings that there is no satisfactory mathemat-... 

The influence of EOF nonuniformity on efficiency of CE in the capillary with the zeta potential of the wall being the function (x) of the longitudinal coordinate x was studied in Ref. 5. To calculate the EOF velocity profile, an important approximation was justified by the fact that usually ka 1 in CE. Thus, the doublelayer region was neglected and the following boundary condition was formulated ... 

It is important that, to optimize the collection efficiency, the gas distribution across the frontal area of the precipitator must be as uniform as possible, although some recent work has indicated that for certain conditions a skewed velocity profile can be advantageous. It is not easy to produce a typical operational gas velocity of around 1.5m/s, which has been decelerated from approximately 15m/s in the inlet approach ductwork, and an acceptable standard of distribution is an RMS deviation of 15%. This standard can be achieved through field corrective testing, large-scale model tests, or the more recent CFD approaches.f ... 

In practice, the fluid velocity profile is rarely flat, and spatial gradients of concentration and temperature do exist, especially in large-diameter reactors. Hence, the plug-flow reactor model (Fig. 7.1) does not describe exactly the conditions in industrial reactors. However, it provides a convenient mathematical means to estimate the performance of some reactors. As will be discussed below, it also provides a measure of the most efficient flow reactor—one where no mixing takes place in the reactor. The plug-flow model adequately describes the reactor operation when one of the following two conditions is satisfied ... 

In the circulation efficiency, Eq. (14.228), the factor [/(ri/j)] /4/3, which has the value unity for the uniform mass velocity profile, increases rapidly with Vg, thus reducing the circulation efficiency. 

The turbine exhaust gas/combustion air velocity profile af the duct burner plane must be within certain limits to ensure good combustion efficiency, and in cogeneration applications this is rarely achieved without flow straightening devices. Even in nonfired configurations, it may be necessary to alter the velocity distribution to make efficient use of boiler heat transfer surface. Figure 26.7 shows a comparison of flow variation wifh and without flow straightening. 

Output Data. Basically, concentration maps of all dissolved substances can be computed. Yet, because of the previously described simplifying assumptions, the computation will proceed routinely via the direct calculation of collision efficiency factors as functions of location. Transport parameters, such as dissipation and kinetic energy, are likewise computed as functions of location at the predetermined grid points. These parameters, too, are on the one hand, intermediary results in the computation of particle aggregation and aggregate transport, but on the other hand, the basis for computed velocity profiles (see Table I). 

The combustor validation during steady state and transient conditions is performed in a test rig at ON ERA, France, where the high pressure/temperature conditions can be achieved. As was pointed out earlier,in order to obtain high hetero/homogenous combustion efficiency with low emission values it is important to create an even velocity profile at the catalytic section inlet. Extensive... 

The Influence of Non>UnKbrmity of the Velocity Profile on the Efficiency Coefficient of Gravitational Separators... 

Summarizing, we should make the following observation the expression for the efficiency coefficient clearly implies that for a horizontal gravitational separator, this coefficient does not depend on the velocity profile - assuming that the gas fiow rate is constant. 

The movement of a liquid, when in contact with a charged surface, situated in a strong electric field is called electro-endosmosis. The flow of liquid through a silica tube under electro-endosmosis is of plug form, and does not exhibit the parabolic velocity profile that normally occurs in Newtonian flow. As a result of this, there is little, or no, resistance to mass transfer similar to that in open tubular columns. It follows, that there is very little band dispersion when the flow is electrosmotically driven and consequently extremely high efficiencies can be attained. 

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