Flow pattern efficiency

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... 

The value of the flow pattern efficiency is shown as a function of the spacing between the streams ia Figure 15a. It can be seen that the flow pattern efficiency is a maximum when the position of the upflowiag stream is chosen such that /T2 is equal to 0.5335. For this particular case the flow pattern efficiency assumes the value 6p = 0.8145. 

Fig. 15. (a) Values of the flow-pattern efficiency for the two-sheU model, (b) The dependence of the flow-pattern efficiency on the dimensionless... 

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 separation parameters have been calculated for a centrifuge in which the behavior of the circulating gas is described by Martin s equation. The flow pattern efficiency is shown in Figure 15(b) as a function of the dimensionless parameter M, where M is equal to (ME /2RT). In this case the maximum flow pattern efficiency attainable is 0.956. 

The flow pattern efficiency decreases from 0.56 at = 400 m/s to 0.19 at 700 m/s. When combined with the in the first factor of Eq. (14.226), the overall effect is to cause the separative capacity per unit length to vary as over this range of v, instead of as Vg. 

We will now introduce a few parameters in CGC such as the flow pattern efficiency E/ and the flow number Nf Then we will focus on the separation achieved in a CGC under total reflux. The flow pattern efficiency E/ is defined as... 

The internal flow rate M has another useful application. It serves as a scale factor for the integrals in Eqs. (54) and (55). The flow pattern efficiency is defined by... 

The flow pattern efficiency E of Eq. (63) depends only on the shape of the flow function, and not on its magnitude ... 

The optimal flow function is the one which produces a flow pattern efficiency E of unity. It can be deduced without considering the fluid mechanics of the centrifuge. 

Figure 14 shows a typical flow function for = 10 as calculated from Eq. (158) of the simplified Berman model. Note that this curve is quite different from the form F( ) required by Eq. (105) for maximum flow pattern efficiency. 

The flow pattern efliciencies are plotted on Fig. 15 for the various long bowl models (the two dashed curves result from calculations which will be discussed in the next section). The spot calculations on the simplified long bowl methods agree satisfactorily with the Parker calculation. The latter shows a maximum value of = 0.81 at = 5.4. At large ( > 20), the flow pattern efficiency curve of Fig. 15 varies as jA. ... 

Because the rotor wall does not appear explicitly in Martin s analysis, the flow function of Eq. (173), like the optimum flow function of Eq. (105), does not satisfy the restraint of Eq. (99). However, the flow pattern efficiency may be computed by substituting Eq. (173) into Eq.(63) ... 

To this approximation, the flow pattern efficiency for AT = constant is given by... 

The separative properties of the centrifuge depend upon two fluid mechanical characteristics of the device, the flow pattern efficiency E and the internal circulation parameter m. Both of these parameters depend upon double integrals of the axial velocity profile. The efficiency E requires knowledge of the shape of the velocity profile. In addition, calculation of m is possible only if the magnitude and shape of the axial velocity profile are known. 

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