Interdisciplinary Applied Mathematics

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(a)    x 10    (b)

FIGURE 6.28. Pressure (a), streamwise velocity (b) variations along the midline of the channel (line p1-p2 of Figure 6.27) for filters 1, 2, and 4.

Effect of Channel Length

Dependence of the flow characteristics on channel length was investigated using filters 1, 2, and 4, which have identical channel height (1 p,m), but different channel lengths (1, 5 and, 10 p,m) (see Table 6.2). A pressure difference of 0.3 atm was applied through these filter elements in all simulations.    In    Figure    6.28,    we    present    the    pressure    (a)    and channel    center

velocity (b) variation along the midline of the channel (line p1-p2 of Figure 6.27). To facilitate comparisons between the different cases, the x and y axes are shifted so that the center point for each channel is at x = y = 0.

The pressure drop in filters 1, 2, and 4 is shown in Figure 6.28 (a). Filter 1 has    the    smallest    lc/hc    ratio    of the    studied cases.    Thus,    the    presence    of

undeveloped flow can be easily observed in the left figure. For this filter, the pressure drop is nonlinear and extends beyond the membrane channel. The flows in filters 2 and 4 exhibit typical developing compressible flow for large sections of the channel, which results in almost linear pressure drop, and a smoothly increasing velocity profile. The nonlinear pressure distribution, which is observed in compressible channel flows with large pressure drop, is not observed due to the small input-to-output pressure ratio. As a result, it can be concluded that for these filters the pressure distribution is very close to linear, unless the filter length-to-height ratio introduces undeveloped flows.

Flowrate Comparisons

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