Interdisciplinary Applied Mathematics

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(Yang et    al.,    1999b)    were    able    to    fit    their    experimental    and    numerical


simulation data to an empirically determined scaling law, given in the following (Yang et al., 1999b):


0.28



к



в



73.5


Re



+ 1.7



(6.24)


where к is the pressure drop nondimensionalized with the dynamic head,


i.e.,


AP


к


T~0    7/2”’


2lJoouoo and h and t are the hole diameter and thickness of the filter, respectively. For three-dimensional cases the Reynolds number is defined as


Re


Poo UCO


pfi


where the subscript ж indicates upstream conditions. For a two-dimensional geometry the opening factor becomes the ratio of the hole opening length to the center-to-center filter separation distance L (в = h/L), resulting in


P<X> U<x>L


Re =-.


P


Using the scaling law presented by equation (6.24) leads to higher pressure drops than the experimentally determined values. The assumptions and the parameters utilized in development of this scaling law were:


1.    2-D geometry,


2. Opening factor: 0.1 < в < 0.45,


3. t/h ratio: 0.08 < t/h < 0.5,


4.    Reynolds number: 1 < Re < 100,


5.    Knudsen number: 0.005 < Kn < 0.015.


In a follow-up study, (Yang et al., 2001) proposed the following modified scaling law based on detailed studies of the filter geometry, experimental data, and three-dimensional numerical simulations:


« = r2(3.5t+3)(g+0.2,Y    (6.25)


Although most of the experimental data fit this relation, there were some deviations for low Reynolds number flows. This scaling law did not explicitly incorporate the rarefaction effects as a function of the Knudsen number.

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