Environmental Engineering Reference
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grids with 3D low. Investigations with numeric calculations of resistance for various 3D grids
[84,85] were carried out in the latter half of the 1990s.
The irst step on the way of analytical description of resistance in the 3D grid was executed in
Ref. [86]. Simple analytical expressions for drag force were obtained for the case when the pair lay-
ers are turned in their plane relative to the impair ones. These expressions describe qualitatively the
model ilters resistance which is being observed experimentally.
Hydrodynamic low in the polydisperse 3D ibrous porous medium was analytically scrutinized
for the irst time in Ref. [87]. The theory of self-consistent ield was applied to study averaged equa-
tions of liquid low in isotropic medium and in anisotropic ibrous ilter. One of the important practi-
cal results that follow this research is determination of the Reynolds number, when self-similarity
low mode in the ilter with the given packing density is deranged. It is of particular importance to
know the onset of the self-similarity derangement to evaluate the inertia particles deposit during
analytical iltration, that is, at high low velocities.
Speciic character of low in the 3D model ilter was studied in Ref. [35] as well. Numerical
methods were used to determine the relationships between hydrodynamic resistance and a step and
distance between rows for a model ilter consisting of two rows of parallel cylinders perpendicular
to the Stokes low direction, cylinders being turned through −90° in their planes relative to each
other. Approximation equations were obtained for the cylinder drag force in the adjoining rows:
−
1
⎧
2
3
4
⎫
⎪
⎪
⎛
⎜
2
a
h
⎞
⎟
−
a
h
⎛
⎜
a
h
⎞
⎟
−
⎛
⎜
a
h
⎞
⎟
+
⎛
⎜
a
h
⎞
⎟
⎪
⎪
F
=
8
π
1 1 5
−
.
ln
7 48
.
+
26
37 5
.
21
(17.22)
at
a/h
< 0.6 and
−
5 2
/
−
1
9
2 2
π
⎛
⎜
a
h
⎞
⎟
⎛
⎜
a
h
⎞
⎟
−
F
=
1
−
+
10 34 1
.
−
10 45
.
(17.23)
at
a/h
> 0.6. Equations 17.22 and 17.23 can be used to calculate the resistance of thin nets.
Studies of the fan-type model resistance at tenuous air low showed that gas sliding effect exerts
in this model more notably than in the parallel one. Proportionality factor considering interaction of
air molecules with the iber surface and calculated from the angle of slope of the linear relationship
between 1/
F
f
and
Kn
equals 1.43 instead of 1.18 for the parallel model [66].
The air low and the particle deposition process are similar for the fan and the real ilter. In par-
ticular, a very important common feature is discovered: diffusive aerosol deposition eficiency for
the fan model ilter does not depend on the packing density in a wide range of α from 0.01 to 0.15,
the capture coeficient being determined as per the equation [7]:
η
f
−
2 3
/
(17.24)
=
2 7
.
Pe
While collating
F
for real ilters with
F
f
for the fan-type model, it was found that the force character
dependent on the packing density is described correctly by the equation for the fan-type model,
however, absolute magnitudes
F
f
>
F
, which is caused by inhomogeneity of the real ilters. Paper [88]
provides theoretical support for the diffusive deposition law in disorder ibers system with ibers
perpendicular the low, which is being experimentally observed. It has been shown that in the area
of low packing densities α the capture coeficient dependence on α is really rather weak.
The simple view of the Equation 17.7 contributed to the wide spread of the diffusive method of
sampling submicron aerosol particles by means of diffusive grid batteries [52-54].
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