Case Studies in the Human Respiratory System - Computational Fluid and Particle Dynamics in the Human Respiratory System - page 258

Table 8.4 Shape of
agglomerate of spheres to
model pollen particles

where P p is the projected perimeter of the particle in its direction of motion. The
empirically defined correlation for the drag coefficient is given as

0 . 42 d d n 2

1

Re p 0 . 687

d A
d n

24
Re p

d A
d n

0 . 15
√ c C D = + +

√ c 1

42500 d d n Re p − 1 . 16
(8.18)

+

The application of this model for pollen particles assumes the non-spherical shape
to be an agglomerate of spheres that form a shape referred to as close-to-sphere
particles. The resulting terms, d A / d n and c, for the representative pollen particle are
given in Table 8.4 .
During the pollen season, pollen in the air can either be wet or dry according to
the stage of pollen development. The dry pollen lacking water content was found
to have a density of 550 kg/m 3 (Crawford 1949) while wet pollen has a density
of 1,320 kg/m 3 (Harrington and Metzger 1963). In the current simulation only the
dry pollen was considered because this is more justifiable in terms of the developed
pollen drifting in the air. The effects of a higher density will lead to an increase in
the aerodynamic diameter which will enhance the impactability of the particle.
For fibres , the approach by Tran-Cong et al. (2004) is again used here, since
it has been reported that the accuracy of the Haider-Levenspiel method, Eq. (8.13)
decreases as the shape factor decreases (Gabitto and Tsouris 2007). The fibre is repre-
sented by spherical aggregate particles clustered into a cylindrical bar configuration.
The resulting terms, d A / d n and c, which satisfy the drag coefficient in Eq. (8.18)
for a representative fibre having a length of 7 d and a diameter of 1 d, are given in
Table 8.5 .