Strona 2_redak - Instytut Agrofizyki im. Bohdana Dobrzańskiego ...

87
Experimental airflow resistance as a function of air velocity for three types of seeds
and centric filling is shown in figure 11.2. The lowest was airflow resistance of
soybeans and the highest – that of wheat. This order does not correspond exactly to
the determined porosities that were 0.37, 0.40 and 0.39 for wheat, corn and
soybeans, respectively. Higher airflow resistance of corn despite its higher porosity
in respect to soybeans may be the result of more complex geometry of pore space
due to more irregular shape of corn kernels as compared to the roughly spherical
shape of soybeans.
Fig. 11.2. Airflow resistance as a function of airflow velocity for centric filling of grain column with:
red soft wheat, corn and soybeans
11.3. Ergun’s equation
Pressure drop data for airflow through agricultural products are usually presented
as curves or equations [5, 23, 121]. These formulations imply that pressure drop per
unit of height is independent of the depth of the grain. This assumption is not correct,
because the density and porosity of grain in the silo changes along the height due to
compaction from grain load. Fluctuations of filling stream may introduce additional
non-homogeneity of the bedding. Li and Sokhansanj [95] concluded that Ergun’s
equation could be the basis for a generalized model of airflow resistance through
agricultural products. Ergun [49] hypothesized that the pressure drop was the summation
of viscous and kinetic energy loses. The general equation takes a form as [95]:
û3
L
⎛
2
2
2 1 − % !90
k1
1 − % !90
= aV0
+ bV0
= 2fE
= 2⎜
+ k ⎟
3
2
,
3
% D
p
( Re) (11.1)
dp
% dp
where:
û3 – pressure drop,
L – length,
⎝
⎞
⎠