160
D. Markauskas and H. Kruggel-Emden
Table 1
(continued)
Model number and origin
Major equations
Adjustable
parameters
Features
12. Soldinger; not
resolving undersized
fractions [9]
E
j+1
= k
j B
j
t
j+1
− t
j
+ E
j
t
j
= l
j
/v
B
j+1
= B
j
+
c
j
1
− S
j
− k
j B
j
t
j+1
− t
j
j:
time index
k
j
= b
1
− E
j
; c
j
= f
w q
, w d
B:
fractional mass of undersized particles in bottom layer
S:
fractional mass of undersized particles stratified into bottom layer
E:
fractional mass of undersized particles passed through apertures
v
(transport
velocity)
w
q (dependent
on proportion of
undersized
material)
w
d (dependent
on width of
particle size
distribution)
b
(dependent on
particle size)
history dependent,
bed depth,
stratification
13. Soldinger; resolving
undersized fractions [10]
E
i, j+1
= k
i, j B
i, j
t
j+1
− t
j
+ E
i, j ; t
j
= l
j
/v;
i:
particle class; j:
time index
E
j
=
n
i=1 E
i, j ; B
j
=
n
i=1 B
i, j ; n:
number of undersized particle classes
B
i, j+1
= B
i, j
+
c
i, j
S
i,∞
− S
i, j
− k
i, j B
i, j
t
j+1
− t
j
;
k
i, j
= b
i
1
− E
i, j
; c
i, j
= f
w q
, c
d,i
B
i : fractional mass of undersized particles in bottom layer
S
i : fractional mass of undersized particles stratified into bottom layer
E
i : fractional mass of undersized particles passed through apertures
v
(transport
velocity)
w
q (dependent
on proportion of
undersized
material)
b
1, …, b
n
(dependent on
particle diameter
and aperture size)
History
dependent,
fractioned, bed
depth,
stratification