5 Development of a Dynamic-Physical Process Model for Sieving
175
The initial (base) case with delayed/shifted particle passage and a resulting flat
fraction retained curve is comparatively easy to model. This results in minor deviations for most of the investigated models. Also simulation cases with immediate
particle passage and strongly decreasing fraction retained curves show no major
discrepancies between models and DEM results, likewise. Greater differences occur
when the fraction retained curves stagnate over a certain length of the screen or when
they are decreasing unevenly. The models that account for the division of undersized
particle fractions, in particular models Nos. 8–10, have greater difficulties when the
differences between the passage rates of undersized particles are erratic. This could
be the case, if the particles are transported with higher velocity on the screen when
e.g. a large amplitude, frequency or inclination angle is used.
In the considered cases using double cones (Fig. 13b) the models by Grozubinsky
et al. (Nos. 5, 7) and Andreev et al. (No. 2) followed by the model by Subasinghe et al.
(No. 6) are adjusted to the simulation results with the smallest deviations. Although
model No. 4 needs many adjustable parameters, it demonstrates comparatively large
deviations because it does not consider the shape of the particles. Again, model No.
11 is the model with lowest deviations which accounts for the division of undersized
particles in fractions without adjusting parameters for each size class. For the case of
double cones, however, it leads to larger deviations and model No. 8 by Subasinghe
et al. achieves nearly the same results with less computations. With the models by
Nakajima et al. (No. 9) and Deghani et al. (No. 10), the largest deviations are obtained
again.
The models by Grozubinsky et al. (Nos. 5, 7) demonstrate the smallest deviations for volume equivalent cylinders (Fig. 13c). Here, the probabilistic model No.
7 achieves slightly better results than the deterministic model, since the dispersion
of the particles is taken into account. Unlike the two former investigated shapes
(spheres and double cones), model No. 12 by Soldinger does not get the lowest
deviations caused by randomly passing particles with an equivalent diameter larger
than the aperture size. For the same reason, model No. 13 by Soldinger shows more
deviations in comparison to the other shapes. Again, model No. 3 by Trumic and
Magdalinovic reveals comparatively large deviations because of its simplicity and
not considering the particle shape. For the volume equivalent cylinders, model No. 11
by Ferrara et al. shows only slightly larger deviations in the comparison to model
No. 4 by Standish, which requires much more adjustable parameters. In addition,
model No. 11 has much lower deviations than model No. 3, in which only the undersized fraction as a lumped entity is considered. For volume equivalent cylinders,
model No. 10 by Deghani et al. shows the largest deviations due to its condition for
the probability function and because the use of only one parameter for all particle
size classes. The revised model No. 9 with a similar model structure and the same
number of model parameters gives comparatively lower deviations.
175
The initial (base) case with delayed/shifted particle passage and a resulting flat
fraction retained curve is comparatively easy to model. This results in minor deviations for most of the investigated models. Also simulation cases with immediate
particle passage and strongly decreasing fraction retained curves show no major
discrepancies between models and DEM results, likewise. Greater differences occur
when the fraction retained curves stagnate over a certain length of the screen or when
they are decreasing unevenly. The models that account for the division of undersized
particle fractions, in particular models Nos. 8–10, have greater difficulties when the
differences between the passage rates of undersized particles are erratic. This could
be the case, if the particles are transported with higher velocity on the screen when
e.g. a large amplitude, frequency or inclination angle is used.
In the considered cases using double cones (Fig. 13b) the models by Grozubinsky
et al. (Nos. 5, 7) and Andreev et al. (No. 2) followed by the model by Subasinghe et al.
(No. 6) are adjusted to the simulation results with the smallest deviations. Although
model No. 4 needs many adjustable parameters, it demonstrates comparatively large
deviations because it does not consider the shape of the particles. Again, model No.
11 is the model with lowest deviations which accounts for the division of undersized
particles in fractions without adjusting parameters for each size class. For the case of
double cones, however, it leads to larger deviations and model No. 8 by Subasinghe
et al. achieves nearly the same results with less computations. With the models by
Nakajima et al. (No. 9) and Deghani et al. (No. 10), the largest deviations are obtained
again.
The models by Grozubinsky et al. (Nos. 5, 7) demonstrate the smallest deviations for volume equivalent cylinders (Fig. 13c). Here, the probabilistic model No.
7 achieves slightly better results than the deterministic model, since the dispersion
of the particles is taken into account. Unlike the two former investigated shapes
(spheres and double cones), model No. 12 by Soldinger does not get the lowest
deviations caused by randomly passing particles with an equivalent diameter larger
than the aperture size. For the same reason, model No. 13 by Soldinger shows more
deviations in comparison to the other shapes. Again, model No. 3 by Trumic and
Magdalinovic reveals comparatively large deviations because of its simplicity and
not considering the particle shape. For the volume equivalent cylinders, model No. 11
by Ferrara et al. shows only slightly larger deviations in the comparison to model
No. 4 by Standish, which requires much more adjustable parameters. In addition,
model No. 11 has much lower deviations than model No. 3, in which only the undersized fraction as a lumped entity is considered. For volume equivalent cylinders,
model No. 10 by Deghani et al. shows the largest deviations due to its condition for
the probability function and because the use of only one parameter for all particle
size classes. The revised model No. 9 with a similar model structure and the same
number of model parameters gives comparatively lower deviations.