5 Development of a Dynamic-Physical Process Model for Sieving
173
Benchmarking of Steady State Spatially Resolved Screening Models
In a second step, the simulation results presented in section “Numerical Investigations” are used to benchmark the steady state spatially resolved screening process
models described in Sect. 3.2.2. Thereby the fraction retained on the continuous
screening apparatus in dependence on screen length obtained from the DEM simulations is compared with data from spatially resolved phenomenological models which
are fitted to the DEM results by adjusting their respective model parameters. For the
benchmarking of a larger number of investigations, an average deviation of the simulated and process model predicted fraction retained is calculated for models, where
the whole fine material is considered as one lumped undersized fraction by using
j
k=1 |E mod (k) − E sim (k)|
/j, where j is the total number of considered positions
along the screen k. For models in which the different undersized particle classes i are
considered as fractions (Nos. 4, 8, 9, 10, 11, 13), the average of the obtained fractional
deviations is calculated by using
l
i=1
j
k=1 |E mod (i, k) − E sim (i, k)|
/( j · r ),
where r is the total number of undersized fractions. The screen of length 0.35 m in
this process is divided into intervals of 0.01 m.
In Fig. 13 the summed up particle passage deviations between steady state spatially
resolved screening models according to Sect. 3.2.2 and discrete element simulations
for spheres (Fig. 13a), double cones (Fig. 13b) and volume equivalent cylinders
(Fig. 13c) for all investigated variations (see Table 4) are shown.
Regardless of shape, the models that do not account for the division of undersized particle fractions (Nos. 1, 2, 3, 5, 6, 7 and 12) are the fastest to adjust and
get low deviations as only the lumped fraction retained curve is to be fitted to the
simulation results instead of the fraction retained curves of all undersized particle
classes. Among these models, the model by Soldinger (No. 12) followed by Andreev
et al. (No. 2), Subasinghe et al. (No. 6) and Grozubinsky et al. (Nos. 5, 7) show the
lowest overall deviations when spheres as shape are considered (Fig. 13a). All of
these models use more than one adjustable parameter. The models Nos. 5 and 7 can
be easily reduced to the rate law (model No. 1); for the screening intensity β 1 the
term ex p(−βt) becomes zero (see [122]). In both models the additionally introduced
coefficient of proportionality q provides an improvement in accuracy for screening
if many different size classes are under consideration. The model by Trumic and
Magdalinovic (No. 3) shows the largest deviations of the models, which does not
take into account the division of undersized particle fractions due to the use of only
one adjustable parameter.
For a model that accounts for the division of undersized particle fractions, relatively low deviations are obtained by the model of Standish (No. 4). This is achieved
by using one adjustable parameter per size class. Although the model by Ferrara
et al. (No. 11) exhibits overall minor deviance and accounts for different particle size
classes as well as uses only a few adjustable parameters, it has the disadvantage of
a long adjustment time because it has to be fitted iteratively. Slightly larger deviations are visible for the fractioned model by Soldinger (No. 13) with the benefit of a
shorter fitting time. The probabilistic model by Subasinghe et al. (No. 8) is adjusted
173
Benchmarking of Steady State Spatially Resolved Screening Models
In a second step, the simulation results presented in section “Numerical Investigations” are used to benchmark the steady state spatially resolved screening process
models described in Sect. 3.2.2. Thereby the fraction retained on the continuous
screening apparatus in dependence on screen length obtained from the DEM simulations is compared with data from spatially resolved phenomenological models which
are fitted to the DEM results by adjusting their respective model parameters. For the
benchmarking of a larger number of investigations, an average deviation of the simulated and process model predicted fraction retained is calculated for models, where
the whole fine material is considered as one lumped undersized fraction by using
j
k=1 |E mod (k) − E sim (k)|
/j, where j is the total number of considered positions
along the screen k. For models in which the different undersized particle classes i are
considered as fractions (Nos. 4, 8, 9, 10, 11, 13), the average of the obtained fractional
deviations is calculated by using
l
i=1
j
k=1 |E mod (i, k) − E sim (i, k)|
/( j · r ),
where r is the total number of undersized fractions. The screen of length 0.35 m in
this process is divided into intervals of 0.01 m.
In Fig. 13 the summed up particle passage deviations between steady state spatially
resolved screening models according to Sect. 3.2.2 and discrete element simulations
for spheres (Fig. 13a), double cones (Fig. 13b) and volume equivalent cylinders
(Fig. 13c) for all investigated variations (see Table 4) are shown.
Regardless of shape, the models that do not account for the division of undersized particle fractions (Nos. 1, 2, 3, 5, 6, 7 and 12) are the fastest to adjust and
get low deviations as only the lumped fraction retained curve is to be fitted to the
simulation results instead of the fraction retained curves of all undersized particle
classes. Among these models, the model by Soldinger (No. 12) followed by Andreev
et al. (No. 2), Subasinghe et al. (No. 6) and Grozubinsky et al. (Nos. 5, 7) show the
lowest overall deviations when spheres as shape are considered (Fig. 13a). All of
these models use more than one adjustable parameter. The models Nos. 5 and 7 can
be easily reduced to the rate law (model No. 1); for the screening intensity β 1 the
term ex p(−βt) becomes zero (see [122]). In both models the additionally introduced
coefficient of proportionality q provides an improvement in accuracy for screening
if many different size classes are under consideration. The model by Trumic and
Magdalinovic (No. 3) shows the largest deviations of the models, which does not
take into account the division of undersized particle fractions due to the use of only
one adjustable parameter.
For a model that accounts for the division of undersized particle fractions, relatively low deviations are obtained by the model of Standish (No. 4). This is achieved
by using one adjustable parameter per size class. Although the model by Ferrara
et al. (No. 11) exhibits overall minor deviance and accounts for different particle size
classes as well as uses only a few adjustable parameters, it has the disadvantage of
a long adjustment time because it has to be fitted iteratively. Slightly larger deviations are visible for the fractioned model by Soldinger (No. 13) with the benefit of a
shorter fitting time. The probabilistic model by Subasinghe et al. (No. 8) is adjusted