180
D. Markauskas and H. Kruggel-Emden
strongly lengthened. For double cones, it can be seen exemplarily that residence
times are increased in the bottom layer for larger amplitudes (Fig. 15c) which reduces
overall particle passage (Fig. 15a).
The second study (Fig. 15b) deals with the variation of the frequency (Table 5).
Here, also the two lowest frequencies result in the least particle passage with under
50% after t = 40 s, due to a low stratification. In addition, the particles are in
an immobile state, leaving them few opportunities to come in direct contact with
apertures, forcing them to reside an extended period of time in the bottom layer
independent of particle shape (Fig. 15d). All the other settings show similar results
for the overall passage throughout the first 10 s of the investigation, but with final
residual mass on the screen varying between 0 and 20% at the end of the screening
time. The frequency value of 27.6 Hz shows the best passage ability over more than
half of the simulation time, before being surpassed by the frequency of 34.5 Hz.
Initially, the simulations use a stroke angle of 90° to the horizontal (Table 5)
which in the third investigation is changed to an oscillating movement consisting
of two stroke angles with varying horizontal and vertical components (Fig. 16a).
An alternating stroke angle of 45°/135° significantly improves the particle passage
for spheres, however reduces the passage of complex shaped particles. In contrast,
a stroke angle of 30°/150° increases the screening efficiency of all particle shapes
because particles have enhanced chances to enter an aperture and pass it. Using an
angle of 60°/120° significantly reduces the passage only for cylindrical particles.
The above mentioned observations can also be confirmed by the enhanced residence
times of non-spherical particles in the case of 60°/120° and 45°/135° stroke angles
as well as by the reduced residence times in the bottom layer for spheres for stroke
angles of 45°/135° and for all particle shapes for stroke angles of 30°/150° (Fig. 16c).
In general, a combination of a stronger horizontal with a less intense vertical motion
component as e.g. for 30°/150° facilitates more possibilities to pass the screen openings for all undersized particle shapes, while a combination of a stronger vertical with
a weaker horizontal motion forces the oversized elongated non-spherical particles
to align vertically with the screening surface, which leads to pronounced pegging of
the apertures.
The fourth investigation deals with a variation of total particle mass (Fig. 16b).
Due to a lower bed height and thus a faster stratification, the application of a lower
mass leads to a faster particle passage. In comparison, particles in a thicker bed layer,
which is caused by a larger particle mass, take extra time to stratify and then to pass.
The probability of pegging is larger for particle masses with more oversized particles
being present. As a result, the undersized particles remain longer in the bottom layer
when more mass is applied to the screen (Fig. 16d).
Comparison of Phenomenological Screening Process Models
The simulation results described in section “Numerical Investigations” are used
to benchmark the phenomenological screening models as outlined in Table 2. An
average deviation of the simulated and model predicted mass is calculated for
D. Markauskas and H. Kruggel-Emden
strongly lengthened. For double cones, it can be seen exemplarily that residence
times are increased in the bottom layer for larger amplitudes (Fig. 15c) which reduces
overall particle passage (Fig. 15a).
The second study (Fig. 15b) deals with the variation of the frequency (Table 5).
Here, also the two lowest frequencies result in the least particle passage with under
50% after t = 40 s, due to a low stratification. In addition, the particles are in
an immobile state, leaving them few opportunities to come in direct contact with
apertures, forcing them to reside an extended period of time in the bottom layer
independent of particle shape (Fig. 15d). All the other settings show similar results
for the overall passage throughout the first 10 s of the investigation, but with final
residual mass on the screen varying between 0 and 20% at the end of the screening
time. The frequency value of 27.6 Hz shows the best passage ability over more than
half of the simulation time, before being surpassed by the frequency of 34.5 Hz.
Initially, the simulations use a stroke angle of 90° to the horizontal (Table 5)
which in the third investigation is changed to an oscillating movement consisting
of two stroke angles with varying horizontal and vertical components (Fig. 16a).
An alternating stroke angle of 45°/135° significantly improves the particle passage
for spheres, however reduces the passage of complex shaped particles. In contrast,
a stroke angle of 30°/150° increases the screening efficiency of all particle shapes
because particles have enhanced chances to enter an aperture and pass it. Using an
angle of 60°/120° significantly reduces the passage only for cylindrical particles.
The above mentioned observations can also be confirmed by the enhanced residence
times of non-spherical particles in the case of 60°/120° and 45°/135° stroke angles
as well as by the reduced residence times in the bottom layer for spheres for stroke
angles of 45°/135° and for all particle shapes for stroke angles of 30°/150° (Fig. 16c).
In general, a combination of a stronger horizontal with a less intense vertical motion
component as e.g. for 30°/150° facilitates more possibilities to pass the screen openings for all undersized particle shapes, while a combination of a stronger vertical with
a weaker horizontal motion forces the oversized elongated non-spherical particles
to align vertically with the screening surface, which leads to pronounced pegging of
the apertures.
The fourth investigation deals with a variation of total particle mass (Fig. 16b).
Due to a lower bed height and thus a faster stratification, the application of a lower
mass leads to a faster particle passage. In comparison, particles in a thicker bed layer,
which is caused by a larger particle mass, take extra time to stratify and then to pass.
The probability of pegging is larger for particle masses with more oversized particles
being present. As a result, the undersized particles remain longer in the bottom layer
when more mass is applied to the screen (Fig. 16d).
Comparison of Phenomenological Screening Process Models
The simulation results described in section “Numerical Investigations” are used
to benchmark the phenomenological screening models as outlined in Table 2. An
average deviation of the simulated and model predicted mass is calculated for