170
D. Markauskas and H. Kruggel-Emden
is released. Although the support for horizontal transport is lower, a stronger vertical
motion component (vibration plane tilted by 60°) speeds up the transport of spheres
and thereby also improves the particle passage due to a faster removal of pegged
particles. For double cones, the change in the stroke angle in both directions leads
to delayed particle passage. A stroke angle of 30° leads to particle accumulation and
therefore slower particle transport and longer residence times. In contrast, a stroke
angle of 60° leads to delayed/shifted passage. For volume equivalent cylinders, a
decreased stroke angle has only minor effects on the passage of particles, although
particle accumulation is observed. An increased stroke angle leads to a reduced
transport, delayed particle passage and less near mesh particles in the overflow.
The fourth variation takes into account the particle mass flow rate (Fig. 11b).
The probability of pegging for spheres is increased for larger particle mass flows
with more near orifice sized particles being present. Due to a larger bed height and
therefore a greater necessity for stratification, the use of higher mass flow results
in delayed/shifted particle passage and flat fraction retained curves (Fig. 11b). In
comparison, spheres in a shallower bed caused by a lower particle mass flow require
less time for stratification and hence passage, especially with so few near mesh sized
particles present that pegging is a rare event. If the mass flow is further increased from
˙
m = 150 g/s to ˙
m = 200 g/s, the percentage of undersized particles remaining on the
screen does not appear to change for spheres (Fig. 11b). Due to the higher mass flow
˙
m ≥ 100 g/s, the undersized particles, but also the oversized particles entrained in the
bed layer remain longer on the screen with slightly increased transport. An increase in
the mass flow in the case of complex shaped particles also leads to a delayed/shifted
particle passage (comp. Fig. 11b). However, the fraction retained curves remain steep
compared to spheres as there is no pegging of particles or blocking on the screen.
Benchmarking of Steady State Separation Curve Screening Models
In a first step, the steady state separation curve screening models are fitted and then
benchmarked against the data obtained in section “Numerical Investigations” by
the DEM. For the benchmarking over a larger number of investigations in case of
separation curve models an average deviation of the simulated and model predicted
separation curves is calculated with
r S
i S =1 |T sim (i S ) − T mod (i S )|
/r S where r S is
the total number of considered particle classes i S . Figure 12 shows the summed
up deviations between steady state separation curve screening models according to
Sect. 3.2.1 and simulations using the DEM with spheres (Fig. 12a), double cones
(Fig. 12b) and volume equivalent cylinders (Fig. 12c) according to Table 4.
With exception of model No. I by Dehghani et al., the investigated steady state separation curve screening models do not consider the particle shape. Nevertheless, the
differences between the adjusted models and the DEM results remain small because
the separation curve models are adjusted separately for each simulation since they do
not have any predictive capabilities. Separation curve screening models can easily
represent partition numbers forming an ideal separation curve (unit step function) or
a symmetrical S-shaped curve. For spheres (Fig. 12a), the closest result to an ideal
D. Markauskas and H. Kruggel-Emden
is released. Although the support for horizontal transport is lower, a stronger vertical
motion component (vibration plane tilted by 60°) speeds up the transport of spheres
and thereby also improves the particle passage due to a faster removal of pegged
particles. For double cones, the change in the stroke angle in both directions leads
to delayed particle passage. A stroke angle of 30° leads to particle accumulation and
therefore slower particle transport and longer residence times. In contrast, a stroke
angle of 60° leads to delayed/shifted passage. For volume equivalent cylinders, a
decreased stroke angle has only minor effects on the passage of particles, although
particle accumulation is observed. An increased stroke angle leads to a reduced
transport, delayed particle passage and less near mesh particles in the overflow.
The fourth variation takes into account the particle mass flow rate (Fig. 11b).
The probability of pegging for spheres is increased for larger particle mass flows
with more near orifice sized particles being present. Due to a larger bed height and
therefore a greater necessity for stratification, the use of higher mass flow results
in delayed/shifted particle passage and flat fraction retained curves (Fig. 11b). In
comparison, spheres in a shallower bed caused by a lower particle mass flow require
less time for stratification and hence passage, especially with so few near mesh sized
particles present that pegging is a rare event. If the mass flow is further increased from
˙
m = 150 g/s to ˙
m = 200 g/s, the percentage of undersized particles remaining on the
screen does not appear to change for spheres (Fig. 11b). Due to the higher mass flow
˙
m ≥ 100 g/s, the undersized particles, but also the oversized particles entrained in the
bed layer remain longer on the screen with slightly increased transport. An increase in
the mass flow in the case of complex shaped particles also leads to a delayed/shifted
particle passage (comp. Fig. 11b). However, the fraction retained curves remain steep
compared to spheres as there is no pegging of particles or blocking on the screen.
Benchmarking of Steady State Separation Curve Screening Models
In a first step, the steady state separation curve screening models are fitted and then
benchmarked against the data obtained in section “Numerical Investigations” by
the DEM. For the benchmarking over a larger number of investigations in case of
separation curve models an average deviation of the simulated and model predicted
separation curves is calculated with
r S
i S =1 |T sim (i S ) − T mod (i S )|
/r S where r S is
the total number of considered particle classes i S . Figure 12 shows the summed
up deviations between steady state separation curve screening models according to
Sect. 3.2.1 and simulations using the DEM with spheres (Fig. 12a), double cones
(Fig. 12b) and volume equivalent cylinders (Fig. 12c) according to Table 4.
With exception of model No. I by Dehghani et al., the investigated steady state separation curve screening models do not consider the particle shape. Nevertheless, the
differences between the adjusted models and the DEM results remain small because
the separation curve models are adjusted separately for each simulation since they do
not have any predictive capabilities. Separation curve screening models can easily
represent partition numbers forming an ideal separation curve (unit step function) or
a symmetrical S-shaped curve. For spheres (Fig. 12a), the closest result to an ideal