352
M. Weers et al.
and Mular [10]. In this context, the formation of particle layers, the so called stratification, where finer particles move downwards across the openings between larger
particles, has to be considered. In this way, fine particles may pass the meshes or may
be reflected by collisions with the sieve wires. According to the model by Molerus
[4] the fractional separation efficiency T(x) can be described by:
T(x) = 1/[1 + (x t /x)
2 exp(k[1 − (x t /x)
2
])]
(1)
where x is the particle size, x t the cut size and k represents a coefficient for the
sharpness of cut.
Also for the deflector wheel separators, the model by Molerus [4] was applied.
It was later improved by Rumpf [11], Senden [12, 13], Schubert [14] and finally by
Husemann [15]. As a simplification, all these models assume a steady state process,
for which the classification corresponds to a counter flow separation of single particles. The forces at work are on the one side the drag force of the gas flow radially
passing the wheel blades inwards and on the other hand, the centrifugal force directed
outwards deflecting coarser particles.
In his theoretically based model, Husemann considered the geometry and operational parameters where, however, also four fitting parameters were used. In this way,
a calibration is necessary to find the appropriate parameter values for the separation
characteristics of a classification process. In addition, particle-particle interactions
and particle-wall collisions with the blades of the deflector wheel were neglected.
However, since deflector wheel separators are usually operated at high loadings [16]
other approaches need to be developed to capture the underlying physical principles
in a sound manner.
The objectives of this chapter are to give deeper insights into the characteristics
and the analogy of flow and sieve classification and to develop optimized models for
steady state and instationary operations of the classification processes. For flow and
sieve classification the model by Molerus (Eq. 1) will serve as starting point, but it
will experience some modifications.
2 Deflector Wheel Classifier
2.1 Model Considerations
The deflector wheel separator used here is an ATP 50 (Hosokawa Alpine) which is
schematically shown in Fig. 2 (left). The powder, which is added by a conveying
screw, approaches the rotating wheel carried by an air stream. Between the blades,
the particles experience a drag force inwards by the carrier air which is counteracted
by the centrifugal force originating from the vortex induced by the rotating wheel
(Fig. 1, left). Therefore, it is tempting to calculate the cut size from a force balance on
individual particles as done by Molerus leading to the Eq. (1). However, for the ATP
50 used here, previous investigations have shown that, especially for particles with
M. Weers et al.
and Mular [10]. In this context, the formation of particle layers, the so called stratification, where finer particles move downwards across the openings between larger
particles, has to be considered. In this way, fine particles may pass the meshes or may
be reflected by collisions with the sieve wires. According to the model by Molerus
[4] the fractional separation efficiency T(x) can be described by:
T(x) = 1/[1 + (x t /x)
2 exp(k[1 − (x t /x)
2
])]
(1)
where x is the particle size, x t the cut size and k represents a coefficient for the
sharpness of cut.
Also for the deflector wheel separators, the model by Molerus [4] was applied.
It was later improved by Rumpf [11], Senden [12, 13], Schubert [14] and finally by
Husemann [15]. As a simplification, all these models assume a steady state process,
for which the classification corresponds to a counter flow separation of single particles. The forces at work are on the one side the drag force of the gas flow radially
passing the wheel blades inwards and on the other hand, the centrifugal force directed
outwards deflecting coarser particles.
In his theoretically based model, Husemann considered the geometry and operational parameters where, however, also four fitting parameters were used. In this way,
a calibration is necessary to find the appropriate parameter values for the separation
characteristics of a classification process. In addition, particle-particle interactions
and particle-wall collisions with the blades of the deflector wheel were neglected.
However, since deflector wheel separators are usually operated at high loadings [16]
other approaches need to be developed to capture the underlying physical principles
in a sound manner.
The objectives of this chapter are to give deeper insights into the characteristics
and the analogy of flow and sieve classification and to develop optimized models for
steady state and instationary operations of the classification processes. For flow and
sieve classification the model by Molerus (Eq. 1) will serve as starting point, but it
will experience some modifications.
2 Deflector Wheel Classifier
2.1 Model Considerations
The deflector wheel separator used here is an ATP 50 (Hosokawa Alpine) which is
schematically shown in Fig. 2 (left). The powder, which is added by a conveying
screw, approaches the rotating wheel carried by an air stream. Between the blades,
the particles experience a drag force inwards by the carrier air which is counteracted
by the centrifugal force originating from the vortex induced by the rotating wheel
(Fig. 1, left). Therefore, it is tempting to calculate the cut size from a force balance on
individual particles as done by Molerus leading to the Eq. (1). However, for the ATP
50 used here, previous investigations have shown that, especially for particles with