Extraction characteristics of bulk materials from silos Part 2: Experimental results

4 Test results
The test results for test series 1 and 4 are given below (Table 1; part 1). A complete evaluation can be found in [18].
 
4.1 Flow profiles
Knowledge of the flow profiles is very important for explaining and interpreting the stresses that occur in silos. The relationship between the flow profiles and the corresponding stresses is known from mass flow and funnel flow silos [6]. During the trials to determine the flow profiles the test silo described in Part 1 was first filled uniformly up to the specified mark. The sloping surface of the bulk material caused by the central filling was then levelled off and covered with a layer of black plastic pellets (Fig. 10a). This procedure for recording flow profiles is often used in the literature, sometimes in modified form, for observing emptying processes [19, 21, 22]. The bulk material was then extracted and immediately returned again to the top of the test silo. The surface of the bulk material was continuously levelled (Fig. 10b) in order to prevent the sloping surface of the bulk material from influencing the flow profile. Figure 11 shows a diagrammatic representation of the flow profile that was obtained during test series 1. The screw geometry used had a constant pitch and did not lead to a uniform extraction rate over the intake length of the screw. As expected, the extraction took place principally from the rear section. This confirmed the supposition that in each case the first flight of the screw in the rear part fills with bulk material and essentially no more bulk material is extracted over the rest of the intake length. This results in a dead zone in the front part of the silo that hardly moves at all. Funnel flow is established. The flow profiles for screw geometry S2 (Fig. 8; part 1), i.  e. with graduated progression, were meas­ured in test series 4 and 5. Figure 12 shows the flow profile that was obtained in test series 4. The screw geometry used had a graduated, uniform, extraction rate over the entire intake length. In contrast to the flow profile of test series 1 (Fig. 11) no dead zone is formed and the bulk material flow extends over the entire cross-section of the silo. With the flow profile of test series 1 there were significant differences in movement between the front wall and the rear wall, but this did not occur in test series 4. The bulk material sinks down virtually identically at the front and rear walls. The extraction of the bulk material also takes place uniformly over the width of the silo. Mass flow is established.
 
4.2 Wall normal stresses
The investigations described in this section were carried out during the emptying process from the test silo. The measurements were made during the steady-state emptying condition, i.e. the bulk material that had been extracted was immediately recycled back to the top of the test silo. This kept the level of material in the silo at a constant height. The surface of the bulk material was constantly levelled to exclude any influence of the sloping surface. The steady-state emptying condition is defined as the state at which there are no more substantial changes in the measured wall normal stresses. After the first test series it was apparent that varying the screw rotational speeds had no significant effect on the measured wall normal stresses. The rest of the investigations were therefore carried out at constant screw speed. As expected, however, the screw geometry and screw pairing were seen to have an effect. Each of the trials was ended when the measured wall normal stresses no longer changed with time.
 
The measured wall normal stresses in the steady-state emptying condition for extraction screws with constant flight pitch (test series 1) are shown in Figure 13. As shown in Figure 7, the front wall is the end at which the bulk material is extracted. The rear wall of the test silo is shown on the right. The wall normal stresses on the two side walls are also shown. The radii of the circles are proportional to the stresses. The centre point of each circle shows the respective positions of the stress meas­uring cells. The stress distribution for test series 1 can be reconstructed with the aid of the observed flow profiles (see Section 4.1). Uneven extraction of the bulk material was obtained for the extraction screws with constant flight pitch, as ­already described in Section 4.1. The flow profile for test series 1 shown in Figure 11 confirms the uneven extraction of bulk material. The convergent flow of bulk material in the rear part of the silo means that an effectively radial stress field is formed there. The moving bulk material is supported on the static bulk material and causes additional loading of the static bulk material. As a result, larger wall normal stresses are formed at the dead zones than at the moving zones [5, 8]. This relationship is reflected in the wall normal stresses. The bulk material is only extracted from the rear, so very small stresses are formed at the rear wall and the rear part of the two side walls. The wall normal stresses rise sharply in the direction of transport. The largest stresses occur at the lower part of the front wall. This is caused partly by the formation of dead zones, where the stresses are always larger than in moving regions. A second effect, however, is caused by the extraction screws. The equilibrium of forces means that shear stresses acting in the direction of transport due to the rotation of the screws are transmitted to the bulk material located above the screws. This causes the wall normal stresses to increase continuously in the direction of transport. The shear forces are governed by the transport angle, which is obtained through the pitch.
 
The measured wall normal stresses are shown in Figure 14 for the steady-state emptying condition using extraction screws with progressive pitch (test series 4). As already described for the test series in the previous section, the stress distribution for the test series using extraction screws with progressive pitch can also be explained with the aid of the observed flow profiles (Fig. 12). It can be seen from the flow profile that the bulk ­material is extracted evenly over the entire length of the silo. This explains the more uniform stress distribution throughout the silo. This becomes particularly clear at the side walls in ­Figure 14. The measured wall normal stresses are of the same order of magnitude, especially in the two upper measuring levels.
 
What cannot be explained by the flow profiles are the substantially higher wall normal stresses at the front wall and the front corners of the two side walls (Fig. 14). Although no dead zones are formed, progressively higher wall normal stresses than in the rear part of the silo occur in the direction of transport. This relationship can be explained by the shear stresses that act in the direction of transport due to the rotation of the screws. Because of the equilibrium of forces the shear stresses acting in the direction of transport due to the rotation of the screws are transmitted to the bulk material located above the screws. This causes the wall normal stresses to increase continuously in the direction of transport. The shear forces are governed by the transport angle, which is obtained through the pitch. The dimensionless wall normal stress S is shown below as a function of distance from the front wall. Only the lowest level of measuring cells is taken into account. The dimensionless normal stress S is defined as follows:
 
S =  w(1)
       f
where:
w    =    wall normal stress in the steady-state emptying condition
f    =    wall normal stress in the filling state
 
The dimensionless wall normal stresses for test series 1 and 4 are compared in Figure 15. The horizontal straight line, which intersects the ordinate at the value 1, corresponds to the filling state. The values at distances 0 mm and 1500 mm correspond to the wall normal stresses at the front wall and rear wall respectively. By referring the stress values to the filling state it can be seen clearly from Figure 15 that the bulk material is extracted from the rear. In test series 1, i.  e. using extraction screws with constant pitch, the wall normal stresses drop to values that are about 50  % below the wall normal stresses in the filling state. The wall normal stresses increase again with decreasing distance from the front wall and at both side walls eventually reach about 2.5-times the stresses in the filling state. At the front wall the wall normal stresses in the steady-state emptying condition are actually 3.25-times the stresses in the filling state.
 
The dimensionless wall normal stress for test series 4 basically follows a similar pattern. The difference, however, is that the stress curve is flatter from back to front. In the rear part of the silo the stresses do not drop as far as in test series 1. In fact the wall normal stress in the steady-state emptying condition remains at virtually the same order of magnitude as the stress in the filling state. As already explained, this is because with extraction screws with constant pitch an effectively radial stress field (passive stress state) is obtained in the rear part of the silo. For the extraction screws with progressive pitch the bulk ma­terial is extracted over the entire length of the silo. No passive stress state is obtained and the active stress state is retained even during extraction of the bulk material.
 
4.3 Characteristic torque curve
When dimensioning silo extraction systems the determination of the size of the drive is the most important criterion alongside the consideration of the process engineering aspects. The determining parameters when selecting the drive are the rotational speed and the torque. The rotational speed is dictated by the process engineering requirements, but the requisite torque is a parameter that is specific to the plant and the bulk material. All the torque curves shown exhibit basically the same features. After the extraction screw has been switched on the torque rises directly to the maximum value and then drops immediately again to a lower, steady-state, value. During the rest of the test period the torque remains close to this steady-state value (Figs. 16, 17). The initial torque peak is termed the start-up torque and characterizes the peak value when the plant is started up or switched on. The start-up torque is usually given as a multiple of the subsequent, ideally constant, torque:
 
S/A =  Mstart-up(2)
           Maverage
The start-up torque phenomenon has also been observed by Schumacher [23] and Bortolamasi & Fottner [24]. As explained by Schwedes and Schulze [6], the reason lies essentially in the changeover from active to passive stress state that occurs during the first start-up after the filling. The greatest vertical stress v occurs after a silo has been filled, as explained in [13] for a silo with cone. After the emptying has started the active stress state that is present changes over to the passive stress state and the vertical stress at the outlet cross-section drops abruptly. There is a corresponding abrupt drop in the extraction force Fh for the extraction device, which initially has to overcome the large vertical stress after the filling. The start-up peak can be as much as 10-times the steady-state value [5, 6]. This changeover is due to the transition from the active to the passive stress field and therefore always occurs in silos with conical bases. There is actually no cone in the rectangular test silo used but, as explained above, there is a convergent flow of bulk material in the rear part of the silo when using extraction screws with constant pitch, so that the bulk material forms a cone there. This also explains the increased start-up torque for the extraction screws with constant pitch (test series 1 to 3) when compared with steady-state operation. An oscillation, which is caused by the high measurement rate, is superimposed on the torque curve (Fig. 16). This superimposed oscillation is a result of the rotation of the extraction screws. Tests with different rotational speeds confirm that the frequency is directly proportional to the screw rotational speed.

Figure 16 shows the torque curve for test series 1, i.  e. when the two extraction screws with constant pitch rotate towards the centre. The short-term torque peak after the start-up and the subsequent drop in torque to a steady-state value are clearly recognizable. If the start-up torque is correlated with the average, steady-state, torque then a value of 1.83-times the steady-state torque is obtained for the right-hand extraction screw and 1.85-times for the left-hand extraction screw. If the steady-state torque is correlated with the start-up torque then values of 55  % and 54  % respectively are obtained for the steady-state torques of the two extraction screws.

The torque curves for test series 4, using extraction screws with progressive pitch, are shown in Figure 17. The two extraction screws rotate towards the centre. Torque peaks can also be detected here at the start, followed by a drop to steady-state torques. These torque peaks are attributable to the initial changeover from the active to the passive stress state in the same way as for the explanations given above for the extraction screws with constant pitch. The superimposed oscillations that also occur and are caused by the rotation of the extraction screws each exhibit relatively large amplitudes and, as with test series 1, are in phase with each other. The relatively large amplitudes are attributable to the vertical movement of the bulk material in the extraction screws over the entire length of the silo. The symmetrical loading of the two extraction screws leads to virtually identical values. The start-up torque of the right-hand extraction screw is 2.36-times its steady-state torque and that of the left-hand extraction screw is 2.29-times its steady-state torque. If the steady-state torque is correlated with the start-up torque then values of 42.4  % and 43.6  % respectively are obtained for the steady-state torques of the two extraction screws.
Comparison of the torque curves in Figures 16 and 17 leads to the following conclusions:
 
–    If funnel flow is present (test series 1), then the steady-state torques are larger than for mass flow (test series 4)
–    The large amplitudes of the superimposed oscillations for mass flow are attributable to the fact that the shearing at the screw flight/outlet edge area is subject to greater fluctuations when the bulk material flows into this area from above
 –    The differences between mass flow and funnel flow are greater when the silo consists of a vertical shaft and cone and/or if the working length of the screw is greater [18]
 
5    Conclusions
Experimental investigations were carried out with a rectangular silo as part of this work. The focus was on the stress states during emptying by two silo extraction screws and the relationships between the wall normal stresses, the flow profiles and the requisite torques of the extraction screws. A series of tests were carried out in the test silo using different extraction screws. Extraction screws with and without progression in the direction of transport were used, in which the progression was obtained by changing the pitch. The direction of rotation of the extraction screws in the test series was also varied. At first the two extraction screws both rotated towards the centre and then they both rotated towards the outside. For the extraction screws with constant pitch a test series was also carried out with both extraction screws rotating in the same direction. When determining the flow profiles it was established that for the extraction screws with constant pitch the bulk material was, as expected, extracted almost exclusively from the rear. The convergent bulk material flow observed in the rear part of the silo corresponds to the classical funnel flow profile and is independent of the direction of rotation of the extraction screws. The direction of rotation of the extraction screws only affects the bottom part of the silo. With the extraction screws with progressive pitch the bulk material was extracted over the entire length of the silo, thereby ensuring mass flow.
 
In agreement with the measured flow profiles it was established that the wall normal stresses are lower in the moving zones than in the static zones. For the extraction screws with constant pitch, with which the bulk material is extracted mainly from the rear part of the silo, this can be explained by the radial stress field that is formed there. The moving bulk material is supported on the static bulk material and therefore causes additional loading on the static bulk material. Rising wall normal stresses in the direction of transport were observed for all test series. Shear stresses acting in the direction of rotation are transferred to the bulk material above the screws by the rotation of the screws. This causes a progressive increase in the wall normal stresses in the direction of rotation. The shear forces acting at the outer circumference of the extraction screws are formed in accordance with the transport angle (determined by the pitch). As a result the direction of rotation of the extraction screws has an influence on the stress distribution in the front part of the silo.
 
Qualitative and quantitative information about the increases in stress in the test silo caused by the extraction by the two extraction screws were derived from the measurements of the wall normal stresses in the test silo. The expected stress changes caused by the extraction are shown qualitatively in [18] for other silo geometries. During the determination of the torques it was shown that the extraction screws with constant pitch, which cause funnel flow, basically require a higher torque than the extraction screws with progressive pitch that lead to mass flow. A dependence on the direction of rotation was also established for all extraction screws. The extraction screws rotating towards the centre required higher torques than the extraction screws rotating towards the outside.
 
Further investigations have already been carried out with other bulk materials. In particular, the investigations included bulk materials with poor flow characteristics, such as sewage sludge and secondary fuels that had been processed in different ways. The findings and relationships obtained can be applied reliably to industrial plants.