Discharge productivity for loose materials from a vessel

Abstract

UDC 622.831 Discharge (delivery) productivity with free flow of loose materials from a vessel is characterized by the throughput of the opening. It is necessary to consider this in planning storage capacity, unloading devices, units for processing loose materials, etc. However, until now there has been no satisfactory method for calculating discharge productivity. As a rule calculation is performed using empirical equations (nine equations from different authors are given in [1] containing 19 parameters in total) which give actual delivery values only for a narrow range of materials within a limited band of particle and discharge opening dimensions. The problem of discharge productivity for loose materials is closely connected with the distribution of particle velocities within the cross section of the discharge opening. Therefore the lack of success in resolving it mainly follows from the inadequacy of the ideas adopted as a basis about the distribution of velocities within the region of the discharge opening. It is assumed in [2-4] that particle velocities during outflow from an opening obey a parabolic rule and they have a maximum at the center of the hole. A basis for this was the hypothesis of dynamic arches which form above opening during discharge [5]. Outflow with this approach is represented as a result of the free fall of particles with a parabolic arch contour which also leads to a parabolic rule for velocity distribution at the instant particles pass through the discharge opening. However, the doubtful claims of the calculation methods used as a basis for the assumed distribution are placed in question by the following. Even in the case of the actual existence of dynamic arches there is no basis for unambiguous confirmation with respect to the features of velocity distribution in the space below the arch. The actual picture of these distribution may only be obtained from special experiments. We consider the results of experiments directed at resolving this problem. Tests were performed in a unit represented by a transparent rectangular bunker with a discharge opening located in its horizontal flat bottom fitted with a plunger. The bunker had a length (front dimension) b = 60 mm, width (side dimension) a = 10 mm, and height h = 100 mm. The width of the channel (discharge opening) was equal to the width a of the vessel, and length l could be varied within the limits of vessel length b. The loose material used was marble chips of fractions 0.1-0.25 mm; 0.25-0.5; 0.5-1; 0.7-1 mm. The average particle size d found by the standard procedure [7] for these fractions was 0.2; 0.35; 0.61; 0.8 mm, respectively. On loading the bunker in each test a layer of colored chips was formed at the front face at height h' < 1 (h' ~ 5 mm). The deformation picture for this layer realized with plunger movements served as a basis for conclusions with respect to particle velocity distribution within the cross section of the opening. Presented in Fig. 1 are the characteristic discharge stages for chip fraction 0.25-0.5 mm through openings of three sizes: l = 30, 15, and 6 mm. All of the pictures relate to the instant when particles of the control (colored) layer reached the discharge opening. It can be seen that the picture of layer deformation, and consequently also curves of velocity distribution for its component particles depend on size 1 of the opening. With the larger of them (Fig. la) part AA of the layer drawn into movement separates into a central zone BB of different velocities and two boundary zones with width M = (AA BB)/2 embracing it within whose limits velocities fall linearly to zero. A reduction in size 1 of the hole from 30 to 15 mm (Fig. lb) only leads to the same reduction in magnitude of the zone of different velocities whereas the geometry of boundary zones remains constant. Finally in view of retention of the same features with l = 6 mm = 2M the boundary zones merge with each other without leaving a zone of different velocities (see Fig. lc). Experiments performed with particles of different sizes showed that the deformation picture in these cases did not basically differ from that in question. There is only a change in width M of the boundary zone. It increases with an increase in panicle size and falls with a reduction in size. This may be explained by the fact that boundary zones are nothing but slip