Hoppers conical

SpiralTlevator Materials are moved upward by the centrally located spiral-type conveyor in a cylindrical or cone-shaped Nautamix vessel (Fig. 37c and d). Blending occurs by the downward movement at the outer walls of the vessel. The vessel serves the dual purposes of blending and storage. In these mixers the screw impeller actively agitates only a small portion of the mixture and natural circulation is used to ensure all the mixture passes through the impeller zone. In the case of Nautamix, an Archimedian screw lifts powder from the base of a conical hopper while progressing around the hopper wall. 

Conica.1 Hoppers. Design charts for conical hoppers typically are plots of wall friction angles, ( ), vs hopper angle, 9. Charts such as that in... 

Wed e Hoppers. Different design charts are used for wedge hoppers (Fig. 7b) than for conical hoppers. Values of hopper angle 0 (measured... 

The area of influence of a vibrating discharger is limited to a cylinder, the diameter of which is roughly equal to the top diameter of the discharger. Hence, if a vibrating discharger is mounted onto a conical hopper section, flow is confined predominantly to a central flow channel located directly above the discharger. This is tme unless the slope and smoothness of the static cone meet requirements for mass flow, or the diameter of the flow channel exceeds the critical rathole diameter for the material. 

A useful approximation of B for a conical hopper is B = 22f/a, where a is the bulk density of the stored product. The apparatus for determining the properties of solids has been developed and is offered for sale by the consulting firm of Jenike and Johansen, Winchester, Massachusetts, which also performs these tests on a contract basis. The flow-factor FF tester, a constant-rate-of-strain, direct-shear-type machine, gives the locus of points for the FF cui ve as well as ( ), the... 

Figure 10 Mass flow/funnel flow design chart for a conical hopper handling a bulk material with a 40 effective angle of internal friction.

The onset of powder motion in a hopper is due to stress failure in powders. Hence, the study of a hopper flow is closely related to the understanding of stress distribution in a hopper. The cross-sectional averaged stress distribution of solids in a cylindrical column was first studied by Janssen (1895). Walker (1966) and Walters (1973) extended Janssen s analysis to conical hoppers. The local distributions of static stresses of powders can only be obtained by solving the equations of equilibrium. From stress analyses and suitable failure criteria, the rupture locations in granular materials can be predicted. As a result, the flowability of granular materials in a hopper depends on the internal stress distributions determined by the geometry of the hopper and the material properties of the solids. 

Janssen s analysis can be extended to the stress analysis of conical hoppers. Walker (1966) proposed a differential slice with vertical sides, as shown in Fig. 8.7(a), where the cross-sectionally averaged force balance in the vertical direction results in... 

The axisymmetric nature of conical hoppers results in es = 0 and, according to Eq. (2.20), cre = (compatibility requirement, i.e., the relationship of strains. This relation, with the aid of constitutive relations between stress and strain (e.g., Hooke s law), provides an additional equation for stress so that the problem can be closed. However, the compatibility relation for a continuum solid may not be extendable to the cases of powders. Thus, additional assumptions or models are needed to yield another equation for stresses in powders. 

Example 8.1 Three sets of yield loci under different consolidation conditions are obtained for a sample of powder of bulk density 1,500 kg/m3, as shown in Fig. E8.1. If a conical hopper is to be designed, determine the wall slope of the hopper and the opening size necessary to ensure a steady mass flow. The angle of wall friction is 15°. The design diagram for mass flow conical hoppers is given in Fig. E8.2 [BMHB, 1988]. 

Figure E8.2. Design diagram for mass flow conical hopper (from BMHB, 1988) (a) Flow factor (b) Angle of wall friction.

Therefore, to ensure mass flow of the given powder in a conical hopper, the half angle of the hopper should be no more than 35° and the circular opening should be larger than 0.21 m to prevent the formation of a stable arch that can span the opening. 

As mentioned, the flow rate in a standpipe depends on the solid feed device as well as the flow control valve. In this section, we discuss the gas-solid flows in a simple standpipe system where the feed device is a mass flow hopper and the solid flow regulator is a discharge orifice [Chen et al., 1984]. As shown in Fig. 8.15, the entrance of the vertical standpipe is connected to a conical hopper feeder of half angle solids flow patterns are considered. One is a dilute suspension flow, and the other is a solid moving bed. In this case, the following additional assumptions are needed ... 

Nguyen, T. V., Brennen, C. and Sabersky, R. H. (1979). Gravity Flow of Granular Materials in Conical Hoppers. Trans. ASME, J. Appl. Mech., 46,529. 

A conical hopper of a half angle 20° and an angle of wall friction 25° is used to store a cohesionless material of bulk density 1,900 kg/m3 and an angle of internal friction 45°. The top surface of the material lies at a level 3.0 m above the apex and is free of loads. Apply Walker s method to determine the normal and shear stresses on the wall at a height of 1.2 m above the apex if the angle between the major principal plane at that height and the hopper wall is 30°. Assume a distribution factor of 1.1. 

Considering the equilibrium of a stable arch, show that the minimum diameter of the orifice in a conical hopper, d,ma, which is defined to account for the arching, can be related to the unconfined yield stress of the bulk material by the relation... 

It is required to design a mass flow conical hopper with the volume capacity of 100 m3 to store a cohesionless material of bulk density 1,700 kg/m3 and an angle of internal friction 40°. Four sets of shear tests have been conducted on the material and results for the unconfined yield strength and the corresponding consolidating stress are as follows ... 

Consider a conical hopper flow where there is no-slip between the gas and the particle. Determine the distribution of mean stress of particles in the hopper flow. The particles can be assumed to be in a moving bed condition. 

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