Rathole diameter

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. 

If the bin discharges in funnel flow, the bin outlet diameter should be sized to be larger than the critical rathole diameter (Of) to prevent a stable rathole from forming over the outlet. For a funnel flow bin with a circular outlet, sizing the outlet diameter to exceed the Of will also ensure that a stable arch will not form (.since a rathole is inherently stronger than an arch). The Of value is calculated in Equation (2), and additional details of the calculation are provided in Ref. 1. 

FIGURE 13 Plot of derived function G(ikt) u.sed to calculate critical rathole diameter for funnel flow bins. 

Reduce the material level in the bin Since the critical rathole diameter typically decreases with a reduction in the major consolidation pressure (require using multiple smaller bins to handle the bulk solid. 

In order to avoid the formation of a stable rathole, it is necessary that the size of the flow channel exceed the critical rathole diameter, DF, which is calculated as follows ... 

There are a number of considerations when sizing the bin outlet. If arching is a concern (either in mass flow or funnel flow), the discharge frequency must be considered since this sets the maximum time that the bulk solid will remain at rest within the vessel. If a funnel flow vessel is being designed, the critical rathole diameter will also be needed to set the minimum outlet dimensions. 

By measuring the force required to shear a bed of powder that is under various vertical loads, a relationship describing the cohesive strength of the powder as a function of the consolidating pressure can be developed (4). This relationship, known as a flow function, FF, can be analyzed to determine the minimum outlet diameters for bins to prevent arching and ratholing. 

If funnel flow develops instead of mass flow, the minimum outlet diameter is given by the tendency for a stable rathole to occur, because this diameter is usually larger than that required to overcome arching. In this case, the minimum outlet diameter is... 

The flow function that describes the cohesive strength (unconfined yield strength, F ) of the powder as a function of the major consolidating pressure (cti). The flow function is one of the parameters used to calculate the minimum outlet diameter/width for bins, press hoppers, blender outlets, etc. to prevent arching and ratholing. The calculation of the minimum outlet diameter/width is discussed in more detail below. 

Ratholing index [m], RI, = diameter of the circular exit hole from a hopper that will ensure rathole failure and cleanout in a funnel-flow bin or mixer, values range from 0-9 m. (If RI > 3 then likely lumps .)... 

Erratic flow obstructions alternating between arching and ratholing/cohesive material plus [sequential arching then ratholing] /noncohesive plus bin walls not steep enough to produce flow at the wall/noncohesive plus star feeder draws only from one wall/noncohesive plus constant pitch screw conveyor with diameter < exit hole from hopper. 

Archingf particle diameter large compared to outlet/cohesive particles probably caused by moisture or compaction/AI too high/AI > conical hopper outlet diameter. [Ratholing] cohesive particles probably caused by increased moisture or by compaction (fine powders < 100 pm such as pigments, additives and precipitates)/ outlet diameter from hopper < RI/HK steepest hopper angle (as measured from the vertical). 

Semi-stable ratholing] outlet diameter of hopper slightly larger than RI and HI < steepest hopper angle and AI < conical hopper outlet diameter. 

A third flow pattern, expanded flow, is a combination of funnel flow and mass flow (see Figure 2.6). Usually this is achieved by placing a small mass flow hopper below a funnel flow hopper. The mass flow hopper section expands the flow channel from the outlet up to the top cross section of the mass flow hopper. It is important to ensure that this cross-sectional area is sufficiently large so as to avoid ratholing in the funnel flow hopper section. Expanded flow designs are generally considered only when the cylinder diameter exceeds 6 m or so. 

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