Sharpness index

AH three parameters, the cut size, sharpness index, and apparent bypass, are used to evaluate a size separation device because these are assumed to be independent of the feed size distribution. Other measures, usually termed efficiencies, are also used to evaluate the separation achieved by a size separation device. Because these measures are dependent on the feed size distribution, they are only usefiil when making comparisons for similar feeds. AH measures reduce to either recovery efficiency, classification efficiency, or quantitative efficiency. Recovery efficiency is the ratio of the amount of material less than the cut size in the fine stream to the amount of material less than the cut size in the feed stream. Classification efficiency is defined as a corrected recovery efficiency, ie, the recovery efficiency minus the ratio of the amount of material greater than the cut size in the fine stream to the amount of material greater than the cut size in the feed stream. Quantitative efficiency is the ratio of the sum of the amount of material less than the cut size in the fine stream plus the amount of material greater than the cut size in the coarse stream, to the sum of the amount of material less than the cut size in the feed stream plus the amount of material greater than the cut size in the feed stream. Thus, if the feed stream analyzes 50% less than the cut size and the fine stream analyzes 95% less than the cut size and the fine stream flow rate is one-half the feed stream flow rate, then the recovery efficiency is 95%, the classification efficiency is 90%, and the quantitative efficiency is 95%. 

There are relationships between the independent size separation device parameters and the dependent size separation efficiencies. For example, the apparent bypass value does not affect the size distribution of the fine stream but does affect the circulation ratio, ie, the ratio of the coarse stream flow rate to the fine stream flow rate. The circulation ratio increases as the apparent bypass increases and the sharpness index decreases. Consequendy, the yield, the inverse of the circulating load (the ratio of the feed stream flow rate to the fine stream flow rate or the circulation ratio plus one), decreases hence the efficiencies decrease. For a device having a sharpness index of 1, the recovery efficiency is equal to (1 — a). 

There is a unique d value which produces a fine stream having a specific 95% passing size from a feed stream. The feed size distribution should analyze at least 50% less than the 95% passing size of the product (5). However, the necessary d value varies with the sharpness index value. In general, the required d decreases, as the sharpness index decreases (eq. 2) ... 

Data for dry screening on a 20-mm square aperture vibrating screen (8) indicate that the screen is relatively efficient, giving an apparent bypass value of 0.5%, sharpness index of 0.8, and a cut size of 20 mm. On the other hand, results (9) from a plant operating an 8 ft x 20 ft (2.4 m x 6.1 m) double-deck screen with 16 mm woven wire bottom screen deck gave an apparent bypass of 4%, sharpness index of 0.56, and a cut size of 17 mm. Data (10) for smaller... 

Centrifuges. Sohd-bowl centrifuges have been proposed as an alternative classifying device to hydrocyclones for cut sizes below 10 pm. The results appear to be mixed (21). In one apphcation, where the cut size was 6.5 pm and the sharpness index 0.7, there was essentially no apparent bypass. However, in other apphcations operating at higher feed concentrations, the cut size ranged from 5—8 pm, but the sharpness index was between 0.3—0.5 and the apparent bypass between 10—30% or higher (22). Smaller cut sizes have also been reported (23). 

Analysis of this type of classifier (15) suggests that the sharpness index is between 0.5 and 0.6, consistent with calculated results, because the degree of turbulence can be high in these devices (16). A DSF Dorr classifier (1.8 m x 7 m), operating at 19 strokes per minute and having a weir depth of 100 cm and a slope of 19.4 cm/m, produced a cut size equal to 240 im, a sharpness index of 0.5, and an apparent bypass of approximately 26% when the water split was 26% (15). 

For a properly designed and operated cyclone, the sharpness index is constant, typically 0.6. The cut size and apparent bypass are a function of the cyclone geometry, the volumetric feed rate, the material relative density, the feed solids concentration, and the slurry rheology. The relationship for a standard cyclone geometry, where if D. is the cylinder diameter in cm and inlet area = 0.05 D vortex finder diameter = 0.35 Dc ... 

It is quite common in the designs for fine classification to recontact the coarse stream transversely or in counterflow with air before discharging it (see Fig. 9). This removes dry fine particles not removed in the primary classification. That is, these particles are swept back into the feed and given another chance to exit with the fine particles. Such an arrangement increases the overall sharpness index and reduces the overall apparent bypass. Another variation is to reenter the air from the solid/gas separation of the coarse stream. 

A measure of the slope of the probability function at the cut size is the Sharpness index, s, which is the ratio of size of the particles whose... 

An ideal classifier would have a sharpness index of 1.0 reed classifiers have values less than this. Industrial classifiers operating properly will have sharpness index values between 0.5 and 0.8. Actual sharpness index values will change as a function of the properties of the feed and operating conditions. 

The other type of classifier inefficiency is apparent bypass, a. If, because of mutual interference or other reasons, some of the feed material bypasses the separation and reports to either the fine or the coarse streams, then a certain percentage of one of the product streams will have the same particle size distribution as the feed materiaL Both the apparent bypass and the sharpness index dictate the performance of classifiers. 

Analysis of various tj s of industrial classifiers has led to the observation that the sharpness index is essentially constemt for a classifier (with a fixed geometrical configuration) over its normal operating range. Assuming that bypass is minimal, only two things affect the size distribution of the fine stream the size distribution of the feed and the cut size. Hence, if the size distribution of the feed is constant, only the cut size (c 5o) will affect the size distribution of the fines. Bypass can be minimized by proper design and operation of the classifier. 

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