Grade efficiency curves

Fig. 7. Cyclone generalized grade-efficiency curves. The soHd line is for the Lapple cyclone dimension ratios given in Figure 9. The dotted line is theoretical...

Cyclone Efficiency. Most cyclone manufacturers provide grade-efficiency curves to predict overall collection efficiency of a dust stream in a particular cyclone. Many investigators have attempted to develop a generalized grade-efficiency curve for cyclones, eg, see (159). One problem is that a cyclone s efficiency is affected by its geometric design. Equation 15 was proposed to calculate the smallest particle size collectable in a cyclone with 100% efficiency (157). 

This equation is for Eigure 9 cyclone dimension ratios. The term the effective number of spirals the gas makes in the cyclone, was found to be approximately 5 for Lapple s system (134). The soHd line grade-efficiency curve of Eigure 7 is also used with Lapple s cyclone, which is a somewhat taller, less compact cyclone than many commercial designs. 

Practically all cyclone performance data have been related to a present cyclone set of geometric ratios. One model for cyclone grade-efficiency curves has been tested against reported commercial cyclone efficiencies (159). A good fit was obtained. 

It should be noted, however, that the cut size is an idealization. In practice perfect separation does not occur some smaller particles than expected will be present in the underflow whilst some larger than predicted occur in the overflow leading to a blurring of the separation in a grade efficiency curve (Figure 4.23). 

A typical plot of efficiency versus particle diameter is shown in Fig. 12-8. This is called a grade efficiency curve. Although the efficiency varies with the particle size, a more easily determined characteristic is the cut diameter (d50), the particle size that is collected with 50% efficiency. 

Grade-efficiency curve, in sedimentation design methods, 22 57... 

A typical grade efficiency curve, shown in Figure 1.10, rises from some minimum value, at small particle size, in a sigmoidal manner to a value of 1, at a size usually defined as dm. ) and G(d) = 1. 

Figure 1.10. Typical grade efficiency curve for a particle separation...

Figure 1.55. Typical grade efficiency curves for cyclones and a self-induced spray wet collector 53)...

The experimental results reported in this paper demonstrate the ability of a flat-bottom hydrocyclone to separate the coarse fraction of ammonium sulfate crystals from a slurry which contains crystals of a wide size range. It appears that the grade efficiency curve, which predicts the probability of a particle reporting to the underflow of the cyclone as a function of size, can be adjusted by a change in the underflow diameter of the hydrocyclone. These two observations lead to the suggestion to use hydrocyclone separation to reduce the crystal size distribution which is produced in crystallisers, whilst using a variable underflow diameter as an additional input for process control. 

This paper presents the grade-efficiency curves of a 75 n flat bottom cyclone (RWB 1613) provided by the Amberger Kaolin Werke (AKW). It is tested for the ammonium sulfate-water system for both fines removal and product classification. Its results will be compared with the results for fines removal obtained when using an... 

From these grade efficiency curves the nominal cut size, that is the size with an efficiency of 50% and the classifier imperfection can be determined. The imperfection is defined by ... 

The shape of this classification function is identical to the shape of the grade efficiency curve for product classification but the ordinate values are changed. 

A typical grade efficiency curve for the product classification step is given in Figure 4. A value of nearly 100 percent is attained at large sizes, whereas normally a value equal to or larger than the so-called dead flux is attained at small sizes. This is caused by the diluted discharge of the coarse fraction. It represents the minimum amount of residual fines in the product after one separation stage. 

Figure A typical grade efficiency curve for the product classification step.

The effect of throttling, is significant, as Indicated in Figure 8, which indeed suggests that an additional process-input can be created. A shift of the grade efficiency curve of about plus or minus 50 pm is found. 

Figure 7. Three grade efficiency curves for the product classification step at the flow rates indicated, while using an apex diameter of 10 mm.

The matrix of classification C was introduced on the basis of the formula by Molems and Hoffmann [11] for the grade efficiency curve ... 

The definition of the grade efficiency (Equation 9) is similar to the total efficiency definition, but it applies only to a given bioparticle size. Figure 11.5 shows a typical grade efficiency curve ... 

Grade efficiency curve for Rf equal to 0% (A) and greater than 0% (B). 

Through Equations (10), (13), and (15), it is possible to obtain the grade efficiency curve based on the total efficiency E and the size distributions of two out of three streams (j,yp andyc)-... 

For separators which operate with Rf > 0, the grade efficiency curve does not start at G = 0% (Figure 11JB). This is because the separator operation always gives a minimum efficiency almost equal to the flow ratio Rf. The reduced grade efficiency G may be obtained in the same way as the reduced total efficiency E ... 

Reduced grade efficiency curve and reduced cut size (c/50). 

These equations are used to determine the grade efficiency of a classifier provided the total efficiency and the size distributions of two of the streams are known. Results are usually plotted as grade efficiency curves of G (jc) or Gj(x) against jc [3]. Since the classifier separates on the basis of Stokes diameter it is preferable to carry out the size determinations, for grade efficiency evaluations, on the same basis. 

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