Technical Note -
A generalised model for hydrocyclone classifiers
By K NAGESWARARA0 1 (Le/Dc)°·15 6o. 20 } ({P/ppgD e) } -0.22 AO.93)
INTRODUCTION A generalised mathematical model for hydrocyclone classifiers was developed by the author (Nageswararao, 1978) using dimensionless groups which include phenomenological characteristics as independent variables. This model is incorporated in JKSimMet, the steady state mineral processing simulator developed by JKTech.
3.
Recently, when this model was rewritten (Lynch and Morrell, 1992), in terms of variables other than those used by the author, a few errors have crept in. For example, while the exponent of (Du/Dc) in the equation for d50e should be negative (-0.47), it was recorded as positive (0.47). Also, the exponent of (DoIDe) in the equation for pressure drop should be 0.67 and not 0.60. In the same equation, the exponent of Dc would turn out to be -0.10 and not 0.15. These are clearly attributable to typographic and rounding off errors, while transforming the original equations.
4.
More recently, Cilliers (pers comm) has done a comprehensive evaluation of the major semi-empirical models for hydrocyclones. He observed that the major difference between the cyclone model developed by the author and other models lies in the method of quantifying the effect of spigot diameter on d50e. He noted that while all other models predict an increase in d50e with a decrease in the spigot diameter, the model as cited by Lynch and Morrell (1992) predicts just the opposite. However, he conjectured correctly that the discrepancy could be due to a typographic error. As the model is still unpublished, it is felt that the original model equations should be recorded with the correct exponents, so that errors in predictions other than those due to the limitations of the model itself could be avoided. They are given hereunder.
MATHEMATICAL MODEL FOR HYDROCYCLONE CLASSIFIERS The performance of industrial hydrocyclone classifiers can be completely described by the following equations in which [ ] are used for scale factors, { } for design variables and ( ) for operating variables.
I.
Pressure -
Recovery of water to underflow, Rr:
Rr= Kwo [Dc 0.00] { (Do/Dc
r1.l 9 (D u/Dc l40 (D j/De )-0.50
. '(Le/Dc) 0.22 6-o·24 } ({P/(ppgD e)
r O.53 AO.I.7)
Volumetric recovery of feed pulp to underflow, Rv:
Rv = Kvo [Dc 0.00] { (Do/Dc )-0.96 (D u/D e )1.83 (D /Dc )-0.25
5.
(Le/Dc) 0.22 6-0.24} ({P/(PpgDe)}·0.31) Reduced efficiency curve In general, the reduced efficiency curve can be represented by the following equation:
E c (d/d50e)= 100 (ea.· d/dSOc _ l )/ (ea.· where
d/dsOc + ea._
2)
KQo, Kdo, Kwo and Kvo are material specific constants dependent on the characteristics of feed solids such as specific gravity, size distribution etc; Dc, Do, Du and Dj are the diameters of cyclone, vortex-finder, spigot and inlet respectively; Le, 6
are the length of the cylindrical section and full cone angle respectively;
P
is the pressure drop across the cyclone;
g
is the acceleration due to gravity;
Pp
is the density of feed slurry;
A
is ~ / (l_~)3, ~ being the volumettric fraction of solids in the feed slurry; and
ex
is the shape factor in the equation for the reduced efficiency curve.
throughput relationship:
REFERENCES (Le/De)0.20 6-o.IO} «P/p p ) 0.5~ 2.
Corrected classification size, d50e:
d50e/D e = KdO [Dc -0.65] { (D o/D e)0.52 (Du/Dc) -0.47 (Dj/Dc) -0.40
1.
Nonferrous Materials Technology Development Centre, PO Kanchanbagh, Hyderabad 500 058, India.
2.
Original manuscript submitted July 1994.
3.
Revised manuscript received July 1995.
The AusIMM Proceedings
Lynch, A J and Morrell, S, 1992. The understanding of comminution and classification and its practical application in plant design and operation, in Comminution - Theory and Practice, Proceedings of Annual Meeting, pp 405-426 (The American Institute of Mining, Metallurgical and Petroleum Engineers: Warrendale, Pennsylvania). Nageswararao, K, 1978. Further developments in the modelling and scale-up of industrial hydrocyclones, PhD thesis, University of Queensland.
No 21995
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