ABSTRACT
A mathematical model is proposed to calculate the total separation effectiveness in terms of GT for a disk stack centrifuge taking account of the variation of the centrifugal force with a position in the disk. In practice, the centrifuge ability/force is often referred as Relative Centrifugal Force (RCF) or G number, which is a multiple of the centrifugal acceleration over the gravitational acceleration. As the radial velocity varies it is important to integrate the relative centrifuge force, here in terms of the G number along the path taking account of the change in velocity. The separation effectiveness, GT is defined as an integrated product of local G number, G(x) and local residential time (dt), where dt is the time taken for the bulk fluid to traverse a distance from r to r+ dr. The GT value calculated for a disk type centrifuge can be compared with the GT value of others and compared with a bench top fixed rotor centrifuge. An industrial centrifuge would be expected to be able to deliver similar separation performance to a pilot or a lab scale one, if operated at the same/similar value of GT. This would allow the performance of a full-scale clarifier to be predicted. This model is, in essence, a simple alternative to the Sigma concept.
KEYWORDS:
Nomenclature
Effectiveness GT | = | an integral of Gdt over the length of the flow path, second |
G | = | gravitational acceleration 9.8 m s−2 |
G | = | ratio of local acceleration over gravitational acceleration, dimensionless |
N | = | number of discs |
n | = | disk rotation rate, rotation per second, rps |
r0: | = | inner radius of discs m |
R | = | outer radius of discs m |
RCF | = | relative centrifugal force |
s | = | time, second |
ε | = | disc spacing m |
vf | = | linear velocity of fluid ms−1 |
V | = | volumetric feed flow rate m3s−1 |
ω | = | angular velocity, 2πn |