Analysis and estimation/prediction of the disk stack centrifuge separation performance – Scaling from benchtop fixed rotor type to disk stack centrifuges

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:

• Centrifuge
• separation scaling

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