A mathematical model of a continuous sugar centrifuge

Centrifuges are used in sugar factories to separate sugar crystals from their viscous mother liquor. In this thesis, a mathematical model of a continuous sugar centrifuge has been developed.
The model comprises several modules which describe the various operations occurring in a sugar centrifuge:-

(i) Filtration and sedimentation - Hindered settling and centrifugal filtration rate equations have been coupled and solved incrementally by approximating the inclined screen of a continuous sugar centrifuge by a series of stepwise cylindrical elements. Values for the screen resistance and the voidage and specific cake resistance of beds of sugar crystals have been determined experimentally.

(ii) Drainage - Based on experiments carried out using a laboratory batch centrifuge, correlations have been developed to enable the residual saturations and drainage rates of spun beds of sugar crystals to be predicted.

(iii) Flow over the screen - Cine photographic and shear cell studies have led to the development of a combined viscous flow- "plug" flow model to describe the motion of the massecuite, molasses and crystal bed layers over the basket screen.

(iv) Crystal motion across the sugar chamber - Equations of motion describing the crystal trajectory across the annular gap between the basket discharge point and the casing impact zone have been formulated and solved using a Runge-Kutta numerical scheme. Experiments have been carried out to determine the drag coefficient of sugar crystals and to measure the windage generated by the rotation of the basket in a continuous centrifuge.

(v) Crystal breakage - The breakage of sugar crystals on single impact has been investigated in both laboratory and factory studies. The size distributions of the broken crystals have been modelled by a halves, quarters and fines mechanism and correlations have been developed linking the mass fractions of halves, quarters and fines to the crystal kinetic energy prior to impact. These correlations have been incorporated into a breakage model capable of predicting the size distribution after impact from a knowledge of the impact velocity and the initial size distribution.

Results obtained using the filtration, sedimentation, drainage and screen flow modules (which model the behaviour on the basket) have been found to be in reasonable agreement with experimental evidence and these modules have been used to predict the effect of altering various operating parameters on the purity of the sugar discharged from the basket. The crystal trajectory and breakage modules (which model the behaviour in the sugar chamber) have been employed to predict the change in the sugar crystal size distributions resulting from casing impact in both high and low grade continuous centrifuges and have also proven useful in assessing the effectiveness of several anti-breakage schemes relying on drag enhancement.