# Batch Centrifual Comparison and Evaluation

The purpose of this article is to propose a method to compare and evaluate the operational performance of a number different makes of batch centrifugal machines. A whole range of things will have to be assumed in order to make the method usable, these assumptions will of course limit the the valididty of the results this method yields. Some of the assumptions are; charge time, acceleration time, plough time are the same for all machines.

## Definitions

- D= Basket Shell Internal Diameter [m]
- R= Basket Shell Radius [m]
- t= Massecuite thickness [m]
- d= Massecuite ID [m]
- R= Equivalent Radius [m]
_{m} - ω= Maximum Basket Speed [rad/s]
- G= G force
- θ= Time of Drying
- μ= Mother Liquor Viscosity [Pa s]
- MA= Crystal Size as Mean Aperture [mm]

where

R = D/2

d = D - 2·t

R_{m} = ^{2}/_{3} (R^{3} - r^{3}) / (R^{2} - r^{2})

G = ω^{2}·R_{m}/g

In Table 36.13 of Hugot, pg 741 3rd ed, Hugot gives G-force and cycle time for various sized machines. Assuming these are all on the same massecuite we can develop a regression model and use this as a basis of comparison for the fugals we are comparing. Part of this table is reproduced below.

On pg 721 of Hugot Equ 36.15 states

^{2}

^{2}

G force (G) |
Cycle Time [seconds] (θ) |
log(G) | log(θ) |
---|---|---|---|

645 | 202 | 2.809559715 | 2.305351369 |

1026 | 170 | 3.011147361 | 2.230448921 |

542 | 210 | 2.733999287 | 2.322219295 |

792 | 180 | 2.898725182 | 2.255272505 |

1238 | 165 | 3.092720645 | 2.217483944 |

542 | 215 | 2.733999287 | 2.33243846 |

792 | 185 | 2.898725182 | 2.267171728 |

497 | 230 | 2.696356389 | 2.361727836 |

620 | 210 | 2.792391689 | 2.322219295 |

741 | 190 | 2.869818208 | 2.278753601 |

905 | 180 | 2.956648579 | 2.255272505 |

A linear regression on the log data above yields the following regression curve

θ = 10^{(-0.35837·log(G) + 3.312263)}

The correlation coefficient, r^{2} = 0.9494

The G force is calculated from the data supplied by centrifugal machine vendors and the equations detailed above. From the calculated G force an expected cycle time can be calculated from the regression curve given above. The cycle time can be translated to a massecuite throughput rate assuming a massecuite density (ρ=1500 kg/m^{3} is assumed). The massecuite throughput rate can be used as a criterion for selection of the centriugal. All the four machines compared are nominally 1750 kg charge machines. These calculations are summarised in the table below.

Machine | D | t | ω | R | r | R_{m} |
G | θ | cycles per hr | charge volume | massecuite throughput | G/t |
---|---|---|---|---|---|---|---|---|---|---|---|---|

[mm] | [mm] | [rpm] | [mm] | [mm] | [mm] | [sec] | [litre] | [ton/h] | [mm^{-1}] |
|||

A | 1524 | 254 | 1000 | 762 | 508 | 643.5 | 719.3 | 194.3 | 18.53 | 1158 | 32.2 | 2.83 |

B | 1600 | 264 | 1050 | 800 | 536 | 676.7 | 834.0 | 184.2 | 19.54 | 1182 | 34.6 | 3.16 |

C | 1600 | 215 | 1100 | 800 | 585 | 698.1 | 944.2 | 176.2 | 20.43 | 1141 | 35.0 | 4.39 |

D | 1540 | 230 | 1080 | 770 | 540 | 661.7 | 862.8 | 182.0 | 19.78 | 1107 | 32.8 | 3.75 |

It is clear that machines from vendors B and C have a greater expected massecuite throughput. This information is useful in deciding which machine to choose, but clearly it cannot be the only factor considered. Do these calculations on-line to compare your machines

However Broadbent in their *Raw Sugar Course Notes* derive a formula for the volume of molasses driven off the massecuite.

V = MA^{2}·G·θ/μ/t

This formula can be used to compare centrifugal operation. In the cases being considered above; the crystal size (MA), spin time (θ) and mother liquor viscosity (μ) will not vary. So in order to compare the four fugals we can simplify the formula above to G/t. These values are shown in the last column of the table above. According to this criterion machine C followed by D are the best performers.

## Other Points to be Considered

The following are a number of points Phil Thompson has suggested be kept in mind when doing a technical adjudication of centrifugal machine tenders.

### The capability of the drive system must be assessed.

The ability of the variable speed drive system to deliver the necessary rate of acceleration and deceleration to achieve the specified cycles/hour must be confirmed. There are some weak drives systems installed and on offer that will limit the machine to 15 charges/hour in practice.

### Time Efficiency of the Cycle

As well as acceleration / deceleration limits of the drive there is the time to plough, feed, screen wash etc. Some manufacturers offer machines with 15 seconds of screen washing, others have two seconds of screen wash that occurs while accelerating to feed speed (no delay at all). Phil also claims to have fallen asleep watching machines in a refinery, where 30 seconds of screen washing was required to remove sugar left behind by the plough.

### Purging of the Massecuite

Purging of the massecuite during feeding means that the actual charge is significantly more than the litres of basket space suggest. A 10% increase on nominal size is possible where the massecuite is free purging and the basket has enough drainage capability (hole size, open area etc).

### Two Phases of Fugal Operation

There are two distinct phases to consider; the initial purging and washing occurs below spin speed, while drying occurs at spin speed. Purging and washing are influenced by cake thickness and permeability (function of crystal size and CV). Drying is heavily dependent on G-force combined with MA/CV of sugar and the ventilation of the fugal and its conveyors.

### Plough Efficiency

A plough which leaves 5 kg of sugar per cycle behind means you need more cycles per hour to make the same amount of sugar. Low yield means more massecuite per ton of sugar and the fugal has a big influence on the overall yield figure.

Two papers on this topic are worth reading:

- Moor StC B and Greenfield MS,
*A Financial Evaluation Applied to Selection of "A" Centrifugals*, SASTA 62, pg 45, 1988. - Currie AF,
*Experiences with the BMA G1500 Centrifugal on "A"-Massecuite*, SASTA 60, pg 43, 1986