Sugar Centrifuge Basket

What is modelled

In a batch sugar centrifuge a perforated basket spins and throws the syrup out of a mass of sugar crystals, leaving a cake of crystals on the wall. The spinning produces an outward acceleration of hundreds of g, which acts like a very strong gravity and pushes syrup through the narrow channels between the crystals (Darcy flow). Capillary forces hold some syrup in the channels, so the cake never dries completely. The basket rim, a thin steel ring, must carry its own centrifugal load.

Equations

• Centrifugal acceleration a = ω² R; liquid head ΔP = ½ ρ ω² (R² - r²).
• Darcy flow through the wet part of the cake Q = 2π H k (ΔP - Pc) / (μ ln(R/r)).
• Liquid front ε 2π H r dr/dt = Q; it stops at r = √(R² - 2Pc/(ρω²)).
• Rotor energy ½ J ω² with J = m R² (thin ring, as in the 3D model); spin-up time J ω / torque.
• Thin-ring hoop stress σ = ρsteel ω² R².

Checks run in the page

• The spin-up integrated step by step: time and motor work against the closed forms.
• The hoop stress from adding up the centrifugal force on a half ring.
• The liquid front stepped under Darcy flow against the capillary stopping radius, plus the Darcy pressure gradient integrated across the cake.
• The acceleration from the second difference of the rim position and the wall pressure integral.

Honest simplifications

The cake is uniform with one permeability and porosity, it does not compress or wash, the syrup is Newtonian at a fixed viscosity, capillary retention is one number, the basket is a flat ring with no floor, there is no air drag or bearing loss and the rim stress ignores the cake and the wall holes. The drained state is not dry sugar: a real cycle also washes the cake. Draining is shown 40 times faster than real time. The 3D factory is an illustrative model of the machinery.

• Choose Slow rotor: the g-force falls with the square of the speed and the cake holds much more syrup.
• Choose Cold viscous syrup: the same pressure drains it far more slowly.
• Choose Small lab basket: the speed is high, but the stress and the energy stay small because the radius is small.