A fluidised centrifugal concentrator uses a rotating bowl to intensify density separation. Slurry enters through a central feed tube, while collection rings and supplied water support the separation process. This cutaway explains the feed, bowl, spindle and overflow paths; the calculator explores centrifugal field and ideal relative settling scaling.
Centrifugal Separator Interactive Calculator
Set bowl speed and target field to calculate the required effective radius and rim speed. Change particle density and diameter to compare an ideal settling scale, without treating it as predicted recovery.
Equation Used
- Constant angular speed and acceleration evaluated at the calculated effective radius.
- Relative settling scale assumes equal fluid viscosity and density, with fluid SG 1.
- The Stokes-type size/density scaling is a comparison only; its creeping-flow regime is not verified for these settings.
- Flow markers indicate routes, not velocities, particle trajectories or separation efficiency.
- Illustrative ring count and proportions; no manufacturer operating setting is prescribed.
The diagram is a generic fluidised-bowl concentrator, not a dimensional reconstruction of a particular model. Radius and rim speed follow the selected speed and target field. The relative settling scale is not a recovery prediction.
Reading the concentrating-bowl cutaway
The central tube carries feed toward the bowl base. The cone rotates on the lower spindle. Material moves toward the wall and collection rings, while overflow enters the surrounding casing and leaves through the tailings outlet.
The drawing uses blue markers for the feed and overflow route, and amber marks for a retained dense fraction. Water enters at the rings. These marks explain the paths; their number or speed does not predict mineral recovery. The axial section remains upright while the rim witness mark and spindle show rotation.
The cutaway shows a central feed, rotating cone, collection rings, drive and surrounding casing. Its simplified proportions explain the flow paths; they are not manufacturing dimensions. The FLS references below show commercial concentrating-cone arrangements.
Density concentration
FLS describes Knelson concentrators as gravity-concentration equipment for recovering free gold and other target minerals using centrifugal force and fluidised cones. Equipment selection depends on the feed and the selected process.
Density alone does not determine recovery. Particle size, liberation, fluid properties and bed conditions matter. The calculator does not identify a universal speed, water pressure, throughput or recovery percentage.
Field, radius and a relative settling scale
For angular speed ω = 2πN/60, radial acceleration is a = ω²r. Expressed in multiples of gravity, G = ω²r/g. This calculator solves the inverse problem: r = Gg/ω² for the selected speed and target field. Rim speed is v = ωr.
At fixed G, increasing speed reduces the calculated radius. That is different from speeding up an existing fixed-radius bowl, where field increases with speed squared.
For isolated small spheres in the Stokes regime, settling-speed scaling contains density difference, particle diameter squared and acceleration. With the same liquid of SG 1 and the same viscosity, the relative factor used here is S = (SG−1)d²G / [(19−1)50²300].
This comparison does not verify the Stokes regime or predict capture in a fluidised bed. A value above 1 means a larger algebraic settling scale than the chosen reference, not more than 100% recovery. The index has no inherent maximum of 1.
Example radius and field calculation
At 2000 rpm and a target 300 g, angular speed is 209.4395 rad/s. Radius is 300 × 9.80665 / 209.4395² = 0.06707 m, or 67.07 mm. Radial acceleration is 2941.995 m/s² and rim speed is 14.047 m/s.
At the same target field, reducing speed to 1000 rpm requires four times the radius, 268.28 mm, and twice the rim speed. This is a different bowl geometry, not a prediction for slowing a fixed machine.
SG 19 and 50 µm at 300 g give the reference settling scale 1. A 200 µm particle of SG 2.65 gives 1.467 at the same field: a larger, less-dense particle can have a greater value of this simple scaling. That illustrates why density alone cannot establish which particles a real separator captures.
What the model leaves out
The acceleration equation is kinematic. It does not calculate recovery, concentrate grade, water demand, feed capacity, mechanical stress or acceptable operating speed.
The relative settling factor omits viscosity, non-spherical particles, turbulence, hindered settling, liberation and residence time. Manufacturer settings and process tests are needed for a particular concentrator and feed. The illustration does not supply hole dimensions, pressure prescriptions or maintenance intervals.
Calculator questions
Why does radius change when I change speed?
Target field is an input here, so the calculator solves for the radius needed at the chosen speed. It is not holding an existing bowl’s radius constant.
Does relative settling scale mean capture probability?
No. It is a normalized size, density and acceleration expression. It is not bounded by 1 and is not a recovery percentage.
Does the feed tube rotate with the bowl?
The generic cutaway keeps the feed delivery tube fixed while the bowl and its drive rotate. The surrounding casing collects the overflow.
Why do the colored particles follow simplified routes?
They identify feed, retained fraction and overflow. Their paths do not solve fluid flow or particle dynamics.
Can I use this to select fluidisation water pressure?
No. Water pressure and flow are not calculated. They depend on equipment and process requirements.
Separate positioning equipment
The concentrating bowl uses a rotary drive. Its field and radius calculations do not determine the stroke or force of a linear actuator.
If a separate installation needs a powered cover or positioning linkage, calculate that mechanism’s own load and travel with the FIRGELLI actuator force calculator. Plan its electrical controls with the linear actuator wiring diagram generator, or compare an existing actuator with the linear actuator replacement finder. These tools do not size the bowl drive or predict mineral recovery.
References & Further Reading
- FLS Knelson GX concentrating-cone product datasheet: manufacturer cutaway showing central feed, ringed cone, spindle and surrounding casing.
- FLS gravity-concentration equipment: fluidised-cone concentration and mineral-recovery context.
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