Chemical Forums
Specialty Chemistry Forums => Chemical Engineering Forum => Topic started by: Help123 on March 06, 2019, 11:31:39 AM

How can i find the size of a rotor in a tubular centrifuge?
any relevant equations to use..
bear in mind, this is only for a uni project so nothing that is too overcomplicated.
Would i have to make an assumption for the size ?
by size i would assume radius and diameter.
Any help is appreciated.

the radius and the speed of rotation.

The separation equilibrium doesn't depend on the size, only on the azimuthal speed. If you want to separate a suspended powder from the liquid, as in your other discussion, the probably the equilibrium is trivial and needs only a ridiculous azimuthal speed.
So the size and speed depend only on the desired kinetics. You need to evaluate how quickly the powder particles drift under the centrifugal field, as a consequence of the density difference, particle size and fluid viscosity. It's probably a laminar regime, for which algebraic solutions exist, if assimilating the particles to spheres.
I don't expect one solution that results from the design needs. You have to engineer something sensible and efficient, and many possibilities exist, with big variations. More azimuthal speed separates the particles faster, but above Mach 0.7 aerodynamic losses increase more steeply. Probably not necessary for a suspension. You also may want to decide early if you want liquidtight joints where one end rotates and the other doesn't (difficult and it restricts the possible speeds) or if you can disconnect all hoses before starting the rotation, which is easier with human intervention.
One nontrivial estimate is how imbalanced the rotor will be, especially if a powder is to settle at the wall. This decides much the rotation speed, the bearings, the wall resistance.
So, what is the input mix, especially densities and grain size? Throughput?

Help123 sent me a personal message, in essence:
Separate amoxicillin 1600 kg/m^{3}
hydroxyphenylglycine 1396 kg/m^{3}
water 1000 kg/m^{3}
and again, no sorry, there is no "equation" telling a diameter and angular speed for that.
You must determine a particle size that tells how quickly the particles drift due to the centrifugal force. Without that, nothing is possible.
Combined with the desired throughput, you get a range of possible designs, where more azimuthal speed can reduce the machine's size but complicate other design aspects. Much engineering subjectivity and choice in it. Many smaller centrifuges can be better than a single big one.
The physical needs combine with the ease of design, construction, use. Technological limitations like rotating seals, wall resistance, aerodynamic losses and their solutions, bearings... drive fundamentally the choice of the operation parameters.

In the personal message,
"I have found this equation for RCF:
RCF = 1.118 x 10^5 * Radius (rotational radius) * RPM"
looks like Rω^{2}/g, the centripetal acceleration relative to Earth's gravity, where
(2π/60)^{2}/9.806=1.118×10^{3} in S.I. units
and the square is missing on the angular speed.
Sorry Help123, but if you need to search for a formula to compute a centrifugal force, then your chances of designing a centrifuge are zero. At best, I could imagine that your course or a book gives some rough relations or curves about existing centrifuge designs, where you could locate where your process needs is and try to infer a size.
Allegedly a university project... I just wonder how this assignment landed on you. In a company, I'd say: buy from a supplier or find a subcontractor.