Engineering task and calculation objective
This module calculates cyclones for separating solid particles from gases according to Section L3.4 of the VDI-Wärmeatlas (VDI Heat Atlas, 12th edition, 2019). Gas cyclones are the most widely used centrifugal separators in process engineering: robust, with no moving parts, usable at high temperatures and dust loadings – for example downstream of fluidized bed reactors, spray dryers, mills, or as pre-separators upstream of filters. Anyone who wants to design a cyclone separator or calculate the separation efficiency of a cyclone needs, besides the geometry, above all the particle size distribution of the feed.
The calculation follows the model documented in the VDI Heat Atlas (after Muschelknautz): from the inlet velocity, the friction factors with and without dust and the mean centrifugal acceleration, the cut size of the inner vortex is determined. The overall separation efficiency is composed of several contributions – separation by exceeding the limit loading at the wall, fractional separation in the inner vortex, vortex finder (immersion tube) and secondary flow separation – which the module reports individually.
As a result, the calculation delivers the overall separation efficiency, the fractional separation efficiencies per particle class and the clean gas emission, i.e. the dust mass flow leaving the cyclone – the key quantity for demonstrating compliance with emission requirements and for sizing downstream filter stages.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Characterize the feed: Particle density, median diameter, slope parameter of the residue curve (e.g. RRSB distribution), minimum and maximum particle diameter and the number of particle classes describe the feed. Inlet loading and dust mass flow define the solids load.
- Determine operating data and flow quantities: From gas flow rate, gas density and viscosity follow the inlet velocity, Reynolds and Froude numbers and the mean centrifugal acceleration in the cyclone; the friction factors are determined separately for pure gas and for the dust-laden flow.
- Check limit loading and wall separation: If the inlet loading exceeds the limit loading of the swirling flow, the excess solids are separated directly as a strand at the wall; this share enters the balance as a separate separation efficiency and dominates in highly loaded cyclones.
- Calculate fractional separation in the inner vortex: For each particle class, the settling velocity or cut size is determined from the equilibrium of centrifugal force and drag force, and from it the fractional separation efficiency of the inner vortex as well as, additionally, the separation at the vortex finder and in the secondary flow.
- Set up the overall balance: From wall, vortex, vortex finder and secondary flow separation, the overall separation efficiency, the mass fractions in fines and coarse material per particle class and the emission (clean gas loading or dust mass flow in the clean gas) are calculated.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Flow rate | V\u0307 | m³/s |
| Inlet width | be | m |
| Inlet height | he | m |
| Inlet velocity | ve | m/s |
| Outside radius of cyclone | ra | m |
| Inlet radius | re | m |
| Load ratio at inlet | μE | kg/kg |
| Constriction factor | α | - |
| Outer tangential velocity | ua | m/s |
| Friction factor of pure gas | λ0 | - |
| Friction factor with dust | λs | - |
| Radius of gas outlet pipe | ri | m |
| Friction area of cyclone | AR | m² |
| Inner tangential velocity | ui | m/s |
| Density (gas) | ρG | kg/m³ |
| Pressure drop separation area | ΔpE | Pa |
| Velocity in gas outlet pipe | vi | m/s |
| Pressure drop immersion tube | Δpi | Pa |
| Total pressure drop | Δpges | Pa |
| Particle density | ρS | kg/m³ |
| Viscosity | ηG | mPa·s |
| Height of cylinder | hZyl | m |
| Cut size for separation in primary flow | d* | m |
| Length of immersion tube | ht | m |
Calculation options
Type of inlet
Slotted inlet · Spiral inlet · Half spiral inlet · Axial inlet
Particle size distribution
0 · 1
Frequently asked questions
Why does the overall separation efficiency increase with increasing inlet loading?
Above the limit loading the swirling flow can no longer carry the solids completely; the excess is separated as a strand at the wall regardless of particle size. In highly loaded cyclones (e.g. downstream of fluidized beds) the majority of the dust is thus separated via the limit loading, and only the remainder has to be classified by the inner vortex.
What is the cut size of a cyclone?
The particle size that is separated in the inner vortex with 50 % probability: for it, centrifugal force and flow drag balance each other at the vortex finder radius. Finer particles are predominantly carried out with the clean gas, coarser ones are predominantly separated. The cut size decreases with increasing tangential velocity and smaller vortex finder diameter – but at the price of a higher pressure drop.
What are typical sources of error in cyclone calculations?
Frequently the particle size distribution of the feed is set incorrectly (laboratory measurement after dispersion instead of the agglomerated operating state), the gas density is not converted to operating temperature and pressure, or false air at the rotary valve discharge is ignored. Leakage air at the dust discharge re-entrains already separated dust and can drastically worsen the real separation efficiency.
Where are the limits of the cyclone compared with filters and electrostatic precipitators?
Cyclones separate particles below about 5 to 10 µm (depending on design and operating point) only incompletely; very fine dusts require downstream fabric filters or electrostatic precipitators. In return, cyclones are insensitive to high temperatures, loadings and abrasive dusts and are therefore preferred as pre-separators or product separators.