Engineering task and calculation objective
This module calculates droplet separation in cyclones according to Section L4.3.3 of the VDI-Wärmeatlas (VDI Heat Atlas, 12th edition, 2019). Liquid cyclones of this type separate entrained droplets from gas or vapor streams – a standard task downstream of evaporators, columns, scrubbers and quenches, and upstream of compressors whose impellers are endangered by droplet impact. Anyone who wants to design a droplet separator as a cyclone must demonstrate which droplet size range is reliably separated and which residual fraction passes the vortex finder.
The working principle corresponds to the gas cyclone: the tangential inflow generates a swirling flow whose centrifugal acceleration flings the droplets to the wall, where they run off as a liquid film and are drawn off via the sump. Compared with solids cyclones, droplet-specific effects come into play: droplets can shatter on impact or be re-entrained from the wall, and the separated film must be drained reliably against the upward core flow.
The module provides the calculation options of the VDI Heat Atlas for this design and supplies the basis for weighing separation performance and pressure drop against alternative designs such as vane-type (lamellar) or wire mesh separators.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Define operating data and fluid properties: Gas flow rate, density and viscosity of the gas, density of the liquid as well as the incoming droplet loading and droplet size distribution (for example from upstream atomization or entrainment from a column) form the input data.
- Choose cyclone geometry and calculation option: The option selection defines the design variant or calculation path; inlet cross-section, cyclone diameter and vortex finder dimensions determine the tangential velocity and the residence time of the swirling flow.
- Calculate flow quantities: From the inlet velocity and the geometry follow the tangential velocity and the mean centrifugal acceleration; together with the drag law they determine the radial migration velocity of the droplets.
- Determine the separation limit: From the equilibrium of centrifugal force and flow drag follows the limiting droplet diameter that just reaches the wall; smaller droplets are partially carried out with the clean gas, larger ones are separated in the liquid film.
- Check operating limits: Finally it is verified that the gas velocity stays below the limit at which separated liquid is re-entrained from the wall (re-entrainment), and that the liquid drain is dimensioned reliably against the swirl.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Flow rate | V̇ | m³/s |
| ⇒ Inlet velocity | ve | m/s |
| Outside radius of cyclone | ra | m |
| Inlet radius | re [4] | m |
| Load ratio at inlet | μe | – |
| Coefficient of contraction | α [2] | – |
| Tangential velocity (outside) | ua = | m/s |
| Coefficient of friction pure gas | λ0 | – |
| Coefficient of friction with liquid | λf [6] | – |
| Radius of gas outlet pipe | ri | m |
| Friction area of cyclone | AR | m² |
| Tangential velocity (inside) | ui [5] | m/s |
| Density (gas) | ρg | kg/m³ |
| Pressure drop separation compartment | Δpe = [15'] | Pa |
| Velocity in gas outlet pipe | vi = | m/s |
| Pressure drop gas outlet pipe | Δpi = [17'] | Pa |
| Total pressure drop Δ ptot | = [14'] | Pa |
| Density (liquid) | ρf | kg/m³ |
| Viscosity | ηg | mPa·s |
| Height of separation compartment | hi | m |
| Cut size main stream | d* | m |
| Length of gas outlet pipe | hT | m |
| Cut size boundary layer around gas outlet pipe | dT* | m |
| Area of cyclone wall | Aw | m² |
Calculation options
Options
Pressure drop · Separation efficiency
Frequently asked questions
How does a droplet cyclone differ from a dust cyclone?
The centrifugal principle is identical, but the boundary conditions differ: droplets coalesce at the wall into a film that must drain off, yet they can shatter or be re-entrained at too high a gas velocity. For the droplet cyclone, therefore, besides the cut size, the re-entrainment limit is the main design criterion, and the liquid drain must be decoupled hydraulically from the clean gas path.
When is a cyclone preferable to a vane-type or wire mesh separator?
At high liquid loadings, fouling or solids-containing media and high pressures or temperatures: the cyclone does not clog and has no internals that can foul. Wire mesh and vane-type separators, in turn, usually achieve better separation efficiencies at lower pressure drop for small droplets (below about 10 µm or in the aerosol range).
Which droplet size should the design be based on?
The droplet size distribution that actually occurs – it depends on how the droplets are generated (entrainment from bursting bubbles at liquid surfaces, atomization at nozzles, condensation). A common source of error is assuming droplets that are too coarse: secondary droplets from shattering and tear-off processes are often much finer than the primary droplets and determine the residual emission.
What limits the gas velocity in a droplet cyclone at the upper end?
Re-entrainment of the wall film: if the shear stress of the gas at the film surface exceeds a critical value, droplets are torn out of the film and carried out with the clean gas – the separation efficiency collapses despite higher centrifugal acceleration. In addition, the pressure drop grows with the square of the velocity, which sets the economic upper limit.