Cyclone design

Q: What is the cut-off diameter (d50) in a cyclone separator?

The cut-off diameter, or d50, is the particle size collected by the cyclone separator at exactly 50% efficiency. Particles larger than the d50 are captured with higher efficiency, while smaller particles are progressively lost in the clean air outlet stream. The Bohnet method evaluates this parameters by solving the balance of centrifugal force against drag velocity at the vortex finder boundary.

Step by step design guide and cyclone shortcut calculation tool

Section summary

1. Introduction

2. Applications of cyclones

3. Cyclone Standard Geometry

4. Cyclone Step by Step design guide

5. Interactive Cyclone Sizing & Design Tool

Section summary
1. Introduction
2. Applications of cyclones
3. Cyclone Standard Geometry
4. Cyclone Step by Step design guide
5. Interactive Cyclone Sizing & Design Tool

1. Introduction

Cyclones and their design

There are different processes for collecting the dust in a gas stream (see global overview here), among them, cyclones are probably one of the most widespread solution, in any industry. Cyclone dust collectors are fairly simple from a mechanical point of view and therefore generally provide a cost effective solution. However, assessing the performance of a cyclone and designing a new equipment for a particular application is not always well understood and only partial literature is often found. The objective of this page is to provide a step by step approach to cyclone dust collector design. This can be sufficient to check quickly the performance of an existing cyclone or during pre-design, one should however reckon that the methodology below is not suited for detailed design which should be carried out with a reputable supplier which will likely have refined the original calculation codes provided in literature and made them more precise. One should also remark that the method given is only one among several published models which may have different accuracy.

The calculation methodology presented on this page relies on the widely accepted Bohnet model (1997), which performs calculations for parameters such as gas wall friction, inlet restriction dynamics, and radial characteristic velocities to determine cyclone separation efficiency and pressure drop.

2. Applications of cyclones

Where are used cyclones ?

Cyclones dust collectors are particularly used in the following applications :

Plastics : after transport of pellets, to catch plastic dust
Wood industry : to collect dust from sawmills
Chemicals : to collect dust from a process or at the end of a pneumatic conveying line to control emissions
Agriculture : to dedust the air used to convey material to a silo

3. Cyclones standard geometry

What are the standard dimensions of cyclones ?

Cyclones efficiency is directly related to their geometry, which has been the object of various research. From these research papers, a set of STANDARD dimensions have been defined. Those dimensions, or rather proportions, constitute the basis of most of the design across the industry. It is recommended to keep those standard configurations, or some adaptation by reputable suppliers, and not modify it. Specific design can still be developed for specific high value applications (FCC for example) but it goes beyond the methodology presented here, requiring modelization, pilot trials...etc...

The table below is due to Koch and Licht (1977) and is summarizing the work of different authors (Lapple, Stairmand...)

Dimensions Ratio	Standard			High Efficiency
Dimensions Ratio	Lapple	Swift	Peterson Whitby	Stairmand	Swift
Inlet Height Ratio: H_c / D_c = K_H	0.5	0.5	0.583	0.5	0.44
Inlet Width Ratio: B_c / D_c = K_B	0.25	0.25	0.208	0.2	0.21
Vortex Finder Depth Ratio: S_c / D_c = K_S	0.625	0.6	0.583	0.5	0.5
Gas Outlet Diameter Ratio: D_i / D_c = K_i	0.5	0.5	0.5	0.5	0.4
Cylinder Height Ratio: L_c / D_c = K_L	2.0	1.75	1.333	1.5	1.4
Cone Height Ratio: Z_c / D_c = K_Z	2.0	2.0	1.84	2.5	2.5
Dust Outlet Diameter Ratio: D_s / D_c = K_D	0.25	0.4	0.5	0.375	0.4

Table 1 : Standard cyclone geometries for a tangential inlet

All the dimensions of the cyclones are related to the diameter Dc. A standard geometry is then selected and the diameter Dc is adjusted to get the desired performance.

Cyclone dimensional engineering schematic showing variables for body diameter Dc, inlet height Hc, inlet width Bc, vortex finder depth Sc, outlet diameter Di, cone height Zc, and dust outlet Ds.

Figure 1 : Cyclone drawing and nomenclature of characteristic geometry

4. Cyclones step by step design guide

How to design cyclones ?

This design guide is based on the works published by Bohnet in 1997. The approach is valid for standard cyclones with squared tangential inlets and with a small dust load in the order of max 10 g/m³. For different types of inlet or higher dust loads, some corrections are necessary.

Validity of the model : as mentioned above it is a good model for estimating the performance of a cyclone in basic design or troubleshooting but gives errors up to 40% vs experiments, depending on the conditions, thus detail calculations should be done with the help of a company specializing in cyclone design and having improved the calculation code.

4.1 Calculate K ratios

If you design a new cyclone, chose one of the standard geometry in table 1 and assume a diameter Dc. If you test an existing cyclone, determine the different ratios for the actual equipment you are evaluating.

K ratios : K_H, K_B, K_S, K_i, K_L, K_Z, K_D from table 1 or actual cyclone dimension

4.2 Calculate the following geometrical dimensions

Cyclone geometric relationship formulas for inlet/outlet area ratio Ae/Ai, vortex finder radius ratio Ri/re, and friction area ratio Af/Ai.

With :

A_e = product inlet section area (m²)

A_i = gas outlet section area (m²)

R_i = radius of gas outlet pipe (m)

r_e = average radius of the fluid vein (m)

A_f = area of friction of powder on the sides of the cyclone (m²)

K_B = B_C/D_c

K_H = H_C/Dc

K_i = D_i/D_c

K_L = L_c/D_c

K_Z = Z_c/D_c

K_S = S_c/D_c

D_c = diameter of the cyclone (m)

4.3 Calculate inlet and outlet velocities

Inlet gas velocity uCe and outlet gas velocity uCi formulas as a function of volumetric flow rate, cyclone diameter, and geometric ratios.

With :

V_c = volumetric flow of the continuous phase (gas) (m³/s)

u_Ce =inlet velocity (m/s)

u_Ci =outlet velocity (m/s)

K_i = D_i/Dc

K_B = B_C/Dc

K_H = H_C/Dc

Dc = diameter of the cyclone (m)

4.4 Calculate friction coefficients

Cyclone friction coefficient Cf, gas contraction coefficient Ce, wall boundary velocity uCC, and cyclone Reynolds number ReC formulas.

With :

C_e = coefficient of contraction at inlet

K_i = D_i/Dc

K_B = B_C/Dc

K_H = H_C/Dc

u_Ce =inlet velocity (m/s)

u_CC =cyclone walls velocity (m/s)

Re_c = Reynolds number

μ_c = viscosity of the continuous phase (gas) (Pa.s)

Dc = diameter of the cyclone (m)

ρ_c = density of the continuous phase (kg/m³)

C_f = friction coefficient

4.5 Calculate the characteristics velocities

Formulas for cyclone radial gas velocity uCri at vortex finder radius and the tangential velocity ratio uC_theta_i/uCi.

With :

u_Cri = gas velocity at the radius Ri (m/s)

V_c = volumetric flow of the continuous phase (gas) (m3/s)

K_i = D_i/D_c

K_L = L_c/D_c

K_Z = Z_c/D_c

K_S = S_c/D_c

D_c = diameter of the cyclone (m)

u_Cθi = (m/s)

u_Ci =outlet velocity (m/s)

C_e = coefficient of contraction at inlet

A_e = product inlet section area (m2)

A_i = gas outlet section area (m2)

R_i = radius of gas outlet pipe (m)

r_e = average radius of the fluid vein (m)

C_f = friction coefficient

A_f = area of friction of powder on the sides of the cyclone (m2)

4.6 Calculate the cut off diameter

Particles having a diameter equal to the cut off diameter are captured with an efficiency of 50%. It means that the cyclone will capture 50% of the particles having this diameter in the gas stream and will let through the other 50%.

Bohnet model cyclone cut-off diameter dc formula for 50% separation efficiency.

With :

u_Cri = gas velocity at the radius R_i (m/s)

μ_c = viscosity of the continuous phase (gas) (Pa.s)

K_i = D_i/D_c

Dc = diameter of the cyclone (m)

Δρ = difference in densities (kg/m³)

u_Cθi = (m/s)

4.7 Calculate the efficiencies

The efficiencies are calculated relatively to the cut off diameter. Bigger particles will lead better efficiencies. Smaller particles to lower efficiencies. A factor Г is used in the calculation and is usually in the order of 3 (+/- 1).

Cyclone grade separation efficiency formula eta as a function of particle diameter di, cut-off diameter dc, and steepness factor Gamma.

d_i = particle of diameter i for which the efficiency is calculated (m)

d_c = cut off diameter (m)

4.8 Calculate the pressure drop

Bohnet model pressure drop calculation formulas including cyclone wall friction coefficient, inlet/outlet coefficients, and total pressure drop xi_C.

With :

ΔP_c = cyclone pressure drop (Pa)

ξ_c = total pressure drop coefficient of the cylone

ξ_ce = pressure drop coefficient in the inlet and inside the cyclone

ξ_ci = pressure drop coefficient in the outlet of the cyclone

C_fi = 0.70 to 0.75

5. Cyclone design Excel calculation & Interactive Tool

Download Cyclone Sizing Excel Spreadsheet

Get the Bohnet design template offline. Customize geometric parameters, calculate cut-off diameters, and generate printable reports. Note that this tool cannot be used for detail design as stated in the file, always link with a commercial company to confirm the design.

Download Excel Tool Requires Excel 2010 or newer (No Macros)

Interactive Bohnet Cyclone Sizing Tool

FOR EDUCATIONAL PURPOSE ONLY — NO WARRANTY — ALWAYS CONSULT A REPUTABLE SUPPLIER

1. Process Stream Properties

Gas Volumetric Flowrate (m³/h):

Gas Density (kg/m³):

Gas Dynamic Viscosity (Pa·s):

Solid Particle Density (kg/m³):

2. Cyclone Configuration

Cyclone Diameter D_c (m):

Standard Geometry Preset:

K_H (H_c/D_c):

K_B (B_c/D_c):

K_S (S_c/D_c):

K_i (D_i/D_c):

K_L (L_c/D_c):

K_Z (Z_c/D_c):

3. Design Calculations

Inlet Height (H_c):	- m
Inlet Width (B_c):	- m
Vortex Finder Depth (S_c):	- m
Gas Outlet Diameter (D_i):	- m
Cylinder Height (L_c):	- m
Cone Height (Z_c):	- m

4. Performance Outputs

Cut-off Diameter (d₅₀)
- µm

Pressure Drop (ΔP_c)
- Pa

Inlet Gas Velocity (u_Ce):	- m/s
Outlet Gas Velocity (u_Ci):	- m/s
Wall Boundary Velocity (u_CC):	- m/s
Cyclone Reynolds Number (Re_c):	-

Legal Disclaimer & Limitation of Liability The results provided by this tool are for educational and preliminary estimation purposes only. NO WARRANTY: PowderProcess.net makes no warranties, express or implied, regarding the accuracy or applicability of these results to any specific engineering project. LIMITATION OF LIABILITY: PowderProcess.net SHALL NOT BE LIABLE for any direct, indirect, incidental, or consequential damages arising from the use of this data. All results MUST be independently verified by a qualified professional engineer before implementation in any industrial or physical environment.

Frequently Asked Questions (FAQ)

How do you calculate cyclone collector efficiency?

Cyclone collector efficiency is calculated by establishing the grade efficiency function relative to the cut-off diameter (d₅₀). Under the Bohnet model, the efficiency curves are calculated for discrete particle size classes using the ratio of particle diameter to cut-off diameter, mapped against a steepness coefficient (usually Γ = 3). This helps engineers project the total recovery percentage of a specific powder size distribution.

What is the cut-off diameter (d₅₀) in a cyclone separator?

The cut-off diameter, or d₅₀, is the particle size collected by the cyclone separator at exactly 50% efficiency. Particles larger than the d₅₀ are captured with higher efficiency, while smaller particles are progressively lost in the clean air outlet stream. The Bohnet method evaluates this parameters by solving the balance of centrifugal force against drag velocity at the vortex finder boundary.

What are the limitations of the Bohnet cyclone model?

The Bohnet cyclone model is primarily valid for standard cyclones with tangential inlets and low dust loadings (below 10 g/m³). While it offers an excellent mathematical framework for sizing and verification, calculations can vary up to 40% against physical experimental data at high concentrations or alternative inlet geometries. For dense phase process operations, secondary correction factors are required.