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# Sizing of dust separation cyclones

## Step by step calculation guide

Section summary
1. Introduction : Leith & Licht method
2. Domain of validity
3. Cyclone Standard Geometry
4. Leith & Licht model Step by Step design guide
5. Cyclone design Excel calculation tool

## 1. Introduction

### Leith & Licht method

There are different methods published in the literature to design cyclones. The method presented in this page was developped by Leith & Licht in the 70s. The calculation principle is based on a force balance on the particles that need to be separated in the cyclone [Altmeyer]. From comparative of cyclone design methods that have been published in literature, the Leith & Licht method is not always the most precise [Altmeyer] [Dirgo]. However its quite simple calculation method makes it an interesting method for quick assessment.

The method presented gives approximate results and should not be used for detail design. It is presented to illustrate the principles of designing a cyclone and for a rough estimation of the design performance. A specialized company should always be consulted for detail design prior to construction of a cyclone.

Another method is presented in this page, it can be interesting to check different models.

## 2. Domain of validity

### In which conditions can be use the method of Leith & Licht to design cyclones ?

The method of Leith & Licht was based on the following range of experimental data [Altmeyer] :

• Gas flowrate : 0.06 < V < 0.13 m3/s
• Temperature : 310 < T < 422 K
• Pressure : atmospheric

## 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...)

 Standard Geometries for cyclones with tangential inlet Standard High efficiency Dimensions Lapple Swift Peterson Whitby Stairmand Swift a/D 0.5 0.5 0.583 0.5 0.44 b/D 0.25 0.25 0.208 0.2 0.21 S/D 0.625 0.6 0.583 0.5 0.5 De/D 0.5 0.5 0.5 0.5 0.4 h/D 2 1.75 1.333 1.5 1.4 (H-h)/D 2 2 1.84 2.5 2.5 B/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 D. A standard geometry is then selected and the diameter D is adjusted to get the desired performance.

Figure  1 : Cyclone drawing and nomenclature of characteristic geometry

## 4. Leith & Licht model : cyclone step by step performance calculation method

### 4.1 Gather input data

The following data are required to be able to calculate a cyclone efficiency and cut off diameter with the model of Leith and Licht :

• Inlet gas flowrate
• Particle diameter
• Particle density
• Temperature
• Pressure
• Gas density
• Gas viscosity

The calculation method proposed is reported in [Dirgo]

### 4.2 Calculate the cyclone dimensions

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

All the individual length (a, b, S, de, B, h, H) must be determined.

### 4.3 Calculate the natural length l of the cyclone

The natural length l of a cyclone is farthest distance from the gas outlet that the gas goes while spinning.

With :

l = natural length of the cyclone (m)
De = diameter of gas outlet (m)
D = diameter of the cyclone (m)
a = vertical dimension of the gas inlet (m)
b = horizontal dimension of the gas inlet (m)

Note : if l > (H-S) then l is replaced by H-S in the equations.

### 4.3 Calculate the cone diameter dc at the natural length

With :
dc = diameter of the cyclone at the natural length l (m)
D = diameter of the cyclone (m)
B = diameter of the product outlet (m)
S = cyclone gas outlet duct length (m)
l = cyclone natural length (m) as calculated in paragraph 4.2
H = cyclone height (m)
h = cyclone cylinder height (m)

### 4.4 Vortex exponent n

With :
n = vortex exponent (-)
D = cyclone diameter (m)
T = temperature (K)

### 4.5 Calculate the cyclone inertia parameter Ψ

With :
Ψ = cyclone inertia parameter (-)
ρp = particles density (kg/m3)
d = particles diameter (m)
vi = gas inlet velocity (m/s)
n = vortex exponent (-) as calculated in paragraph 4.5
μ = gas viscosity (Pa.s)
D = cyclone diameter (m)

### 4.6 Calculate the cyclone geometry parameter C

With :
C = Geometry parameter (-)
De = diameter of gas outlet (m)
D = diameter of the cyclone (m)
B = diameter of the product outlet (m)
S = cyclone gas outlet duct length (m)
l = cyclone natural length (m) as calculated in paragraph 4.2
H = cyclone height (m)
h = cyclone cylinder height (m)

### 4.7 Calculate the efficiency

The efficiency of the cyclone can then be calculated thanks to the parameters given above.

η = cyclone efficiency
n as calculated in paragraph 4.4
Ψ as calculated in paragraph 4.5
C as calculated in paragraph 4.6

### 4.8 Calculation of the cut off diameter

The calculation of the cut off diameter in the model of Leith and Licht is given by the following equations [Altmeyer] :

With :
Nt = number of times the gas turns around in the cyclone in between the inlet and outlet
V0 = gas inlet volumetric flowrate (m3/s)
a = vertical dimension of the gas inlet (m)
b = horizontal dimension of the gas inlet (m)
dpc = cut off diameter of the cyclone (m)
μ = gas viscosity (Pa.s)
D = cyclone diameter (m)
ρp = particles density (kg/m3)
ρ = gas density (kg/m3)

### 4.9 Calculation of the pressure drop

The pressure drop in the cyclone is given, according to Leith and Licht by the following formula [Altmeyer] :

With :
ΔP = cyclone pressure drop (Pa)
V0 = gas inlet volumetric flowrate (m3/s)
a = vertical dimension of the gas inlet (m)
b = horizontal dimension of the gas inlet (m)
De = diameter of gas outlet (m)

## 5. Leith & Licht model Excel calculation tool

A simplified version of the calculation tool can be found here. 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.

Sources

[Dirgo] Cyclone Collection Efficiency: Comparison of Experimental Results with Theoretical Predictions, Dirgo & Leith, Aerosol Science and Technology, 2007

[Altmeyer] Comparison of different models of cyclone prediction performance for
various operating conditions using a general software, Altmeyer et al, Chemical Engineering and Processing, 2004