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

The cut-off diameter (dpc or d50) is the aerodynamic particle size at which the cyclone achieves exactly 50% collection efficiency. Particles coarser than d50 are collected at higher percentages, while finer particles are more likely to escape through the vortex finder.

Why is the Leith and Licht model widely used for cyclone design?

The Leith and Licht model formulates a continuous radial particle concentration profile and accounts for turbulent re-mixing in the vortex through an empirical vortex exponent n and geometric parameter C, giving realistic efficiency curves without complex CFD simulations.

What are optimal inlet velocities for industrial gas cyclones?

Standard industrial practice recommends inlet gas velocities between 15 and 22 m/s (approx. 50 to 72 ft/s). Velocities below 12 m/s lead to centrifugal loss and poor separation, while velocities exceeding 25 m/s cause severe wall erosion, particle attrition, and dust re-entrainment due to vortex disruption.

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Sizing of Dust Separation Cyclones

Leith & Licht Method

Step-by-step calculation guide: How to design and rate a cyclone for gas-solid separation

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Section summary
1. Introduction: Leith & Licht Method
2. Domain of Validity
3. Cyclone Standard Geometries (Stairmand, Lapple, Swift)
4. Leith & Licht Model: Step-by-Step Design Guide & Formulas
5. Interactive Cyclone Sizing Calculator (#calc-app)
6. Industrial Rules of Thumb & Operational Safety Limits
7. Downloadable Cyclone Design Excel Calculation Tool

1. Introduction

Leith & Licht Method

There are different methods published in the literature to design cyclones. The method presented on this page was developed by Leith & Licht in the 1970s. The calculation principle is based on a dynamic force balance on the particles that need to be separated in the vortex, accounting for turbulent back-mixing within the outer gas stream [Altmeyer]. From comparative studies of cyclone design methods published in academic literature, the Leith & Licht method provides an excellent analytical framework for evaluating fractional efficiencies and cut-off points without requiring complex computational fluid dynamics (CFD) [Altmeyer, Dirgo].

The method presented gives reliable preliminary results and should be utilized for equipment sizing and performance verification. A specialized cyclone vendor or engineering consultant should be consulted for final fabrication detailing.

Another cyclone design method (Lapple / Stairmand classic approach) is presented here to compare alternative calculation models.

2. Domain of Validity

In which conditions can the Leith & Licht method be used?

The model of Leith & Licht was validated against experimental pilot and industrial data within the following typical envelope [Altmeyer]:

Gas volumetric flowrate: \(0.06 < V_0 < 0.13 \text{ m}^3/\text{s}\) (per cyclone body in primary test runs, scalable via standard dimensional similitude)
Gas temperature: \(310 < T < 422 \text{ K}\)
Static pressure: atmospheric to moderate pressure
Solids loading: dilute to moderate dust concentrations (typically \(< 20 \text{ g/m}^3\))

3. Cyclones Standard Geometry

Standard Dimensional Proportions of Tangential Inlet Cyclones

Cyclone collection efficiency and hydraulic resistance are directly governed by internal dimensional ratios. Over decades of industrial testing, standard families of dimensions have been established (Koch and Licht, 1977; Lapple; Stairmand; Swift). These geometric proportions constitute the industry benchmark for standard tangential-entry cyclones.

	Standard Geometries for Cyclones with Tangential Inlet
	Standard Efficiency			High Efficiency
Ratio	Lapple	Swift	Peterson-Whitby	Stairmand	Swift (HE)
Inlet Height: \(a/D\)	0.5	0.5	0.583	0.5	0.44
Inlet Width: \(b/D\)	0.25	0.25	0.208	0.2	0.21
Vortex Length: \(S/D\)	0.625	0.6	0.583	0.5	0.5
Gas Outlet Dia.: \(D_e/D\)	0.5	0.5	0.5	0.5	0.4
Cylinder Height: \(h/D\)	2.0	1.75	1.333	1.5	1.4
Cone Height: \((H-h)/D\)	2.0	2.0	1.84	2.5	2.5
Dust Outlet Dia.: \(B/D\)	0.25	0.4	0.5	0.375	0.4

Table 1: Standard cyclone geometries for tangential inlet designs (Koch & Licht, 1977)

Standard cyclone dimensions and nomenclature

Figure 1: Cyclone geometry drawing and characteristic nomenclature

4. Leith & Licht Model: Step-by-Step Calculation Method

4.1 Gather Input Data

The calculation requires the gas operational state, particulate physical properties, and flow geometry:

Inlet volumetric gas flowrate: \(V_0 \text{ (m}^3\text{/s)}\)
Gas temperature \(T \text{ (K)}\) and operating pressure
Gas density \(\rho \text{ (kg/m}^3\text{)}\) and gas dynamic viscosity \(\mu \text{ (Pa}\cdot\text{s)}\)
Particle true density \(\rho_p \text{ (kg/m}^3\text{)}\) and representative particle diameter \(d \text{ (m)}\)
Selected body diameter \(D \text{ (m)}\) and geometric ratios

4.2 Cyclone Dimensions

From the cyclone body diameter \(D\) and the selected family ratios (Table 1), calculate: inlet height \(a\), inlet width \(b\), vortex finder length \(S\), vortex finder diameter \(D_e\), cylinder height \(h\), overall height \(H\), and dust discharge diameter \(B\).

4.3 Natural Length \(l\) of the Cyclone

The natural length \(l\) represents the lowest boundary of the vortex spinning down into the conical hopper before reversing up toward the vortex finder:

l = 2.3 \cdot D_e \cdot \left(\frac{D^2}{a \cdot b}\right)^{1/3}

Calculation of the natural length of a cyclone

Note: If the computed \(l > (H - S)\), the vortex terminates at the dust discharge boundary, and \(l\) is set equal to \((H - S)\) in subsequent expressions.

4.4 Cone Diameter \(d_c\) at Natural Length

The internal cone diameter at the lowest point reached by the vortex is given by linear geometric interpolation:

d_c = D - \frac{(D - B)\cdot(S + l - h)}{(H - h)}

Calculation of the cyclone diameter at the natural length

4.5 Vortex Exponent \(n\)

The tangential velocity distribution follows \(v_\theta \cdot r^n = \text{constant}\). Alexander's empirical correlation accounts for body diameter and gas temperature:

n = 1 - \left[\left(1 - 0.67 \cdot D^{0.14}\right) \cdot \left(\frac{T}{283}\right)^{0.3}\right]

Calculation of the vortex exponent of a cyclone

Where \(D\) is in meters and \(T\) is in Kelvin.

4.6 Cyclone Inertia Parameter \(\Psi\)

The dimensionless centrifugal inertia parameter characterizes the balance between centrifugal migration and Stokes viscous drag:

\Psi = \frac{\rho_p \cdot d^2 \cdot v_i \cdot (n + 1)}{18 \cdot \mu \cdot D}

Calculation of the cyclone inertia parameter

Where \(v_i = \frac{V_0}{a \cdot b}\) is the gas inlet velocity.

4.7 Cyclone Geometry Parameter \(C\)

Parameter \(C\) describes the effective volume and residence trajectory of the gas within the annular and conical chambers:

C = \frac{\pi \cdot D^2}{a \cdot b} \cdot \left[ 2 \cdot \left\{1 - \left(\frac{D_e}{D}\right)^2\right\}\left(\frac{S}{D} - \frac{a}{2 \cdot D}\right) + \frac{1}{3}\left(\frac{S+l-h}{D}\right)\left(1 + \frac{d_c}{D} + \frac{d_c^2}{D^2}\right) + \frac{h}{D} - \left(\frac{D_e}{D}\right)^2 \frac{l}{D} - \frac{S}{D} \right]

Calculation of cyclone geometry parameter

4.8 Cyclone Collection Efficiency \(\eta\)

The fractional collection efficiency for particle size \(d\) is calculated using the Leith & Licht modified exponential formulation:

\eta = 1 - \exp\left(-2 \cdot (C \cdot \Psi)^{1/(2 \cdot n + 2)}\right)

Calculation of the cyclone efficiency according to Leith and Licht

4.9 Calculation of Cut-Off Diameter (\(d_{pc}\) / \(d_{50}\))

The cut-off size \(d_{pc}\) (the particle aerodynamic diameter collected at 50% efficiency) is derived via the effective number of vortex turns \(N_t\):

N_t = \frac{V_0}{a \cdot b} \times \left(0.1079 - 0.00077 \cdot \frac{V_0}{a \cdot b} + 1.924 \cdot 10^{-6} \times \left(\frac{V_0}{a \cdot b}\right)^2\right)

d_{pc} = \sqrt{\frac{9 \cdot \mu \cdot D \cdot a \cdot b}{4 \cdot \pi \cdot N_t \cdot V_0 \cdot (\rho_p - \rho)}}

Calculation of the cyclone cut off diameter according to Leith and Licht

4.10 Calculation of Cyclone Pressure Drop (\(\Delta P\))

The gas pressure loss across the tangential inlet and central vortex finder tube is estimated using the Leith & Licht / Altmeyer relationship:

\Delta P = 0.5 \cdot \rho \cdot \left(\frac{16 \cdot V_0^2}{a \cdot b \cdot D_e^2}\right)

5. Interactive Cyclone Sizing Calculator

⚠️ ENGINEERING NOTICE & EDUCATIONAL DISCLAIMER: This interactive calculator is provided exclusively for preliminary estimation and educational purposes. It is not intended for detailed design or equipment procurement without certified vendor rating. No warranty, expressed or implied, is provided, and no liability is assumed.

Unit System: SI Metric (m, m/s, kg/m³, Pa, °C) US Customary (in, ft, ft/s, lb/ft³, psi, °F)

Standard Cyclone Family

Cyclone Body Diameter \(D\) (m)

Gas Flowrate \(V_0\) (m³/s)

Gas Temperature (°C)

Particle Diameter \(d\) (μm)

Particle True Density \(\rho_p\) (kg/m³)

Gas Density \(\rho_g\) (kg/m³)

Gas Viscosity \(\mu\) (Pa·s)

Calculated Results & Dimensions

Collection Efficiency (\(\eta\))
-- %

Cut-Off Size (\(d_{50}\) / \(d_{pc}\))
-- μm

Inlet Velocity (\(v_i\))

-- m/s

Pressure Drop (\(\Delta P\))

-- Pa

Vortex Exponent (\(n\))

Natural Length (\(l\))

-- m

Overall Height (\(H\))

-- m

Inlet Size (\(a \times b\))

-- × --

🛠️ Practical Industrial Rules of Thumb & Safety Limits

Inlet Velocity Window: Target gas inlet velocity \(v_i\) strictly between 15.0 and 22.0 m/s (50 to 72 ft/s). Velocities \(< 12 \text{ m/s}\) drop centrifugal separation force sharply, while velocities \(> 25 \text{ m/s}\) provoke severe wall erosion, particle attrition, and dust re-entrainment from the cone apex.
Pressure Drop Tolerance: High-efficiency cyclones (e.g. Stairmand) typically operate between 1,000 and 1,800 Pa (4 to 7 in. w.g.). A pressure drop exceeding 2,500 Pa requires excessive booster fan electrical power and often signals an undersized body diameter.
Hopper Discharge Sealing: Up to 15% efficiency loss occurs if the bottom dust discharge permits air in-leakage. Always use a counter-weighted double flap valve, an airtight rotary airlock valve, or an airtight discharge canister with pressure-balancing vents.
ATEX & Dust Explosion Safety: Cyclones handling combustible organic or metallic powders (Kst > 0) generate high electrostatic charges due to high-speed swirling friction. The entire cyclone body, vortex finder, and hopper must be bonded and grounded to earth (\(R < 10\ \Omega\)) and fitted with certified explosion venting or suppression ducts where required by NFPA 68 / 69 or ATEX 2014/34/EU.
Solids Loading Effect: At higher solids concentrations (\(> 50 \text{ g/m}^3\)), coarse particles form agglomerating descending ribbons that sweep fine particles into the hopper, actually increasing overall efficiency beyond dilute Leith & Licht predictions.

7. Leith & Licht Model Excel Calculation Tool

A downloadable spreadsheet version implementing the Leith & Licht formulas is available for engineering studies:

📥 Download Cyclone Design Excel / ODS Tool

Note: This engineering model is designed for preliminary sizing and academic rating. Always collaborate with a certified cyclone manufacturer to validate aerodynamic geometries for erosive, sticky, or high-temperature bulk solids.

References:

[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.

[Koch & Licht] New Approach to Cyclone Design and Specification, Koch, W.H. and Licht, W., Chemical Engineering, Vol. 84, pp. 80-88, 1977.