Cyclone separators and gas cleaning equipment
Cyclone principle, Lapple cut size and grade-efficiency curve, overall efficiency, pressure drop in velocity heads, and comparison with bag filters, scrubbers and ESPs.
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Why it matters
Dust must be removed from gases to recover product (spray dryers, cement kilns, fluid catalytic cracking), to protect downstream equipment and to meet emission limits. Cyclones are the cheapest, most robust workhorse, but their efficiency collapses for fine particles, so engineers must estimate the cut size and know when to move to bag filters, scrubbers or electrostatic precipitators.
Key ideas
How a cyclone works. Dusty gas enters tangentially through a rectangular inlet (height H, width B) near the top of a cylinder of diameter D. It spirals down the wall in an outer vortex, turns near the bottom of the cone and rises in an inner vortex to leave through the central vortex finder (gas outlet). Particles are thrown outward by the centrifugal field, reach the wall, slide down and leave through the dust outlet. There are no moving parts; the centrifugal acceleration V²/r can reach hundreds or thousands of g in small cyclones.
Cut size and grade efficiency. A particle is collected if it can travel across the inlet width B to the wall during the time the gas makes its N_e effective turns in the outer vortex. The cut size d_pc is the diameter collected with 50% efficiency. Larger particles are collected almost completely; much smaller ones mostly escape. The grade (fractional) efficiency curve η(d) shows this, and the overall efficiency follows by weighting η(d) by the mass fraction of the dust in each size band.
Lapple's model gives d_pc from a Stokes-law balance, and an empirical grade-efficiency curve. Design trends that follow from it:
- Smaller cyclones (smaller B for the same proportions) give smaller cut sizes — hence banks of small cyclones in parallel (multicyclones) for fine dust.
- Higher inlet velocity and denser particles lower d_pc.
- Higher gas viscosity (hot gas) raises d_pc, so efficiency falls with temperature.
- Efficiency rises with inlet velocity only up to a point (often around 15–25 m/s), beyond which re-entrainment and the steep rise in pressure drop make it uneconomic.
Pressure drop. The cyclone pressure loss is expressed as a number of inlet velocity heads N_H, depending only on geometry; Δp rises with V_i². Typical values are around 0.5–2.5 kPa. Correlation constants (K in the Shepherd–Lapple formula, N_e) should be taken from your data book or textbook for the chosen design.
Other gas-cleaning equipment.
- Gravity settling chambers: only for coarse particles (roughly > 50 µm); used as pre-cleaners.
- Fabric (bag) filters: dust forms a cake on woven or felted bags; very high efficiency (> 99%) down to sub-micron sizes; limited by temperature and moisture; cleaned by shaking, reverse air or pulse jet.
- Wet scrubbers (spray towers, venturi scrubbers): particles impacted on droplets; also absorb soluble gases; high-energy venturis collect fine particles at high pressure drop; they create a liquid effluent.
- Electrostatic precipitators (ESP): particles are charged by a corona discharge and migrate to grounded collecting plates; very high efficiency for fine dust at low pressure drop with huge gas volumes (power stations, cement); efficiency depends on dust resistivity. The Deutsch equation η = 1 − exp(−w·A/Q) relates efficiency to migration velocity w, plate area A and gas flow Q.
Formulas
Lapple cut size: d_pc = [9·μ·B / (2π·N_e·V_i·(ρ_p − ρ))]^(1/2)
Effective turns (Lapple estimate): N_e = (1/H)·(L_b + L_c/2)
Grade efficiency: η(d) = 1 / [1 + (d_pc/d)²]
Overall efficiency: η_o = Σ xᵢ·η(dᵢ)
Pressure drop (Shepherd–Lapple): Δp = N_H·ρ·V_i²/2, N_H = K·H·B / D_e² (K ≈ 16 for a tangential inlet)
ESP (Deutsch): η = 1 − exp(−w·A/Q)
- d_pc: cut diameter (m); μ: gas viscosity (Pa·s); B, H: inlet width and height (m); N_e: effective turns (−); V_i: inlet velocity (m/s); ρ_p, ρ: particle and gas density (kg/m³); L_b, L_c: cylinder and cone lengths (m); xᵢ: mass fraction in size band i; D_e: gas-outlet diameter (m); N_H: velocity heads (−); w: migration velocity (m/s); A: plate area (m²); Q: gas flow (m³/s).
Worked examples
Example 1 (standard): cut size of a standard cyclone. A Lapple cyclone with D = 0.5 m has B = D/4 = 0.125 m, H = D/2 = 0.25 m, L_b = L_c = 2D = 1.0 m. Air (μ = 1.8 × 10⁻⁵ Pa·s, ρ = 1.2 kg/m³) enters at 15 m/s carrying dust of density 2500 kg/m³. Find d_pc and the efficiency for 10 µm particles.
- N_e = (1/0.25)(1.0 + 1.0/2) = 6.
- d_pc = [9 × 1.8 × 10⁻⁵ × 0.125/(2π × 6 × 15 × 2498.8)]^(1/2) = [2.025 × 10⁻⁵/1.413 × 10⁶]^(1/2) = 3.79 µm.
- η(10 µm) = 1/[1 + (3.79/10)²] = 1/1.143 = 0.875 (87.5%).
Example 2 (GATE level): overall efficiency and pressure drop. The same cyclone treats a dust with mass fractions 0.10, 0.20, 0.30, 0.25 and 0.15 in bands of mean size 2.5, 5, 10, 20 and 40 µm. Find the overall efficiency and the pressure drop (D_e = D/2 = 0.25 m).
- Grade efficiencies with d_pc = 3.79 µm: 2.5 µm → 0.304; 5 µm → 0.636; 10 µm → 0.875; 20 µm → 0.965; 40 µm → 0.991.
- η_o = 0.10 × 0.304 + 0.20 × 0.636 + 0.30 × 0.875 + 0.25 × 0.965 + 0.15 × 0.991 = 0.030 + 0.127 + 0.262 + 0.241 + 0.149 = 0.81 (81%).
- N_H = 16 × 0.25 × 0.125/0.25² = 8.
- Δp = 8 × 1.2 × 15²/2 = 1080 Pa. The fines below 5 µm account for most of the loss; a bag filter downstream would be needed for high overall efficiency.
Common mistakes
- Inventing formulas such as η = 1 − (d_p/D)²; efficiency depends on d_p/d_pc, not on the ratio to the cyclone diameter.
- Taking Δp = ρV²/2. A cyclone loses several velocity heads, not one.
- Using particle density alone instead of (ρ_p − ρ) (harmless for gases, but wrong in principle) and forgetting to convert µm to m.
- Assuming efficiency always rises with velocity; re-entrainment and pressure drop limit it.
- Assuming hot gas behaves like cold gas: higher viscosity at high temperature raises d_pc.
For GATE CH
Expect: Lapple cut size; grade efficiency at a given size; overall efficiency from a size distribution; pressure drop in velocity heads; effect of scaling the cyclone diameter or velocity on d_pc (d_pc ∝ √(B/V_i)); and comparison of gas-cleaning devices by size range and efficiency. Practise the overall-efficiency table quickly.
Quick check
- What is the grade efficiency of a particle whose size equals the cut size?
- If all cyclone dimensions are halved at the same inlet velocity, how does d_pc change?
- Which device collects sub-micron dust at very low pressure drop from huge gas flows?
- Why does cyclone efficiency fall for hot gases? Answers: 1. 50%. 2. It falls by a factor √2 (d_pc ∝ √B, N_e unchanged). 3. The electrostatic precipitator. 4. Gas viscosity rises with temperature, increasing d_pc.
Interview questions
All Mechanical Operations interview questionsTry answering each one aloud before you open it.
1.What is a cyclone separator and how does it work?Concept
A cyclone separator is a device used to remove particulates from an air, gas, or liquid stream without the use of filters, through vortex separation. Rotational effects and gravity are used to separate mixtures of solids and fluids. The air stream enters the cyclone tangentially, creating a spiral flow. Particles are forced to the outer wall by centrifugal force and fall to the bottom, while the cleaned air exits through the top.
2.Explain the principle of operation of gas cleaning equipment.Concept
Gas cleaning equipment operates on the principle of removing contaminants from gas streams to meet environmental and process requirements. This can be achieved through various methods such as filtration, scrubbing, electrostatic precipitation, and adsorption. Each method targets specific types of contaminants and operates based on different physical or chemical principles, such as impaction, diffusion, or electrostatic attraction.
3.Why are cyclone separators commonly used in industrial applications?Application
Cyclone separators are commonly used in industrial applications because they are simple, cost-effective, and require minimal maintenance. They can handle large volumes of gas and are effective at removing large particles. Cyclones are also robust and can operate under a wide range of temperatures and pressures, making them suitable for various industrial processes.
4.What factors affect the efficiency of a cyclone separator?Application
The efficiency of a cyclone separator is affected by factors such as the particle size distribution, the density of the particles, the velocity of the gas stream, and the design of the cyclone itself (e.g., dimensions and shape). Smaller particles are harder to separate, and higher gas velocities can improve separation but may also lead to increased pressure drop.
5.What happens if the inlet velocity of a cyclone separator is too low?Application
If the inlet velocity of a cyclone separator is too low, the centrifugal force generated may be insufficient to effectively separate the particles from the gas stream. This can lead to reduced separation efficiency, with more particles remaining in the cleaned gas. Additionally, low velocities may cause particles to settle in the cyclone, leading to blockages and maintenance issues.
6.How does the design of a cyclone separator influence its performance?Application
The design of a cyclone separator, including its dimensions, shape, and the angle of the inlet, significantly influences its performance. A well-designed cyclone will optimize the balance between pressure drop and separation efficiency. For example, a longer cyclone body can improve separation efficiency for smaller particles, while a larger diameter can handle higher flow rates but may reduce efficiency.
7.Explain the difference between a wet scrubber and a dry scrubber in gas cleaning.Concept
A wet scrubber uses a liquid, typically water, to remove pollutants from a gas stream by absorption or chemical reaction. It is effective for removing gases and particulates. A dry scrubber, on the other hand, uses dry reagents or sorbents to capture pollutants, often through chemical reactions. Dry scrubbers are typically used for acid gas removal and are preferred when water use is a concern.
8.Estimate the cut diameter of a cyclone with an inlet width of 0.125 m, inlet velocity 15 m/s and 5 effective turns, for dust of density 2500 kg/m³ in air (viscosity 1.8 × 10⁻⁵ Pa·s, density 1.2 kg/m³).Numerical
Lapple's model gives d_pc = [9μB/(2π·N_e·V_i·(ρ_p − ρ))]^(1/2). Substituting, d_pc = [9 × 1.8 × 10⁻⁵ × 0.125/(2π × 5 × 15 × 2498.8)]^(1/2) = (2.025 × 10⁻⁵/1.177 × 10⁶)^(1/2) ≈ 4.1 × 10⁻⁶ m, about 4 µm. Particles of this size are collected with 50% efficiency; the inlet width and number of turns must be included, since a formula without them is dimensionally wrong.
9.What is the role of electrostatic precipitators in gas cleaning?Concept
Electrostatic precipitators are used in gas cleaning to remove fine particles from gas streams by applying a high-voltage electrostatic charge to the particles. The charged particles are then attracted to and collected on oppositely charged plates. This method is highly effective for removing small particles and is commonly used in power plants and industrial processes to reduce particulate emissions.
10.If a cyclone separator is not achieving the desired separation efficiency, what steps can be taken to improve it?Application
To improve the separation efficiency of a cyclone separator, one can increase the inlet velocity to enhance centrifugal forces, adjust the cyclone dimensions to optimize flow patterns, or install a series of cyclones in parallel or series to handle larger volumes or finer particles. Additionally, ensuring proper maintenance and operation can prevent blockages and maintain optimal performance.
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