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Cyclone Calculator

Effective turns equals pi over h times 2 cylinder length plus cone length

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Effective Turns

Calculates the number of effective turns the gas makes inside the cyclone based on inlet height, cylinder length, and cone length.

N = π/h × (2L_cyl + L_cone)

Cut Diameter

Determines the particle size at which the cyclone achieves 50% collection efficiency.

d_cut = √(9μ_g W / 2πN v_i (ρ_p − ρ_g))

Radial Velocity

Describes how fast particles migrate outward due to centrifugal force.

v_r = (ρ_p − ρ_a) r ω² d² / 18μ

Pressure Drop

Quantifies the energy cost of operating the cyclone.

P_drop = 3950 K Q² P ρ_g / T

Separation Factor

Compares radial velocity to settling velocity. A factor greater than 1 indicates effective separation.

S = v_r / v_s

How It Works

A cyclone separator spins dirty gas at high speed so that centrifugal force pushes heavier particles outward against the wall while clean gas exits through a central vortex. Five core equations govern cyclone design: effective turns, cut diameter, radial velocity, pressure drop, and separation factor.

Example Problem

A cyclone has an inlet height of 0.5 m, cylinder length of 1.5 m, and cone length of 2.5 m. How many effective turns does the gas make?

  1. Identify the knowns. Inlet height h = 0.5 m, cylinder length L_cyl = 1.5 m, and cone length L_cone = 2.5 m — the three geometric parameters that govern vortex turn count.
  2. Identify what we're solving for. We want the effective number of turns N the gas makes inside the cyclone before exiting through the central vortex.
  3. Write the effective turns formula: N = (π / h) × (2 × L_cyl + L_cone). The path length scales with the cylinder length doubled (gas spirals down and back up the cylinder) plus the cone length.
  4. Substitute the known values: N = (π / 0.5) × (2 × 1.5 + 2.5) = 6.2832 × 5.5.
  5. Simplify the arithmetic: 2 × 1.5 + 2.5 = 5.5 m of vertical sweep, and π / 0.5 = 6.2832 turns per meter.
  6. Compute the product: N = 6.2832 × 5.5 ≈ **34.6 turns** — typical for a high-efficiency cyclone where more turns mean more centrifugal exposure and finer particle capture.

Key Concepts

Cyclone separators exploit centrifugal force to remove particles from a gas stream. Dirty gas enters tangentially, creating a vortex that pushes heavier particles outward against the wall while clean gas exits through a central tube. Performance depends on five interrelated parameters: the number of effective turns the gas makes, the cut diameter (particle size at 50% efficiency), radial migration velocity, pressure drop, and separation factor.

Applications

  • Industrial air pollution control: removing dust and particulates from factory exhaust streams
  • Woodworking shops: separating sawdust and chips from air before it reaches the dust collector bag
  • Grain handling: removing chaff, dust, and lightweight debris from grain in agricultural processing
  • Cement and mining: pre-cleaning kiln exhaust and crusher dust before baghouse or ESP treatment
  • Oil and gas: separating sand and liquid droplets from natural gas in production facilities

Common Mistakes

  • Expecting high efficiency on fine particles — standard cyclones struggle below 5 µm; PM2.5 requires high-efficiency designs or downstream filters
  • Ignoring the pressure drop trade-off — higher inlet velocity improves efficiency but increases fan power consumption and operating cost
  • Using air-density values for process gases — gas density and viscosity vary with temperature and composition, significantly affecting cut diameter
  • Oversizing the cyclone — too large a diameter reduces centrifugal force and degrades collection efficiency

Frequently Asked Questions

What does cut diameter mean in a cyclone separator?

The cut diameter d_cut is the particle size at which the cyclone achieves 50% collection efficiency. Particles larger than d_cut are mostly captured against the wall; smaller particles mostly escape with the clean-gas exit stream. Standard cyclones cut at 5–25 µm; high-efficiency designs push d_cut below 5 µm.

How does inlet velocity change cyclone performance?

Higher inlet velocity multiplies centrifugal acceleration (v_i² / r), which boosts radial particle migration and collection efficiency. The trade-off is a roughly quadratic rise in pressure drop and fan power. Typical inlet velocities stay between 15 and 25 m/s — fast enough to separate, slow enough to keep ΔP manageable.

Can a cyclone reliably remove PM2.5?

Standard cyclones are not efficient below ~5 µm. For PM2.5 control you need high-efficiency cyclone designs (smaller body diameter, longer cone, higher inlet velocity) often as a pre-cleaner, with a baghouse or electrostatic precipitator polishing the remaining fines downstream.

What is the role of the number of effective turns N?

N counts how many times the dirty gas spirals around the body before reaching the exit. More turns means longer residence time in the high-G zone, which gives finer particles more chances to migrate to the wall. N = π/h × (2 L_cyl + L_cone) ties N directly to body geometry.

How does separation factor S compare to gravity settling?

S = v_radial / v_settling tells you how many g's the cyclone applies relative to terrestrial gravity. A small industrial cyclone easily reaches S = 50–500, meaning particles separate at 50–500 times their gravitational settling rate — that's why cyclones are vastly more compact than gravity settling chambers.

Why does pressure drop matter for cyclone economics?

Every Pa of ΔP costs continuous fan power: P_fan = Q × ΔP / η. A cyclone that improves efficiency by 5 percentage points but adds 1000 Pa of ΔP may double the operating cost over the equipment's life. ΔP scales with K, Q², gas density, and inversely with absolute temperature — hot gases reduce ΔP automatically.

What happens if I oversize a cyclone?

Larger body diameter reduces tangential velocity for the same volumetric flow (Q = v × A_inlet), which cuts centrifugal acceleration and degrades collection efficiency. Multi-cyclone arrangements — many small high-G cyclones in parallel — outperform one big low-G cyclone for the same total flow.

Worked Examples

Air Pollution Control — Fly Ash

What cut diameter does a 0.3 m-wide industrial cyclone achieve on coal fly ash with N = 5 effective turns and 18 m/s inlet velocity?

A coal-fired boiler exhausts fly ash (ρ_p ≈ 2300 kg/m³) into a primary cyclone before the electrostatic precipitator. With inlet width W = 0.3 m, effective turns N = 5, inlet gas velocity v_i = 18 m/s, gas viscosity μ_g = 1.8×10⁻⁵ Pa·s, and gas density ρ_g = 1.2 kg/m³, compute the 50%-cut particle diameter.

  • Knowns: μ_g = 1.8×10⁻⁵ Pa·s, W = 0.3 m, N = 5, v_i = 18 m/s, ρ_p = 2300 kg/m³, ρ_g = 1.2 kg/m³
  • d_cut = √(9 × μ_g × W / (2π × N × v_i × (ρ_p − ρ_g)))
  • d_cut = √(9 × 1.8×10⁻⁵ × 0.3 / (2π × 5 × 18 × (2300 − 1.2)))
  • d_cut = √(4.86×10⁻⁵ / 6.50×10⁶)
  • d_cut = √(7.48×10⁻¹²)

d_cut ≈ 2.7 × 10⁻⁶ m = 2.7 μm

Particles larger than d_cut are collected with > 50% efficiency; particles smaller than d_cut pass through. Cement, fly ash, and grain dust cyclones typically target d_cut in the 5–15 μm range — finer than that needs a venturi scrubber or baghouse downstream.

Cyclone Geometry — Effective Turns

How many effective turns does a Stairmand high-efficiency cyclone with h = 0.6 m, L_cyl = 1.5 m, L_cone = 1.5 m make?

Cyclone collection efficiency rises with the number of effective gas-rotation turns N. For a Stairmand-style design with inlet height h = 0.6 m, cylindrical section length L_cyl = 1.5 m, and conical section length L_cone = 1.5 m, compute N from the geometric path formula.

  • Knowns: h = 0.6 m, L_cyl = 1.5 m, L_cone = 1.5 m
  • N = (π / h) × (2 × L_cyl + L_cone)
  • N = (π / 0.6) × (2 × 1.5 + 1.5)
  • N = (π / 0.6) × 4.5
  • N = 5.236 × 4.5

N ≈ 23.6 turns

Stairmand high-efficiency cyclones typically achieve 5–10 effective turns; conventional cyclones run 2–6. Doubling the cylinder length raises N but also raises pressure drop and fabrication cost — diminishing returns set in around N = 8.

Cyclone Performance — Separation Factor

What separation factor does a cyclone provide when the radial velocity is 5 m/s and the gravitational settling velocity is 0.02 m/s?

The separation factor S compares cyclone-driven radial velocity v_r to free-settling velocity v_s of the same particle in air. With v_r = 5 m/s and a 10 μm fly-ash particle whose Stokes settling velocity is about 0.02 m/s, compute S to see how many g’s of effective acceleration the cyclone provides.

  • Knowns: v_r = 5 m/s, v_s = 0.02 m/s
  • S = v_r / v_s
  • S = 5 / 0.02

S = 250

A separation factor of 250 means the cyclone separates the particle 250× faster than gravity alone — equivalent to roughly 250 g of centrifugal acceleration on the particle. Industrial cyclones typically run S between 100 and 1000; the higher the inlet velocity and the smaller the cyclone diameter, the larger S becomes.

Cyclone Separator Formulas

Five interrelated equations describe how a cyclone separator captures particulate from a gas stream:

N = (π / h) × (2 Lcyl + Lcone)Effective number of turns inside the body
dcut = √( 9 μg W / (2π N vi (ρp − ρg)) )Cut diameter (50% collection efficiency)
vr = (ρp − ρa) r ω² d² / (18 μ)Radial migration velocity of a particle
ΔP = 3950 × K × Q² × P × ρg / TPressure drop across the cyclone
S = vr / vsSeparation factor (centrifugal vs. gravity)

Where:

  • N — effective turns the gas makes inside the body (dimensionless)
  • h — inlet height (m); Lcyl, Lcone — cylinder and cone lengths (m)
  • dcut — cut diameter — particle size collected at 50% efficiency (m or µm)
  • μg, μ — gas dynamic viscosity (Pa·s)
  • W — inlet width (m)
  • vi — inlet (tangential) gas velocity (m/s)
  • ρp, ρg, ρa — particle, gas, and air density (kg/m³)
  • vr — radial particle velocity (m/s); vs — gravitational settling velocity (m/s)
  • r — radial position inside the cyclone (m); ω — angular velocity (rad/s)
  • d — particle diameter (m)
  • ΔP — total pressure drop (m H₂O)
  • K — proportionality factor (dimensionless, ~12–18 for standard designs)
  • Q — volumetric flow rate (m³/s); P — absolute gas pressure (atm internally); T — absolute gas temperature (K)
  • S — separation factor (dimensionless); S >> 1 indicates effective centrifugal separation

These design relations assume Stokes-regime particle motion (small, spherical particles in laminar relative flow) and a steady, swirling gas core. Real high-efficiency cyclones add corrections for vortex finder diameter, gas re-entrainment, and turbulent re-mixing, but these five equations remain the textbook starting point for sizing and optimization.

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