OpenSpecEngineering

Finds the cut diameter of a cyclone dust collector, the particle size it catches half of, and its collection efficiency for one particle size, by the Lapple method. Process and air-pollution engineers use it to size a cyclone for a dust load, to compare standard designs, and to judge whether a cyclone alone will do or a bag filter must follow it.

Equations

d₅₀ = √(9·μ·W/(2π·N_e·v_i·(ρ_p − ρ_g)))

η = 1/(1 + (d₅₀/d_i)²)

d₅₀ is the cut diameter [1], [3]. μ is the gas viscosity and W the width of the inlet. N_e is the effective number of turns the gas makes in the cyclone, and v_i the gas velocity in the inlet. ρ_p and ρ_g are the particle and gas densities. η is the fraction of particles of diameter d_i that the cyclone catches, from Lapple’s efficiency curve as fitted by Theodore and DePaola [3].

Inputs

• Choosing a Standard Cyclone Design fills in N_e from its proportions: N_e = (L_b + L_c/2)/H, where H is the inlet height and L_b and L_c the lengths of the body and cone [3]. The menu shows each design’s inlet width as a fraction of the body diameter D, so W follows from D.
• Choosing a Gas or a Dust fills in its properties [4]–[6]. Use the solid density of the dust, not its bulk density.
• The inlet velocity is the gas flow divided by the inlet area. Most cyclones run at about 15–25 m/s [2].

Limits and common mistakes

• The result is for one particle size. For a real dust, find η for each size band and weight it by the mass in that band to get the overall efficiency [3].
• A higher inlet velocity gives a smaller cut size, but the pressure drop grows with v_i². Above about 25–30 m/s, dust bounces and is picked up again, and efficiency falls.
• The Lapple model is a first estimate. Heavy dust loads usually collect better than it predicts; sticky or very fine dust can do worse.

Worked example

Cement dust in air at 20 °C goes to a Stairmand high-efficiency cyclone of 600 mm diameter, with an inlet velocity of 18 m/s. What is its cut size, and how much 5 µm dust does it catch?

1. Enter Inlet Gas Velocity 18 m/s.
2. The Stairmand inlet is 0.2D wide, so enter Cyclone Inlet Width 120 mm.
3. Choose Standard Cyclone Design Stairmand high efficiency. N_e fills in as 5.5.
4. Choose Gas Air, 20°C, 1 atm (0.018 cP and 1.2 kg/m³) and Dust Portland cement (3150 kg/m³).
5. Enter Particle Diameter of Interest 5 µm and press Solve. The Solution shows: Cut diameter d50: 3.15042 µm
   Collection efficiency at di = 5 µm: 0.715817
   Collection efficiency: 71.5817 %

Check by hand: 9 × 1.8×10⁻⁵ × 0.12 = 1.944×10⁻⁵, and 2π × 5.5 × 18 × 3148.8 = 1.959×10⁶. The square root of their ratio is 3.15×10⁻⁶ m, or 3.15 µm. Then η = 1/(1 + 0.630²) = 0.716. A cut size of a few microns is typical of a high-efficiency cyclone.