Gas & Particle Operating Conditions
Stairmand (1951) high-efficiency & Lapple cyclone separation models
Separation Cut-Point & Pressure Drop
Lapple cut-point (d₅₀), fractional recovery, and fan draft loss
Worked Lapple & Stairmand Separation Derivations
Centrifugal cut-point, fractional efficiency, and velocity head equations evaluated live
Per Stairmand (1951) and Lapple (1951), gas entering tangentially creates a high-velocity outer vortex spinning downward to the cone apex before reversing into an inner clean gas vortex core.
1. Inlet Duct Area & Velocity: For a cyclone barrel diameter D = 0.90 m with Stairmand standard inlet height a = 0.5D (0.45 m) and width b = 0.2D (0.18 m):
v_i = Q / A_inlet = 17.15 m/s (3,375 ft/min)
2. Flue Gas Viscosity (μ) & Density (ρ_g): At operating temperature 150°C (Sutherland Law):
3. Lapple Cut-Point Diameter (d₅₀): Effective vortex turns N_e = 5.5 turns, particle density ρ_p = 2,500 kg/m³:
4. Overall Fractional Collection Efficiency: Evaluated across log-normal particle distribution with MMD = 18.0 μm:
5. Shepherd-Lapple Static Pressure Drop (ΔP): Velocity head coefficient N_H = 6.4 heads:
5 Fatal Traps in Industrial Cyclone Operation
EPA AP-42, Stairmand, and industrial ventilation dust collection guidelines
Cyclones operate under negative pressure (suction) created by the induced draft fan. Even a 2% air leak through a worn rotary airlock or unsealed dump gate at the hopper bottom collapses collection efficiency by 30% to 50%. In-leaking atmospheric air rushes up through the discharge spout, re-entraining settled dust and jetting it straight up into the clean gas exit vortex.
Engineers often assume higher inlet velocity guarantees better separation because centrifugal force scales as v². In reality, pushing inlet velocity above 22–25 m/s (4,500 ft/min) creates severe turbulence at the boundary layer. Dust particles bounce off the barrel wall (saltation) instead of sliding down into the cone, cutting efficiency while abrasive dust wears holes through the steel shell.
Operating an uninsulated cyclone on boiler flue gas or kiln exhaust near the water/acid dew point causes moisture to condense on internal walls. Dry dust combines with sulfuric or hydrochloric acid droplets to form sticky, corrosive mud that bridges the cone apex within hours. Always maintain cyclone wall temperatures at least 15°C (25°F) above the acid dew point.
Fabrication shortcuts that alter the vortex finder insertion depth (S ≠ 0.5D) or barrel transition angles destroy cyclone fluid dynamics. If the vortex finder does not extend past the inlet duct, raw dusty gas short-circuits directly into the outlet without spinning. If it extends too deep into the cone, it intercepts the returning dust stream, discharging uncollected particulate.
Cyclones are inertial separators governed by Stokes' Law: aerodynamic drag on particles smaller than 3 to 5 microns overcomes centrifugal force. For PM₂.₅ and PM₁₀ regulatory compliance, a single cyclone can never replace a fabric filter baghouse or electrostatic precipitator (ESP). Treating a cyclone as an absolute filter rather than a coarse pre-cleaner leads to guaranteed environmental EPA non-compliance.