Description

Reverse-flow cyclone of standard Lapple proportions, for gas–solid separation. Every dimension is a fixed multiple of the body diameter $D_c$, which makes the Lapple model the classical basis for the preliminary design of dust cyclones.

Lapple cyclone

Calculation methods

• Sizing for a target cut size: body diameter and number of cyclones in parallel required to reach a given cut size within the maximum inlet velocity and pressure drop; also the pressure drop, blower power and principal dimensions.
• Dimensions: cut size, inlet velocity, pressure drop, blower power and principal dimensions of a cyclone of known diameter.
• Grade efficiency curve: collection efficiency as a function of particle size.
• Dust split from the cyclone diameter and from the cut diameter: division of a particle size distribution into the collected (underflow) and escaping (overflow) streams, with the overall collection efficiency.

Model

For $N$ identical cyclones in parallel, each receiving $q = Q/N$:

$V_i = \frac{q}{H W} = \frac{8 q}{D_c^2} \qquad d_{50} = \sqrt{\frac{9 \mu W}{2 \pi N_e V_i (\rho_p - \rho)}} = \sqrt{\frac{3 \mu D_c^3}{128 \pi q (\rho_p - \rho)}}$

$\Delta P = N_H \frac{\rho V_i^2}{2},\ N_H = 8 \qquad \eta(d) = \frac{1}{1 + (d_{50}/d)^2}$

where $V_i$ is the inlet velocity, $N_e = 6$ the number of effective turns, $N_H = K H W / D_e^2$ the number of inlet velocity heads ($K = 16$), $\rho_p$ and $\rho$ the particle and gas densities and $\mu$ the gas viscosity. Standard proportions: $L_1 = L_2 = 2D_c$, $H = D_e = D_c/2$, $W = D_d = D_c/4$, $L_3 = 5D_c/8$.

Design criteria

• Inlet velocity between 15 and 25 m/s and pressure drop up to 2.5 kPa; both limits may be changed under Design coefficients. With $N_H = 8$, a pressure drop of 2.5 kPa in air corresponds to an inlet velocity of about 23 m/s, so the pressure limit generally governs the sizing.
• Default properties: air at 20 °C and 1 atm, quartz particles (2650 kg/m³).
• The model neglects mass loading and bypass and tends to overestimate the collection of the finest particles; it is intended for preliminary design.