2.1.3 Pressure drop

Pressure drop across the cyclone is of much importance in a cyclone separator. The pressure drop significantly affects the performance parameters of a cyclone. The total pressure drop in a cyclone will be due to the entry and exit losses, and friction and kinetic energy losses in the cyclone. Normally most significant pressure drop occurs in the body due to swirl and energy dissipation. There have been many attempts to predict pressure drops from design variables. The idea is that having such an equation, one could work back and optimize the design of new cyclones. The empirical equation given by Stairmand (1949) can be used to estimate the pressure drop.

 

............................(5.5)

ΔP = cyclone pressure drop

ρ_f = gas density; u₁ = inlet duct velocity; u₂ = exit duct velocity

r_t = radius of circle to which the centre line of the inlet is tangential; r e = radius of exit pipe

Φ = cyclone pressure drop factor

Ψ = f_c (A_s /A₁)

f_c = friction factor, taken as 0.005 for gases

A_s = surface area of cyclone exposed to the spinning fluid

For design purposes this can be taken as equal to the surface area of a cylinder with the

same diameter as the cyclone and length equal to the total height of the cyclone

A_t = area of inlet duct

 

Above equation is for the gas flowing alone, containing no solids. The presence of solid will increase the pressure drop over that calculated using equation (5.5), depending on the solids loading.

Alternative design equation for cyclones occasionally used is:

 

......................(5.6)

Where q = volumetric flow rate

B_c = inlet width, H_c = inlet height, D_c = outlet diameter, Z_c = cone length, L_c = cylinder length

In this equation k_c is a dimensionless factor express of cyclone inlet vanes.

K_C = 0.5 for cyclones without vanes; K_C = 1.0 for cyclone vanes that do not expand the entering gas or touch the outer wall; however K_C = 2.0 for cyclone vanes that expand and touch the outlet all. The above equation when compared with experimental data shows poor correlation coefficient (Theodore, 2008 ).

Another form of the empirical pressure drop an equation which is being widely used:

............................................................................(5.7)

K_C = a proportionality factor, if the is measured in inches, it varies from 0.013 to 0.024, with 0.024 the norm.