2.1.2 Collection efficiency
The collection or separation efficiency is most properly defined for a given particle size. As mentioned, fractional efficiency is defined as the fraction of particles of a given size collected in the cyclone, compared to those of that size going into the cyclone. Experience shows that collection efficiency of cyclone separator increases with increasing particle mean diameter and density; increasing gas tangential velocity; decreasing cyclone diameter; increasing cyclone length; extraction of gas along with solids through the cyclone legs.
Several equations have been developed to predict the collection efficiency in cyclones through correlation equations. The following section describes two methods of calculating cyclone efficiency. First the theory proposed by Leith and Licht (1973) for calculating fractional efficiency will be discussed and then a convenient graphical method developed by Lappel (1951) will be presented.
The fractional efficiency equation of Leith and Licht is given as:
......................(5.3)
Where c = cyclone dimension factor
Ψ = impaction parameter
n = vortex exponent
.........................................(5.4)
In this expression, c is a factor that is a function only of the cyclone's dimensions. The symbol ψ expresses characteristics of the particles and gas and is known as inertia or impaction parameter. The value of n is dependent on the cyclone diameter and temperature of the gas stream. And ρp times vi expresses the particle's initial momentum. Although the calculation involved in this method are tedious but are straightforward.
A more popular and an older method of calculating cyclone fractional efficiency and overall efficiency was developed by Lappel (1951). He first computed the ratios dp /[dp ]cut from equation 5.2 and it is observed that cyclone efficiency correlates in a general way with this ratio. For a typical cyclone, efficiency will increase as the ratio increases. The preceding correlation has been found to agree well with experimental data. To calculate fractional efficiency, the following procedure given below should be used. The sum of the products in the rightmost column will give the overall efficiency.
Lappel calculation procedure |
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dp range |
Wt fraction in range |
dp /[dp ]cut |
Ei for each dp from experiment or Lappel's method, % |
Wt fraction × Ei |