The overall collection efficiency of an ESP is given by the famous Deustsch Anderson equation.
where, f = specific collection area of the electrode
and Ud = average migration velocity of the charges dust particles towards the collection electrode.
where, n = number of channels used in parallel to the gas stream in a stage,
l = length of the plates and
h = height of the plates.
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From equation (5.19) it becomes clear that by increasing the length of the plate and/or the migration velocity, we expect and increase in the collection efficiency and vice-versa. If U sub d and h remain constant, an increase in efficiency from 60 to 907.5% will entail an increase of the length of the plates by 4 times.
Deustsch-Anderson equation is based on the condition of mass equilibrium, uniform dust concentration, size distribution and charging conditions in the separating, and layer formation and trapping conditions, as also the constant value of migration velocity irrespective of size distribution, voltage and field distribution and physico-chemical characteristics of gas and dust. It also does not take into account the rapping conditions and consequent re-entrainment of the particles.
With the known efficiency and employing a representative model Esp under similar gas operating conditions, dust concentrations, size distribution and rapping mechanism, and field strength, the effective migration velocity Ud for the dust particles, maybe as certained.
This drift velocity, may then be used to calculate the dimensions of the actual precipitator. It may be noted, however, that the empirically determined values of Ud should always be treated with caution, for any attempt to generalize the values prove to be utterly misleading.
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The Ud is a strong function of particle size, field strength and viscosity of the gas, generally given as,
where C cunningham correction factor for particle slip and is given by,
where λ is mean free path of air, µ m and dp is also in µm
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Eo = charging field strength, V/m
Ep = collecting field strength, V/m
p = viscosity of the gas tream pq.s
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Mean Drift or migration velocity of some of the industrial dust is given in Table 9.4.
For a known size distribution of particles, the cumulative efficiency can be determined as,
where Xi is the weight fraction of particles of average size dp.