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Graseby-Andersen Mark III cascade impactor for particle size classification

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In this method, particulate matter is withdrawn under isokinetic
conditions and segregated by size in an cascade impactor. The Andersen
Mark III cascade impactor uses the principle of inertial separation
to size segregate particulate samples from the gas stream. The impactor
has eight stages for particle size determination. Each stage gives
a cut-point based on aerodynamic diameter of the particle.

Aerodynamic diameter is defined as the diameter of a sphere of unit density ( 1 g/cm3 ) that attains the same terminal settling velocity (vs) at a low Reynolds number as the actual particle under consideration. For mathematical modeling purposes, it is convenient to express the behavior of an irregularly shaped particulate specimen as if it were a spherical particle. Use of such common denominators makes it easier to predict, compare and correlate various materials. The Stokesian, or Equivalent, Diameter is the diameter of a sphere having the same terminal settling velocity and density as the particle under consideration. Typically, the density of a particulate sample is not known during field sampling. All calculations in the field are therefore performed assuming unit particle density ( 1 g/cm3 ).

During sampling, the particles are driven (jetted) toward a collecting surface where they may cling. By changing the velocity (orifice size of the jet), the size of the particles collected is controlled. The size of the jets within each stage is constant, but for each succeeding stage the jets get smaller. Impaction occurs when the particle's inertia overcomes the aerodynamic drag. Otherwise, the particle remains in the air stream and proceeds to the next stage. To keep the cut-point for each stage constant, the impactor must be operated at a constant flow rate. At each stage, the particle impacts on a desiccated, tared, Whatman 934AH glass fiber mat. Following sampling, the samples are cooled in a desiccator and weighed to 0.00001g.

Test time for particle size distribution is dependent on the actual grain loading of the gas stream. The following definitions are given to aid in the understanding of sampling methodology and data interpretation.

*Reynolds Number (Orifice Flow)*

The Reynolds number is a dimensionless quantity that establishes
the proportionality between fluid inertia and the sheer stress due
to viscosity. It's significance in this application is that it can
be used to determine whether or not the flow through the orifice
was laminar or turbulent. One strives to avoid turbulence within
the impactor as this could disturb the particulate on the individual
stages. As a general rule of thumb, Reynolds numbers greater than
4000 represent totally turbulent conditions, whereas values in the
range of 1000 to 2000 represent laminar flow. In the region between
these two values, the flow contains both laminar and turbulent components.

*Cut Diameter (D50) of Various Particle Sizes*

Cut diameter is calculated for each stage. It is the particle diameter
for which the efficiency and the penetration is 50% or where half
these size particles are captured and half penetrate the collector.

*Reynolds Number (Particle)*

This quantity is a dimensionless number used to characterize the
movement of a particle in a system where the containing walls have
essentially no effect on the motion of the particle (as is the case
in an ESP). During impactor data reduction, the terminal setting
velocity of the particles must be calculated. This velocity is used
to determine the first stage cut diameter (D50). These calculations
involve a dimensionless drag coefficient (often called the particle
friction factor) which is dependent on the particle Reynolds number.

*Knudsen Number (Particle)*

This dimensionless number is used to indicate how far a gaseous
system (including the particles) deviates from a continuous system.
When this value is less than 0.1 (larger particles), the gas flow is in
the continuum regime and one set of equations are used to obtain velocity.
When the Knudsen number is between 0.1 and 1 (smaller particles), the gas
flow is considered to be in the slip flow regime and a correction to the
equations for the continuum regime is used when calculating velocity. With
slip flow, the particle appears to "slip through" the gas molecules.

*dM/dlogD*

This is the differential particle size distribution. It assumes
that all mass captured on a given stage in the impactor consists
of material with diameters greater than the D50 of that stage and
less than the D50 of the previous stage. Since the intervals between
these D50s are logarithmically related, the change in mass (dM)
divided by the change in size (dlogD) gives an approximation of
the amount of material contained in that size band. By comparing
these values for inlet and outlet test runs, fractional efficiencies
(efficiencies for given size bands) for the pollution control device
can be easily obtained.

*Geometric Mean Diameter*

Most aerosols (e.g., fly ash in flue gas) have particle size distribution
that are approximately log-normal. That is, they have a bell-shaped
curve if the number of particles of a given size are plotted as
a function of the logarithm of their diameter. The diameter corresponding
to the center of the bell-shaped curve for this distribution is
called the geometric mean diameter. In addition, a geometric mean
diameter can be calculated for each size band of the differential
size distribution (see above). These individual diameters are then
used to plot each value of dM/dlogD (for a given impactor stage)
as a function of the logarithm of the geometric mean for that size
interval.

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