Chemical Engineering August 2019 - 29

recent studies typically find that the
pumping number is a characteristic
of the type of impeller, independent
of D/T, and is often related to the impeller
power number.
The literature on liquid mixing describes
a pumping number or flow
number in a few different ways [13],
depending on the impeller type and
flow pattern. A measured average
velocity across the swept circular
area of an axial discharge impeller
or the cylindrical area around a radial
discharge impeller can be used
to define a discharge pumping number,
NQ. As soon as the flow leaves
the discharge of an impeller, it begins
to entrain surrounding fluid, increasing
the effective volumetric pumping
capacity. Depending on the impellerto-tank
diameter ratio, D/T, the entrained
flow will recirculate and can
be described by a circulating pumping
number. The circulating pumping
of an impeller is important for both
the velocity and flow pattern in the
tank. For example, the motion above
a down-pumping, axial-flow impeller
is a result of circulating flow.
Call the
Solids Mixing
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The experimental and analytical
methods for defining mixing properties
often create empirical relationships
that, while useful for basic
analysis, often fail to include the effect
of volume on mixer size or effectiveness.
The impeller power number
and pumping number are both
commonly reported impeller characteristics.
The dimensionless impeller
power number, NP, contains the
obviously important mixer variables:
power, P; rotational speed, N; impeller
diameter, D; and fluid density, ρ.
To make the power number dimensionless
using U.S. customary units
requires a large conversion factor.
(1)
The power number is effectively a
constant for a given impeller geometry
under turbulent conditions in a
baffled tank. Impeller geometry factors,
such as number of blades, blade
width and blade angle, do affect the
power number, but D/T has a relatively
minor effect in most cases. No
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27
amount of manipulation of the variables
in the power number will tell you
if a mixer will provide sufficient mixing
or not, because the relationship is independent
of tank size.
Even the obvious effect of viscosity
on power is not reflected in the
power number. Instead, the power
number is typically correlated as a
function of impeller Reynolds number,
NRe.
(2)
The conversion factor in the Reynolds
number makes it dimensionless
when using U.S. customary units
with density, ρ, in specific gravity
and viscosity, μ, in centipoise. Power
number correlations can be found in
a number of references, but some of
the more relevant ones are in mixing
handbooks such as Refs. 14 and 15.
The impeller Reynolds number is
similar in concept to a pipe Reynolds
number but has entirely different
values. Turbulent conditions in a
stirred tank exist for NRe > 20,000.
Q ual
191
ity &
Since
1
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Chemical Engineering August 2019

Table of Contents for the Digital Edition of Chemical Engineering August 2019
