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NWe crit for low-viscosity fluids commonly ranges from 10 to 20, with
the larger value for a free-fall condition and the smaller for a sudden
acceleration. High liquid viscosity also increases NWe crit.
Droplet breakup via impingement appears to follow a similar relationship,
but much less data is available. This type of breakup can
result from impingement on equipment walls or compressor blades.
In general, there is less tendency to shatter on wetted surfaces.
Droplet Size Distribution Instead of the single droplet size
implied by the discussion above, a spectrum of droplet sizes is produced.
The most common ways to characterize this spectrum are:
• Volume median (mass median) Dvm. This has no fundamental meaning
but is easy to determine since it is at the midpoint of a cumulative-volume
plot.
• Sauter mean D32. This has the same ratio of surface to volume as the
total drop population. It is typically 70 to 90 percent of Dvm. It is frequently
used in transport processes and is used here to characterize
drop size.
• Maximum Dmax. This is the largest-sized particle in the population.
It is typically 3 to 4 times D32 in turbulent breakup processes, per
Walzel [International Chemical Engineering, 33, 46, (1993)]. It is
the size directly calculated from the power/mass relationship. D32 is
estimated from Dmax by
D32 = 0.3⋅Dmax
(14-193)
and Dvm is estimated from it by
Dvm = 0.4⋅Dmax
(14-194)
However, any average drop size is fictitious, and none is completely
satisfactory. For example, there is no way in which the high surface
and transfer coefficients in small drops can be made available to the
larger drops. Hence, a process calculation based on a given droplet
size describes only what happens to that size and gives at best an
approximation to the total mass.
There are a variety of ways to describe the droplet population. Figures
14-88 and 14-90 illustrate one of the most common methods, the
plot of cumulative volume against droplet size on log-normal graph
paper. This satisfies the restraint of not extrapolating to a negative
drop size. Its other advantages are that it is easy to plot, the results are
easy to visualize, and it yields a nearly straight line at lower drop sizes.
Cumulative volume over the range of 1 to 50 percent can also be
shown to vary approximately as D2 . This is equivalent to finding that
the number of droplets of a given size is inversely proportional to the
droplet area or the surface energy of the droplet.
Atomizers The common need to disperse a liquid into a gas has
spawned a large variety of mechanical devices. The different designs
emphasize different advantages such as freedom from plugging, pattern
of spray, small droplet size, uniformity of spray, high turndown
ratio, and low power consumption.
As shown in Table 14-19, most atomizers fall into three categories:
1. Pressure nozzles (hydraulic)
2. Two-fluid nozzles (pneumatic)
3. Rotary devices (spinning cups, disks, or vaned wheels)
These share certain features such as relatively low efficiency and
low cost relative to most process equipment. The energy required to
produce the increase in area is typically less than 0.1 percent of the
total energy consumption. This is because atomization is a secondary
process resulting from high interfacial shear or turbulence. As droplet
sizes decrease, this efficiency drops lower.
Other types are available that use sonic energy (from gas streams),
ultrasonic energy (electronic), and electrostatic energy, but they are
less commonly used in process industries. See Table 14-19 for a summary
of the advantages/disadvantages of the different type units. An
expanded discussion is given by Masters [Spray Drying Handbook,
Wiley, New York (1991)].
Special requirements such as size uniformity in prilling towers can
dictate still other approaches to dispersion. Here plates are drilled
with many holes to develop nearly uniform columns.
Commonly, the most important feature of a nozzle is the size of
droplet it produces. Since the heat or mass transfer that a given dispersion
can produce is often proportional to (1/Dd) 2 , fine drops are
usually favored. On the other extreme, drops that are too fine will not
PHASE DISPERSION 14-93
settle, and a concern is the amount of liquid that will be entrained
from a given spray operation. For example, if sprays are used to contact
atmospheric air flowing at 1.5 m/s, drops smaller than 350 mm
[terminal velocity = 1.5 m/s (4.92 ft/s)] will be entrained. Even for the
relative coarse spray of the hollow-cone nozzle shown in Fig. 14-88,
7.5 percent of the total liquid mass will be entrained.
Hydraulic (Pressure) Nozzles Manufacturers’ data such as
shown by Fig. 14-88 are available for most nozzles for the air-water
system. In Fig. 14-88, note the much coarser solid-cone spray. The
coarseness results from the less uniform discharge.
Effect of Physical Properties on Drop Size Because of the
extreme variety of available geometries, no attempt to encompass this
variable is made here. The suggested predictive route starts with airwater
droplet size data from the manufacturer at the chosen flow rate.
This drop size is then corrected by Eq. (14-195) for different viscosity
and surface tension:
Dvm, system
� Dvm, water
=� � 0.25
� � 0.25
σsystem µ�
where Dvm = volume median droplet diameter
σ=surface tension, mN/m (dyn/cm)
µ� = liquid viscosity, mPa⋅s (cP)
(14-195)
The exponential dependencies in Eq. (14-195) represent averages of
values reported by a number of studies with particular weight given to
Lefebvre ([Atomization and Sprays, Hemisphere, New York (1989)].
Since viscosity can vary over a much broader range than surface tension,
it has much more leverage on drop size. For example, it is common
to find an oil with 1000 times the viscosity of water, while most
liquids fall within a factor of 3 of its surface tension. Liquid density is
generally even closer to that of water, and since the data are not clear
that a liquid density correction is needed, none is shown in Eq.
(14-195). Vapor density also has an impact on dropsize but the impact
is complex, involving conflicts of a number of effects, and vapor density
is commonly omitted in atomizer dropsize correlations.
Effect of Pressure Drop and Nozzle Size For a nozzle with a
developed pattern, the average drop size can be estimated to fall with
rising ∆P (pressure drop) by Eq. (14-196):
∆P2 1/3
= � �
(14-196)
For similar nozzles and constant ∆P, the drop size will increase with
nozzle size as indicated by Eq. (14-197):
D 1
� D2
D1
� D2
� 73
� ∆P1
orifice diameter1
orifice diameter2
1/2
= �� � �
(14-197)
Once again, these relationships are averages of a number of reported
values and are intended as rough guides.
The normal operating regime is well below turbulent breakup
velocity. However the data of Kennedy [J. of Engineering for Gas Turbines
and Power, 108, 191 (1986)] at very high pressure drop in large
nozzles shows a shift to a higher dependence on pressure drop. This
data suggests that turbulent droplet breakup can also be governing
with hydraulic spray nozzles, although this is unusual.
Spray Angle A shift to a smaller-angle nozzle gives slightly larger
drops for a given type of nozzle because of the reduced tendency of
the sheet to thin. Dietrich [Proc. 1st Int. Conf. Liq. Atomization Spray
Systems, Tokyo (1978)] shows the following:
Angle 25° 50° 65° 80° 95°
Dvm, µm 1459 1226 988 808 771
In calculating the impact point of spray, one should recognize that
the spray angle closes in as the spray moves away from the nozzle. This
is caused by loss of momentum of the spray to the gas.
� 1.0