IMPROVE Critical Orifice Flow Control

Author: Robert Eldred, CNL, University of California,
Davis (__raeldred@ucdavis.edu)__

Date: May 4, 1998

The IMPROVE Critical Orifice Control System

__Summary__: The primary purpose of flow control is to keep
the volume flow rate through the cyclone or PM_{10} inlet as close as
possible to the nominal rate for the 2.5 or 10 µm cut. There are several
factors producing a variation in the flow rate for a critical orifice: the
diurnal and seasonal variation of ambient temperature, the change in pressure
drop across the filter associated with variation in clean filters, and the
change in pressure drop across the filter associated with mass loading. The
estimated total variation in inlet flow rate with a critical orifice controller
from all three factors is generally less than 3%. This is similar to the
standard deviation in flow rates observed in the network. **The conclusion is
that a critical orifice system is reasonable if a variation in flow rate of
approximately 3% is acceptable.**

In the current IMPROVE sampler, the flow rate is measured before and after collection, but is not monitored during the sampling period. The secondary purpose of flow control is to assure that the measured flow rate represents the true average flow rate. That is, the flow controller must eliminate all unusual changes in flow rate during sampling. Measurements made at an eastern site in summer 1997 indicate that the flow rate behaves normally even with high mass loading and high relative humidity. In the new version of the IMPROVE sampler, to be installed during 1998, the flow rate will be monitored throughout the sampling period, making this purpose unnecessary.

The two major advantages of a critical orifice system is reliability and minimal maintenance. The reliability has been verified over the ten years of the IMPROVE network. The traditional mass flow control system is an unsatisfactory alternative, partly because it does not control the volume flow rate as well as a critical orifice system and partly because of high maintenance. The volume flow control systems proposed by several manufacturers for the FRM sampler appear to do an excellent job of controlling the volume flow rate. The maintenance requirements are less than with earlier mass flow systems, but still greater than with the critical orifice system. We have considered using a similar system, but have decided to wait until the reliability of these controllers has been verified in the FRM network. We will also wait to see if this method significantly increases the precision of the measurements.

__I. Flow Rate and Particle Size Cut__

Section I will examine the variation in flow rate for the IMPROVE sampler as it affects the particle size cut by the cyclone. The relationship between flow rate and the 50% aerodynamic diameter for the IMPROVE cyclone is

, (1)

On the other hand, the accuracy and precision of the air volume depends on how well the measured flow rates represent the true average flow rate, rather than how the flow rate compares to the nominal. Possible errors and uncertainties in volume will be discussed in Section II.

__Equations__: The volume flow rate *at the critical
orifice* depends on the geometry of the orifice (primarily the diameter) and
the square root absolute temperature of the air at the front of the orifice, but
not on the pressure at the orifice:

Q' = k * , (2)

where k is a constant and Tc is the temperature at the critical orifice. Tests at Davis have shown no significant difference between the temperature at the cyclone and the temperature at the critical orifice. Therefore the subscript can be dropped.

The flow rate at the critical orifice differs from the volume
flow rate *at the inlet and cyclone* because of the pressure across the
filter. Because there is very little pressure drop across the cyclone, the
volume flow rate after the cyclone is equal to the volume flow rate at the
inlet. The volume flow rate *at the cyclone* is:

Q = Q' * = k * , (3)

where P is the decrease in pressure before the orifice and P is the ambient pressure.

To account for the pressure drop of the clean filter, each critical orifice is adjusted during calibration to give the desired flow rate with a typical clean filter appropriate for the module. If the nominal pressure drop used in calibration is Pcal, the flow rate during calibration is:

Qcal = k * , (4)

Combining Equations 2 and 3 and eliminating k, the flow rate is given by:

Q = Qcal * . (5)

Expanding the pressure term and dropping terms beyond the second order:

1 - = 1 - (6)

where P is the variation of the pressure drop from the nominal used in calibration.

The critical orifice controller is calibrated to provide a flow rate of 23 L/min for an ambient temperature of 20C and for the elevation of the site. (This yields a 2.5 µm cut point at 15°C.) The equation for the flow rate at the cyclone is then

Q = 23.0 * * . (7)

The pressure term of Equation 7 depends on the variation in the pressure drop across the filter from the nominal. There are two reasons for nonzero P: (1) the pressure drop for a given clean filter may vary from that of the nominal filter, and (2) the loading of the filter will increase the pressure drop. The variation in ambient pressure at the site is a lower order effect and can be safely ignored.

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__Variation in Pressure Drop for Clean Filters__: The effect
of the variation in clean filters can be estimated from the standard deviation
of the pressure drops of the initial readings in the field. This was done for
select sites during 1992 and 1997. For the PM_{2.5} Teflon and quartz
filters, the resulting variation in flow rate was 0.7% and 1.4%, respectively,
corresponding to a change in cut point of less than 0.1 m. The
values for Teflon included both full 35 mm filter and those masked to 2.2 cm^{2}.
For the 47mm nylon filters used in 1992, the variation was 1.1%. In 1994, we
shifted from 47mm to 25 mm filters. Recently there has been some quality
control problems with nylon filters, producing a larger variation in pressure
drop. Thus, in 1997, the variation increased to 3.9%. If quality control
problems persist, we will shift back to 47 mm filters in the new version of the
sampler. This larger uncertainty in the nylon flow rate will affect the IMPROVE
concentrations for sulfate and nitrate. We have investigated the relationship
between sulfate measured on nylon and sulfur measured on Teflon, comparing the
period with 47 mm nylon with the period using 25 mm nylon. Figure 1 plots the
distributions of the ratios of the difference between S*3 and SO_{4} for
1993 and 1997. Also shown is the theoretic fit expected for a Gaussian. If
there had been a major shift in the uncertainty for sulfate on nylon, the 1997
distribution would become more spread out. The two years are nearly identical.
The conclusion is that the change in the uncertainty in sulfate-on-nylon is too
small to detect.

Figure 1. Distribution of the difference between the sulfate measured on Teflon (sulfur times 3) and sulfate measured on nylon. Also shown is the expected Gaussian fit. In 1993, the nylon filters were 47 mm, while in 1997 they were 25 mm.

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__Change in Pressure Drop because of Filter Loading__: The
filter loading pressure effect can be estimated from mean difference between the
initial and final pressure drop readings for the same samples. For the Teflon
and quartz filters, the effect on flow rate has generally been small: 1% for
Teflon, and 0.1% for quartz. These small values were obtained with full 25 mm
Teflon filters at eastern sites and with the collection area masked to 2.2 cm^{2}
at most western sites. The effect was slightly larger for 25 mm nylon filters,
3% at most sites and 8% at Shenandoah and Dolly Sods.

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__Temperature Effects__: The temperature effect in flow rate
is proportional to the square root of the absolute temperature. Table 1 gives
the variation in flow rate Q and d50 as
a function of temperature, for the typical system in the IMPROVE network, which
is calibrated to provide a cut point of 2.5 µm at 15°C,
the median temperature for the IMPROVE network.

Table 1: Flow rate
and 50% aerodynamic diameter *vs*. temperature

T (C) -20 -10 0 10 20 27 30 40

Q (L/min) 21.4 21.8 22.2 22.6 23.0 23.2 23.4 23.8

d50 (m) 3.0 2.8 2.7 2.5 2.4 2.3 2.3 2.2

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For the entire network in 1997, the extreme temperatures at the time of the sample change ranged from -20°C to 40°C, the range used in Table 1. Eighty percent of the samples had temperatures between 0°C and 27°C, corresponding to cut points of 2.7 and 2.3 µm. In addition, we examined the variation in temperature at the Grand Canyon IMPROVE meteorological site for 1990; the standard deviation in absolute temperature over the year was 3.8%. Since the variation in flow rate depends on the square root of this, the standard deviation in flow rate was less than 2%.

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__Conclusions on the variation in flow rate__: For the
critical orifice the quadratic sum of pressure and temperature contributions
give a total variation in flow rate of less than 3% for Teflon and quartz
filters. The variation is also below 3% for 47mm nylon filters, but has
recently risen to about 6% for 25 mm nylon, partly because of quality control in
the filter material. In practice, the current critical orifice controllers
maintain the flow rate as predicted. The mean measured flow rates for all PM_{2.5}
samples for 6 years from March 1991 to February 1996 was 22.4 L/min with a
standard deviation of 0.7 L/min (3%). This corresponds to a mean and standard
deviation in d_{50} of 2.6
0.3 m.

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__II. Accuracy and Precision of Volume Calculation__

The current method is to measure the flow rate before and after sample collection using two independent gauges. The mean flow rate during sampling is defined as the mean of the two values. The two major assumptions with this method are (1) the average temperature during sampling does not significantly vary from the temperatures at the two sample changes, and (2) the flow rate behaves reasonably. In 1998, the IMPROVE sampler will monitor the flow rate continuously. Thus, this section will no longer be applicable. It will also provide useful information to quantify the effect for the past 10 years.

__Temperature Bias during
Sample Change__: If the average temperature during the two sample changes
differs from the average temperature for the sampling period, the volume
calculation will be incorrect. We examined 1990 Grand Canyon meteorological
data, comparing the mean square root of absolute temperature for the Wednesday
and Saturday sampling periods with those for various change hours on Tuesday.
The largest single possible error for the year was less than 3%. There could be
a systematic bias if the operator always changed samples during the warmest or
coolest hours. If every change were done at 9 AM, there would be no difference
for the means. The largest changes would have occurred if the changes were
always performed at 2 PM; the error would be 0.6%. The conclusion is that the
temperature assumption does not introduce significant error.

__Unmeasured Fluctuations in
Flow Rate__: The assumption that the flow rate behaves reasonably throughout
the sample collection can be verified using a data logger. This will be done
for every sample in the modified IMPROVE sampler to be installed in 1998. One
test was made at Dolly Sods Wilderness, WV, during summer 1997. This site ranks
near the top in the IMPROVE network for both gravimetric mass and relative
humidity. The primary purpose was to check that the pressure drop across the
filter did not make any sudden changes because of high humidity. For example, a
possible scenario is that the pressure drop for heavily loaded filters would
suddenly increase rapidly as the RH approached 1. This was not observed.

Figure 2 gives the flow rates for
modules A and B (Teflon and nylon), temperature, and relative humidity at Dolly
Sods Wilderness, July 26, 1997. The mass concentration for this sample, 45 µg/m^{3},
was the highest in the study. In 1997, only three samples in the entire network
(all in the east) had higher concentrations. Since the flow rate was monitored
on a sampler with a reduced collection area, an ambient concentration of 70 µg/m^{3}
would be needed to give the same mass per unit area; no samples were at this
level. Thus, this is an extreme case. While there is a steady decrease in flow
rate as the filter loaded (6%), there was no unusual changes associated with
high humidity. The average of initial and final flow rates differed from the
true average by <1%.

Figure 2. Flow rate for modules A and B (Teflon and nylon), temperature, and
relative humidity at Dolly Sods Wilderness, July 26, 1997. The mass
concentration for this sample, 45 µg/m^{3}, was the highest in the
study.

Figure 3 gives the same plots for July 26, 1997, which had
the lowest mass concentration for the Dolly Sods study, 9 µg/m^{3}.
However, this is still a heavily loaded sample, above the median mass
concentration for eastern sites, and larger than 93% of all samples at western
sites. There is a smaller decrease in flow rate (3%) over the sampling period.

Figure 3. Flow rate for modules A
and B (Teflon and nylon), temperature, and relative humidity at Dolly Sods
Wilderness, July 30, 1997. The mass concentration for this sample, 9 µg/m^{3},
was the lowest in the study.

Figure 4 gives the plots for the period with the highest
average relative humidity in the study. The sample is heavily loaded compared
to typical concentrations, corresponding the 97^{th} percentile for
eastern sites and 99^{th} percentile for western sites. Once again
there is no significant error in using the average of the initial and final
readings compared to using the true average.

Figure 4. Flow rate for modules A and B (Teflon and nylon), temperature, and
relative humidity at Dolly Sods Wilderness, August 13, 1997. The relative
humidity was the highest in the study, at about 85% throughout the period.
The temperature remained near 18°C
throughout the period. The mass concentration for this sample was 17 µg/m^{3}.

__III. RELIABILITY, OPERATING CONDITIONS, AND MAINTENANCE__

The critical orifice is a simple passive device that operates at all temperatures, that cannot lose its calibration, and that requires minimal maintenance. At the present time we are operating very efficiently, with a recovery rate of 95%. No samples have been lost because of the critical orifice.