EPA-AA-TEB-87-01
USE OF HEATED CRITICAL FLOW VENTURI SAMPLE PROBES
TO MAINTAIN PROPORTIONAL FLOW
by
Walter Andrew Adams
February 1987
Test and Evaluation Branch
Emission Control Technology Division
Office of Mobile Sources
U.S. Environmental Protection Agency
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Abstract
The Notice of Proposed Rule-Making (NPRM) for
raethanol-fueled vehicles proposes using sample probes heated to
235°F when sampling for methanol or formaldehyde. When using a
critical flow venturi constant volume sampler (CFV-CVS) to
measure exhaust flow, critical flow venturi (CFV) sample probes
must be used to obtain a constantly proportional exhaust
sample. The gas temperature at the sample CFV must be the same
as that of the bulk stream for the sample flow to be constantly
proportional (when a heat exchanger is not used to control
dilute exhaust temperature). Tests conducted with a sample CFV
heated to 235°F indicated that the gas temperature at the CFV
was not the same as the bulk steam temperature. This caused a
measurable (approx. 3%) change in flow through the CFV. The
conclusion is that a heated CFV may not be able to maintain
constantly proportional flow if the temperature of the dilute
exhaust stream varies. There are viable alternatives to this
approach, such as using a heat exchanger in the CVS or
insulating the venturi from the heated sample line.
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Foreword
The Notice of Proposed Rule-Making (NPRM) for
methanol-fueled vehicles (ref. 1) requires:
1. Proportional sampling of dilute exhaust for methanol
and formaldehyde, and
2. Using heated probes (235 +_ 15 F) when sampling for
these two pollutants. If a critical flow venturi constant
volume sampler (CFV-CVS) is used, the NPRM suggests simply
heating standard CFV sample probes.
In CFV-CVS units which do not use a heat exchanger to
control dilute exhaust temperature (as is the case with most
light-duty CVS units), critical flow venturi sample probes are
used to obtain a constantly proportional exhaust sample. If
applying heat to the venturi causes a change in the temperature
of the gas flowing through it, the flow through the venturi
will no longer be constantly proportional to that of the bulk
stream, as is required by the NPRM. Testing was needed to
determine if a CFV could be heated without affecting the
temperature of the gas flowing through it. This report gives
the results of the testing, documents the difference, and
recommends ways to obtain a heated, constantly proportional
exhaust sample.
Summary
The test results indicate that heating a critical flow
venturi (CFV) does change the flow characteristics of the
venturi (other than those due to thermal expansion). The data
obtained indicate that a sample CFV cannot be used to maintain
constantly proportional flow if it is heated (without
temperature control of the bulk stream), and that other
alternatives will have to be explored if we wish to heat the
probes used for methanol and formaldehyde sampling.
The most viable alternatives are:
1. Using a heat exchanger in the CVS. This would
eliminate the need for CFV's in the sample lines.
2. Not heating the critical flow venturi and insulating
it from the heated sample line. Sample losses should not occur
at the venturi due to the high gas velocity.
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I. Introduction and Theory
Exhaust from methanol-fueled vehicles contains
significant amounts of methanol and formaldehyde. EPA wishes
to regulate emissions of these two pollutants for vehicles
running on blends of 50% or more methanol. Current exhaust gas
sampling systems used for testing gasoline vehicles are not
equipped to measure methanol or formaldehyde.
The NPRM published in August 1986 outlines equipment and
procedures required for methanol and formaldehyde sampling. In
each case, one of the requirements is that sample collection
lines and probes (including venturies) be heated to 235°F in
order to avoid losses in the collection equipment (reference 1).
The theory of operation of critical flow venturi
constant volume samplers (CFV-CVS) requires that the gas
temperature at the inlet to all venturies be the same unless
the temperature of the dilute exhaust stream is controlled (see
Appendix C for theory of operation of constant volume
samplers). The question this report addresses is: "Will the
gas temperature at the orifice of the sample venturi be the
same as at the bulk stream venturi if the sample venturi is
heated?" If it is not, the sample obtained will no longer be a
constantly proportional sample, which the NPRM requires.
II. Apparatus and Procedure
It is very difficult to accurately measure the gas
temperature at a critical flow orifice without altering the
flow conditions. It is much easier to simply measure the flow
through the orifice when heated and unheated. A change in gas
temperature through the orifice can be seen as a change in flow.
The apparatus used for testing the probe in an unheated
condition is shown in Figure 1. A 20 CFH smooth approach CFV
was attached to the inlet of a Metal Bellows Pump Model MB-158
(standard equipment used for drawing bag samples at MVEL) . The
pump outlet was connected to a laboratory wet test meter.
Instrument connections were made using 1/4" 316 stainless steel
tubing and Swagelok fittings.
The apparatus used for testing the heated probe was
identical except for the addition of a 95VAC heat tape and an
Athena temperature controller set at 235°F. A type "J"
thermocouple was attached to the outside surface of the probe,
with the heat tape wrapped over it, to supply the feedback
signal to the controller. Other temperature measurements were
made using a fine tip "J" thermocouple and digital readout.
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Digittl B*rom«Ur
ViJidyu
Prwrun Trwuductr
20CFH
Critical Flow
MB-158
2.3 SCFM
Cipwity Pump
Vtt T«t
Mtt«r
FIGURE 1. Unheated Test Configuratioi
LA5T 2 mCKIS OJ
VTHTUII VEAJJZD
wrnt 95 VAC
HZAT TAJZ
szz
A.TKZHA. PBOIOBTBOHAJ.
TZMIZBA.TUIZ
COHTBOIIZB
to
AtmospLtrt
ZZZDBA.CK
TKZBMOCOUTLZ
KZAT TA1Z (NOT SKOWK)
WBAJPZD OVZB LAST
TWO IHCHZS OZ PBOBZ
riNZ-TII J T/C
FOB BZADIKO
VTNTUBI ZA.CZ
TEMPZBA.TUBZ
U JT/C
ZOB BZADIKC
IBOBZ SUB7ACZ
TZMIZBATUBZ
FIGURE 2. Hea^d Test Configuration
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The sample pump was started approximately 20 minutes
before any data was collected and allowed to run for the
duration of the experiment (approximately 75 minutes).
Experimental runs were performed by simultaneously taking an
initial wet test meter reading and starting the stop watch,
followed by stopping the watch and taking a final reading.
There are three main differences between the test set-up
and the way a sample would really be collected in a CVS:
1. The temperature of the bulk steam would be 20-30°F
higher than ambient temperature and would fluctuate (in this
experiment the ambient air from which the sample is drawn is
analogous to the bulk stream),
2. The bulk steam would be moving very fast, rather
than not at all as in the test set-up,
3. The sampling systems to be heated will have flow
rates on the order of 2 to 10 CFH, not 20 CFH as in the test
set-up.
These differences are unimportant for the purpose of
this test, which was to determine if heating the probe changed
the gas temperature at the probe inlet. The apparatus used was
sufficient for this purpose.
Ill. Presentation and Discussion of Results
A seguence of nine tests were run as follows: tests 1,
2, and 3 were conducted with an unheated probe; tests 4, 5 and
6 followed immediately using a heated probe; finally, runs 7, 8
and 9 were made with an unheated probe as a check for any
unforeseen changes in the equipment or surroundings.
The results for all runs are contained in Table 1.
There appears to be a significant difference in flow for
unheated and heated configurations. The results from Table 2
confirm this; there is a difference in flow of about 3 percent
between heated and unheated runs, while the coefficient of
variance is on the order of 0.1 percent.
Could the difference in flow be due to anything other
than a change in gas temperature? The only other effect that
could cause a change in flow is thermal expansion of the probe
during heating. Calculations contained in Appendix B show that
the inside radius of a cylinder increases as the temperature
increases for materials with positive coefficients of thermal
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expansion. This would cause the area available for flow to
increase and, therefore, the flow would tend to increase as
well. Since the flow decreased when the orifice was heated, it
must be concluded that the change in flow was not the result of
thermal expansion of the probe.
A further check on the consistency of the data is to
calculate the temperature of the gas flowing through the
venturi during heated runs. This calculation is shown in
appendix B; the gas temperature was about 103°F for runs 4-6.
This correlates very well with the observed face temperature of
the probe which was about 105°F (data in App. A).
Table 1. Flow through CFV in Heated and Unheated Configurations
RUN
1
2
3
4
5
6
7
8
9
PROBE
HEATED?
NO
NO
NO
YES
YES
YES
NO
NO
NO
FLOW
(SCFH)
18.255
18.188
18.215
17.625
17.664
17.629
18.124
18.130
18.145
Table 2. Statistical Analysis of CFV Flow Data
RUNS
1-3
4-6
7-9
HEATED?
NO
YES
NO
MEAN
FLOW
(SCFH)
18.219
17.639
18.133
SDEV
0.027
0.017
0.009
C.O.V,
o, '
0.150
0.099
0.048
% CHANGE
FROM
RUNS 1-3
-3.18
% CHANGE
FROM
RUNS 6-9
-2.72
In concluding this discussion, I feel I should address a
question posed by several engineers when told of this problem,
which is: "How can a gas moving at sonic velocity (1000 ft/s)
have time to heat up as it moves through the venturi?"
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It did not seem to make intuitive sense at the time, although
it does if we think of this as a classical heat transfer
problem. The pertinent heat transfer equation here is:
q/A= h(twai 1 - tgas)
where q is the rate of heat transfer (BTU/hr), A is the heat
transfer area (ft2), and h is the local heat transfer
coefficient (BTU/hr-ft2-F) . h is a function of fluid
properties only; a typical correlation for predicting h is
Dittus-Boelter (see reference 4), which is:
Nu = .023 Re' 8Pr "4
Nu = hd. Re = pvd, Pr = joCp
k y k
then h= .023 /vd\ 8 /CP\ "4 k
d
where
/
\
h=.023(pv) • 8 /CP\ -4
Re = Reynolds number, dimensionless
Nu = Nusselt number, dimensionless
Pr = Prandtl number, dimensionless
h = heat transfer coefficient, BTU
hr-ftz-°F
d = diameter, ft
k = thermal conductivity, BTU
ft-hr-°F
p = density, Ib
ft3
v = velocity, ft
• hr
jj = viscosity, Ib
ft-hr
Cp = heat capacity, BTU
lb-°F
This correlation says that the heat transfer coefficient
is proportional to velocity to the 0.8 power. In other words,
h is almost directly proportional to the gas velocity, which
reaches a maximum at the venturi. It is not surprising at all
that the gas temperature changes significantly before it can
move through the venturi because of this effect.
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Recommendations
There appear to be three ways to circumvent the problem of
sampling proportionally without using a heated CFV.
1. Use a Heat Exchanger in the CVS - Using a heat
exchanger to hold the temperature of the dilute exhaust stream
constant eliminates the need for CFV sample probes, so sampling
can be done at a constant flow rate using a heated static
probe. Appendix C gives the physical relationships that prove
the validity of this method.
2. Do not heat the CFV - Heat the sample line up to the
dilution tunnel, but don't heat the CFV sample probe. Sampling
losses should not occur within the probe because of the high
gas velocity, and also because the temperature within the
dilution tunnel is high enough to ensure that water
condensation will not occur within the probe. (Absorbtion by
condensed water is thought to be the main source of methanol
sampling losses. Formaldehyde losses are thought to occur due
to both absorption by condensed water as well as polymerization
in the presence of liquid water.)
3. Use feedback control - By putting a flow controller in
the sample line which gets its set point from the CVS flow
computer, proportional flow can be maintained as long as the
response time of the controller is very fast. This method
requires some modification of existing equipment, as well as a
mass flow controller or equivalent flow control device for the
sampling system. It is also not a true proportional method in
the strictest sense, since there will always be some lag time
between a change of flow through the bulk stream venturi and
the controller's response to that change. However, for a
controller with relatively fast response (95% of full scale in
one second or less is typical for a good quality mass flow
controller), the lag time should be negligible.
Of the three alternatives listed above, the first one is
the most technically sound; it would also meet all requirements
in the NPRM as it is now written. The only unresolved
technical question is whether or not a heat exchanger affects
methanol and formaldehyde emissions. It is unlikely that a
heat exchanger would have an effect unless there were
condensation occurring within the heat exchanger due to
inadequate dilution of the raw exhaust.
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10
References
NPRM-Methanol Fueled Vehicles, ECTD, QMS, Summer 1986,
Sec. 86.109-88. Published in Federal Register,
August 29, 1986, Vol. 51, No. 168.
Paulina, Carl. "Non-Proportional Sample Rates in a
Critical Flow Venturi Constant Volume Sampler." EPA,
QMS, EOD, TPB, January, 1982.
Perry, Robert H. Perry's Chemical Engineers' Handbook.
New York: McGraw-Hill, 1984, p.5-14
Bennett, Carroll O., and Myers, John E., Momentum, Heat,
and Mass Transfer. New York: McGraw-Hill, 1982,
p.384.
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11
Appendix A. Raw Data Inputs and Calculated Outputs
PROBE
RUN HEATED?
1
2
3
4
5
6
7
8
9
NO
NO
NO
YES
YES
YES
NO
NO
NO
VI
(CU FT)
V2
(CU FT)
16
18
19
32
33
35
38
39
40
.500
.000
.400
.300
.800
.500
.100
.300
.800
17
19
20
33
35
39
39
40
41
.500
.300
.900
.600
.400
.200
.200
.700
.800
189
247
285
255
313
216
210
267
191
.86
.72
.42
.64
.94
.26
.35
.64
.01
WET TEST
METER TEMP
(PEG F)
73
73
73
73
73
73
73
73
73
VENTURI
FACE TEMP
(PEG F)
73
73
73
105
105
105
73
73
73
PROBE
SURFACE
(PEG F)
73
73
73
182
182
182
73
73
73
DELTA P
(IN H20)
0
0
0
0
0
0,
0
0
0.1
PI
(IN HG)
ABSOLUTE
29.078
29.078
29.078
29.078
29.078
29.078
29.078
29.078
29.078
P2
(IN HG)
GAUGE
-13.0
-13.0
-13.0
-13.0
-13.0
-13.0
-13.0
-13.0
-13.0
P2/P1*
ABS PRESS
RATIO
0.553
0.553
0.553
0.553
0.553
0.553
0.553
0.553
0.553
FLOW
(SCFH)
18
18
18
17
17
17
18
18
255
188
215
625
664
629
124
130
18.145
*According to fluid mechanics textbooks, the critical pressure
ratio, PC, required for sonic flow of air is 0.528 or less
(ref. 3). However, this is really the ratio required for an
orifice; the ratio can be much hiqher for a venturi, depending
on the venturi design. For the sample venturies used at MVEL,
PC is about 0.6 , a number arrived at by experimentation with a
margin of safety included (see reference 2). A PC of 0.553 is
well below the ratio required to maintain sonic flow for this
type of venturi.
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12
Appendix B. Calculations
1. Thermal Expansion of Heated Probe
Calculation of the change in size of the sampling probe
orifice due to thermal expansion would require a detailed
equation based on probe geometry, material, and temperature
change. Unfortunately, equations available for calculating
thermal expansion of solids are limited to the linear case. In
order to more accurately predict the effect of heating under
the conditions of the test, a simplified model was developed
which attempted to take into account the cylindrical geometry
of the orifice. The derivation is long and arduous, and it
goes beyond the scope of this report to present it here. There
were two important results that pertain to the problem at hand:
a. The formula for calculating the change in radius of a
cylinder is:
r2 = r,(BAt + 1)
where rt = old radius
r2 = new radius after heating
0 = thermal expansion coefficient
At = temperature change
This is the same equation one would arrive at by assuming
that the radius expands linearly with temperature.
b. If At and B are both positive, r2 will always be
greater than r(. The orifice size will always increase as
temperature increases. This means that the decrease in flow
seen when the probe was heated could not have been due to
thermal effects, since the orifice had to increase in size upon
heating.
What was the maximum change in orifice size for this
experiment? Since
Atmax = 235 - 73 = 162 deg F
B = 9.6E-6 deg F"'
ri = .016 inches
r2 = .016((9.6E-6)(162) + 1)
r2 = .0160248 inches
The maximum % change in area available for flow would be
%AAF = (irr| - -rrr2 )/(irr2)
%AAF = (.01602482 - .0162)/.0162
%AAF = .3113%
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13
2. Calculation of Gas Temperature at Venturi for Heated
Runs
For a CFV at a given upstream pressure and gas
composition, the mass flow rate through the venturi will be
m = K
Where n = mass flow rate, Ib/hr
K = proportionality constant based on gas
temperature and venturi design,
T = absolute gas temperature
Subscripts: 1 = unheated
2 = heated
(1) mi = K (2) mz = K
Dividing eqn. (1) by eqn. (2),
mt = K
mz Jf
JT1
* 1 =fTl
\ K JT,
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14
Since
m = Qp
where Q = volumetric flow rate, SCFH
p = density of air at standard conditions
substituting for m in the previous equation yields
Q2p
fli =
Qz JT,
Qi = 18.133 SCFH (runs 7-9)
Q2 = 17.639 SCFH (runs 4-6)
T! = 73°F = 533°R
T2 =?
18.133 = T
17.639 >J533
T2 = 563.3°R
T2 = 103.3°F
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15
Appendix C. Theory of Operation
of Constant Volume Samplers
Constant volume samplers (CVS) use one of two methods to
measure dilute exhaust flow and obtain sample at a rate
proportional to the dilute exhaust flow. These two methods are
described below:
1. Critical Flow Venturi. A sketch of a CFV-CVS is shown
in Figure 3. As the raw exhaust flow rate varies, the
temperature and pressure of the dilute exhaust stream changes.
VMK
DILUTION
AIR
1
RAV EXHAUST
DILUTE EXHAUST
Ts-J
BAG SAMPLE
Fif ore 3. Critical Flov Yenturi Constant Volume Sampler
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16
The equation for flow of an ideal
orifice is (see references 2 and 3):
gas at a critical flow
Q = CA
\
gck RT
\k-
t. +/k-i\B2]
\—) J
P-'
V t 1
\ J\. J.
where Q = Volumetric flow rate (ftVsec)
C = Coefficient of discharge (dimensionless)
A = Cross-sectional area of orifice (ft2)
gc = gravitational constant (32.2 ft/S2)
k = ratio of specific heats (dimensionless)
R = ideal gas constant (1545 ft-lbf/°R-mol)
M = Molecular weight of gas (Ib/lb-mol)
T = Absolute gas temperature (°R)
B = ratio of orifice diameter to pipe diameter
(dimensionless)
For values of B less than 0.2 (the usual case), the
bracketed term on the right is approximately equal to unity.
For a given orifice and pipe size. A, B, and C are constants.
For a given gas, k and M are constants.
The only variable left in the equation is T; therefore,
for a given gas and orifice (or venturi), this equation takes
the form
Q =
where K is a dimensional
and venturi properties.
constant that incorporates gas
For the venturies in the CFV-CVS, the flows through each
would be
Qb = K
and Qs = KsNJT?
where the subscripts (b
sample streams, respectively.
Dividing, we get
and s) refer to the bulk and
Q
= Kb
KS
then
If the venturies are located near each other, Tb = T.
= 1
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17
and Qb = Kb = a constant
Q, Ks
Since the ratio Qb/Qs is a constant, the flows through
the sample and bulk stream venturies will be constantly
proportional to one another as long as the gas temperatures at
each venturi are equal.
Notice that if the temperatures of the bulk and sample
streams remain constant, it is no longer necessary that the
temperatures of the two streams be equal. The flow will remain
constantly proportional because all terms on the right hand
side of the equation will be constant.
2. Positive Displacement Pump. A sketch of a PDP-CVS is
shown in Figure 4. Dilute exhaust passes through a heat
exchanger and reaches a constant temperature before entering
the PDP. The unit is designed to maintain a relatively
constant pressure at the pump inlet. Since T and P are
constant, sampling of the dilute exhaust can be done with a
static probe at a constant flow rate.
DILUTION
AIR
I
VMK
RAV EXHAUST
WATTS W (r) (p)
—M-I-
DILUTE EXHAUST
WATER OUT
PDP
BAG SAMPLE
Figure 4. Positive Displacement Pump Constant Volume Sampler
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