Expansion chamber method and apparatus for eliminating accuracy errors when testing gaseous flowmeters

A properly designed expansion chamber is mounted in a flowmeter test equipment configuration to quench or prevent pulsations from resonating the acoustic cavities in the configuration and, thereby, eliminate resonation errors in testing the accuracy of the flowmeter. The invention is particularly though not exclusively adapted to use with a testing configuration including a prover master meter and a conduit connecting the inlet of the prover master meter to the outlet of the gaseous flowmeter being tested. In the practice of the present invention, the pulsation frequencies can be quenched before the acoustic cavity within the conduit can be excited by introducing an expansion chamber at one or both ends of the conduit.

BACKGROUND OF THE INVENTION 
This invention relates to methods and apparatus for testing gaseous 
flowmeters and, more particularly, it concerns an improved method and 
apparatus for eliminating accuracy errors caused by standing waves of 
sound encountered when testing gaseous flowmeters. 
Public Utility Companies delivering natural gas to industrial complexes, 
factories, office buildings, hotels, apartments, hospitals, stores, homes, 
etc., are required to periodically verify the accuracy of the gas 
flowmeters used to bill the customers for the quantity of gas delivered. 
Accuracy of the meters must be verified before being put in service and at 
specified intervals determined by the regulatory commissions of the 
states, cities, or local governmental authorities. A widely accepted 
method for testing is by the use of a portable transfer prover. This 
instrument system includes a very accurate "master meter" which is 
connected in series with the meter to be tested, so that a flow of air or 
natural gas may be transferred through both meters at various flow rates. 
Portability of the proving system is important so that the transfer prover 
can be positioned near the installation site of the meter to be tested. 
Valves and fittings are normally provided so that the meter to be tested 
can be isolated from the gas line and a suitable pipe or flexible hose 
connection can be used to transfer the same gaseous flow through both 
meters in series. The volume readout of each meter can be compared after 
being corrected for temperature and pressure values of the flow through 
each meter. The accuracy determination is normally expressed as a 
percentage equivalent of the result indicated by the transfer prover 
master meter which has been calibrated to be 100% accurate at all flow 
rates. 
The most accurate master meters are the positive displacement type. In this 
design the air or gas at the inlet of the meter is allowed to successively 
fill one cavity after another as they rotate to discharge each captured 
volume to the meter outlet. The cavities are rigid in shape and size, 
hence the name "positive displacement" meter. 
A common form for this type of meter has two rotating impellers, each with 
two lobes which will produce four very small pulses in the air or gas 
stream for each complete revolution of the rotor assembly. Therefore, the 
frequency of the pulsations will be four times the revolutions per second 
of the meter impellers. When the displacement of the meter is known (cubic 
feet per revolution, CFR) and the flowrate is known (cubic feet per hour, 
CFH), the pulsation frequency can be easily determined: 
##EQU1## 
The impeller rotors in the positive displacement meters will appear at all 
times as a solid closure to a pressure wave-front travelling at the speed 
of sound in air or natural gas. 
With reference to FIG. 1 of the drawings, if the inlet of a rotary positive 
displacement meter 10 is connected to a hose, tubing, or pipe 12 with the 
inlet to the tubing open to free space, the tube becomes a tuned 
one-quarter wavelength cavity. Such a cavity will resonate with sound 
waves at a fundamental frequency with a wavelength of four times the 
length of the cavity: 
##EQU2## 
1130 is the speed of sound in air, feet per second (or 1460 feet per 
second in natural gas) 
L is the length of the cavity in feet 
F is the frequency of the sound wave (Hz) 
.DELTA. is the pipe open end correction which is equal to 
##EQU3## 
D is the pipe diameter in feet 
When small pressure pulses occur at a rate which will resonate the cavity 
length, a standing wave sound will be sustained with a pressure node at 
the closed end and a velocity loop at the open end. This cavity will 
resonate only at "odd" harmonics of the fundamental frequency (3rd, 5th, 
7th, etc.). 
The true accuracy of the meter is not affected by these conditions, the 
problem lies in our inability to measure the true instantaneous pressure 
captured in each of the measuring chambers of the metering rotors. At or 
near resonant conditions, this pressure value will be different from the 
measured average flowing pressure which is normally used for pressure 
correction in test results. When the pressure correction is made with an 
incorrect pressure value, the accuracy of the test is also in error. 
With reference to FIG. 2 of the drawings, if the inlet of a rotary positive 
displacement meter 14 is connected to a hose, tubing, or pipe 16 coupled 
to the outlet of another positive displacement meter 18, the tubing 16 is 
effectively closed at both ends for sound waves and becomes a tuned 
one-half wavelength cavity. Such a cavity will resonate with sound waves 
at a fundamental frequency with a wavelength of two times the length of 
the cavity: 
##EQU4## 
1130 is the speed of sound in air, feet per second (or 1460 feet per 
second in natural gas) 
L is the length of the cavity in feet 
F is the frequency of the sound wave (Hz) 
When the small pressure pulses occur at a rate which will resonate this 
cavity length, a standing wave of sound will be sustained with pressure 
nodes at both "closed" ends. This cavity will resonate at all harmonics of 
the fundamental (2nd, 3rd, 4th, 5th, 6th, etc.). 
With reference to FIG. 3 of the drawings, if the inlet of a rotary positive 
displacement meter 20 is connected to a hose, tubing, or pipe 22 coupled 
to the outlet of a turbine meter 24, the tubing 22 is effectively closed 
to sound waves only at the positive displacement meter and is open through 
the turbine meter which is transparent to the sound waves at the velocity 
loop of the standing wave. Hence, the tubing 22 is closed at one end and 
open at the other and becomes a tuned one-quarter wavelength cavity. This 
cavity will resonate with sound waves at a fundamental frequency with a 
wavelength of four times the length of the cavity: 
##EQU5## 
1130 is the speed of sound in air, feet per second (or 1460 feet per 
second in natural gas) 
L is the length of the cavity in feet 
F is the frequency of the sound wave (Hz) 
.DELTA. is the pipe open end correction which is equal to 
##EQU6## 
D is the pipe diameter in feet 
The resonant harmonic frequencies will be only the 3rd, 5th, 7th, etc. odd 
harmonics of the calculated fundamental. 
In order to reach typical meter locations conveniently, the length of the 
hose or tubing required to interconnect the prover master meter with the 
meter to be tested will be 20 or 30 feet. This range of cavity length, 
when excited by the wide range of pulsation frequencies of a positive 
displacement meter, will combine to pass through many harmonic resonant 
points over the range of flow rates to be used for testing meter accuracy. 
As such, when gaseous flowmeters are tested for determining the metering 
accuracy over the full range of flow rates, acoustic resonance at certain 
flow rates prevents accurate test results from portions of the range of 
flow rates which are necessary to validate the true measuring accuracy of 
the device. 
Although an experienced and skilled technician can sometimes audibly sense 
flow rate regions where acoustic resonance may be a problem and select 
other flow rates by trial and error to locate flow rates not producing 
acoustic resonance, this is not only time-consuming but leads to a lower 
confidence factor for the overall accuracy of the test. 
In light of the foregoing, there is a need for an improved method and 
apparatus for testing gaseous flowmeters. 
SUMMARY OF THE INVENTION 
In accordance with the present invention, the problems associated with 
errors due to pulsations resonating acoustic cavities are substantially 
overcome by an improved apparatus and method providing an expansion 
chamber in the test configuration to quench or prevent the resonations. 
The invention is particularly though not exclusively adapted to use with a 
testing configuration including a prover master meter and a section of 
hose or tubing connecting the prover master meter to the gaseous flowmeter 
being tested. 
In the practice of the present invention, the pulsation frequencies can be 
quenched before the acoustic cavity can be excited by introducing an 
expansion chamber at one or both ends of the cavity. 
Accordingly, a principal object of the present invention is to provide an 
improved method and apparatus for eliminating accuracy errors caused by 
standing waves of sound when testing gaseous flowmeters. Another and more 
specific object of the invention is the provision of an expansion chamber 
at one or both ends of the cavity interconnecting a prover master meter 
and the meter being tested. Other objects and further scope of 
applicability of the present invention will become apparent from the 
detailed description to follow taken in conjunction with the accompanying 
drawings in which like parts are designated by like reference characters.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
In accordance with the present invention, a properly designed expansion 
chamber is mounted in a flowmeter test equipment configuration to quench 
or prevent pulsations from resonating the acoustic cavities in the 
configuration and, thereby, eliminate resonation errors in testing the 
accuracy of the flowmeter. 
In FIG. 4 of the drawings, an exemplary gaseous flowmeter testing 
configuration incorporating the expansion chamber of the present invention 
is generally designated by the reference numeral 30 and shown to include a 
rotary positive displacement master meter 32 connected to a rotary 
positive displacement meter 34 being tested via a pipe or tubing 36. An 
expansion chamber 38 is connected at its inlet to the tubing 36 and at its 
outlet to a short section of pipe or tubing 40 which in turn is connected 
to the inlet of the master meter 32. 
The energy present in the sound pressure wavefront of meter pulsations is 
finite over the cross-sectional area of the pipe or tubing carrying the 
gaseous flow. If the cross-sectional area of the tubal cavity is abruptly 
increased to a value seven or more times as great, the energy per unit of 
area drops suddenly and is spread over a radially changing particle 
velocity, tending to destroy the uniform sound wavefront. The result is 
similar to the effect of the sound wave pressure front leaving the open 
end of pipe or tubing into the atmosphere, where the resonance would be 
lost. 
With reference again to FIG. 4 of the drawings and in accordance with a 
preferred embodiment of the present invention, the cross-sectional area 
S-2 of the expansion chamber 38 should be seven or more times as great as 
the cross-sectional area S-1 of the tubing 40. 
##EQU7## 
The length of the expansion chamber 38 is required to provide maximum 
attenuation at the maximum driving frequency: 
##EQU8## 
where L.sub.e is length of the expansion chamber in feet, C is the 
velocity of sound in air 1130, or natural gas 1460 feet per second, and f 
is the frequency of pulsations. For the rotary positive displacement 
meter, the frequency is 4 times the maximum rotor revolutions per second 
(4.times.Rmax). 
##EQU9## 
The length L.sub.p of the passage 40 from the rotating positive 
displacement elements of the meter, to the beginning of the expansion 
chamber L.sub.e, must be kept short to ensure that no resonant 
amplification occurs in this pipe when driven by the positive displacement 
meter at its maximum rotational speed. 
For the pipe length L.sub.p, the meter end is effectively closed by the 
positive displacement rotors. The end connected to the expansion chamber 
38 is open and the L.sub.p fundamental quarter-wavelength resonant 
frequency is given by: 
##EQU10## 
where C is the sonic velocity in the gas 
.DELTA.is the pipe end correction equal to 
##EQU11## 
D being the pipe diameter in feet 
The skirts of resonance extend from 
##EQU12## 
therefore the resonant frequency F must be equal to or greater than 
##EQU13## 
The calculation for the length L.sub.p, specifies the marginal limit for 
this value and a valuable safety margin will be achieved if the length is 
reduced as far as possible. Thus, it is preferred to use the shortest 
length that can be readily assembled below the calculated value to 
maximize the safety margin preventing tubing resonance. 
For the larger industrial sized meters with capacities from 10,000 to 
1,000,000 cubic feet per hour, portable equipment for testing on site is 
not practical. Meters of this size range will be tested at permanent 
installations in central meter shops maintained by the Utility company. At 
these installations, the expansion chamber usually takes the form of an 
acoustic filter to reduce interaction from any pulsation developed by 
either meter. 
In FIG. 5 of the drawings, another embodiment of a flowmeter testing 
configuration in accordance with the present invention is generally 
designated by the reference numeral 50 and shown to include an expansion 
chamber 52 and 54 at each end of a section of tubing or pipe 56 
interconnecting a positive displacement master meter 58 and a positive 
displacement meter 60 being tested. 
An interesting demonstration can be performed with a typical 3-M, 5-M, 7-M 
etc., positive displacement rotary meter being tested by a transfer 
prover. The usual set-up will be with a length of hose coupling the master 
meter to the discharge flange of the meter under test. The normal 
recommendation is to leave the inlet flange of the meter under test, open 
to the atmosphere. The accuracy curve developed by several tests covering 
the flow range of the meter will show a reasonable fit to the 
manufacturers furnished data. 
Next, a short length of pipe, for example approximately three feet, should 
be flanged-up to the inlet of the meter under test. An accuracy curve run 
under this condition will show a very severe sag of the accuracy curve in 
a flow rate region where the impellers of the meter under test are turning 
at approximately 23.4 revolutions per second (1400 RPM). 
The cause of this test error is the resonance of the short length of pipe 
at the meter inlet. When the small meter pulsations occur at a frequency 
which is close to the resonant frequency of the inlet pipe length, a 
standing wave of sound is created in the pipe with the peak pressure 
located at the entrance to the meter measuring chambers. As a result, the 
meter rotors are capturing air volumes at a higher pressure than an 
average air pressure measurement would indicate. The higher pressure 
packets of air will allow the meter to run slower while discharging more 
volume to the master meter. If the meter under test runs slower than the 
rate indicated by the master meter, the test will run longer than it 
should (the revolutions of the meter under test determine the start and 
the end of the test) and the proof count will be greater for the test run. 
For pressure correction between the meters, the average pressure is 
normally used, but the true pressure of the measured volume at the meter 
under test is distinctly higher and is not available for proper pressure 
correction. When the greater than expected Corrected Proof count is 
converted to Corrected Accuracy, the value is lower than expected. The 
Accuracy curve will then exhibit a pronounced negative drop through the 
resonance region. 
This experiment demonstrates the reason for recommending the length of air 
passage from the atmosphere to the inlet of the meter under test, should 
be very short so that the highest flow rate to be used, generates small 
pressure pulses too low in frequency to resonate the inlet passage, and 
normal average pressure measurements are accurate for the test. 
When a turbine meter is to be tested with a rotary positive displacement 
master meter, attention should be paid to the tuned one-quarter wavelength 
tubular cavity which is now in place at the inlet to the master meter. The 
air path through the turbine body is never closed to sound frequencies and 
the prover hose length will be closed to sound frequencies at the master 
meter. The length of the resonant cavity extends from the inlet of the 
turbine body to the inlet of the master meter. This dimension is the 
length of the one-quarter wavelength tuned cavity for calculating the 
fundamental resonant frequency and the order of odd harmonics. At 
resonance frequencies there will be pressure pulses at the closed end and 
smooth air velocity changes (not pressure changes) at the open end into 
the atmosphere (the inlet of the turbine). The inertia of the turbine 
rotor is sufficient to prevent responding to even the lowest sound 
frequencies and will indicate a steady average flow rate. The resonant 
peaks of the air in one-quarter wavelength cavity will now affect the 
rotary positive master meter. The result will be slower than average 
rotations in the resonant flow rate regions, causing a lower Proof count 
at these test points. Of course, a low Proof count converts to a high 
Accuracy result. Therefore, at these resonant points, the accuracy curve 
will have positive error peaks. 
The use of a long hose will produce a low frequency for the fundamental 
resonance and therefore closer spacing of the flow rates for the odd 
harmonic points, resulting in erroneous test points which are more closely 
spaced. Use of a much shorter hose will raise the fundamental frequency of 
the tuned cavity, and much greater spacing of the odd harmonic regions. 
The result will be a considerable increase in the valid flow rates that 
are acceptable to define a valid accuracy curve. An even better result can 
be achieved in accordance with the present invention by adding an 
expansion chamber between the hose and the inlet of the master meter. 
As shown in FIG. 6 of the drawings, a turbine meter testing configuration 
in accordance with the present invention is generally designated by the 
reference numeral 70 and includes a master meter 72 interconnected with a 
turbine meter 74 being tested by a hose 76. An expansion chamber 78 has an 
inlet connected to the hose 76 and an outlet connected to a short tube or 
pipe 80 which in turn is connected to the inlet of the master meter 72. 
The expansion chamber 78 serves to quench or prevent the error causing 
resonant peaks. 
Thus it will be appreciated that as a result of the present invention, a 
highly effective testing error eliminating apparatus and method is 
provided by which the principal object and others are completely 
fulfilled. It is contemplated and will be apparent to those skilled in the 
art from th foregoing description and accompanying drawing illustrations 
that variations and/or modifications of the disclosed embodiment may be 
made without departure from the invention. Accordingly, it is expressly 
intended that the foregoing description and accompanying drawings are 
illustrative of a preferred embodiment only, not limiting, and that the 
true spirit and scope of the present invention be determined by reference 
to the appended claims.