AbstractThis paper presents the establishment and verification of a primary low-pressure gas flow standardwith the capacity of 0.005 L/min to 24 L/min (at 23 °C and 101.325 kPa), newly established atNational Institute of Metrology of Thailand (NIMT). This facility is a mercury-sealed piston proverconsisting of three precision-machined glass cylinders. Flow measurement can be carried out manuallyor semi-automatically. The electronics were installed in a separate console to minimize their thermalimpact on the gas temperature. Special care was taken in designing the facility to ensure sound andrepresentative gas pressure and temperature measurement. The relative expanded uncertainty of massflow measurement was evaluated to be less than 0.13%. To verify the measurement capability andperformance of the new facility, a bilateral comparison with the piston prover at Center for MeasurementStandards (CMS), Taiwan was conducted. The transfer standard used was a set of three critical flowventuris with dedicated thermometers. Eight flow rates of dry air ranging from 42 mL/min to 14.5 L/min at 0 °C and 101.325 kPa (0.055 g/min to 18.87 g/min) were tested. Comparison results showedthat the En values for the flow measurements at NIMT with reference to CMS were all well less thanunity, demonstrating good agreement between the two participants.
To support the needs of gas flowmeter calibrationsand establish the traceability chain to SI units of gasflow measurement within Thailand, the NationalInstitute of Metrology (Thailand), i.e., NIMT,established a mercury-sealed piston prover as theprimary standard for low pressure gas flow in 2009.The facility was designed and manufactured byCenter for Measurement Standards, Industrial
MAPAN - Journal of Metrology Society of India, Vol. 26, No. 3, 2011; pp. 173-186ORIGINAL ARTICLE
Technology Research Institute (CMS/ITRI), Taiwan.The capacity of the system covers the range of flowfrom 0.005 L/min to 24 L/min (at 296.15 K and 101.325kPa) with some overlapped flows between variouscolumns. The calibration gases are dry air andnitrogen. The relative expanded uncertainty of massflow measurement is less than 0.13 % and will bedelineated in detail in this paper.
To verify the measurement capability andperformance of the newly established piston prover,
Chun-Min Su, Win-Ti Lin and Sutham Masri
174
a bilateral comparison between NIMT and CMS wasconducted. The standard facility of CMS, who servesas the pilot laboratory in this comparison, is also apiston prover. A set of three critical flow venturis(CFV's), or sonic nozzles, with dedicated thermometerswas used as the transfer standard (TS) for thiscomparison. The comparison was made at eight flowrates of dry air ranging from about 0.055 g/min to18.87 g/min. As will be demonstrated later, themeasurement results of the two participants were ingood agreement, and thus the claimed measurementcapabilities were deemed valid.
2. Establishment of the Low-Pressure Gas FlowStandard at NIMT
2.1 Gas Piston Prover Design
Typically, mercury-sealed piston provers of earlierdesign perform measurements based on glasscylinders having uniform diameters and graduatedscales to determine, usually facilitated by opticalswitches installed in pairs, the collection volumes.When the incoming gas pushes the piston upward,the light reflected by the mercury ring generatessignals to start and stop the timing. Systems of thiskind generally suffer from the following shortcomings.
i) Errors due to manual adjustment of theinstallation positions of the optical switches incorrespondence with the graduation marks.
ii) The distance between the pair of optical switchesmay differ from the actual distance travelled bythe piston since the trigger signals are affected bythe mercury surface condition and the reflectionintensity, leading to compromised systemreproducibility.
iii) Difficulties in calibrating the graduated scale andthe installation effect due to differences betweenoperation and calibration conditions.
iv) Inappropriate installation position of thethermometer, which problem degrades thecorrectness of gas temperature measurement.
v) Inappropriate installation position of the pressuretap, which problem degrades the correctness ofgas pressure measurement, especially at highflows that cause significant pressure loss in thepiping.
vi) All the columns in a set of piston prover generallyadopt a common connecting piping whichoccupies significant proportion relative to thecollection volumes of small glass cylinders,resulting in augmented storage effect andincreased measurement uncertainty.
vii) The bypass valve usually opens immediately afterthe triggering of the second optical switch. Thispractice affects, in a degree that is difficult toevaluate, the measurements of temperature andpressure at the end of the calibration.
viii) The environment temperature, when differsconsiderably from the gas temperature, wouldaffect the temperature of the gas in the glasscylinder, which is practically difficult to measurewith accuracy, especially at low flows withprolonged calibration time.
The new gas piston prover established at NIMT,as shown in Fig. 1, is designed to overcome, to theextent possible, the aforementioned problems. Theprover consists of three precision bore glass cylinders,about 85 cm long, with measured inner diameters of19.0448 mm, 44.4507 mm and 143.7143 mm and amercury-sealed piston in each cylinder. The roomwhere the system is installed is controlled at the
Fig. 1. A photo of the full system of NIMT'smercury-sealed piston prover
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Establishment and Verification of a Primary Low-Pressure Gas Flow Standard at NIMT
temperature of (23 ± 1.5) °C. The designed capacity ofthe system is from 5 mL/min to 24 L/min at thereference condition. The applicable ranges of flow are(5 to 200) mL/min, (50 to 1500) mL/min and (0.5 to24) L/min for the small, medium and large cylinders,respectively.
Figure 2 shows the simplified schematic of thepiston prover. The piston can move up and downfreely, for accommodating the incoming gas andtriggering the timing device. The travelling distanceof the piston is measured by a Laser Doppler Scale(LDS) installed on the top of the piston prover body.The LDS was chosen because of its low cost with highperformance, high signal quality, compactness, feweroptical components and easy faster setup andalignment. A corner cube is placed on top of the pistonas a movable reflector for the LDS system. The axles ofthe glass cylinders are installed in coplanar mannerso that the laser beam of LDS can be easily switchedamong the three cylinders through simple optics for
piston travelling distance measurement. Two digitalfiber photo sensors, actuated by the mercury ring,control the start and stop of an electronic digital timerand synchronize data acquisition (DAQ) for flowmeasurement. A third photo sensor is also installedfor emergency vent to prevent the piston from leavingthe cylinder it resides accidentally. At the bottom ofeach column, a dedicated pressure tap andtemperature sensor are situated, allowingmeasurements taken to best represent the conditionof the gas within the cylinder. Moreover, to mitigatethe storage effect resulted from inventory volume, eachof the columns uses separate connecting piping witha calibre compatible to corresponding flow rate rangeand collection volume.
Operationally, the flow, once stabilized, isdiverted from the bypass passage into the glasscylinder, causing the piston to rise at a constantvelocity. The distance traversed by the piston, andthus the collection volume, are dictated by triggering
Fig. 2. Simplified schematic of NIMT's mercury-sealed piston prover
Stop
Meter Under Test
Flow
Bypass Valve
Start
T
Glass Cylinder
Piston with Mercury Seal
Piston Traveling Distance 123.4567 mm.
Corner Cube
EmergencyVent
LDS
P
Chun-Min Su, Win-Ti Lin and Sutham Masri
176
of two photo sensors and measured simultaneouslyby the LDS system. This distance is measured for eachand every flow calibration run. The piston prover isalso designed to allow another two operation modes:(a) use a fixed and predetermined distance betweenthe two photo sensors, and (b) assign an arbitrarydistance (a lower limit and a higher limit) to the LDSsystem which, when criterion is met, sends outtriggering signal and synchronizes the DAQ process.These two additional modes allow the facility tooperate without the LDS and photo sensors,respectively.
Based on the measured distance, collection time,gas pressure inside the cylinder at the beginning andat the end of flow calibration, averaged gastemperature, and the pre-determined glass cylinderinner diameter, the standard mass flow rate can bedetermined as follows;
c c I Il,mm
2IIc
c v,l4
⋅ ∆ ⋅= + + =
× × × ∆ ×+ + ×
⋅
V Vq qt tD L V qt t
ρ ρ
ρ π ρρ (1)
where qm is the mass flow rate; Vc is the collectionvolume; VI is the inventory volume, which is thevolume between the exit of the meter under test andthe start location of the glass cylinder (Fig. 2), t is thecollection time; cρ is the density of the gas in the
collection volume; is the change in density of thegas in the inventory volume; qm,l is the mass leak ratefrom the system; D is the diameter of the glass cylinder;L is the travelling distance of the piston, and qv,l is thevolume leak rate.
2.2 Experimental Setup of the Piston Prover at NIMT
Figure 3 shows the schematic of the experimentalsetup at NIMT. The LDS sits steadily on top of the
Fig. 3. Schematic of the experimental setup of the piston prover at NIMT
I∆ρ
BV
InterchangeableMetering Valve
Filter BV
Filter
Metering valve
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Establishment and Verification of a Primary Low-Pressure Gas Flow Standard at NIMT
piston prover, and a set of specially designed guidingoptics is used to direct the laser beam to the column ofinterest. A universal measured value display unit(HEIDENHAIN ND281B) receives the output signalof the LDS and displays the measured distancetraversed by the piston. Four digital indicatingcontrollers (CHINO DB1000) are used, in combinationwith custom-made 4-wire Pt-100 sensors, to measurethe temperatures of the gas at each of the three glasscylinder and at the device under test (DUT). The timingdevice used is a red lion CUB5T miniature electronicpreset timer and cycle counter. A two-channel digitalpressure gauge (mensor 2500) is used to measure thepressure at the standard and the DUT.
2.3 Uncertainty Evaluation of the Piston Prover at NIMT
From Eq. (1), the relative combined uncertainty ofthe mass flow measurement can be derived as follows.
2 2c m c
m c
2 2I2
c
v,l2 2 1/2II2 2
c
( ) 2 ( ) ( ) ( )[( ) ( ) ( )
( ) ( )4( ) ( )
4 ( )4 ( )( ) ( ) ]
= + +
− Δ+ +
× ××Δ
+ +× × × ×
I
u q u D u L uq D L
u t uVt D L
t u qu VD L D L
ρρρ
π ρρρ π π
(2)
where u represents the standard uncertainty. The massflow measurement uncertainty of the gas piston proverdepends on the diameters of the glass cylinder,travelling distance of the piston, density of the gas,time, storage effects of the inventory volume and theleakage. The analysis, based on ISO/IEC guide 98 (ISOGUM) [1] and other references [2-3], is as follows.
2.3.1 Inner diameters of the glass cylinders
The inner diameters of the glass cylinders weremeasured by bore gauges which are traceable to ringgauges calibrated by Dimension Laboratory of NIMT.For each cylinder, diameters at 9 or 12 cross-sections,each about 5 cm apart, were measured. A total of 10measurements at two perpendicular directions weretaken for each cross-section. The average of alldiameter measurements at various cross-sections wasused as the estimation of the diameter of each cylinder.
Uncertainty contributions from traceability of the ringgauges, repeated measurements of the diameters,variation in the cylinder diameter along the axialdirection, thermal expansions of the glass cylindersand the ring gauges, temperature control andmeasurements were included in the analysis. Theresulting contributions of the diameter measurementsto the standard uncertainties of the collection volumesare 0.012 %, 0.006 % and 0.004 % for the small, mediumand the large cylinders, respectively.
2.3.2 Piston travelling distance
The LDS uses a He-Ne laser source. The wavelength of the laser was calibrated by Wave LengthLaboratory, Dimensional Department of NIMT. Theeffects of the environmental changes, i.e., pressure,temperature and humidity [4], and cosine error to themeasured distance were also taken into consideration.Collectively, these uncertainties contribute 0.001 % tothe standard uncertainty of the collection volume.
2.3.3 Gas density
The gas density is used to convert the volumetricflow to mass flow. The density value is calculatedbased on the measured pressure and temperatureusing the following equation.
c ( , )=
PMZ P T RT
ρ (3)
where P and T are the absolute pressure and absolutetemperature, respectively, of the gas in the collectionvolume; M is the gas molecular weight; R is theuniversal gas constant; and Z(P,T) is thecompressibility factor of the gas. The uncertaintycontributions from these components are elucidatedas follows.
2.3.3.1 Temperature measurement
The temperature sensors were calibrated by theTemperature Laboratory of NIMT. The standarduncertainty which takes into consideration thetraceability, residuals of curve fitting, resolution,effects of the environment to the temperaturedistribution of the gas inside the glass cylinder anddrift of sensors is estimated to be 0.13 K (0.044 %, basedon a reference temperature of 296.15 K).
Chun-Min Su, Win-Ti Lin and Sutham Masri
178
2.3.3.2 Pressure measurement
The absolute pressure transducers, calibrated bythe Pressure Laboratory of NIMT, are used to measurethe pressure of gas collected in the glass cylinder.Contributions from traceability, residuals of curvefitting, resolution, drift of the transducer and the effectof installation position are combined to yield astandard uncertainty of 17 Pa (0.017%, based on areference pressure of 100 kPa).
2.3.3.3 Molecular weight and gas constant
The molecular weight and universal gas constantare regarded as constants. Taken from publishedreference [3], the uncertainty of universal gas constantis 0.0002 %, and those of the molecular weight of dryair and nitrogen are 0.0001 % and 0.019 %, respectively.The calculation of compressibility factor of dry airand nitrogen over the temperature range of 270 K to330 K at 100 kPa has a relative standard uncertainty of0.001 % [3].
Combining the above-mentioned componentswith root-sum-of-squares (RSS) technique yieldsrelative standard uncertainties of 0.051 % and 0.048 %for the calculated density of air and nitrogen,respectively. In this analysis, 0.051 % is used as theuncertainty of calibration gas density.
2.3.4 Collection time
The timer with a resolution of 0.001 s is tested bycomparing with a universal counter which wascalibrated by the Time and Frequency Laboratory ofNIMT. Taking into consideration the traceability andthe test results, resolution, and start/stop responsetime of the timer, the standard uncertainty forcollection time measurement is 0.0014 s (0.007 %, basedon a minimum collection time of 20 s).
2.3.5 Storage effects
The storage effects account for two parametersthat would affect the measurement result, i.e., thevariation of gas density in the inventory volume andthe inventory volume measurement. The maximumpressure and temperature variations are assumed tobe 30 Pa and 0.20 K during the collection time. As aresult, the relative standard uncertainty of the gasdensity variation is 0.045 %. The inventory volume is
calculated based on the sizes of the piping, connectorand the glass cylinder, and those for the small,medium and the large columns are estimated to be 70cm3, 200 cm3 and 2000 cm3, respectively,corresponding to ratios of 0.68, 0.26 and 0.23,respectively, to the collection volumes. These causecontributions of 0.031 %, 0.012 % and 0.010 %,respectively, to the standard uncertainty of mass flowdetermination. The maximum relative deviation of theinventory volume measurement is estimated to be 40 %,resulting in contributes of 0.007 %, 0.003 % and0.002% for small, medium and large columns,respectively, to the standard uncertainty of the massflow.
2.3.6 Leakage
The leak is tested by lifting and holding the pistonmidway in the glass cylinder and monitoring itsfalling speed. Results show that the leak is less than0.02% of the minimum flow to be measured by thepiston prover. In practice, the leakage is ignored witha relative uncertainty contribution of 0.012 %.
2.3.7 Combined and expanded uncertainties
Table 1 gives a summary of the uncertaintycomponents described above. The combineduncertainties of mass flow rate, obtained by RSS of allstandard uncertainties, are 0.063 %, 0.055 % and0.054 % for small, medium and large cylinders,respectively. With a coverage factor of 2, whichcorresponds to a level of confidence of approximately95 %, the expanded uncertainties of mass flowmeasurement by NIMT's piston prover areaccordingly 0.13 %, 0.11 % and 0.11 %.
3. Verification of the Low-Pressure Gas Flow Standard through Bilateral Comparison
3. 1 Bilateral Comparison Scheme
Figure 4 is a photo of the TS used in thiscomparison. Each of the CFV's has been installed inrespective stainless steel holder. On the holder, acustom-made 4-wire Pt-100 thermal sensor is installedand connected to a handheld digital display. Twoquick connector type taps have also been administeredfor the measurement of pressure upstream anddownstream of the CFV.
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Establishment and Verification of a Primary Low-Pressure Gas Flow Standard at NIMT
The three CFV's have measured throat diametersof 0.035 mm, 0.106 mm and 0.585 mm, and wereidentified as SN-003, SN-010 and SN-060, respectively.The CFV's were chosen as the TS flowmeter due totheir robustness, long term stability and well-understood and relatively small sensitivities, and thefact that they have often been used in inter-comparisons [5-7]. The DAQ at CMS was carried outusing a self-developed, LabVIEW based program. Arevised and compiled version of this program wasused in the system at NIMT. The property databasedeveloped by the National Institute of Standards andTechnology (NIST), Refprop (Version 8.0), was usedto obtain the gas properties.
The TS was used, with dry air as the test fluid, ateight flows ranging approximately from 42 mL/minto 14.5 L/min at standard condition of 0 °C and101.325 kPa (about 0.055 g/min to 18.87 g/min). Thespecific TS used, nominal operation (inlet) pressureand corresponding approximate volume flow rate foreach flow point are listed in Table 2.
The first measurement was carried out at CMSfrom 13 to 14 August 2009. The TS was then carried toNIMT where measurement with its piston prover wasconducted from 30 September 2009 to 1 October 2009.The last measurement took place back at CMS from 6to 8 October 2009. The second CMS data set was used
Fig. 4. A photo of the transfer standard (TS) used in the bilateral comparison
Table 1Uncertainty budget for mass flow measurement of NIMT's piston prover
Sources of uncertainty Small column Medium column Large column(%) (%) (%)
1 I.D. of glass cylinders 0.012 0.006 0.0042 Piston traveling distance 0.00090 0.00089 0.000893 Gas density 0.051 0.051 0.0514 Collection time 0.007 0.007 0.0075 Storage effects 0.032 0.012 0.0106 Leakage 0.012 0.012 0.012
as the reference value for the comparison.The parameter compared is the averaged dischargecoefficient of the CFV's. Note that for the measurementat NIMT, the nozzles SN-003, SN-010 and SN-060were calibrated on small, medium and large columns,respectively.
3.2 Primary Low-Pressure Gas Flow Standard at CMS
The CMS primary standard used in thiscomparison is a piston prover consisting of fiveprecisely manufactured glass cylinders. The systemis installed in a room with controlled temperature at(23 ± 1) °C and relative humidity at (45 ± 10) % and iscapable of measuring flows ranging from 2 mL/minto 24 L/min at the reference condition (296.15 K and101.325 kPa). Table 3 lists the mean cylinder innerdiameter (I.D.), applicable range of flow andmeasurement uncertainty for each column.
Figure 5 shows the experimental setup at CMS. Aself-assembled interferometer system, which uses a633 nm laser from MELLES GRIOT and ND281Bdisplay unit from HEIDENHAIN, located at the topof the piston prover is used to measure the pistontravelling distance. The interferometer is installed on
a positioning system which allows the laser beam tomove to the column intended to be used. HP 3457Adigital multi-meter and HP 34970A data acquisition/ switch unit are used, in combination with custom-made 4-wire Pt-100 sensors, to measure thetemperatures of the gas flowing into the glass cylinderat various locations of the standard and, if applicable,at the DUT. HP 53132A universal counter serves asthe timer. Two DHI RPM3 digital pressure gauges areused to measure the pressure at the standard and theDUT. With 95 % level of confidence, the claimedrelative expanded uncertainty for the entire flow rangecovered is 0.10 %. For the measurements at CMS inthis comparison, the nozzles SN-003 and SN-010 werecalibrated on column no. 3 and the nozzle SN-060 oncolumn no. 5.
3.3 Methods of Comparison and Data Analysis
3.3.1 Measurement parameter
In this comparison, mass flow measurements bythe two participating labs, NIMT and CMS, arecompared using the discharge coefficient, Cd, for thethree CFV's.
Table 2Measurement arrangement of the bilateral comparison
Flow point TS Operation pressure (kPa) Approximate flow rate (mL/min)
Establishment and Verification of a Primary Low-Pressure Gas Flow Standard at NIMT
m ,s m ,sd * *
m ,th 0 0( / )q q
Cq A C P R M T
= = (4)
where qm,s is the mass flow rate measured by thestandard system; qm,th is the theoretical CFV massflow; T0 is the gas stagnation temperature; A* is thethroat area of the CFV; C* is the critical flow functionof sonic nozzle; and P0 is the gas stagnation pressure.
The air supply in both labs were dehumidified toa dew point temperature of -40 °C or lower, therefore,the molecular weight and C* were calculated basedon dry air composition. Three repeated calibrationsfor the eight flows were carried out at each lab, yieldinga total of 24 data points in each of the three set ofmeasurements conducted in this comparison. Thethree Cd values for each CFV at each flow were
averaged to obtain dC , which was then used for thecomparison
3.3.2 Uncertainty analysis
The uncertainty of the discharge coefficient wasevaluated in accordance with the CIPM CCM.FF-K6comparison report [6]. The components of theuncertainty include:
i) the mass flow measured by the participating lab,ii) the standard deviation of the mean of repeated
measurements at each flow, andiii) factors related to the determination of theoretical
mass flow rate by the TS.
Starting from Eq. (4), the relative standarduncertainty of Cd can be expressed as follows.
(5)
Fig. 5. Schematic of the experimental setup of the piston prover at CMS
2 2m,s m,thd
d m,s m,th
( ) ( )( ) −= +
u q u qu CC q q
Chun-Min Su, Win-Ti Lin and Sutham Masri
182
The uncertainty of theoretical mass flow rate,u(qm,th), as given in Eq. (6), can be further evaluated bycomponents that can be grouped into two categories:(a) the first order effects of the parameters appear inEq. (4), u1(qm,th), and (b) the second order effects of theparameters and other factors unaccounted for in thephysical model, u2(qm,th).
2 2m,th 1 m,th 2 m,th( ) ( ) ( )≡ +u q u q u q (6)
For the uncertainty originated from mass flowmeasurement, the capabilities of the two participatinglaboratories described in earlier were used. Moreover,the maximum of the standard deviation of the meanof three Cd values obtained at each flow set point fromeach laboratory was used to evaluate the uncertaintyassociated with reproducibility of the measurement.
The term u(qm,th) can be evaluated based on Eq. (4)and the method of propagation of uncertainties.Uncertainties related to the determination of P0, T0, C*and M have been considered and attributed to u1(qm,th).Temperature and critical flow effects as well as leakshave also been taken into account and attributed tou2(qm,th). The sources and magnitudes of these sevencomponents are elucidated below.
i) Pressure: The pressure at the inlet of the CFV'swas measured using the participants' ownpressure gauge. Contributions from traceability,curve-fitting and drifting were considered. As aresult, the relative standard uncertainties of thepressure measurement, with reference to anoperation pressure of 450 kPa / 300 kPa fornozzles SN-003 / SN-010 & SN-060, are 0.006 %/ 0.008 % and 0.011 % / 0.015 % for CMS andNIMT, respectively.
ii) Temperature: Both CMS and NIMT used the sametemperature sensors in the comparison and thuscalibration biases are correlated. Observationsshowed that the temperature variation during asingle calibration was well within 0.05 °C. Arelative standard uncertainty of 0.01 % withreference to the room temperature of 296.15 K canthus be obtained. The sensitivity coefficient ci is0.5 since temperature appears under the squareroot in Eq. (4).
iii) Critical Flow Function: The real critical flowfunction was calculated according to the
international standard ISO 9300 [8] and was usedin this comparison for both participants.However, as a conservative measure, the value0.008 % from [6] was adopted in this comparisonas the relative standard uncertainty.
iv) Molecular Weight: The value 0.011 % from [6]was adopted in this comparison. Appearanceunder the square root in Eq. (4) gives M asensitivity coefficient of 0.5.
v) Temperature Effects: The uncertainty due totemperature effects for the CFV's used in K6 wasdeliberately studied in [9] and was incorporated inthe K6 report [6]. The values 0.016 % and 0.006 %for the small and large CFV's, respectively, weregiven in the K6 report. Due to considerationspertaining to temperature variation, sizes of thenozzles and their installation, the value 0.016 %was used for all the CFV's in this comparison.
vi) Critical Flow Effects: A preliminary study at CMSshowed that the critical back pressure ratio(CBPR), defined as the downstream to upstreampressure ratio at which the discharge coefficientis 0.1 % below the initial value in the chokingcondition, of the CFV's SN-003, SN-010 and SN-060 were, as shown in Fig. 6, approximately 0.34,0.57 and 0.47, respectively, under an inlet pressureof about 300 kPa. At a back pressure ratio largerthan CBPR, the nozzles will no longer be critical.In this comparison, as can be derived from Table2, the maximum back pressure ratio was about0.22 for SN-003 and 0.33 for SN-010 and SN-060,which were well below their corresponding CBPR.Therefore, the uncertainty due to breakdown ofchoke condition was considered negligible.
vii) Leaks: Leak check on the CFV's was preformedprior to the comparison. The design of the CFVholder allows minimum rearrangement of the TSpiping and gives us the confidence that the leakswere controlled to less than 0.01 % of all flowstested.
Since both NIMT and CMS used the same valuesof the universal gas constant and CFV throat diameter(cross-sectional area at throat) in the calculation ofCd, uncertainties related to these components can beignored.
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Establishment and Verification of a Primary Low-Pressure Gas Flow Standard at NIMT
Taking the root-sum-square of the aforementionedcomponents and sources, as depicted in Eqs. (5) and(6), gives the relative standard uncertainty of themeasurement of Cd. Table 4 summarizes theevaluation results for the three CFV's calibrated byCMS and NIMT. The relative standard uncertaintiesfor Cd measurements by CMS were all 0.056 %, andthey were 0.068 %, 0.062 % and 0.061% for SN-003,SN-010 and SN-060, respectively, for measurementsby NIMT
3.4 Measurement and Comparison Results
3.4.1 Measurement results
Figures 7-9 show the Cd measurement results fornozzle SN-003, SN-010 and SN-060, respectively,plotted versus the inverse square root of the theoreticalReynolds number, Reth, which is defined as follows.
m ,thth
0
4=
qRe
πdμ (7)
Fig. 6. Normalized Cd vs. back pressure ratio at 300 kPa inlet pressure for the three CFV's
Table 4Uncertainty budget for Cd measurement of the three CFV's
Fig. 7. Results of Cd vs. Reth-0.5 for nozzle SN-003
Fig. 8. Results of Cd vs. Reth-0.5 for nozzle SN-010
where d is the throat diameter of the sonic nozzle, and0μ is the viscosity of gas the upstream of the sonic
nozzles at stagnation temperature and pressure. Inthese figures, the first and second measurements byCMS are marked as blue triangle (CMS-#1) and bluecircle (CMS-#2), respectively, and the measurementby NIMT is represented by red crosses. The resultsshow that, in general, the first measurement carriedout at CMS has the lowest Cd value, where as themeasurement by NIMT has the highest and isrelatively close to the second measurement conductedat CMS. Differences between the two measurementsby CMS are within 0.05 %, showing that the TS wasstable during the circulation. Since extra care was
taken for temperature equilibrium and measurementin the CMS-#2 calibrations, this set of data wasconsidered more reliable and thus was used as thereference values in this comparison.
3.4.2 Comparison results
As mentioned earlier, the comparison was madebetween the averaged discharge coefficient at each
flow and the reference value based on CMS-#2data set. Since the operational conditions among thethree sets of measurement differed slightly, NIMT's
Establishment and Verification of a Primary Low-Pressure Gas Flow Standard at NIMT
CMS-#2 data at the same Re-0.5 values. The slope0.5
d / ( )−dC d Re used for the adjustment was based on
NIMT's data. The dC values were then normalizedby the reference values. The degree of equivalence forNIMT with reference to CMS, denoted as DNIMT, wascalculated as follows.
(8)
where Re th (CMS-#2)is the Reynolds numbercorresponding to the actual operational condition of
the CMS-#2 data set; dδC is the correction applied tomake the aforementioned adjustment. The
approximate 95 % confidence level (k = 2) uncertaintyof DNIMT, U(DNIMT), can be expressed in terms of othercomponents by the following equation.
(9)
The degree of equivalence of NIMT to the referencewas further examined by the En value, adimensionless parameter defined as the differencebetween the participant's result and the referencevalue divided by the expanded uncertainty of thedifference. The En values for NIMT's measurementresults were calculated according to Eq. (10). Table 5summarizes the bilateral comparison results at eachflow.
Fig. 9. Results of Cd vs. Reth-0.5 for nozzle SN-060
Table 5Summary of the comparison results between NIMT and CMS
In Table 5, the flows specified are approximatevalues at standard condition of 0 °C and 101.325 kPa.
d NMIT )-U(C and d CMS-#2 )-U(C were quoted from Table4, and d )U(δC was obtained through statistic analysisof those data for the linear regression. As can be seen,all the values of DNIMT are less than 0.06 % and wellwithin the stated uncertainty. All the En values aresmaller than 0.4.
4. Conclusion
A mercury-sealed piston prover was establishedas a primary low-pressure gas flow standard inThailand, covering the flow of 5 mL/min to 24 L/min(at 23 °C and 101.325 kPa). Evaluation detailed inthis paper showed that the mass flow measurementuncertainty of the facility is less than 0.013 % (k = 2).A bilateral comparison between NIMT and CMS wasconducted to verify the measurement capability of thesystem. With the use of a set of three CFV's as thetransfer standard, the comparison was carried outbased on calibrations of eight flows covering the rangeof 42 mL/min to 14.5 L/min (at 0 °C and 101.325kPa). Discharge coefficient (Cd) was used as theparameter for the comparison and the measurementuncertainties for both participants were evaluated. Therelative expanded uncertainty for Cd measurementsby CMS was 0.12 % for all three CFV's, and those byNIMT were less than 0.14 %.
The difference between NIMT's averageddischarge coefficient at each flow and correspondingreference value based on CMS's second calibrationdata set, both normalized by the reference value, andthe En values were analyzed to evaluate the degree ofequivalence. Results showed that the difference wasless than 0.06 % throughout the flow range tested,and the En values at all flows were well smaller thanunity. Flow measurements by both participants of thiscomparison are in good agreement and themeasurement capabilities claimed are thus consideredvalid.
Acknowledgement
The authors gratefully thank colleagues at NIMTand CMS/ITRI for their support and contribution inthe collaboration project.
References
[1] ISO/IEC Guide 98-3:2008, Uncertainty ofMeasurement - Part 3: Guide to the Expressionof Uncertainty in Measurement (GUM:1995),International Organization for Standardization,Geneva, Switzerland, (2008).
[2] J.D. Wright and G.E. Mattingly, NISTCalibration Services for Gas Flow Meters: PistonProver and Bell Prover Gas Flow Facilities, NISTSpecial Publication 250-49, National Instituteof Standards and Technology, (1998).
[3] J.D. Wright, A.N. Johnson and M.R. Moldover,Design and Uncertainty Analysis for a PVT GasFlow Standard, Journal of Research of theNational Institute of Standards andTechnology, 108 (2003) 21-47.
[5] J.D. Wright, What is the "Best" Transfer Standardfor Gas Flow?, the 12th International Conferenceon Flow Measurement (FLOMEKO), Groningen,Netherlands, (2003).
[6] J.D. Wright, B. Mikan, R. Paton, K.A. Park, S.Nakao, K. Chahine and R. Arias, CIPM KeyComparison for Low-Pressure Gas Flow:CCM.FF-K6 Final Report, WGFF, CIPM, (2007).
[7] T. Morioka and S. Nakao, Protocol for the APMPLow-Pressure Gas Flow Key Comparison(APMP.TCFF-K6), Gas Flow StandardsLaboratory, NMIJ, (2006).
[8] ISO 9300:2005, Measurement of Gas Flow byMeans of Critical Flow Venturi Nozzles,International Organization for Standardization,Switzerland, (2005).
[9] J. Wright, Uncertainty of the Critical VenturiTransfer Standard Used in the K6 Gas Flow KeyComparison, the 14th International Conferenceon Flow Measurement (FLOMEKO),Johannesburg, South Africa, (2007).
