Gas Flowmeter Calibrations with the 26 M3 PVTt Standard

1 Page 1 NIST Measurement Services: Gas Flowmeter Calibrations with the 26 m 3 PVTt Standard NIST Special Publication 250-1046 Aaron N. Johnson and John D. Wright November 25, 2009 U. S. Department of Commerce Technology Administ... Open at page → 2 Page 2 i Table of Contents Gas Flowmeter Calibrations with the 26 m 3 PVTt Standard Abstract.............................................................................................................................1 1 Introd... Open at page → 3 Page 3 1 Abstract This document describes NIST’s 26 m 3 pressure, volume, temperature, and time (PVTt) primary flow standard. This standard is used to calibrate gas flow meters over a range extending from 200 L/min to 77000 L/m... Open at page → 4 Page 4 2 1. Introduction to Gas Flow Measurement at NIST Calibrations of gas flow meters are performed with primary standards [1] that are based on measurements of more fundamental quantities, such as length, mass, and time. Pr... Open at page → 5 Page 5 3 uncertainty of the 26 m 3 PVTt primary flow standard covering the flow range from 200 L/min to 77000 L/min. Details concerning the two smaller PVTt flow standards can be found in the following reference [6]. 2. Descrip... Open at page → 6 Page 6 4 cannot be read with precision any better than 1 %. It is not practical to pay several thousand dollars to obtain a NIST calibration with an expanded uncertainty of 0.09 %. For such a flowmeter, a calibration with an ex... Open at page → 7 Page 7 5 3. Procedures for Submitting a Flow meter for Calibration The FMG follows the policies and procedures described in Chapters 1, 2, and 3 of the NIST Calibration Services Users Guide [9]. These chapters can be found on t... Open at page → 8 Page 8 6 various safety features that prevent overpressurizing the collection tank during a calibration. This allows the PVTt system to safely perform calibrations during non-business hours, thereby allowing a faster turnaround... Open at page → 9 Page 9 7 overlap. The smallest three CFVs in Fig. 2 have a portion of their flow ranges that can be calibrated on both the 677 L and the 26 m 3 PVTt. Agreement between these independent systems adds confidence to the validity o... Open at page → 10 Page 10 8 inlet. As long as the appropriate pressure ratio is maintained across the CFV, the mass flow ( m) remains constant throughout the collection period. If the leak rate is negligible, then the instantaneous rate of mass... Open at page → 11 Page 11 9 where the effect of leaks is omitted in calculating the CFV mass flow, but accounted for in the mass flow uncertainty in section 6.3. Furthermore, by substituting the definitions of T MΔ and I MΔ given in Eqns. (7a) an... Open at page → 12 Page 12 10 of state for dry air to determine the final compressibility factor ( f T Z), and subsequently the final density ( f T ρ). The volume of the collection tank ( T V) is multiplied by the final density to determine the fi... Open at page → 13 Page 13 11 Many of the operating procedures used by the FMG are standard to all blow-down PVTt systems. However, the inventory mass cancellation technique outlined in steps 4 and 6 of the PVTt operating procedures (see section 4... Open at page → 14 Page 14 12 agree reasonably well with measured results, and are used here to explain the inventory matching technique. The time histories of I M and T M are divided into five regions. Region 1 corresponds to steps 1 and 2 in the... Open at page → 15 Page 15 13 Region 2b is the best choice to begin the collection time. Similar arguments can be made to show that Region 4b is the best choice to stop the collection time. Figure 4. Time adjustment factor versus the percent densi... Open at page → 16 Page 16 14 ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − − = minmax minmatch 100 ρρ ρρ ζ ρ (10) determines which of the manifold of possible collection times is used to calculate the mass flow. Here, min ρ and maxρ are the lower and upper limits of the density... Open at page → 17 Page 17 15 evaluated by other means) as described in [12]. Uncertainties having subcomponents belonging to both Type A and Type B are categorized as (A, B) as specified in [12]. 5.1 Reference Parameters ( M, uR, and Z) 5.1.1 Uni... Open at page → 18 Page 18 16 compressibility factor is conservatively estimated to be no more than ()[ ] II ZZu = 100 × 10 -6 . Both of these uncertainty components are Type B. 5.2 Collection Time The collection time, defined previously in Eqn. (... Open at page → 19 Page 19 17 with misalignment of the triggering signal and the valve fully closed positions of either valve are inherently accounted for by the inventory mass cancellation technique. For example, if during the first flow diversio... Open at page → 20 Page 20 18 intervals starts at t = 0 s. The pressure and temperature time traces begin at near ambient conditions, increase as mass accumulates into the inventory volume, and then sharply decrease as the accumulated mass is exha... Open at page → 21 Page 21 19 Below we assess the uncertainty for pressure and temperature measurements in the inventory volume. Since the greatest inventory volume uncertainties occur at the largest flows, the analysis gives the uncertainties at... Open at page → 22 Page 22 20 tank valve ( i.e., 2 nd dead-end interval) just prior to the start of the dead-end periods. Because the CFV mass flow, and the initial inventory pressures, and temperatures are nearly the same during the first and sec... Open at page → 23 Page 23 21 can differ slightly attributed to differences between the initial and final pressures. The relative standard uncertainty of the correlated components of the final pressure include the calibration fit residuals (0.4 %)... Open at page → 24 Page 24 22 5.3.4 Final Temperature in the Inventory Volume The final temperature has the same uncertainty components as the initial temperature and the corresponding uncertainties types are the same. These include the spatial sa... Open at page → 25 Page 25 23 The final pressure in the collection tank is measured using a Paroscientific Model pressure transducer with a full scale of 200 kPa. This transducer is calibrated at six month intervals using a Ruska piston pressure g... Open at page → 26 Page 26 24 Table 10. Uncertainty of the final tank temperature. Uncertainty of Final Tank Temperature Abs. Unc. Rel. Std. Unc. (k=1) Perc. Contrib. Unc. Type Comments Final tank temperature, K294= f T T (mK) (× 10 -6 ) (%) (A or... Open at page → 27 Page 27 25 temperature changes. However, additional temperature measurements suggest that 50 mK is a reasonable upper bound. Moreover, an array of 14 thermocouples distributed along the outer surface of the collection tank verif... Open at page → 28 Page 28 26 Figure 6. Shows eight measurements (four with argon and four with nitrogen) based on gravimetric weighing technique used to determine the collection tank internal volume ( TV), and the standard deviation of repeated m... Open at page → 29 Page 29 27 repeated volume measurements equals to the standard deviation of the mean, N V TV σ = 113 × 10 -6 , where N= 8 are the eight repeated volume measurements. Table 11. Uncertainty of the collection tank volume. Tank Volu... Open at page → 30 Page 30 28 method, the size of the connecting volume was 128.4 cm 3 and its relative standard uncertainty is () [] ccVVu = 58940 × 10 -6 . 5.6.2 Initial Gas Density in the Collection Tank The initial tank density was determined... Open at page → 31 Page 31 29 Before beginning the mass transfer into the collection volume, the connecting volume of nylon tubing was checked for leaks using a soap solution. If no leaks were found, the high pressure cylinders were emptied into t... Open at page → 32 Page 32 30 = ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ 2 )( cyl cylM MuΔ Δ 2 2 )( ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + i air i air cyl i aircyl ref i air cyl i sen i DS i ref u M V M MOM ρ ρ Δ ρ ρ ρ Δ 2 2 )( ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡... Open at page → 33 Page 33 31 5.6.5.3 Density of the Reference and Sensitivity Masses Both reference and sensitivity masses are made of stainless steel and have identical densities equal to 7950 kg/m 3 . The relative standard uncertainty for densi... Open at page → 34 Page 34 32 standard uncertainty is ][ i air i air u ρρ)( = 844 × 10 -6 . The major sources of uncertainty are attributed to the measurement of temperature and relative humidity. The temperature uncertainty is primarily due to te... Open at page → 35 Page 35 33 repeated occurrences of IM Δ in the numerator and denominator of the first term and observing that the correlated terms vanish as IM Δ tends to zero we obtain () () () 22 T T 2 T I 2 t tu M Mu M Mu m )m(u ⎥ ⎦ ⎤ ⎢ ⎣ ⎡... Open at page → 36 Page 36 34 ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + 2222 )()()( f T f T f T f T f T f T T f T Z Zu T Tu P Pu M MΔ () 2 T T V Vu ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + and each component is itemized in Tab... Open at page → 37 Page 37 35 normalized by the density change in the collection tank, T ρΔ, instead of IρΔ=0, to avoid the singularity that would result from dividing by zero. Table 16 itemizes these components and shows that the relative standar... Open at page → 38 Page 38 36 Table 17. Uncertainty components for the inventory volume density difference. Uncertainty of Density Difference Rel. Std. Unc. (k=1) Sen. Coeff. Perc. Contrib. Unc. Type Comments Density Difference, ΔρI =0 kg/m 3 (%)... Open at page → 39 Page 39 37 6.4 Uncertainty Attributed to the Steady Flow Assumption In developing the expression for the measured mass flow ( i.e., Eqn. 8 or 9) we assumed that the flow entering the CFV remained steady for the entire collection... Open at page → 40 Page 40 38 uncertainty are attributed measuring the collection tank volume and the final ( i.e., after filling) temperature of the gas in the tank in the collection tank. Together these contribute more than 60 % of the overall u... Open at page → 41 Page 41 39 are completely automated and able to perform calibrations overnight and on weekends, thereby expediting turnaround time for our customers. Open at page → 42 Page 42 40 REFERENCES [1] International Organization for Standardization, International Vocabulary of Basic and General Terms in Metrology , 2 nd edition, 1993. [2] Brain T. J. S., Macdonald, L. M., Evaluation of the Performance... Open at page → 43 Page 43 41 [17] Wright J. D. and Johnson, A. N., Uncertainty in Primary Gas Flow Standards Due to Flow Work Phenomena , FLOMEKO, Salvador, Brazil (2000). [18] A. Bejan, Convection Heat Transfer, John Wiley and Sons, 1 st edition... Open at page → 44 Page 44 NIST Test Number: 836-123456-04-04 Service ID Number: 18010C Calibrated on July 22, 2004 by Gina Kline, Aaron Johnson, and John Wright Page 1 of 6 SAMPLE CALIBRATION REPORT FOR A CRITICAL FLOW NOZZLE July 22, 2005 Mfg.:... Open at page → 45 Page 45 SAMPLE CALIBRATION REPORT Gas Flow Meter, S/N 1234 Flow Nozzles, Inc. Purchase Order No. A123 NIST Test Number: 836-123456-04-04 Service ID Number: 18010C Calibrated on July 22, 2004 by Gina Kline, Aaron Johnson, and Joh... Open at page → 46 Page 46 SAMPLE CALIBRATION REPORT Gas Flow Meter, S/N 1234 Flow Nozzles, Inc. Purchase Order No. A123 NIST Test Number: 836-123456-04-04 Service ID Number: 18010C Calibrated on July 22, 2004 by Gina Kline, Aaron Johnson, and Joh... Open at page → 47 Page 47 SAMPLE CALIBRATION REPORT Gas Flow Meter, S/N 1234 Flow Nozzles, Inc. Purchase Order No. A123 NIST Test Number: 836-123456-04-04 Service ID Number: 18010C Calibrated on July 22, 2004 by Gina Kline, Aaron Johnson, and Joh... Open at page → 48 Page 48 SAMPLE CALIBRATION REPORT Gas Flow Meter, S/N 1234 Flow Nozzles, Inc. Purchase Order No. A123 NIST Test Number: 836-123456-04-04 Service ID Number: 18010C Calibrated on July 22, 2004 by Gina Kline, Aaron Johnson, and Joh... Open at page → 49 Page 49 SAMPLE CALIBRATION REPORT Gas Flow Meter, S/N 1234 Flow Nozzles, Inc. Purchase Order No. A123 NIST Test Number: 836-123456-04-04 Service ID Number: 18010C Calibrated on July 22, 2004 by Gina Kline, Aaron Johnson, and Joh... Open at page →