Gas Flowmeter Calibrations with the 34 L and 677 L PVTt Standards

1 Page 1 NIST Measurement Services: Gas Flowmeter Calibrations with the 34 L and 677 L PVTt Standards NIST Special Publication 250-63 John D. Wright, Aaron N. Johnson, Michael R. Moldover, and Gina M. Kline U. S. Department of Co... Open at page → 2 Page 2 Table of Contents Gas Flowmeter Calibrations with the 34 L and 677 L PVTt Standards Abstract......................................................................................................................1 1 Introd... Open at page → 3 Page 3 Abstract This document provides a description of the 34 L and 677 L pressure, volume, temperature, and time (PVTt) primary gas flow standards operated by the National Institute of Standards and Technology (NIST) Fluid Fl... Open at page → 4 Page 4 Double diversions were used to evaluate the 677 L system over a range of 300 L/min to 1600 L/min, and the relative differences between single and double diversions were less than 75 × 10 -6 . Key words: calibration, corr... Open at page → 5 Page 5 Customers with no primary standards use their NIST calibrated flowmeters as working standards or reference standards in their laboratory to calibrate other flowmeters. The Fluid Flow Group of the Process Measurements Div... Open at page → 6 Page 6 the old and the new primary standards for customer calibrations. In 2003, the new primary standards and their uncertainty statements were sufficiently validated [Wright 2003A], and we began using the new standards alone... Open at page → 7 Page 7 L PVTt standard, gases are practically limited to air from the compressor and nitrogen from dewars since a very large number of gas cylinders would be necessary to provide gas at 2000 L/min. The gas temperatures are nomi... Open at page → 8 Page 8 standard. The same set point flows are tested on a second occasion, but the flows are tested in decreasing order instead of the increasing order of the first set. Therefore, the final data set consists of six (or more) p... Open at page → 9 Page 9 3 Procedures for Submitting a Flowmeter for Calibration The Fluid Flow Group follows the policies and procedures described in Chapters 1, 2, and 3 of the NIST Calibration Services Users Guide [Marshall 1998]. These chapt... Open at page → 10 Page 10 Figure 1. Arrangement of equipment in a PVTt system. The process of making a PVTt flow measurement normally entails the following steps: 1. Close the tank valve, open the bypass valve, and establish a stable flow through... Open at page → 11 Page 11 6. Wait for stability and then acquire and and hence. f TP f T T f T m By writing a mass balance for the control volume composed of the inventory and tank volumes (see the volume defined by the dashed line in Fig. 1), on... Open at page → 12 Page 12 in the inventory volume () and extremely good cancellation of certain correlated inventory uncertainties. I m∆ The PVTt measurement process can be performed in a “blow down” mode also, where initial and final values of t... Open at page → 13 Page 13 5 Design and Operation of the PVTt Standard Experience with a previous, 26 m 3 PVTt flow standard at NIST indicated that improvements in temperature and pressure instrumentation as well as in the design and operation of... Open at page → 14 Page 14 Figure 2. A schematic of the PVTt collection tanks, water bath, duct, and temperature control elements. In this work, we avoided long equilibration times and the difficult problem of measuring the average temperature of... Open at page → 15 Page 15 Large diverter valves Small diverter valves 677 L collection tank manifold Heating, cooling, and mixing elements 34 L collection tank Figure 3. A photograph of the two PVTt collection tanks submerged in the temperature c... Open at page → 16 Page 16 volume through the unobstructed, 10 cm thick, water-filled spaces between the duct and the sides, the top, and the bottom of the rectangular tank. 297.286 297.287 297.288 297.289 297.29 01 0 Time (min) T (K) 20 Figure 4.... Open at page → 17 Page 17 gasτ= (a/2.405) 2 /DT, where DT is the thermal diffusivity of the gas. This estimate gives gasτ= 80 s for nitrogen in the 677 L tank. This estimate for τgas is too large insofar as it neglects convection, conduction thro... Open at page → 18 Page 18 The manifold linking the 8 cylindrical shells is completely immersed in the water bath. Thus, the gas in the manifold quickly equilibrates to the bath temperature as well. However, each collection system has small, unthe... Open at page → 19 Page 19 of the inventory transients (see Fig. 7) and the mass cancellation method also give uncertainty benefits due to high correlation in the uncertainties of pressure and temperature measurements for ∆mI . We tested our strat... Open at page → 20 Page 20 Figure 6. Experimentally measured data (25 L/min in the 34 L tank) and thermodynamic model predictions for zero and non-zero sensor time constants. The model outputs demonstrate that neglect of sensor response causes sig... Open at page → 21 Page 21 neglects heat transport from the gas to the surrounding structure and non-uniform conditions, such as the jet entering the volume. For Fig. 6, T(t) and P(t) were calculated on the assumption that the diverter valve reduc... Open at page → 22 Page 22 5.2.3 Near Symmetry of Start and Stop Behavior of P(t) Figure 7 shows records of T(t) and P(t) taken during the dead-end time intervals at the start and the stop of a single flow measurement. As before, the data were rec... Open at page → 23 Page 23 acquisition card (see Fig. 8). The trigger signals originate from an LED/photodiode pair and a flag on the valve actuator positioned so that the circuit output rises to a positive voltage when the valve is closed. These... Open at page → 24 Page 24 5.2.4 Insensitivity of to the Match Pressure I m∆ Figure 9 shows the total correction time as a function of the match pressure for two flows in the 34 L system. The 100 L/min flow is very high for the 34 L tank, having o... Open at page → 25 Page 25 Figure 9. The collection time correction versus the match pressure used in the inventory mass cancellation algorithm. Analysis of the thermodynamic model of the inventory and its sensors shows that times later in the dea... Open at page → 26 Page 26 5.3 Measurement of the Tank and Inventory Volumes 5.3.1 Gas Gravimetric Method The volume of the 677 L tank was determined by the gas gravimetric method. In this method, the mass of an aluminum high pressure cylinder was... Open at page → 27 Page 27 and 3820 g respectively. The standard deviation of the six volume measurements (4 with nitrogen, 2 with argon) was 16 × 10 -6 VT. The initial and final masses of the gas cylinder were measured using a substitution proces... Open at page → 28 Page 28 apparent mass in water. The apparent mass of the cylinder in air (with the liquid still inside) was measured using the comparator described above. The density of air with humidity was calculated as previously described.... Open at page → 29 Page 29 5.3.2 Volume Expansion Method The 34 L collection tank volume, the inventory volume for the large collection tank, and the small inventory volume were all determined with a volume expansion method. In this method, a know... Open at page → 30 Page 30 relative standard uncertainty of 60 × 10 -6 to the determinations of the volumes of the collection tanks and to the flow measurements. 6.1 Techniques for Uncertainty Analysis The uncertainty of a mass flow measurement ma... Open at page → 31 Page 31 () () ()()( )∑∑ ∑ = − =+= ∂ ∂ ∂ ∂ +         ∂ ∂ = N i N i N ij jiji ji i i c xxrxuxu x y x y xu x y yu 1 1 11 2 2 ,2 , (9) where r(xi, xj) is the correlation coefficient, ranging from –1 to 1, and equaling zero i... Open at page → 32 Page 32 Most of the equations utilized to calculate flow, mass, volume, and other necessary intermediate quantities for the PVTt standard have been discussed in prior sections. In Fig. 10 the information is summarized in a diagr... Open at page → 33 Page 33 The discharge coefficient resulting from a flowmeter calibration will have additional uncertainties not considered herein due to measurements associated with the meter under test. For instance, if the meter under test is... Open at page → 34 Page 34 in both relative (× 10 -6 ) and dimensional forms. The units of the dimensional values are given in the third column. The relative contribution of each sub-component to the combined uncertainty is listed in the fourth co... Open at page → 35 Page 35 Table 3 presents the uncertainty of flow measurements from the 34 L system for flows between 1 L/min and 100 L/min. The expanded uncertainty varies between 270 × 10 -6 and 440 × 10 m& -6 . At high flows, the significant... Open at page → 36 Page 36 Table 4. Uncertainties for a 100 kPa pressure measurement made with the piston pressure gage used as the standard for pressure calibrations. Uncertainty Category Standard Uncertainty (k = 1) ContribComments Relative (×10... Open at page → 37 Page 37 listed in Table 5. They include the uncertainties from the piston pressure gage, the long term drift of the Paroscientific transducer which has been quantified by periodic re- calibrations, as well as the residuals from... Open at page → 38 Page 38 sensor returns to room temperature (with a time constant of approximately 1 hr). The temperature dependence of the sensor was confirmed by testing with an environmental chamber. Temperature effects also result in a hyste... Open at page → 39 Page 39 Table 6. Uncertainties for the Fluid Flow Group temperature transfer standard. Uncertainty Category Standard Uncertainty (k =1) Contrib Comments Relative (×10 6 ) (mK) (%) Temperature Transfer Standard Temperature value... Open at page → 40 Page 40 related to extrapolation of their calibration data. Uncertainty related to the time response of the thermisters is negligible since the time constant for the sensor is on the order of 10 s and the wait for thermal equili... Open at page → 41 Page 41 Table 7. Uncertainty of average gas temperature in the collection tank with the dedicated temperature sensors. Uncertainty Category Standard Uncertainty (k =1) ContribComments Relative (×10 6 ) (mK) (%) Tank Gas Average... Open at page → 42 Page 42 6.5.2 Compressibility The compressibility factor can be calculated from the following expression: 2 1 nn CBZ ρρ++= , ( 11) where nρis the molar density (mol/ cm 3 ) and B and C are the second and third virial coefficient... Open at page → 43 Page 43 Uncertainty estimates for experimental studies of compressibility are often unavailable, especially for older publications. Comparison of previously compiled compressibility values obtained by various researchers [Dymond... Open at page → 44 Page 44 6.5.3 Molecular Weight The departure of the molecular weight of ultra high purity nitrogen, industrial liquid nitrogen, and ultra high purity argon from the molecular weight of the pure substance was examined using the i... Open at page → 45 Page 45 Table 9. The uncertainty of collection tank gas density for nitrogen and argon. Uncertainty Category Standard Uncertainty (k=1) Contrib Comments Collection Tank Density (N2 & Ar) Relative (×10 6 ) (%) pressure 64 6.45 ×... Open at page → 46 Page 46 the trigger voltage can be any time within a 0.33 ms window. Assuming a rectangular distribution, the post-processing corrections will have a standard uncertainty of 0.19 ms. This uncertainty applies to both the start an... Open at page → 47 Page 47 The uncertainty of this measurement is traceable to the density of distilled water, ambient air, reference masses, and the performance of the mass measuring systems. The uncertainty of the density of ambient air during t... Open at page → 48 Page 48 The uncertainties related to the determination of the external volume of the high-pressure cylinder are listed in Table 13. The 1 × 10 -6 relative standard uncertainty for the apparent mass in air is based on uncertainty... Open at page → 49 Page 49 The relative standard uncertainties of the cylinder mass measurement (Table 14) are quite small (1 × 10 -6 ) with the major components being the reference masses, the room air density (for buoyancy corrections) and the p... Open at page → 50 Page 50 Table 15. Uncertainty of the 677 liter collection tank volume. Uncertainty Category Standard Uncertainty (k =1) Contrib Comments Collection tank volume Relative (×10 6 ) (%) Initial mass of high P cylinder 1 0.00385 g 2... Open at page → 51 Page 51 Significant uncertainties of the volume expansion method are related to density and the measurement of pressure. Many components of the previously given pressure uncertainty are correlated for a pressure change measureme... Open at page → 52 Page 52 The 34 L tank volume uncertainty is summarized in Table 16. The largest uncertainty contributions are from the 677 L volume uncertainty, the density change in the 34 L volume, and the standard deviation of the repeated v... Open at page → 53 Page 53 Not all of the measurement uncertainties of the inventory volume are correlated. For perfect inventory mass cancellation, the pressure and temperature measured at specific locations in the inventory volume must exhibit p... Open at page → 54 Page 54 It is difficult to assess the magnitude of the uncorrelated uncertainties of pressure and temperature between the start and stop diversions in the inventory volume. Our strategy is to estimate the uncorrelated inventory... Open at page → 55 Page 55 Uncertainty Category Standard Uncertainty (k =1) Contrib Comments Relative (×10 6 ) (mK) (%) Inventory Thermocouple Temperature value 297000 sensor calibration 337 100 0 sensor time response 168350 50000 97 from inventor... Open at page → 56 Page 56 of these volumes are large, the sensitivity of the flow measurement to these volumes is small due to the inventory mass cancellation scheme and the relatively small size of VI. For the very small pressure changes used fo... Open at page → 57 Page 57 extremely large since the mass change is nearly zero. The mass change was calculated using the same 3 kPa and 9 K uncorrelated uncertainty values previously discussed. Table 21. Uncertainty of the inventory mass change f... Open at page → 58 Page 58 Throughout the range 3 L/min to 110 L/min, flows were measured independently using the 34 L and the 677 L collection systems, using a set of critical flow venturis (CFV) as transfer standards, and the two systems agreed... Open at page → 59 Page 59 that the two systems differ by about 100 × 10 -6 for flows less than 20 L/min. The RSS of the two relative standard volume uncertainties is 137 × 10 m& -6 (k = 1). Figure 11. Difference in the discharge coefficient of cr... Open at page → 60 Page 60 Figure 11 also shows the tank comparison results from the perspective of time measurement uncertainty rather than the mass. We interpreted the comparison results using the simplified model , where m is the mass collected... Open at page → 61 Page 61 size. This approach adheres to the definition of primary standard for both systems since neither one has been calibrated by a flow measurement against some other flow standard. During some of the comparison flows, we not... Open at page → 62 Page 62 beginning and end of the collection interval in the usual manner. In the second protocol, the collection interval was divided into two subintervals, i.e. each flow measurement had two start and stop diversions. The inter... Open at page → 63 Page 63 flow calibration, including a sample calibration report, as well as sources for instructions for submitting a flowmeter for calibration. The 34 L and 677 L PVTt flow standards have several novel features. The collection... Open at page → 64 Page 64 The uncertainty analysis shows that the 677 L system measures mass flow with an uncertainty between 200 × 10 -6 and 300 × 10m& -6 for a pure gas like nitrogen or argon. The higher uncertainty applies to higher flows as t... Open at page → 65 Page 65 Hilsenrath, J., Beckett, C. W., Benedict, W. S., Fano, L., Hoge, H. J., Masi, J. F., Nuttall, R. L., Touloukian, Y. S., and Woolley, H. W., Tables of Thermal Properties of Gases, NBS Circular 564, 1955. International Org... Open at page → 66 Page 66 Patterson, J. B. and Morris, E. C., Measurement of Absolute Water Density, 1° C to 40° C, Metrologia, 31, pp. 277-288, 1994. Trusler, J. P. M., Wakeham, W. A., and Zarari, M. P., Model Intermolecular Potentials and Viria... Open at page → 67 Page 67 NIST Test Number: 836-123456-03-01 Page 1 of 6 Calibration Date: July 2, 2003 Appendix: Sample Calibration Report REPORT OF CALIBRATION FOR A CRITICAL FLOW NOZZLE July 7, 2003 Mfg.: Meter Builders, Inc. Serial No: 1234 T... Open at page → 68 Page 68 REPORT OF CALIBRATION Gas Flow Meters Flowmasters, Inc. Purchase Order No. A123 and the stagnation pressure, , was calculated via the equation: 0P PP M 01 2 1 1 1 2 =⋅ + − ⋅       −γ γ γ (2) where γ is the specific... Open at page → 69 Page 69 REPORT OF CALIBRATION Gas Flow Meters Flowmasters, Inc. Purchase Order No. A123 where µ has units g / (cm s), and T is in K. The polynomial coefficients, a are in turn polynomial functions of pressure 0 i 3 03 2 02010 Pb... Open at page → 70 Page 70 REPORT OF CALIBRATION Gas Flow Meters Flowmasters, Inc. Purchase Order No. A123 0.9780 0.9800 0.9820 0.9840 0.9860 0.9880 0.9900 35,000 85,000 135,000185,000235,000285,000 Re Cd Figure 2. Calibration results for 0.125 in... Open at page → 71 Page 71 REPORT OF CALIBRATION Gas Flow Meters Flowmasters, Inc. Purchase Order No. A123 calibration result (measurand) so that the sensitivity of the result to uncertainties in the input quantities can be evaluated. The 67 confi... Open at page → 72 Page 72 REPORT OF CALIBRATION Gas Flow Meters Flowmasters, Inc. Purchase Order No. A123 NIST Test Number: 836-123456-03-01 Page 6 of 6 Calibration Date: July 2, 2003 coefficient at each of the nominal flows was used to calculate... Open at page →