Liquid Flow Meter Calibrations Piston Provers

1 Page 1 NIST Special Publication 250-10 39r1 Liquid Flow Meter Calibrations with the 0.1 L/s and the 2.5 L/s Piston Provers Jodie G. Pope John D. Wright Aaron N. Johnson Chris J. Crowley Open at page → 2 Page 2 NIST Special Publication 250-1039r1 Liquid Flow Meter Calibrations with the 0.1 L/s and the 2.5 L/s Piston Provers Jodie G. Pope John D. Wright Aaron N. Johnson Chris J. Crowley Sensor Science Division Physical Measureme... Open at page → 3 Page 3 Certain commercial entities, equipment, or materials may be identified in this document in order to describe an experimental procedure or concept adequately. Such identification is not intended to imply recommendation or... Open at page → 4 Page 4 Liquid Flow Meter Calibrations with the 0.1 L/s and 2.5 L/s Piston Provers Table of Contents Abstract ……………………………………………………………………...…………1 1.0 Introduction ..................................................................... Open at page → 5 Page 5 Abstract This document provides a description of the 2.5 L/s and 0.1 L/s liquid flow calibration standards operated by the National Institute of Standards and Technology (NIST) Fluid Metrology Group to provide flow meter... Open at page → 6 Page 6 0.1 L/s with expanded uncertainty of 0.044 % and a 2.5 L/s LFS that covers flows up to 2.5 L/s with expanded uncertainty of 0.064 % (with a 95 % confidence level) a . The 0.1 L/s and 2.5 L/s LFSs each consist of a fluid... Open at page → 7 Page 7 NIST uses the LFSs described herein to provide liquid flow meter calibrations for flows between 0.003 L/s and 2.5 L/s [4]. The most common flow meter types received for calibrations are turbines, Coriolis meters, and pos... Open at page → 8 Page 8 frequency and temperature instrumentation). NIST-owned and controlled instruments (temperature, etc.) are used as part of the test of a customer’s meter since these have established uncertainty values based on calibratio... Open at page → 9 Page 9 4.0 Description of the Liquid Flow Standards Piston prover systems have long been accepted as primary flow standards for both gas and liquid flow meters [7,8]. Figure 1 shows NIST’s piston provers and Table 1 and Table 2... Open at page → 10 Page 10 D d L c L c t C u p V D d L c L c t C u Q Table 1. Nominal Characteristics of NIST’s 0.1 L/s Liquid Flow Standard c . Volume of the cylinder [cm 3 ], p V 2229 Diameter of the cylinder [cm], 7.62 Diameter of the piston sh... Open at page → 11 Page 11 A) Photograph of the 0.1 L/s LFS. B) Photograph of the 2.5 L/s LFS. Figure 1. NIST’s LFSs. 7 Open at page → 12 Page 12 Figure 2. Sketch of the LFSs with the piston stroking left. The operation of the four-way diverter valve is demonstrated schematically in Figures 2 and 3. The calibration interval begins as soon as flow conditions reach... Open at page → 13 Page 13 (b) Transition from Left to Right Stroke (d) Transition from Right to Left stroke (a) Piston Stroking Left (c) Piston Stroking Right (b) Transition from Left to Right Stroke(b) Transition from Left to Right Stroke (d) Tr... Open at page → 14 Page 14 detect by eye. Because leaks are detected and repaired, errors resulting from undetected leaks are small enough to be neglected during uncertainty analysis. To determine if a visible leak is significant, a graduated cyli... Open at page → 15 Page 15    refenenrefe,e 1 TTLL  (3c) -5 -1 -6 -1 where  st  1.7 × 10 K [9,10] and  en  8 × 10 K[9] are the linear expansion coefficients for the stainless steel shafts and cylinder and for the glass encoder scal... Open at page → 16 Page 16 5) no leaks into or out of the piston-cylinder and test section. NIST operates the LFSs as close as practical to these idealized conditions with the exception of the operating pressure. Steady flow conditions are obtaine... Open at page → 17 Page 17 MUT (MUT). Based on mass conservation, the volumetric flow at the MUT is taken to be equal to the volumetric flow at the cylinder multiplied by the density ratio ( cyl/MUT). A third type of non-ideality results from m... Open at page → 18 Page 18 Figures 4a and 4b show the location of the piston at the start of the measured time interval ( i t ) and at the end of the measured time interval ( f t ). The white dashed lines constitute the control volume where mass c... Open at page → 19 Page 19         cv fffifiii cyl fffifiii                       t VˆVˆVˆVˆ t VˆVˆVˆVˆ  cv fififi cyl fififi                       t VˆVˆ t VˆVˆ  t ˆV t Vˆ t... Open at page → 20 Page 20 Mass Flow and Volumetric Flow at the MUT Equations (7) and (8) for the MUT mass flow and volumetric flow can be compactly expressed by 65432154321 ref Vref MUT SSSSSSRRRRR t NK m ~           e   (9a) and 2165... Open at page → 21 Page 21 Table 3. Correction factors for mass flow in Equation (9a) and volumetric flow in Equation (9b). applies Region of LFS Type of where correction Equation Description correction )( ref en en 1 1 TTR   Reference Axial c... Open at page → 22 Page 22 ref V K cyl V S  cyl V CV V Continuation of Table 3. Region of LFS Type of where correction Equation Description correction applies )( f cy l i cy lst ref V e f cy l 21 1 T ˆ T ˆ KN V S            Radial ch... Open at page → 23 Page 23 e. the calibration interval, Δt c, f. the thermal expansion coefficient of the liquid,  g. and the isothermal compressibility factor of the liquid, κ. Some component uncertainties listed above and in Equations (9a) and... Open at page → 24 Page 24 )x,.....,x,x(fy n21  (10) its first-order Taylor series approximation is,     i i i dx x y dy (11) Thus, the propagation of uncertainty yields )()(2)( )()( 1 1 1 2 1 2 2 1 2 jiij n ij j n i i i n i i n i i i c xuxur... Open at page → 25 Page 25 According to [3], the sources of uncertainty used in assessing the combined standard uncertainty of the measurement process can be classified according to two types: Type A - those which are evaluated by statistical meth... Open at page → 26 Page 26 temperature was controlled to within ± 0.5°C of T ref, and the fluid pressure was 100 kPa ± 9 kPa. For these conditions )1 ref i cyl4 TT ˆ R (  is the only significant correction factor. All of the other reference co... Open at page → 27 Page 27 The 0.1 L/s LFS ref VK was measured on two occasions, one via dimensional analysis in 2005 and one time via the water draw method in April of 2013 (Figure 7). The difference between the two values is < 140 parts in 10 6... Open at page → 28 Page 28 The expression used to calculate the uncertainty of the measured ref VK by the water draw method is given by Equation (15):          2 V V ref ref K Ku)( 2 i i 2 i V V i ref ref                 ... Open at page → 29 Page 29 Table 4. Uncertainty budget for ref VK corresponding to Equation (15) for the 0.1 L/s LFS. Vol. Prover K-factor Kv ref = 0.08099 [cm 3 /pulse] Uncertainty Category Reference masses Reference mass density Room air density... Open at page → 30 Page 30 Table 5. Uncertainty budget for ref VK corresponding to Equation (15) for the 2.5 L/s LFS. Vol. Prover K-factor Kv ref = 0.35432 [cm 3 /pulse] Uncertainty Category Reference masses Reference mass density Room air density... Open at page → 31 Page 31 Temperature Measurement The uncertainty of the temperature measurements made throughout the LFS will contribute to the uncertainty of the calibrator. Platinum resistance temperature detectors (RTDs) are used for all temp... Open at page → 32 Page 32 is classified as a Type B uncertainty for each RTD. During calibration of the RTDs, a minimum of five data points are collected at each temperature set point. The root-sum-square of the uncertainties from the reference s... Open at page → 33 Page 33 Figure 9. Temperatures in a fictitious flow standard to illustrate how to use the average temperature measurements made in a series of flow collections to predict initial and final temperatures for input to an uncertaint... Open at page → 34 Page 34 Time of Piston Displacement The uncertainty of the measurements of time can be separated into two parts: a) that due to the reference clock (including calibration errors and temperature effects) and b) that due to quanti... Open at page → 35 Page 35 stopped, and the total (N) is multiplied by Δt to obtain the time required by the piston to travel the prescribed distance (t Emeas). As for the generic case, this time has a standard uncertainty due to quantization of 6... Open at page → 36 Page 36 Figure 11. Diagram of the process for counting and timing the pulses from the encoder that measures piston displacement and from a pulse generating MUT (e.g., a turbine meter) and their quantization errors. Fluid Propert... Open at page → 37 Page 37 estimated. This process is propagated throughout all the measurement components until the uncertainties of the desired quantities are obtained. After the uncertainties of the sub-measurements are obtained, the one-standa... Open at page → 38 Page 38 Table 6 itemizes each component of uncertainty for the 0.1 L/s LFS and Table 7 for the 2.5 L/s LFS. Table 6. Uncertainty budget for volumetric flow at the MUT for the 0.1 L/s LFS corresponding to Equation (9b). Vol. Flow... Open at page → 39 Page 39 Continuation of Table 6. Uncertainty Category Nom. Rel. Unc. Norm. Sen. Coeff. (Sc) [-] Contribution [%] Comments Value Initial liquid temperature in the fixed connecting volume, T i cv [ ○ C] Final liquid temperature in... Open at page → 40 Page 40 Table 7. Uncertainty budget for volumetric flow at the MUT for the 2.5 L/s LFS corresponding to Equation (9b). Vol. Flow; QMUT [L/s] QMUT = 0.06 [L/s] Rel. Norm. Sen. Nom. Unc. Contribution Uncertainty Category Coeff. (S... Open at page → 41 Page 41 Uncertainty Category Continuation of Table 7. Rel. Nom. Unc. Value (k = 1) [%] Temperature cal records and 20.90 0.017 -0.015 0.008 data from LFS Final liquid temperature in the Temperature cal records and f ○ 20.87 0.01... Open at page → 42 Page 42 Therefore, to determine the uncertainty of a meter factor for a pulse generating MUT, we determine the sensitivity coefficients for each component by partial differentiation of Equation (19). The uncertainty terms are th... Open at page → 43 Page 43 &#3627408482; &#3627408438;(&#3627408454;&#3627408481;) 4 ( ) &#3627408454;&#3627408481; = eff 4 4 (21) &#3627408482;(&#3627408452;) &#3627408482;(&#3627408467;) 4 (&#3627408480; &#3627408452; ) (&#3627408480; &#36274084... Open at page → 44 Page 44 uncertainty claims for a customer’s MUT may be larger than those reported here because the customer’s MUT may not be as repeatable n or reproducible o as NIST’s best existing device. The uncertainties given in a NIST cal... Open at page → 45 Page 45 NIST’s systems, the most significant correction terms are for deviations from reference conditions (R 4 and R 5) for the fluid temperature and pressure. Finally we analyze the uncertainty of the flow standards, give supp... Open at page → 46 Page 46 [13] Taylor, B. N., and Kuyatt, C. E. Guidelines for the evaluating and expressing the uncertainty of NIST measurement results. 1994; NIST TN-1297. [14] Coleman, H. W. and Steele, W. G. Experimentation and uncertainty an... Open at page → 47 Page 47 Appendix A Sample Calibration Report REPORT OF CALIBRATION FOR A LIQUID FLOW METER July 2, 2013 Dual Rotor Turbine Flow Meter Brand X, Model XX/XX S/N: xxx submitted by Company X 666 Calibration Dr. West Gaithersburg, MD... Open at page → 48 Page 48 REPORT OF CALIBRATION Dual Rotor Turbine Flow Meter, Brand X, Model XX/XX, S/N: xxx The LFSs are piston provers that work on a volumetric principle. They determine the volumetric flow by displacing a known volume of liqu... Open at page → 49 Page 49 REPORT OF CALIBRATION Dual Rotor Turbine Flow Meter, Brand X, Model XX/XX, S/N: xxx (4)  21 1 21T        T 10 (5) where,  is the fluid density, in kg/m 3 , ν is the kinematic viscosity, in centistokes... Open at page → 50 Page 50 REPORT OF CALIBRATION Dual Rotor Turbine Flow Meter, Brand X, Model XX/XX, S/N: xxx Figure 2. A photograph of the meter under test installed in the 2.5 L/s LFS. An analysis was performed to assess the uncertainty of the... Open at page → 51 Page 51 REPORT OF CALIBRATION Dual Rotor Turbine Flow Meter, Brand X, Model XX/XX, S/N: xxx To measure the flow meter reproducibility, the standard deviation of 10 measurements was used to calculate the relative standard uncerta... Open at page → 52 Page 52 REPORT OF CALIBRATION Dual Rotor Turbine Flow Meter, Brand X, Model XX/XX, S/N: xxx 5.90 5.95 6.00 6.05 6.10 6.15 6.20 0 20 40 60 80 100 St up Ro upx 10 -4 Upstream Rotor SN 0718 Cox (6/10/2009) 20L (6/10/09) Cox (5/2/06... Open at page → 53 Page 53 REPORT OF CALIBRATION Dual Rotor Turbine Flow Meter, Brand X, Model XX/XX, S/N: xxx 12.7 12.8 12.9 13.0 13.1 13.2 13.3 0 50 100 150 200 St up + down Ro up + downx 10 -4 Upstream + Downstream Rotor SN 0718 Cox (6/10/2009)... Open at page → 54 Page 54 REPORT OF CALIBRATION Dual Rotor Turbine Flow Meter, Brand X, Model XX/XX, S/N: xxx Table 3. Tabulated results from 2.5 L/s LFS for the downstream rotor of meter SN: xxx. V  f Ro x 10 -4 St Uk=2 Tliq   [C] [kg/m3] [... Open at page → 55 Page 55 REPORT OF CALIBRATION Dual Rotor Turbine Flow Meter, Brand X, Model XX/XX, S/N: xxx Table 6. Tabulated results from the 0.1 L/s LFS for the downstream rotor of meter SN: xxx. V  f Ro x 10 -4 St Uk=2 Tliq   [C] [kg/m... Open at page →