Measurement assurance programs (MAPs) are commonly used in metrology to ensure product performance. The following outlines the steps taken by SeaMetrics to establish a MAP for calibrating its flowmeters. Under the program all measurements performed by the transfer system are traceable to NIST. Uncertainty in flowrate was determined by the Law of Propagation of Error, and the calibration system was validated by a proficiency test.

By Jeff Peery & Jim Frederick

The MAP described herin is a liquid flow calibration system used to calibrate liquid flowmeters. It consists of four elements: 1) calibration of measurement devices; 2) statistical process control of measurement devices; 3) a measurement uncertainty analysis; and 4) a proficiency test. The MAP is responsible for process control, maintaining quality of measurements, and traceability to National Institute of Standards and Technology (NIST, www.nist.org) standards.

MAPs are necessary to maintain quality assurance and ties to national standards [1]. They assure quality of all measurement devices and test procedures and assure a state of statistical control of the measurement process. Upon establishing traceability to national standards, a MAP may be implemented to maintain this traceability over time.

The MAP described in this article is used to evaluate and manage SeaMetrics’ (www.seametrics.com) liquid flow calibration system. The Law of Propagation of Error is used to predict measurement uncertainty [2]. A proficiency test is used to validate the system’s measurements. Process control is maintained by Shewart’s Statistical Process Control (SPC) [3]. Under the MAP described here, liquid flowrate and K-factor measurements are traced to NIST, thereby maintaining measurement quality.

Methods

Liquid flowmeter calibrations are performed by driving liquid water at constant flowrate through a system of closed conduit and referencing a primary flowmeter (meter under test) to a secondary flowmeter (flow standard). The calibration system is composed of a storage tank, flow conditioner, pump, one six-inch secondary flowmeter, and one two-inch secondary flowmeter (Figure 1). All components are connected by epoxy-coated steel pipe. The pump is used to drive fluid from the storage tank to the flow conditioner; maximum flowrate is approximately 1.50×10^{-1} m^{3}/s and minimum flowrate is approximately 3.16×10^{-4} m^{3}/s. Exiting the flow conditioner is a section of straight pipe that is sufficient in length to fully develop flow upstream of the primary meter. Downstream of the primary meter the pipe splits into one two-inch line and one six-inch line. Each line leads to a separate secondary meter (six inch and two inch) located at approximately 10 diameters from the bifurcation point to assure fully developed flow. By using two different sizes of secondary meters, a greater operating range is achieved. Two butterfly valves are located at the exit of each bifurcation line and are used to regulate flowrate. Liquid exiting the valves is routed back to the storage tank.

Prior to collecting measurements a thermal steady state, hydrodynamic steady state, and test meter output steady state are obtained. After all steady states are found, volume, time, and primary and secondary meter output are measured.

K-factor and flowrate measurements are traced to NIST through an unbroken chain of comparisons. Comparisons are created annually by calibrating all measurement devices at an accredited laboratory. Traceability is maintained through statistical process control (SPC). Measurement uncertainty is evaluated by an uncertainty analysis. The entire system is validated by a proficiency test.

Statistical Process Control

State of control for the calibration system is assessed using SPC. The system is calibrated monthly against a check standard — currently a new NIST traceable gravimetric liquid flow calibration system is being constructed and will replace the current check standard. Check standard calibrations include four points (four flowrates) and five replicates. Measurements are grouped and plotted using control charts. Upper and lower control limits (Eq. 1-6) for subgroup standard deviation, and subgroup averages are calculated from Shewhart’s control limit factors [3; Table A.5].

(1)

(2)

(3)

(4)

(5)

(6)

Where:

• UCL is upper control limit

• LCL is lower control limit

• CL is control limit

• A_{1} is constant [3; Table A.5]

• B_{3} is constant [3; Table A.5]

• B_{4} is constant [3; Table A.5]

• X is control variable

• s_{n} is standard deviation of subgroup

• Subscripts sn and X refer to control variable and standard deviation of control variable respectively, and bars indicate the average function.

Out-of-control subgroups are evaluated using software and condition five is evaluated visually. Given an out-of-control state, assignable cause is identified and system control is established prior to performing further measurements. All instruments are calibrated annually by an NVLAP (National Voluntary Laboratory Accreditation Program).

Uncertainty Analysis

Law of Propagation of Uncertainty [2] was used to determine uncertainty in flowrate and K-factor measurements. The result was second order accurate (Eq. 7).

(7)

Where:

• δ is differential operator

• η is component of measurement process

• w is uncertainty of η

• S is measurand

• w_{R} is measurement uncertainty.

The uncertainty analysis was simplified by assuming that liquid temperature was equal to pipe temperature. This assumption was valid because Biot number was much less than unity.

Conservation of mass was used to derive a function for flowrate (the method is similar to that given by T. T, Yeh et. al [4]). The calibration system was modeled as a completely closed system (no leaks) and was broken into three components: 1) storage mass; 2) primary mass; and 3) secondary mass. Storage mass was mass contained between the secondary and primary meters, secondary mass was total mass seen by the secondary meter (flow standard), and primary mass was total mass seen by the primary meter (meter under test). Assuming that mass was conserved, the difference in mass passing through the primary meter from test start to test end was obtained by equating the total mass at each time. Differences were expanded by taking the total derivative (Eq. 8).

(8)

Where:

• ρ is density kg/m^{3}

• V is volume m^{3}

• M is mass kg

• Subscripts Pri, S, and Sec refer to the primary meter, storage volume, and secondary meter respectively. Variations in volume and density were assumed to arise from thermal variations with time (Eq. 9-10):

(9)

(10)

Where:

• T is temperature K,

• α is coefficient of thermal expansion 1/K. Equations 9 and 10 were substituted into equation 8 to obtain an expression for the change in primary mass (Eq. 11).

(11)

Where:

• subscripts w, and pi refer to water and pipe material respectively. Volumetric flow rate (Eq. 12) was obtained from equation 11.

(12)

Where:

• t was time s, and Q bar was average volumetric flowrate m^{3}/s.

Flowrate uncertainty was determined by taking the appropriate partial derivatives and substituting their result and the dependant variable uncertainty into equation 7 (tables 1 and 2). Uncertainties represented the 67 percent probability interval for a standard normal distribution.

Results

The greatest uncertainty in flowrate measurement was 0.30 percent (Table 3). Uncertainty of flowrate was most sensitive to uncertainty of test time and uncertainty of secondary meter volume. Test time was maintained at 6.0×101 seconds.

Proficiency test results are listed in tables 1 and 3. K-factors measured by Colorado Experimentation and Engineering Station (CEESI, www.ceesi.com) agreed well with those measured by the system described herein. At each flowrate, the 95 percent confidence interval for measurements collected by CEESI was within the 95 percent confidence interval for measurements collected by SeaMetrics.

About the Author

Jeffrey T. Peery earned his bachelor’s and master’s degrees in Mechanical Engineering from the University of Washington. He published papers regarding thermal modeling in biomechanics while working at the Veterans Affairs Puget Sound Health Care Center and the Center for Excellence in Limb Loss Prevention and Prosthetic Engineering. Mr. Peery currently works as a mechanical engineer at SeaMetrics Inc., a designer and manufacturer of mechanical and electromagnetic liquid flowmeters. His work focuses on flowmeter research and development, design, and experimentation. He can be reached at JeffPeery@SeaMetrics.com or 253 872-0284. James R. Frederick has 20 years of experience as a manufacturing engineer. As one of the founding partners for SeaMetrics, he has designed, built, and tested all of the specialized machines and calibration stands used by the company. Mr. Frederick has a wide background in electronics, hydraulics, machining, pneumatics, and welding. He currently specializes in equipment and process automation.

For More Information: www.seametrics.com

References

1. B. Belanger, “Measurement Assurance Programs Part I: General Introduction,” NBS Special Publication 676-I, U.S. Government Printing Office, Washington, May 1984.

2. S. J. Kline and F. A. McClintock, “Describing Uncertainties in Single-Sample Experiments,” Mechanical Engineering, January, 1953.

3. D. J. Wheeler and D. S. Chambers, Understanding Statistical Process Control, SPC Press, Knoxville TN, May 1984.

4. T. T. Yeh et. al., “An Uncertainty Analysis of a NIST Hydrocarbon Flow Calibration Facility,” Proceedings of the 2004 Heat Transfer/Fluids Engineering Summer Conference, ASME 2004.

5. ANSI/ASTM, Measurement Uncertainty for Fluid Flow in Closed Conduits American Society of Mechanical Engineers, 2001.

6. F. P. Incropera and D. P. Dewitt, Introduction to Heat Transfer, John Wiley & Sons, Inc., 1996.

7. Norman E. Dowling, Mechanical Behavior of Materials. Prentice Hall, 1999.

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