Novel methodology for turbine gas meters error curve modelling across a wide range of operating parameters

Bogdan Blagojevič; Brane Širok; Benjamin Bizjan

doi:10.1515/teme-2021-0083

Artikel

Novel methodology for turbine gas meters error curve modelling across a wide range of operating parameters

Bogdan Blagojevič

Bogdan Blagojevič obtained his PhD in 1996 at the University of Ljubljana, Faculty of Mechanical Engineering. His PhD research was on turbulent transport phenomena of water droplets in air. He began his job at the Faculty of mechanical engineering in the laboratory of Measurement of Process Engineering in 1988. His areas of expertise are experimental design and measurement uncertainty in gas meters. Since 2009 he is the Head of Measurement Department in Plinovodi d.o.o. where he leads the Laboratory for calibration of gas meters in air and volume conversion devices.
, Brane Širok

Brane Širok obtained a master degree in 1985 and a PhD in 1990 at the University of Ljubljana, Faculty of Mechanical Engineering. Since 1996 he has been a professor at the department for hydraulic machinery at the Faculty of Mechanical Engineering in Ljubljana, and also the faculty dean between 2013 and 2017. His main research areas are turbomachinery design and applications, mineral wool production and properties, computer-aided flow visualization techniques and experimental analysis of non-linear chaotic phenomena in fluid dynamics.
und Benjamin Bizjan

Benjamin Bizjan obtained a master degree in 2012 and a PhD in 2014 at the University of Ljubljana, Faculty of Mechanical Engineering. In 2018, he was promoted from teaching assistant to associate professor at the Faculty of Mechanical Engineering in Ljubljana. In 2019, he completed a postdoc project in the field of mineral wool research. He is a member of an interdisciplinary team involved in challenging R&D projects solving complex problems from the industry: mineral wool technology development, flow velocimetry and thermometry solutions, cavitation avoidance and applications, precision farming, seaport environmental studies and big data analytics.

Veröffentlicht/Copyright: 13. Juli 2021

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Abstract

In this paper, performance of turbine flowmeters was investigated for different flowmeter ranges and working gas operating pressures. Variation of these parameters was represented in dimensionless form as a function of Reynolds Number and gas density ratio, while the relative flow measurement error was selected as the most important operating characteristic. A novel error curve model based on turbine machine theory and dimensionless analysis was introduced for the purpose of error data fitting across a wide range of gas flow rates and operating pressures. The main advantage of the presented model is the capability of accurate error data fitting with a single continuous equation, as demonstrated by high R 2 values for the vast majority of flowmeters analyzed in this study. The acceptability criterion was designed based on the fact that the expanded measurement uncertainty of the relative error must not exceed 0.5 %. Besides an accurate interpolation, our model can also be utilized for prediction of turbine flowmeter performance at modified flow conditions (pressure and flow rate, working gas properties), and for assessment of the drift of flowmeter performance over time. The novel error curve model is demonstrated to outperform the standard polynomial-based model regardless of the independent variable used.

Zusammenfassung

In diesem Artikel wurde die Leistung von Turbinendurchflussmessern für verschiedene Durchflussmessbereiche und Arbeitsgasbetriebsdrücke untersucht. Die Variation dieser Parameter wurde in dimensionsloser Form als Funktion der Reynoldszahl und des Gasdichteverhältnisses dargestellt, während der relative Durchflussmessfehler als wichtigstes Betriebsmerkmal ausgewählt wurde. Ein neuartiges Fehlerkurvenmodell, das auf der Theorie der Turbomaschine und der dimensionslosen Analyse basiert, wurde eingeführt, um Fehlerdaten über einen weiten Bereich von Gasdurchflussraten und Betriebsdrücken anzupassen. Der Hauptvorteil des vorgestellten Modells ist die Fähigkeit zur genauen Anpassung von Fehlerdaten mit einer einzigen kontinuierlichen Gleichung, wie durch hohe R 2 -Werte für die überwiegende Mehrheit der in dieser Studie analysierten Durchflussmesser gezeigt wird. Das Akzeptanzkriterium wurde auf Grund der Tatsache entworfen, dass die erweiterte Messunsicherheit des relativen Fehlers 0,5 % nicht überschreiten darf. Neben einer genauen Interpolation kann unser Modell auch zur Vorhersage der Leistung des Turbinen-Durchflussmessers bei veränderten Durchflussbedingungen (Druck und Durchflussrate, Arbeitsgaseigenschaften) und zur Bewertung der zeitlichen Abweichung der Leistung des Durchflussmessers verwendet werden. Es wurde gezeigt, dass das neuartige Fehlerkurvenmodell das auf Polynomen basierende Standardmodell unabhängig von der verwendeten unabhängigen Variablen übertrifft.

Keywords: Turbine flowmeter; natural gas; Reynolds number; calibration; error curves

Schlagwörter: Turbinendurchflussmeter; Erdgas; Reynoldszahl; Kalibrierung; Fehlerkurven

About the authors

Bogdan Blagojevič

Bogdan Blagojevič obtained his PhD in 1996 at the University of Ljubljana, Faculty of Mechanical Engineering. His PhD research was on turbulent transport phenomena of water droplets in air. He began his job at the Faculty of mechanical engineering in the laboratory of Measurement of Process Engineering in 1988. His areas of expertise are experimental design and measurement uncertainty in gas meters. Since 2009 he is the Head of Measurement Department in Plinovodi d.o.o. where he leads the Laboratory for calibration of gas meters in air and volume conversion devices.

Brane Širok

Brane Širok obtained a master degree in 1985 and a PhD in 1990 at the University of Ljubljana, Faculty of Mechanical Engineering. Since 1996 he has been a professor at the department for hydraulic machinery at the Faculty of Mechanical Engineering in Ljubljana, and also the faculty dean between 2013 and 2017. His main research areas are turbomachinery design and applications, mineral wool production and properties, computer-aided flow visualization techniques and experimental analysis of non-linear chaotic phenomena in fluid dynamics.

Benjamin Bizjan

Benjamin Bizjan obtained a master degree in 2012 and a PhD in 2014 at the University of Ljubljana, Faculty of Mechanical Engineering. In 2018, he was promoted from teaching assistant to associate professor at the Faculty of Mechanical Engineering in Ljubljana. In 2019, he completed a postdoc project in the field of mineral wool research. He is a member of an interdisciplinary team involved in challenging R&D projects solving complex problems from the industry: mineral wool technology development, flow velocimetry and thermometry solutions, cavitation avoidance and applications, precision farming, seaport environmental studies and big data analytics.

Appendix A Derivation of the error curve equation

Step-by-step methodology for derivation of error curve equation defined by Eq. (11):

Polynomial adjustment – least square curve fit [23], [24]
(A1) E = a 0 + a 1 x p + a 2 x q + a 3 x r + ... + a n − 1 x n − 1 + ...

For Straatsma: p = − 0 , 2; q = − 0 , 33; r = − 2 and x = Q / Q max .
Calibration curve proposed by PTB (Certificate PTB, XXXXK00A_KS_mit_Anlage.dot 30.01.2004)

The deviation E is calculating according to the equalized error curve with the following equation:
(A2) E = A Q 2 + B Q + C + D · Q + D · Q 2
In the paper [25] different quantities can be used for x:
Q , Q / Q max , log ( R e / 10 6 ) , log ( Q / Q max )
Eqs. (A3) and (A4) can be written:
(A3) E = b 0 + b 1 x − 0 , 2 + b 2 x − 0 , 33 + b 3 x − 2

(A4) E = A x 2 + B x + C + D · x + D · x 2
If Eqs. (A3) and (A4) are compared, E depends on:
(A5) E = E ( x − 0 , 2 , x − 0 , 33 , x − 2 , x − 1 , x , x 2 )
The error curve equation can be written:
(A6) E = a 1 x − 1 + a 2 + a 3 x + a 4 x 2 + a 5 x − 2 + a 6 x − 0.33 + a 7 x − 0.2

Terms 1–5 = Straatsma 1978 (discussed in Van der Grinten [23])

Terms 2, 5, 6, 7 = PTB 2003
Eq. (A6) is a somewhat similar to the Eq. (3) in the paper [26]
(A7) E = b 0 ρ · Q 2 + b 1 ρ · Q + ∑ I = 1 4 a j log ( R e / 10 6 ) + c p Q 2 ρ p
Definition area of Eq. (11)/Eq. (A6):

It depends on experimental data of flowrate, pressure, temperature, viscosity of air at atmospheric condition and from experimental data of flowrate, temperature, pressure, viscosity of natural gas at high pressure. The obtained parameters a 1 , to a 7 are valid only for tested gas meter.

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Received: 2021-05-11

Accepted: 2021-06-30

Published Online: 2021-07-13

Published in Print: 2021-11-30

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Artikel in diesem Heft

https://doi.org/10.1515/teme-2021-0083

Schlagwörter für diesen Artikel

Turbine flowmeter; natural gas; Reynolds number; calibration; error curves