# Mathematical Modelling and Simulation

Working Group 8.41

# Modelling and Simulation of Fluid Flows in Metrology

In computational fluid dynamics (CFD) the Navier-Stokes equations are solved approximatly by means of numerical methods. Applications of flow simulations in the context of metrology are:

• design and optimization of measurement configurations,
• simulation and prediction of experiments, and
• determination of the influence of different parameters on measurement uncertainty.

# Applications

The research is typically motivated by current tasks in metrology, and it is often carried out in collaboration with other working groups at PTB. Some applications, on which Working group 8.41 has been or is currently working on, are listed below.

# Numerical simulation of high-pressure hydrogen flows through critical nozzles

Hydrogen is a promising energy carrier for use in climate-neutral applications in industry and transport. In its gaseous form, it needs to be stored at considerably high pressures (up to 1000 bar) due to its low volumetric energy density. In order to monitor hydrogen consumption, a verifiable flow measurement is required. Critical nozzles are a state-of-the-art secondary standard for the measurement of mass flow rates of gases. However, the international standards are limited to air and natural gases at pressures up to 200 bar.

Therefore, in working group 8.41, numerical simulations are conducted for high-pressure hydrogen flows through critical nozzles as part of the EMPIR project “Metrology infrastructure for high-pressure gas and liquified hydrogen flows” (MetHyInfra). Besides the implementation of a reference data-based real gas model for hydrogen into the open-source software package OpenFOAM, different influences on the mass flow rate –  e. g. laminar-to-turbulent transition, wall roughness, non-ideal nozzle contours, and heat transfer – are investigated to gain more insight into the flow behavior in critical nozzles.

# Influence of uncertain parameters in pipe flow simulations

The flow in a pipe is influenced by different parameters, e.g., uncertain initial and boundary conditions, geometry variations due to manufacturing tolerances, or inaccurate material parameters. The uncertainty in such parameters leads to measurement errors of flow meters. For the application of flow meters under field conditions, which are characterized by disturbed inflow profiles, it must be ensured that the measurement error is below a certain threshold.

Working group 8.41 investigated in cooperation with Working group 7.53 the influence of disturbed inflow profiles on the measurement result of a single-path ultrasonic flow meter. For this, the polynomial chaos method in combination with computational fluid dynamics (CFD) was used. Two subsequent 90° bends were used to create the disturbed profiles. This case is particularly interesting for metrology because combinations of double bends out-of-plane occur quite often in practice, which can lead to significant measurement errors.

# Mathematical modeling and numerical simulation of multiphase flows in metrology

Multiphase flow measurement is a fundamental enabling capability in subsea oil and gas production. However, field measurements exhibit high measurement uncertainty. Therefore, the aim of the project Multiphase Flow Reference Metrology was to reduce measurement uncertainty through harmonisation between different flow laboratories and thereby enhance confidence in multiphase flow meters. Working group 8.41 simulated in close cooperation with the Czech Metrology Institute (CMI) corresponding multiphase flows. Several new modelling approaches improved the agreement between simulation results and experimental data. This leads to more realistic simulations of the formation and evolution of specific flow patterns that might have a negative influence on the measurement process.

# CFD to provide support in particle metrology

Developing a national standard for soot mass concentration and opacity at PTB requires high-sensitivity instrumentation for soot generation in a wide range of particle sizes and particle number concentrations. Such high accuracy soot generators need also well-defined aerosol conditioning, dilution and homogenization process steps in order to vary e.g. the particle number concentration over the legally relevant range. In order to optimize spatial distribution of the soot particles and to develop effective mixing and dilution configurations, three-dimensional CFD simulations were carried out. Mixing characterisitcs have been predicted for different operational parameters. The work was carried out in collaboration with Working Group 3.23.

# Simulation of the temperature distribution in large storage tanks

Storage tanks for mineral oil and its derivatives can have a capacity of more than 50 million liter. Therefore a temperature change to some tenths of percent leads to a volume change of more than thousand liters. The exact measurement of the mean fluid temperature is necessary for the trading of great quantities.
In a scientific project, the mean temperature was measured in a real tank and also determined by extensive simulations. By using the CFD approach it was possible to transfer the measured data to other liquids, different weather conditions, and special filling situations.

# Publications

 • A. Weissenbrunner, A.-K. Ekat, M. Straka;S. Schmelter Metrologia, 2023. • S. Weiss, J. Polansky, M. Bär, K. Oberleithner;S. Schmelter Elsevier International Journal of Hydrogen Energy, 2023. • F. Webner, J. Polansky, S. Knotek;S. Schmelter International Journal of Multiphase Flow, 158 104278, 2023. • M. Olbrich 2022. • S. Schmelter, S. Knotek, M. Olbrich;M. Bär 19th International Flow Measurement Conference (FLOMEKO) 2022. • S. Weiss, B. Mickan, K. Oberleithner, M. Bär;S. Schmelter 19th International Flow Measurement Conference (FLOMEKO) 2022. • H.-B. Böckler, M. de Huu, R. Maury, S. Schmelter, M. Schakel;O. Büker 19th International Flow Measurement Conference (FLOMEKO) 2022. • M. Olbrich, L. Riazy, T. Kretz, T. Leonard, D. van Putten, M. Bär, K. Oberleithner;S. Schmelter International Journal of Multiphase Flow, 2022. • M. Straka, A. Weissenbrunner, C. Koglin, C. Höhne;S. Schmelter Metrology, 2(3), 335-359, 2022. • J. Polansky;S. Schmelter Archives of Thermodynamics, 43(1), 21-43, 2022. • S. Knotek, S. Schmelter;M. Olbrich Measurement: Sensors, 18 100317, 2021. • S. Schmelter, M. Olbrich, S. Knotek;M. Bär Measurement: Sensors, 18 100154, 2021. • M. Olbrich, A. Hunt, T. Leonard, D. S. van Putten, M. Bär, K. Oberleithner;S. Schmelter Measurement: Sensors, 18 100222, 2021. • S. Schmelter, S. Knotek, M. Olbrich, A. Fiebach;M. Bär Metrologia, 58(1), 014003, 2021. [DOI: 10.1088/1681-7575/abd1c9] • S. Schmidt, S. Flassbeck, S. Schmelter, E. Schmeyer, M. E. Ladd;S. Schmitter Magnetic Resonance in Medicine, 85(6), 3154-3168, 2021. [DOI: 10.1002/mrm.28641] • M. Olbrich, E. Schmeyer, M. Bär, M. Sieber, K. Oberleithner;S. Schmelter Flow Measurement and Instrumentation, 76 101814, 2020. • M. Olbrich, M. Bär, K. Oberleithner;S. Schmelter International Journal of Multiphase Flow, 134 103453, 2020. • S. Schmelter, M. Olbrich, E. Schmeyer;M. Bär Flow Measurement and Instrumentation, 73 101722, 2020. • S. Schmelter, M. Olbrich, E. Schmeyer;M. Bär Proceedings of the 18th International Flow Measurement Conference FLOMEKO 2019, 2019. • M. Olbrich, E. Schmeyer, M. Bär, M. Sieber, K. Oberleithner;S. Schmelter Proceedings of the 18th International Flow Measurement Conference FLOMEKO 2019, 2019. • L. Riazy, T. Schäffter, M. Olbrich, J. A. Schueler, F. v. Knobelsdorff-Brenkenhoff, T. Niendorf;J. Schulz-Menger Magnetic Resonance in Medicine, 2019. [DOI: 10.1002/mrm.27756] (advance online publication) • M. Olbrich, E. Schmeyer, L. Riazy, K. Oberleithner, M. Bär;S. Schmelter J. Phys.: Conf. Series, 1065(9), 092015, 2018. • S. Schmelter, M. Olbrich, E. Schmeyer;M. Bär Proceedings of the North Sea Flow Measurement Workshop 2018, 2018. • M. Straka, A. Fiebach, T. Eichler;C. Koglin Flow Measurement and Instrumentation, 60 124--133, 2018. • A. Weissenbrunner, A. Fiebach, M. Juling;P. U. Thamsen Eccomas Proceedia UNCECOMP, (5393), 576--587, 2017. • A. Fiebach, E. Schmeyer, S. Knotek;S. Schmelter Proceedings of the 17th International Flow Measurement Conference FLOMEKO 2016, 2016. • S. Knotek, A. Fiebach;S. Schmelter Proceedings of the 17th International Flow Measurement Conference FLOMEKO 2016, 2016. • A. Weissenbrunner, A. Fiebach, S. Schmelter, M. Bär, P. Thamsen;T. Lederer Flow Measurement and Instrumentation, 2016. • S. Schmelter, A. Fiebach;A. Weissenbrunner tm-Technisches Messen, 83(2), 71-76, 2016. • G. Lindner, S. Schmelter, R. Model, A. Nowak, V. Ebert;M. Bär J. Fluids Eng, 138(3), 031302, 2016. [DOI: 10.1115/1.4031380] • A. Weissenbrunner, A. Fiebach, S. Schmelter, M. Straka, M. Bär;T. Lederer Proceedings of Imeko 2015 XXI World Congress Measurement in Research and Industry, 2015. • S. Schmelter, A. Fiebach, R. Model;M. Bär Int. J. Comp. Fluid. Dyn., 29(6-8), 411-422, 2015. • G. Wendt, R. Jost, S. Schmelter;D. Werner Technische Sicherheit, 11 13--17, 2014. • S. Schmelter, R. Model, G. Wendt;M. Bär Proceedings of Flomeko 2013 16th International Flow Measurement Conference, 2013. • K. Jousten, S. Pantazis, J. Buthig, R. Model, M. Wüest;J. Iwicki Vacuum, 100 14--17, 2013. • R. Model, S. Schmelter, G. Lindner;M. Bär In F. Pavese, M. Bär, J.-R. Filtz, A. B. Forbes, L. Pendrill and K. Shirono, editor, Volume 84 Publisher: World Scientific, New Jersey, 2012. • H. Förster, W. Günther, G. Lindner;R. Model Technische Sicherheit, 1 18--27, 2011. • S. Schmelter, G. Lindner, G. Wendt;R. Model AIP Conf. Proc. Volume 1389 , page 106-109 2011. • R. Model;U. Hammerschmidt Thermal Conductivity 26/Thermal Expansion 14, 346--357, 2005. • R. Model International Journal of Thermophysics, 26(1), 165--178, 2005.
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