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Mathematical Modelling and Simulation

Working Group 8.41

Numerical Simulations of Fluid Flows

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.


As mathematical description of the behavior of Newtonian viscous fluids we have the well known Navier-Stokes equations. Generally, analytic solutions are not available. Therefore, numerical methods as the finite volume method or the finite element method are used. Since the direct numerical solution (DNS) of turbulent flows is extremely expensive, it is limited to relatively simple problems. In case of turbulent flows, characterized by large Reynolds numbers, empirical turbulence models like Reynolds-averaged Navier-Stokes (RANS), unsteady Reynolds-averaged Navier-Stokes (URANS), and large eddy simulation (LES) are commonly used.
As an alternative to expensive experiments, numerical simulations of fluid flows provide the opportunity for

  • prediction and validation of measurements
  • risk evaluation
  • determination of dependencies, e. g. material properties, geometry, cause-effect, case studies
  • optimization of measurement procedures


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. The investigation of such uncertainties is done with the generalized polynomial chaos method together with classical fluid Dynamics.

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 (CAST) 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 the soot spatial distribution and to develop effective mixing and dilution configuration we started to simulate such fluid conditioning units in different configurations.  Three-dimensional CFD simulations are carried out to estimate different mixing characteristics  depending on the incoming flow rates and the angle of inclination at the junction where different pipes join together.  In particular we consider namely mixing of three air flows at different dilution levels, on as short ways as possible, without long, steady flow distances.  To analyse the propagation of mixing the variance for the the approach section is calculated. The work is done in cooperation with the Working Group 3.23 “Aerosols and particle measurements”. 

CFD simulations 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.

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  • EMRP ENG58   Multiphase flow metrology in oil and gas production  (June 2014 - May 2017)
  • EMRP NEW04   Novel mathematical and statistical approaches to uncertainty evaluation  (August 2012 - July 2015)
  • Temperature distribution in large storage tanks  (2010 – 2012)


  • G. Lindner, S. Schmelter, R. Model, A. Nowak, V. Ebert and M. Bär (2016). A Computational Fluid Dynamics Study on the Gas Mixing Capabilities of a Multiple Inlet System. J. Fluids Eng, 138(3), 031302. [DOI: 10.1115/1.4031380
  • G. Wendt, R. Jost, S. Schmelter und D. Werner (2014). Untersuchungen zum Temperaturverhalten von Flüssigkeiten in großen Lagertanks. Technische Sicherheit, Ausgabe 11-12/2014, Seiten 13-17.
  • K. Jousten, S. Pantazis, J. Buthig, R. Model, M. Wüest and J. Iwicki (2013). A standard to test the dynamics of vacuum gauges in the millisecond range. Vacuum , 100, 14-17. [DOI: 10.1016/j.vacuum.2013.07.037].
  • Hildebrandt, M.; Nowak, A.; Lindner, G.; Jordan-Gerkens, A.; Kuntze, A.; Böse, N.; Ebert, V. (2013). Development of a German national aerosol standard for validation and calibration of particle measurement instruments. Combustion Generated Nanoparticles, 17. ETH-Conference, Zürich; [CD-ROM], Nöthinger.
  •  R. Model, S. Schmelter, G. Lindner and M. Bär (2012). Numerical simulations and turbulent modelling for application in flow metrology, in "Advanced Mathematical & Computational Tools in Metrology and Testing IX" , Series on Advances in Mathematics for Applied Sciences vol. 84, eds. F. Pavese, M. Bär, J.-R. Filtz, A. B. Forbes, L. Pendrill, K. Shirono. World Scientific New Jersey.
  • Nowak, A.; Lindner, G.; Jordan-Gerkens, A.; Böse, N.; Ebert, V. (2012). Developing a national standard for soot mass concentration and opacity at PTB in Germany. Combustion Generated Nanoparticles, 16. ETH-Conference, Zürich; [CD-ROM], TTM Mayer, ISBN 978-3-033-035556-0.
  • S. Schmelter, G. Lindner, G. Wendt and R. Model (2011). Numerical investigation of turbulent natural convection in differentially heated square cavity. AIP Conf. Proc., 1389:106-109.
  • H. Förster, G. Werner, G. Lindner and R. Model (2011). Untersuchung zur Explosionsgefahr beim Umschlag von Kerosin Jet A-1. Techn. Sicherheit, 1 (1/2), 18-27Opens external link in new window.
  • G. Lindner, D. Markus and R. Model (2010). Non-reactive free jet flow: Comparison of simulations using different turbulence models with reference measurements. Proc. 5th Europ. Conf. on Comp. Fluid Dynamics

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