# Confidence in virtual flowmeters

## Calculating the uncertainty of a flow simulation

PTBnews 2.2023
02.05.2023
Especially interesting for

flow metrology

mathematical modeling

metrology institutes

A method for calculating the simulation uncertainty of a virtual ultrasonic flowmeter has been developed in PTB's VirtMet Competence Center. This method allows calibration factors relevant to fluid mechanics to be calculated for real measuring devices. The method is based on the comparison of real and virtual measurements and allows the continuous determination of calibration factors with their corresponding expanded uncertainty and confidence interval.

Two ultrasonic clamp-on flowmeters (yellow circles) downstream of a bend configuration. The flow development in the pipe and the fluid mechanical calibration factors of the device are modeled on the basis of a “virtual measurement”.

When a real measurement procedure is reproduced by simulations, it may be referred to as a “virtual measurement”. From a metrological point of view, the question is how to ensure confidence in such virtual measurements. While methods to estimate diverse sources of error in simulations have been developed over the past decades, there has to date been no accepted strategy for meeting the metrological requirements for virtual measuring devices. Now, researchers at PTB have developed a method for calculating the simulation uncertainty of a virtual ultrasonic clamp-on meter for flow rate measurements.

Ultrasonic clamp-on meters have become an established technology for flow rate measurements. Under real, non-ideal flow conditions downstream of bends, valves, etc., the measurement values of flowmeters must be corrected by means of fluid mechanical calibration factors. Because of the variety of relevant flow configurations and installation positions, the experimental determination of these factors is supplemented by simulations. As in the case of real uncertainties, the approach to determining the simulation uncertainty is based on the use of an expanded uncertainty with the associated confidence interval. The simulation errors are determined at discrete measurement positions, and a continuous simulation uncertainty is derived from this, i.e., simulation uncertainties that are applicable to all installation positions of the meter. The newly developed method allows experimental data to be replaced by virtual measurements – a metrologically justifiable approach. This method is not limited only to certain devices and flow configurations in flow rate measurements but is generally also applicable to other areas of metrology to improve confidence in virtual measurement devices.

### Contact

Martin Straka
Department 7.5, Heat and Vacuum
Phone: +49 30 3481-7769
martin.straka(at)ptb.de

### Scientific publication

M. Straka, A. Weissenbrunner, C. Koglin, C. Höhne, S. Schmelter: Simulation uncertainty for a virtual ultrasonic flow meter. Metrology 2, 335–359 (2022)