Ultrasonic clamp-on meters have become an established technology for non-invasive flow measurements. Under disturbed flow conditions, their measurement values must be adjusted with corresponding fluid mechanical calibration factors. Due to the variety of flow disturbances and installation positions, the experimental determination of these factors often needs to be complemented by computational fluid dynamics (CFD) simulations. From a metrological perspective, substituting experiments with simulation results raises the question of how confidence in a so-called virtual measurement can be ensured. While there are well-established methods to estimate errors in CFD predictions in general, strategies to meet metrological requirements for CFD-based virtual meters have yet to be developed. In this paper, a framework for assessing the overall uncertainty of a virtual flow meter is proposed. In analogy to the evaluation of measurement uncertainty, the approach is based on the utilization of an expanded simulation uncertainty representing the entirety of the computational domain. The study was conducted using the example of an ultrasonic clamp-on meter downstream of a double bend out-of-plane. Nevertheless, the proposed method applies to other flow disturbances and different types of virtual meters. The comparison between laboratory experiments and simulation results with different turbulence modeling approaches demonstrates a clear superiority of hybrid RANS-LES models over the industry standard RANS. With an expanded simulation uncertainty of 1.44 × 10⁻², the virtual measurement obtained with a hybrid model allows for a continuous determination of calibration factors applicable to the relevant mounting positions of a real meter at a satisfactory level of confidence.

The 90 ° - bend represents the most common structural element in piping systems and can have a significant impact on the measuring accuracy of flow meters installed downstream. Within the type-approval procedure of water meters, its impact is emulated by means of a segmental orifice plate with a segment area of 7 % (SOP7). In research and development, coverage rates of 33 % (SOP33) or more are sometimes used as an alternative. The purpose of this study is to evaluate the comparability of the flow conditions and their influence on the measurement deviation of flow meters, which is the basic requirement for using SOPs as a substitute for the 90°- bend. We present laser Doppler measurements downstream of an SOP33 and a 90°- bend and describe the flow development in a distance range from 2 to 30 diameters. Besides a quantitative comparison with performance indicators, the measurements are used to model the response of an ultrasonic and electromagnetic flow meter, including recent investigations of an SOP7. The results demonstrate the consistently poor agreement between the SOP7 and the 90°- bend, whereas the SOP33 provides similar flow conditions starting at a distance of 10 diameters. Further studies are necessary to develop a disturbance generator emulating the near-field range.

Most flow metering methods used in industrial applications produce results sensitive to the local velocity profile. In response, manufacturers often implement correction algorithms; however, these are rarely supported by rigorous uncertainty evaluations. This paper presents a Reynolds number-dependent velocity profile correction, applicable under fully developed flow conditions and for the Reynolds-dependent part of the correction in disturbed flows, demonstrated on the example of an ultrasonic clamp-on flow meter. Measurement uncertainties are evaluated and propagated through a regression model using Monte Carlo simulation, in compliance with the Guide to the Expression of Uncertainty in Measurement (GUM). Special care is taken to assess the validity range and impact of assuming fully developed flow conditions at the test rig. A validation case demonstrates the reliability of the correction algorithm and its associated uncertainty within the tested conditions. The proposed approach is applicable to other meter types and can be extended to corrections for specific flow disturbances.