Virtual experiments (VEs) and digital twins (DTs), pivotal for realizing European strategic policies on sustainability and digitalization within Industry 4.0 and the European Green Deal, simulate physical systems and characteristics in a virtual environment, with DTs incorporating dynamic inputs from and outputs to the real-world counterpart. To ensure confidence in their use and outcomes, traceability and methods to evaluate measurement uncertainty are needed, topics that are hardly covered by the literature so far. This paper provides a harmonized definition of VEs and DTs and introduces a framework for evaluating measurement uncertainty. Furthermore, it discusses how to propagate the uncertainty of the contributions coming from the different parts of the DT. For the core part of the DT, the framework derived for VEs can be used. For the physical-to-virtual (P2V) connection and the virtual-to-physical (V2P) connection, additional sources of uncertainty need to be considered. This paper provides a metrological framework for taking all these uncertainty contributions into account while describing a framework to establish traceability for DTs. Two case studies are presented to demonstrate the proposed methodology considering industrially relevant measuring instruments and devices, namely, a coordinate measuring machine (CMM) and a collaborative robot arm (cobot).

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.

Nearly all types of flow measurement devices installed in pipes are affected by the flow conditions at their inlet section, which can lead to measurement errors of several per cent. To evaluate the influence of uncertain inflow profiles on the flow field at different positions of the flow meter, a non-intrusive polynomial chaos approach is applied to simulations of turbulent pipe flow. This allows us to estimate the expected variations of the flow profiles as a function of the distance to the inlet of the pipe in an efficient way. The polynomial chaos approach shows reasonable convergence already for a small number of function evaluations. The results are validated by comparison with a quasi-Monte Carlo method and an exact solution, where available. The approximation error of the polynomial chaos method with 10 function evaluations is smaller than the one for the quasi-Monte Carlo method with 100 runs.

When multiphase flows are modeled numerically, complex geometrical and operational features of the experiments, such as the phase mixing section, are often not resolved in detail. Rather simplified boundary conditions are prescribed, which usually cause less irregular dynamics in the system than present in reality. In this paper, a perturbation that randomly disturbs the secondary components of the velocity vector at the inlet is proposed in order to capture the experimentally observed instabilities at the interface between the phases. This in particular enhances the formation of slugs in the pipe. Different amplitudes of the perturbation are investigated. One observes that, the higher the perturbation amplitude, the earlier the slugs occur. On the other hand, sufficiently far away from the inlet, the flow pattern shows the same dynamics for different perturbation amplitudes. Hence, no specific frequency is imposed by the prescribed perturbation. The simulation results are validated by comparison with liquid level data from a corresponding experiment.