A novel framework for the uncertainty evaluation of virtual flow meters

Abstract The focus on virtual experiments (VEs) utilized for flow measurement in industrial applications is increasingly growing in the context of Industry 4.0 and the European Green Deal. They enable the replacement of cost-intensive physical measurements with computational models. However, the reliability of these virtual flow measurements depends—just as for physical measurements—highly on robust uncertainty quantification. This study introduces a novel framework for uncertainty evaluation that integrates the law of propagation of uncertainty for linear systems and the propagation of distributions for nonlinear systems, following the guide to the expression of uncertainty in measurement. Within this framework, a virtual calibration approach is incorporated that allows the determination of the fluid mechanical calibration factor from VEs instead of cost-intensive measurements. A case study with different Reynolds numbers and geometric configurations demonstrates that the proposed uncertainty evaluation methods perform equally well for an ultrasonic flow meter benchmark application. The proposed approach offers the flexibility to include further error and uncertainty sources, like modeling errors or uncertainties due to missing information in the description of the measurement set-up. Hence, it underscores the potential of VEs in flow measurement towards the virtual calibration of flow meters in complex industrial settings.