About 3D Incompressible Flow Reconstruction from 2D Flow Field Measurements

In this paper, an assessment of the uncertainty affecting a hybrid procedure (experimen-tal/numerical) is carried out to validate it for industrial applications, at the least. The procedure in question serves to depict 3D incompressible flow fields by using 2D measurements of it and computing the third velocity component by means of the continuity equation. A quasi-3D test case of an incompressible flow has been inspected in the wake of a NACA 0012 airfoil immersed in a forced flow of water running in a rectangular open channel. Specifically, starting from a 2D measurement data in planes orthogonal to the stream-wise direction, the computational approach can predict the third flow velocity component. A 3D ADV instrument has been utilized to measure the flow field, but only two velocity components have been considered as measured quantities, while the third one has been considered as reference with which to compare the computed component from the continuity equation to check the accuracy and validity of the hybrid procedure. At this aim, the uncertainties of the quantities have been evaluated, according to the GUM, to assess the agreement between experiments and predictions, in addition to other metrics. This aspect of uncertainty is not a technical sophistication but a substantial way to bring to the use of a 1D and 2D measurement system in lieu of a 3D one, which is costly in terms of maintenance, calibration, and economic issues. Moreover, the magnitude of the most relevant flow indicators by means of experimental data and predictions have been estimated and compared, for further confirmation by means of a supervised learning classification. Further, the sensed data have been processed, by means of a machine learning algorithm, to express them in a 3D way along with accuracy and epoch metrics. Two additional metrics have been included in the effort to show paramount interest, which are a geostatistical estimator and Sobol sensitivity. The statements of this paper can be used to design and test several devices for industrial purposes more easily.