On the accuracy of data assimilation algorithms for dense flow field reconstructions

Abstract

Within the framework of the European Union Horizon 2020 project HOMER (Holistic Optical Metrology for Aero-Elastic Research), data assimilation (DA) algorithms for dense flow field reconstructions developed by different research teams, hereafter referred to as the participants, were comparatively assessed. The assessment is performed using a synthetic database that reproduces the turbulent flow in the wake of a cylinder in ground effect, placed at the distance of one diameter from a lower wall. Downstream of the cylinder, this wall continues either in the form of a flat steady wall, or of a flexible panel undergoing periodic oscillations; these two situations correspond to two different test cases, the latter being introduced to extend the evaluation to fluid–structure interaction problems. The input data for the data assimilation algorithms were datasets containing the particle locations and their trajectories identification numbers, at increasing tracer concentrations from 0.04 to 1.4 particles/mm³ (equivalent image density values between 0.005 and 0.16 particles per pixel, ppp). The outputs of the DA algorithms considered for the assessment were the three components of the velocity, the nine components of the velocity gradient tensor and the static pressure, defined in the flow field on a Cartesian grid, as well as the static pressure on the wall surface, and its position in the deformable wall case. The results were analysed in terms of errors of the output quantities with respect to the ground-truth values and their distributions. Additionally, the performances of the different DA algorithms were compared with that of a standard linear interpolation approach. The velocity errors were found in the range between 3 and 11% of the bulk velocity; furthermore, the use of the DA algorithms enabled an increase of the measurement spatial resolution by a factor between 3 and 4. The errors of the velocity gradients were of the order of 10–15% of the peak vorticity magnitude. Accurate pressure reconstruction was achieved in the flow field, whereas the evaluation of the surface pressure revealed more challenging. As expected, lower errors were obtained for increasing seeding concentration. The difference of accuracy among the results of the different data assimilation algorithms was noticeable especially for the pressure field and the compliance with governing equations of fluid motion, and in particular mass conservation. The analysis of the flexible panel test case showed that the panel position could be reconstructed with micrometric accuracy, rather independently of the data assimilation algorithm and the seeding concentration. The accurate evaluation of the static pressure field and of the surface pressure proved to be a challenge, with typical errors between 3 and 20% of the free-stream dynamic pressure.