Three-dimensional characterisation of macro-instabilities in a turbulent stirred tank flow and reconstruction from sparse measurements using machine learning methods

We apply Proper Orthogonal Decomposition (POD) to characterise rotating, three dimensional, large scale coherent structures inside an unbaffled stirred tank agitated by a Rushton turbine at turbulent flow conditions (Re = 30000). The four leading POD modes come in pairs, with frequencies 0.6 and 0.2 times the impeller rotational frequency (in an inertial reference frame). Investigation of the spatial structure suggest that the two pairs correspond to precessing Macro-instabilities that rotate in a direction opposite to that of the impeller. Four Machine Learning methods are employed to reconstruct the dominant pair from sparse velocity measurements. The pair was reconstructed well by all algorithms using data from 1, 2, and 6 sensors. The performance improved with larger number of sensors. A reduced order model consisting of the mean and the first two modes reconstructs well the largest structures of the flow but, as expected, does not reproduce the finer features.& COPY; 2023 The Author(s). Published by Elsevier Ltd on behalf of Institution of Chemical Engineers. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

This study applies Proper Orthogonal Decomposition (POD) to characterize large scale coherent structures inside a stirred tank agitated by a Rushton turbine at turbulent flow conditions (Re = 30000). The four leading POD modes correspond to precessing Macro-instabilities that rotate in a direction opposite to that of the impeller. Machine Learning methods are utilized to reconstruct the dominant pair from sparse velocity measurements, and the performance improves with a larger number of sensors. A reduced order model consisting of the mean and the first two modes reconstructs the largest structures but not the finer features.