Reconstruction of large-scale flow structures in a stirred tank from limited sensor data

We combine reduced order modeling and system identification to reconstruct the temporal evolution of large-scale vortical structures behind the blades of a Rushton impeller. We performed direct numerical simulations at Reynolds number 600 and employed proper orthogonal decomposition (POD) to extract the dominant modes and their temporal coefficients. We then applied the identification algorithm, N4SID, to construct an estimator that captures the relation between the velocity signals at sensor points (input) and the POD coefficients (output). We show that the first pair of modes can be very well reconstructed using the velocity time signal from even a single sensor point. A larger number of points improves accuracy and robustness and also leads to better reconstruction for the second pair of POD modes. Application of the estimator derived at Re = 600 to the flows at Re = 500 and 700 shows that it is robust with respect to changes in operating conditions.