Investigation of POD bases for flow control on disk wakes

This work investigates the effects of flow control on the near wake region of a disk in a water flow, utilizing the POD reconstructed time dependent velocity fields. Velocity measurements were collected using time resolved particle image velocimetry (TRPIV) at a Reynolds number of 20,000 based on the disk diameter, both with and without control. An open-loop control was applied via periodic synthetic jet excitation from the disk edge. With the advantage of a time resolved velocity database, we have the ability to reconstruct the time dependent velocity fields in the wake of the disk. This reconstruction is done for the baseline and controlled cases using various POD truncations to observe velocity reconstructions, based on the overall energy of the system. In doing so, we will consider the convergence rate of the spatial eigenvalues when conducting our POD reconstruction of the fluctuating velocity fields, for both the baseline and controlled cases. Since a complex flow exists in the wake of the disk, the goal will be to form a state space representation of the flow in the form of a linear time invariant (LTI) system. This model is simply a linearization of the flow around the baseline. Furthermore, our knowledge of the input control signal will allow us to predict the flow at a later instant in time. We would like to extract the most energetic modes of the system and thereby form our observerbased controller to close the loop. In order to accomplish this, and with a rich open-loop dataset at our disposal, we will first form the POD reconstruction of the baseline. We then form a new basis, obtained by taking the actuated (controlled) data and subtracting from it the components of the flow that fall in the subspace spanned by the baseline flow. This will characterize the flow fields by capturing the effect of the control input (actuation), from which the parameters of the LTI system can be identified. Preliminary POD reconstruction shows that 60% of the energy is recovered from 20 POD modes of the total 511 modes for the baseline case; similarly 60% of the energy is also recovered from 100 POD modes of the total 1,024 modes for the actuated case.