Reduced order models for wake control with a spinning cylinder

We study the formulation of reduced order models for a circular spinning cylinder in laminar vortex shedding regime. Proper orthogonal decomposition techniques based on the snapshots generated from velocity fields and a Galerkin projection are used to generate a low dimensional representation of the infinite dimensional system described by the Navier Stokes equation. This kind of problem has generally been studied numerically, without taking into consideration the constraints associated to physical experimental conditions or under the assumption that actuations do not alter significantly the time averaged velocity field. We propose a reduction technique that enables to obtain a control function based on the mean velocity field deviations from the unperturbed reference flow. This function is educed with a Gram Schmidt construction and gives rise to an extended base in which the velocity fields of the perturbed modes are expanded. The analysis allows for easy determination of a suitable model to describe a large range of the control parameter space, without needing to recalculate the coefficients that define the system for new operating conditions.