Global flow stability analysis and reduced order modeling for bluff-body flow control

In the present study, a hierarchy of control-oriented reduced order models (ROMs) for fluid flows is presented. Control design requires simplicity, accuracy and robustness from an online capable Galerkin model. These requirements imply low order of the associated dynamical system. Standard POD (proper orthogonal decomposition) Galerkin models may provide a low-dimensional representation of a given reference state. Yet, their narrow dynamic range and lack of robustness pose a challenge for control design. We propose key enablers to increase the dynamic range of the POD model. An 11-dimensional hybrid model is discussed which includes, in addition to 8 POD modes, a shift mode to resolve base-flow variations, and a complex global stability mode for enhanced description of the transient phase. The dimension is further reduced by a similarly accurate 3-dimensional generalized mean-field model employing a novel continuous mode interpolation technique between POD and stabili ty eigenmodes. This method connects smoothly different operating conditions, different mode bases and even different boundary conditions, allowing the design of least-order, accurate Galerkin model for flow control purposes. The interpolation technique is employed to construct a priori flow model from the stability analysis and the Reynolds equation without the need for flow data.