Low order modelling for flow simulation, estimation and control

The aim is to develop and to test tools having a low computational cost for flow simulation, estimation and control applications. The proper orthogonal decomposition (POD) and a Galerkin projection of the equations onto the POD modes are used to build low order models of the incompressible Navier-Stokes equations. In this work a flow past a square cylinder is considered in two-dimensional and three-dimensional configurations. Two blowing/suction actuators are placed on the surface of the cylinder. Calibration techniques are applied, providing stable and rather accurate models, even for three-dimensional wake flows with complicated patterns. A state estimation method, involving flow measurements, is then developed for unsteady flows. Multi-dynamic calibrations and efficient sampling techniques are applied to build models that are robust to variations of the control parameters. A linear stability analysis by using linearized low order models around a controlled steady state is briefly addressed. The presented techniques are applied to the square cylinder configuration at Reynolds numbers that range between Re = 40 and Re = 300.