Low-dimensional modelling and control of separated shear flows

Abstract

This thesis involves the modelling and control of separated shear flows. The emphasis is on the development of low-dimensional mean-field models that capture essential flow physics and are suitable for nonlinear control design in simulation and experiment. The concept of the mean-field model by Noack et al. (2003) has been generalized to include actuation mechanisms, which are incommensurable with the dominant frequency of the natural flow. This model describes how actuation-induced oscillations can interact with (and suppress) the instability at the natural frequency, only by indirect interaction via the varying mean flow. The framework of mean-field modelling has been applied to three different configurations: the flow around a 2-D circular cylinder, the flow around a 2-D high-lift configuration, and the flow around a D-shaped body. The first two configurations are investigated in numerical simulations, whereas the latter is a windtunnel experiment. For the circular cylinder, a parameterized proper orthogonal decomposition approach (POD) is used to extend the dynamic range of the standard POD. This parameterized model is used to optimize sensor locations. The model is demonstrated in a closed-loop control that targets wake suppression. High frequency open-loop actuation can significantly reduce the separation that is caused by large flap angles of a high-lift configuration. The essence of this mechanism is captured by the generalized meanfield model. This model is used for a set-point control of the lift coefficient. Finally, the generalized mean-field model is adapted for design of a nonlinear controller for set-point tracking of the base pressure coefficient of a bluff body. This illustrates the usefulness of mean-field models in experiment.