Frequency-Domain Analysis, Model Reduction and Control of Time-Periodic Fluid Flows

Abstract

In this dissertation we concern ourselves with the analysis, model reduction, and control of fluid flows that exhibit time-periodic behavior, or that can be modelled as time periodic. These flows are ubiquitous in nature and in engineering. In nature, one of the most remarkable examples of periodic flows may be found in the Von-Karman vortices that form in the wake of an island. A perhaps less spectacular, yet arguably more important example of a flow that can be modelled as periodic, is blood flow, where the periodicity is induced by the beating heart. In engineering applications, examples include flows in turbomachinery and rotorcraft as well as wake flows. Although all these examples belong to widely different classes of application, their time-periodic nature is such that they can all be studied using a very specific class of mathematical tools. These tools will be the focus of this dissertation, where we discuss existing techniques and we introduce novel mathematical and computational methods for the analysis and control of time-periodic fluid flows. This dissertation is divided in two parts. In the first part we provide an overview of existing frequency-domain methods for the analysis, model reduction and control of fluid flows. We begin with popular techniques based on the linearization of the governing equations about steady equilibria, and then we present novel approaches based on the linearization about time-periodic solutions of the governing equations. The second part includes published and submitted manuscripts that contain a more thorough description of the methods and results presented in the first part. The methods discussed herein are demonstrated on two-dimensional incompressible laminar flows that exhibit periodic dynamics as well as on a three-dimensional separated turbulent boundary layer over a flat plate.