Abstract
Fluid flows that exhibit time-periodic behavior, or that can be modeled as time periodic, are ubiquitous in nature and engineering. These flows are usually highly oscillatory and nonlinear, and they exhibit non-trivial coupling between flow structures that oscillate at different frequencies. These are all features that make it difficult to analyze the dynamics of these systems, and to develop reduced-order models that describe the dominant mechanisms that are observed in simulation or experiment. Here, we present a novel frequency-domain framework that allows to fully characterize the input-output dynamics of a nonlinear system in the proximity of a time-periodic orbit. In particular, by linearizing the dynamics about a time-periodic solution of the governing equations, one can assemble a frequency-domain operator - known as the harmonic resolvent operator - that governs the input-output response of the flow across all frequencies. We demonstrate the ability of this framework to reveal flow mechanisms and predict the flow response in two laminar flows: the flow over an airfoil at Re=200 and an axisymmetric jet flow at Re=1500. We also show how this formulation can be used to obtain reduced-order models for control. In particular, we draw a natural connection with the continuous-time balanced truncation framework for linear time-periodic control systems. As a demonstrative example, we compute a reduced-order feedback controller to suppress the vortex pairing instability in the aforementioned axisymmetric jet.
About the Speaker
Alberto Padovan is a postdoctoral research associate working in the Center for Hypersonics & Entry Systems Studies (CHESS) at UIUC under the supervision of Professor Daniel Bodony. Alberto was part of Professor Clarence Rowley’s group at Princeton University, where he obtained his PhD in September 2022. His research interests lie at the intersection of fluid mechanics, controls theory and dynamical systems, and his PhD work focused on the development of input-output methods for the analysis, model reduction and control of fluid flows that evolve in the proximity of time-periodic orbits.
Host: Professor Daniel Bodony
