Network-Theoretic and Data-Based Analysis and Control of Unsteady Fluid Flows
Aditya Nair · 2018
Unsteady fluid flows have complex dynamics due to the nonlinear interactions amongst vortical elements. In this thesis, a network-theoretic framework is developed to describe vortical and modal (coherent structure) interactions in unsteady fluid flows. A sparsified-dynamics model and a networked-oscillator model describe the complex dynamics in fluid flows in terms of vortical and modal networks, respectively. Based on the characterized network interactions, model-based feedback control laws are established, particularly for controlling the flow unsteadiness. Furthermore, to characterize model-free feedback control laws for suppressing flow separation in turbulent flows, a data-driven approach leveraging unsupervised clustering is developed. This approach alters the Markov transition dynamics of fluid flow trajectories in an optimal manner using a cluster-based control strategy. To describe vortical interactions, dense fluid flow graphs are constructed using discrete point vortices as nodes and induced velocity as edge weights. Sparsification techniques are then employed on these graph representations based on spectral graph theory to construct sparse graphs of the overall vortical interactions which maintain similar spectral properties as the original setup. Utilizing the sparse vortical graphs, a sparsified-dynamics model is developed which drastically reduces the computational cost to predict the dynamical behavior of vortices, sharing characteristics of reduced-order models. The model retains the nonlinearity of the interactions and also conserves the invariants of discrete vortex dynamics. The network structure of vortical interactions in two-dimensional incompressible homogeneous turbulence is then characterized. The strength distribution of the turbulence network reveals an underlying scale-free structure that describes how vortical structures are interconnected. Strong vortices serve as network hubs with smaller and weaker eddies predominantly influenced by the neighboring hubs. The time evolution of the fluid flow network informs us that the scale-free property is sustained until dissipation overtakes the flow physics. The types of perturbations that turbulence network is resilient against is also examined. To describe modal interactions in fluid flows, a networked-oscillator-based analysis is performed. The analysis examines and controls the transfer of kinetic energy for periodic bluff body flows. The dynamics of energy fluctuations in the flow field are described by a set of oscillators defined by conjugate pairs of spatial POD modes. To extract the network of interactions among oscillators, impulse responses of the oscillators to amplitude and phase perturbations are tracked. Using linear regression techniques, a networked oscillator model is constructed that reveals energy exchanges among the modes. In particular, a large collection of system responses are aggregated to capture the general network structure of oscillator interactions. The present networked oscillator model describes the modal…