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Full Title

Network-Theoretic and Data-Based Analysis and Control of Unsteady Fluid Flows

Names

Nair, Aditya Gopimohan (author)

Taira, Kunihiko (professor directing dissertation)

Sussman, Mark (university representative)

Cattafesta, Louis N. (committee member)

Oates, William (committee member)

Alvi, Farrukh S. (committee member)

Brunton, Steven L. (Steven Lee), 1984- (committee member)

Florida State University (degree granting institution)

College of Engineering (degree granting college)

Department of Mechanical Engineering (degree granting department)

Date Issued

2018

Format

text

doctoral thesis

Abstract

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 perturbation dynamics more accurately than the empirical Galerkin reduced-order model. The linear network model for nonlinear dynamics is subsequently utilized to design a model-based feedback controller. The controller suppresses the modal fluctuations and amplitudes that result in wake unsteadiness leading to drag reduction. The strength of the approach is demonstrated for a canonical example of two-dimensional unsteady flow over a circular cylinder. The network-based formulation enables the characterization and control of modal interactions to control fundamental energy transfers in unsteady bluff body flows. Finally, unsupervised clustering and data-driven optimization of coarse-grained control laws is leveraged to manipulate post-stall separated flows. Optimized feedback control laws are deduced in high-fidelity simulations in an automated, model-free manner. The approach partitions the baseline flow trajectories into clusters, which corresponds to a characteristic coarse-grained phase in a low-dimensional feature space constituted by feature variables (sensor measurements). The feedback control law is then sought for each and every cluster state which is iteratively evaluated and optimized to minimize aerodynamic power and actuation power input. The control optimally transforms the Markov transition network associated with the baseline trajectories to achieve desired performance objectives. The approach is applied to two and three-dimensional separated flows over a NACA 0012 airfoil at an angle of attack of 9° Reynolds number Re = 23000 and free-stream Mach number M∞ = 0.3. The optimized control law minimizes power consumption for flight enabling flow to reach a low-drag state. The analysis provides insights for feedback flow control of complex systems characterizing global cluster-based control laws based on a data-driven, low-dimensional characterization of fluid flow trajectories. In summary, this thesis develops a novel network-theoretic and data-based framework for analyzing and controlling fluid flows. The framework incorporates advanced mathematical principles from network science, graph theory and dynamical systems to extract fundamental interactions in fluid flows. On manipulating these interactions, wake unsteadiness in bluff body flow is reduced leading to drag reduction. Finally, data-based methods are developed to deduce optimal feedback control laws for post-stall separated flows. The network-theoretic and data-based approaches provides insights on fundamental interactions in fluid flows which paves the way for design of novel flow control strategies.

Keywords

Cluster-based control, Modal interactions, Networked-oscillators, Scale-free networks, Sparsified vortex dynamics

Date of Defense

July 23, 2018.

Submitted Note

A Dissertation submitted to the Department of Mechanical Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy.

Bibliography Note

Includes bibliographical references.

Advisory Committee

Kunihiko Taira, Professor Directing Dissertation; Mark Sussman, University Representative; Louis N. Cattafesta, Committee Member; William S. Oates, Committee Member; Farrukh S. Alvi, Committee Member; Steven L. Brunton, Committee Member.

Publisher

Florida State University

Identifier

2018_Su_Nair_fsu_0071E_14745

Nair, A. G. (2018). Network-Theoretic and Data-Based Analysis and Control of Unsteady Fluid Flows. Retrieved from http://purl.flvc.org/fsu/fd/2018_Su_Nair_fsu_0071E_14745