Flow control and sensing using data-driven reduced-order modeling

Sashittal, Palash

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https://hdl.handle.net/2142/113833 Copy

Description

Title

Flow control and sensing using data-driven reduced-order modeling

Author(s)

Sashittal, Palash

Issue Date

2021-11-17

Director of Research (if dissertation) or Advisor (if thesis)

Bodony, Daniel J.

Doctoral Committee Chair(s)

Bodony, Daniel J.

Committee Member(s)

• Ewoldt, Randy H.
• Heindel, Theodore J.
• Goza, Andres
• Villafane Roca, Laura

Department of Study

Aerospace Engineering

Discipline

Aerospace Engineering

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• flow control
• flow sensing
• reduced-order modeling
• data-driven modeling

Abstract

Transfer operators, such as the Koopman operator, are driving a paradigm shift in how we perform data-driven modeling of fluid flows. Approximations of the Koopman operator provide linear representations even for strongly nonlinear flows, which enables the application of standard linear methods for estimation and control under realistic flow conditions. In the past decade, we have witnessed several breakthroughs in obtaining low-dimensional approximations of the Koopman operators, providing a tractable reduced-order model for complex fluid flows using data from numerical simulations or experiments. In this thesis, we leverage these recent developments in operator-theoretic modeling of fluid flows and provide data-driven solutions to the flow control and sensing problems. The contributions of this thesis can be divided into three parts. In the first part, we introduce a novel method, low-rank Dynamic Mode Decomposition (lrDMD), for data-driven reduced-order modeling of fluid flows. While existing data-driven modeling methods fit an endomorphic linear function on a low-dimensional subspace, lrDMD approximates flow dynamics using a linear map between different subspaces. We show that this approach leads to the design of better reduced-order feedback controllers. We formulate a rank-constrained matrix optimization problem and propose two complementary methods to solve the problem. lrDMD outperforms existing methods in feedback control and optimal actuator placement. In the second part, we present a completely data-driven framework for sensor placement in fluid flows. This framework can be applied in conjunction with any reduced-order modeling technique that constructs a linear model for the flow dynamics. We formulate an optimization problem that minimizes the trace of a data-driven approximation of the estimation error covariance matrix, where the estimates are provided by a Kalman filter. We propose an efficient adjoint-based gradient descent method to solve the optimization problem. We show that sensors placed using our method lead to better performance in important applications, such as flow estimation and control, compared to existing data-driven sensor placement methods. In the third and final part, we propose a new method of interface tracking and reconstruction in multiphase flows using shadowgraphs or back-lit imaging data. First, we show that while traditional modeling methods provide valuable information about the spatio-temporal structure of flow instabilities, they are not able to resolve spatial or temporal discontinuities, such as the liquid-gas interface, in the data. To remedy this, we propose a two-step approach, using data-driven modeling techniques in conjunction with optical flow methods, that preserves sharp interfaces and provides reliable reconstruction and short-time prediction of the flow. We apply our method to an experimental liquid jet with a co-axial air-blast atomizer using back-lit imaging. Our method is able to accurately reconstruct and predict the flow while preserving the sharpness of the liquid-gas interface.

Graduation Semester

2021-12

Type of Resource

Thesis

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http://hdl.handle.net/2142/113833

Copyright and License Information

Copyright 2021 by Palash Sashittal

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