Session G29: Data-Driven Modeling, Control and Analysis for Fluid Dynamics

The neural network fluid dynamicist: networks in feedback for flow control, sensor placement, and flow physics analysis

This talk will discuss a methodology for exploiting neural network architectures to perform a variety of common flow analysis and control tasks. Starting with a nonlinear fluid system equipped with some means of actuation, we first identify a neural network surrogate model for the actuated system. We then use this surrogate to train a second neural network model, designed to achieve a desired control objective. Through an iterative training process for both the model and controller neural networks, we obtain feedback control laws designed to drive unstable, nonlinear systems to their equilibria. Through the application of L1 regularization within the neural network loss function, optimal sensor locations can be identified from a larger set of candidates, allowing for stabilization using a reduced set of real-time measurements. This methodology is validated on several nonlinear systems, including a modified Kuramoto-Sivashinsky equation, spanwise-constant channel flow, and confined cylinder flow. We further show that identified neural-network models can be exploited to find not only unstable equilibria, but also leading linear stability eigenmodes. This demonstrates that rather than just being black-boxes, such neural network models can reveal pertinent flow physics.   

Leveraging Bayesian Optimisation for Expensive Experiments and Simulations in Fluid Dynamics with Uncontrollable Dynamic Variables

The optimisation of physical experiments and computer simulations is a challenge frequently encountered in fluid dynamics. It is a difficult task as the underlying physical processes or mathematical models are often too complex to find an optimum analytically, limiting us to controlling some parameters and observing a response - typically an expensive task.

We introduce NUBO (Newcastle University Bayesian Optimisation), an open-source machine learning framework that takes a data-driven approach to find close-to-optimal parameter values for such problems. It uses a surrogate model to approximate the objective function and heuristics (acquisition functions) to guide the search over the parameter space. This model-based strategy makes NUBO cost-effective and well-suited for expensive simulations and experiments in fluid dynamics.

We apply NUBO to high-fidelity simulations and wind tunnel experiments, where we aim to reduce the skin-friction drag of turbulent boundary-layer flows by optimising multiple actuation parameters (e.g., amplitude, frequency, wavelengths of low-amplitude wall-blowing). We further consider the presence of uncontrollable variables affecting drag, particularly finding optimal control strategies when oncoming wind speeds are changing continually. We will show that NUBO finds strategies yielding significant skin-friction drag reduction that may eventually generate net-energy savings for the system.   

Phase-oscillator-based modeling and control of multi-modal fluid flows

Analysis and control for time-periodic fluid flows have been performed using phase reduction analysis, wherein the high-dimensional periodic flow physics is described as a single scalar phase dynamics. However, most unsteady flows have several dominant frequencies and flow control is challenging owing to the nonlinear interactions. In the present work, we capture the dynamics of unsteady flows with a coupled phase oscillator model, where each dominant mode is represented with an oscillator and the coupling terms quantify the triadic interactions. We demonstrate this approach on a compressible laminar flow over a rectangular cavity with strong triadic interactions. Such flows are characterized by violent pressure fluctuations. Using the developed coupled phase oscillator model, we can identify the phase sensitivity function and the optimal actuation waveform for a rapid shift of the dominant frequency. An actuation jet is introduced at the leading edge using this optimal waveform to modify the dominant physics, which results in a reduction in the triadic interactions, and a 20 percent reduction in pressure fluctuations in the cavity.

This work is supported by the US Air Force Office of Scientific Research (FA9550-21-1-0178) and the US National Science Foundation (2129639).   

Discovering sparse optimal finite-amplitude perturbations in nonlinear flows

Managing flow instabilities is a central challenge in fluid dynamics. Active flow control has been proposed as a means by which unsteady phenomena such as flow separation can be mitigated. However, the design of effective flow control strategies requires an understanding of which physical phenomena should be targeted with actuation. To this end, we propose an optimization framework for finding sparse finite-amplitude perturbations that maximize transient energy growth in nonlinear systems. Using a variational approach, we derive the first-order necessary conditions for optimality, which form the basis of our direct-adjoint looping numerical algorithm. We demonstrate the approach on a reduced-order model of a sinusoidal shear flow. Our framework identifies that energy injection into a single mode yields comparable energy amplification as the non-sparse optimal solution. This analysis establishes the possibility of using such methods to determine actuation strategies for flow control in the future.   

Data-Driven Sensor Placement for Nuclear Reactor Transient Analyses in Digital Twins

Analyzing the effect of transients on reactor core coolant temperature, pressure, and velocity is essential for real-time safety monitoring and control of a nuclear reactor. The strategic placement of sensors critically enables reconstruction of latent reactor flow fields from sparse, heavily constrained measurements. We develop a data-driven optimization procedure for sensor placement that leverages reduced order models (ROMs) of flow physics, including dynamic mode decomposition and autoencoders. These ROMs help reveal the underlying dynamics and behavior of complex nuclear systems, with the goal of constructing a digital twin of the target nuclear asset. The developed methodology is also extended to determine optimal sensing locations and time steps for collecting sparse measurements. The effect of different ROMs on sensor locations and flow reconstruction performance is demonstrated on the Out-of-Pile Testing and Instrumentation Transient Irradiation System (OPTI-TWIST) prototype, which is electrically heated to mimic the neutronic effect, before the TWIST is tested in the Transient Reactor Test Facility (TREAT) at Idaho National Laboratory.