arXiv subjects

Kunihiko Taira

Publications and source records attributed to Kunihiko Taira.

At least 37 records · Page 2Linked to original sources

arXiv2024

Influence of three-dimensionality on wake synchronization of oscillatory cylinder

We investigate the effect of three-dimensionality on the synchronization characteristics of the wake behind an oscillating circular cylinder at Re = 300. Cylinder oscillations in rotation, transverse translation, and streamwise translation are considered. We utilize phase-reduction analysis, which quantifies the phase-sensitivity function of periodic flows, to examine the synchronization properties. Here, we present an ensemble-based framework for phase-reduction analysis to handle three-dimensional wakes that are not perfectly time-periodic. Based on the phase-sensitivity functions, synchronizability to three types of cylinder oscillations is evaluated. In spite of similar trends, we find that phase-sensitivity functions involving three-dimensional wakes are lower in magnitude compared to those of two-dimensional wakes, which leads to narrower conditions for synchronization to weak cylinder oscillations. We unveil that the difference between the phase-sensitivity functions of two- and three-dimensional flows is strongly correlated to the amplitude variation of the three-dimensional flow by the cylinder motions. This finding reveals that the cylinder motion modifies the three-dimensionality of the wake as well as the phase of vortex shedding, which leads to reduced phase modulation. The synchronization conditions of three-dimensional wakes, predicted by phase-reduction analysis, agree with the identification by parametric studies using direct numerical simulations for forced oscillations with small amplitudes. This study presents the potential capability of phase-reduction to study synchronization characteristics of complex flows.

physics.flu-dyn↗

arXiv2024

Single-snapshot machine learning for super-resolution of turbulence

Modern machine-learning techniques are generally considered data-hungry. However, this may not be the case for turbulence as each of its snapshots can hold more information than a single data file in general machine-learning settings. This study asks the question of whether nonlinear machine-learning techniques can effectively extract physical insights even from as little as a {\it single} snapshot of turbulent flow. As an example, we consider machine-learning-based super-resolution analysis that reconstructs a high-resolution field from low-resolution data for two examples of two-dimensional isotropic turbulence and three-dimensional turbulent channel flow. First, we reveal that a carefully designed machine-learning model trained with flow tiles sampled from only a single snapshot can reconstruct vortical structures across a range of Reynolds numbers for two-dimensional decaying turbulence. Successful flow reconstruction indicates that nonlinear machine-learning techniques can leverage scale-invariance properties to learn turbulent flows. We also show that training data of turbulent flows can be cleverly collected from a single snapshot by considering characteristics of rotation and shear tensors. Second, we perform the single-snapshot super-resolution analysis for turbulent channel flow, showing that it is possible to extract physical insights from a single flow snapshot even with inhomogeneity. The present findings suggest that embedding prior knowledge in designing a model and collecting data is important for a range of data-driven analyses for turbulent flows. More broadly, this work hopes to stop machine-learning practitioners from being wasteful with turbulent flow data.

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arXiv2024

On the laminar solutions and stability of accelerating and decelerating channel flows

We study the effect of acceleration and deceleration on the stability of channel flows. To do so, we derive an exact solution for laminar profiles of channel flows with arbitrary, time-varying wall motion and pressure gradient. This solution then allows us to investigate the stability of any unsteady channel flow. In particular, we restrict our investigation to the nonnormal growth of perturbations about time-varying base flows with exponentially decaying acceleration and deceleration, with comparisons to growth about a constant base flow (i.e., the time-invariant simple shear or parabolic profile). We apply this acceleration and deceleration through the velocity of the walls and through the flow rate. For accelerating base flows, perturbations never grow larger than perturbations about a constant base flow, while decelerating flows show massive amplification of perturbations - at a Reynolds number of 500, properly timed perturbations about the decelerating base flow grow $\mathscr{O}(10^5)$ times larger than perturbations grow about a constant base flow. This amplification increases as we raise the rate of deceleration and the Reynolds number. We find that this amplification arises due to a transition from spanwise perturbations leading to the largest amplification, to streamwise perturbations leading to the largest amplification that only occurs in the decelerating base flow. By evolving the optimal perturbations through the linearized equations of motion, we reveal that the decelerating base flow achieves this massive amplification through the Orr mechanism, or the down-gradient Reynolds stress mechanism, which accelerating and constant base flows cannot maintain.

physics.flu-dyn↗

arXiv2024

The effect of Reynolds number on the separated flow over a low-aspect-ratio wing

At high incidence, low-aspect-ratio wings present a unique set of aerodynamic characteristics, including flow separation, vortex shedding, and unsteady force production. Furthermore, low-aspect ratio wings exhibit a highly impactful tip vortex, which introduces strong spanwise gradients into an already complex flow. In this work, we explore the interaction between leading edge flow separation and a strong, persistent tip vortex over a Reynolds number range of $600 \leq Re \leq 10,000$. In performing this study, we aim to bridge the insight gained from existing low Reynolds number studies of separated flow on finite wings ($Re \approx 10^2$) and turbulent flows at higher Reynolds numbers ($Re \approx 10^4$). Our study suggests two primary effects of Reynolds number. First, we observe a break from periodicity, along with a dramatic increase in the intensity and concentration of small-scale eddies, as we shift from $Re = 600$ to $Re = 2,500$. Second, we observe that many of our flow diagnostics, including the time-averaged aerodynamic force, exhibit reduced sensitivity to Reynolds number beyond $Re = 2,500$, an observation attributed to the stabilizing impact of the wing tip vortex. This latter point illustrates the manner by which the tip vortex drives flow over low-aspect-ratio wings, and provides insight into how our existing understanding of this flowfield may be adjusted for higher Reynolds number applications.

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arXiv2024

Data-driven transient lift attenuation for extreme vortex gust-airfoil interactions

We present a data-driven feedforward control to attenuate large transient lift experienced by an airfoil disturbed by an extreme level of discrete vortex gust. The current analysis uses a nonlinear machine-learning technique to compress the high-dimensional flow dynamics onto a low-dimensional manifold. While the interaction dynamics between the airfoil and extreme vortex gust are parameterized by its size, gust ratio, and position, the wake responses are well-captured on this simple manifold. The effect of extreme vortex disturbance about the undisturbed baseline flows can be extracted in a physically-interpretable manner. Furthermore, we call on phase-amplitude reduction to model and control the complex nonlinear extreme aerodynamic flows. The present phase-amplitude reduction model reveals the sensitivity of the dynamical system in terms of the phase shift and amplitude change induced by external forcing with respect to the baseline periodic orbit. By performing the phase-amplitude analysis for a latent dynamical model identified by sparse regression, the sensitivity functions of low-dimensionalized aerodynamic flows for both phase and amplitude are derived. With the phase and amplitude sensitivity functions, optimal forcing can be determined to quickly suppress the effect of extreme vortex gusts towards the undisturbed states in a low-order space. The present optimal flow modification built upon the machine-learned low-dimensional subspace quickly alleviates the impact of transient vortex gusts for a variety of extreme aerodynamic scenarios, providing a potential foundation for flight of small-scale air vehicles in adverse atmospheric conditions.

physics.flu-dyn↗

arXiv2024

Triglobal resolvent-analysis-based control of separated flows around low-aspect-ratio wings

We perform direct numerical simulations (DNS) of actively controlled laminar separated wakes around low-aspect-ratio wings with two primary goals: (i) reducing the size of the separation bubble and (ii) attenuating the wing tip vortex. Instead of preventing separation, we modify the three-dimensional ($3$-D) dynamics to exploit wake vortices for aerodynamic enhancements. A direct wake modification is considered using optimal harmonic forcing modes from triglobal resolvent analysis. For this study, we consider wings at angles of attack of $14^\circ$ and $22^\circ$, taper ratios $0.27$ and $1$, and leading edge sweep angles of $0^\circ$ and $30^\circ$, at a mean-chord-based Reynolds number of $600$. The wakes behind these wings exhibit $3$-D reversed-flow bubble and large-scale vortical structures. For tapered swept wings, the diversity of wake vortices increases substantially, posing a challenge for flow control. To achieve the first control objective for an untapered unswept wing, root-based actuation at the shedding frequency is introduced to reduce the reversed-flow bubble size by taking advantage of the wake vortices to significantly enhance the aerodynamic performance of the wing. For both untapered and tapered swept wings, root-based actuation modifies the stalled flow, reduces the reversed-flow region, and enhances aerodynamic performance by increasing the root contribution to lift. For the goal of controlling the tip vortex, we demonstrate the effectiveness of actuation with high-frequency perturbations near the tip. This study shows how insights from resolvent analysis for unsteady actuation can enable global modification of $3$-D separated wakes and achieve improved aerodynamics of wings.

physics.flu-dyn↗

arXiv2024

An Invitation to Resolvent Analysis

Resolvent analysis is a powerful tool that can reveal the linear amplification mechanisms between the forcing inputs and the response outputs about a base flow. These mechanisms can be revealed in terms of a pair of forcing and response modes and the associated gains (amplification magnitude) in the order of energy contents at a given frequency. The linear relationship that ties the forcing and the response is represented through the resolvent operator (transfer function), which is constructed through spatially discretizing the linearized Navier-Stokes operator. One of the unique strengths of resolvent analysis is its ability to analyze statistically stationary turbulent flows. In light of the increasing interest in using resolvent analysis to study a variety of flows, we offer this guide in hopes of removing the hurdle for students and researchers to initiate the development of a resolvent analysis code and its applications to their problems of interest. To achieve this goal, we discuss various aspects of resolvent analysis and its role in identifying dominant flow structures about the base flow. The discussion in this paper revolves around the compressible Navier-Stokes equations in the most general manner. We cover essential considerations ranging from selecting the base flow and appropriate energy norms to the intricacies of constructing the linear operator and performing eigenvalue and singular value decompositions. Throughout the paper, we offer details and know-how that may not be available to readers in a collective manner elsewhere. Towards the end of this paper, examples are offered to demonstrate the practical applicability of resolvent analysis, aiming to guide readers through its implementation and inspire further extensions. We invite readers to consider resolvent analysis as a companion for their research endeavors.

physics.flu-dyn↗

arXiv2024

Data-driven nonlinear turbulent flow scaling with Buckingham Pi variables

Nonlinear machine learning for turbulent flows can exhibit robust performance even outside the range of training data. This is achieved when machine-learning models can accommodate scale-invariant characteristics of turbulent flow structures. This study presents a data-driven approach to reveal scale-invariant vortical structures across Reynolds numbers that provide insights for supporting nonlinear machine-learning-based studies of turbulent flows. To uncover conditions for which nonlinear models are likely to perform well, we use a Buckingham Pi-based sparse nonlinear scaling to find the influence of the Pi groups on the turbulent flow data. We consider nonlinear scalings of the invariants of the velocity gradient tensor for an example of three-dimensional decaying isotropic turbulence. The present scaling not only enables the identification of vortical structures that are interpolatory and extrapolatory for the given flow field data but also captures non-equilibrium effects of the energy cascade. As a demonstration, the present findings are applied to machine-learning-based super-resolution analysis of three-dimensional isotropic turbulence. We show that machine-learning models reconstruct vortical structures well in the interpolatory space with reduced performance in the extrapolatory space revealed by the nonlinearly scaled invariants. The present approach enables us to depart from labeling turbulent flow data with a single parameter of Reynolds number and comprehensively examine the flow field to support training and testing of nonlinear machine-learning techniques.

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arXiv2024

Phase autoencoder for limit-cycle oscillators

We present a phase autoencoder that encodes the asymptotic phase of a limit-cycle oscillator, a fundamental quantity characterizing its synchronization dynamics. This autoencoder is trained in such a way that its latent variables directly represent the asymptotic phase of the oscillator. The trained autoencoder can perform two functions without relying on the mathematical model of the oscillator: first, it can evaluate the asymptotic phase and phase sensitivity function of the oscillator; second, it can reconstruct the oscillator state on the limit cycle in the original space from the phase value as an input. Using several examples of limit-cycle oscillators, we demonstrate that the asymptotic phase and phase sensitivity function can be estimated only from time-series data by the trained autoencoder. We also present a simple method for globally synchronizing two oscillators as an application of the trained autoencoder.

nlin.AO↗

arXiv2023

Distributed Control of Partial Differential Equations Using Convolutional Reinforcement Learning

We present a convolutional framework which significantly reduces the complexity and thus, the computational effort for distributed reinforcement learning control of dynamical systems governed by partial differential equations (PDEs). Exploiting translational invariances, the high-dimensional distributed control problem can be transformed into a multi-agent control problem with many identical, uncoupled agents. Furthermore, using the fact that information is transported with finite velocity in many cases, the dimension of the agents' environment can be drastically reduced using a convolution operation over the state space of the PDE. In this setting, the complexity can be flexibly adjusted via the kernel width or by using a stride greater than one. Moreover, scaling from smaller to larger systems -- or the transfer between different domains -- becomes a straightforward task requiring little effort. We demonstrate the performance of the proposed framework using several PDE examples with increasing complexity, where stabilization is achieved by training a low-dimensional deep deterministic policy gradient agent using minimal computing resources.

cs.LG↗

arXiv2023

Optimal waveform for fast synchronization of airfoil wakes

We obtain an optimal actuation waveform for fast synchronization of periodic airfoil wakes through the phase reduction approach. Using the phase reduction approach for periodic wake flows, the spatial sensitivity fields with respect to the phase of the vortex shedding are obtained. The phase sensitivity fields can uncover the synchronization properties in the presence of periodic actuation. This study seeks a periodic actuation waveform using phase-based analysis to minimize the time for synchronization to modify the wake-shedding frequency of NACA0012 airfoil wakes. This fast synchronization waveform is obtained theoretically from the phase sensitivity function by casting an optimization problem. The obtained optimal actuation waveform becomes increasingly non-sinusoidal for higher angles of attack. Actuation based on the obtained waveform achieves rapid synchronization within as low as two vortex shedding cycles irrespective of the forcing frequency whereas traditional sinusoidal actuation requires O(10) shedding cycles. Further, we analyze the influence of actuation frequency on the vortex shedding and the aerodynamic coefficients using force-element analysis. The present analysis provides an efficient way to modify the vortex lock-on properties in a transient manner with applications to fluid-structure interactions and unsteady flow control.

physics.flu-dyn↗

arXiv2023

Laminar post-stall wakes of tapered swept wings

While tapered swept wings are widely used, the influence of taper on their post-stall wake characteristics remains largely unexplored. To address this issue, we conduct an extensive study using direct numerical simulations to characterize the wing taper and sweep effects on laminar separated wakes. We analyze flows behind NACA 0015 cross-sectional profile wings at post-stall angles of attack $α=14^\circ$--$22^\circ$ with taper ratios $λ=0.27$--$1$, leading edge sweep angles $0^\circ$--$50^\circ$, and semi aspect ratios $sAR =1$ and $2$ at a mean-chord-based Reynolds number of $600$. Tapered wings have smaller tip chord length, which generates a weaker tip vortex, and attenuates inboard downwash. This results in the development of unsteadiness over a large portion of the wingspan at high angles of attack. For tapered wings with backward-swept leading edges unsteadiness emerges near the wing tip. On the other hand, wings with forward-swept trailing edges are shown to concentrate wake shedding structures near the wing root. For highly swept untapered wings, the wake is steady, while unsteady shedding vortices appear near the tip for tapered wings with high leading edge sweep angles. For such wings, larger wake oscillations emerge near the root as the taper ratio decreases. While the combination of taper and sweep increases flow unsteadiness, we find that tapered swept wings have more enhanced aerodynamic performance than untapered and unswept wings, exhibiting higher time-averaged lift and lift-to-drag ratio. The current findings shed light on the fundamental aspects of flow separation over tapered wings in the absence of turbulent flow effects.

physics.flu-dyn↗

arXiv2023

Grasping Extreme Aerodynamics on a Low-Dimensional Manifold

Modern air vehicles perform a wide range of operations, including transportation, defense, surveillance, and rescue. These aircraft can fly in calm conditions but avoid operations in gusty environments, encountered in urban canyons, over mountainous terrains, and in ship wakes. With extreme weather becoming ever more frequent due to global warming, it is anticipated that aircraft, especially those that are smaller in size, will encounter sizeable atmospheric disturbances and still be expected to achieve stable flight. However, there exists virtually no theoretical fluid-dynamic foundation to describe the influence of extreme vortical gusts on wings. To compound this difficulty, there is a large parameter space for gust-wing interactions. While such interactions are seemingly complex and different for each combination of gust parameters, we show that the fundamental physics behind extreme aerodynamics is far simpler and lower-rank than traditionally expected. We reveal that the nonlinear vortical flow field over time and parameter space can be compressed to only three variables with a lift-augmented autoencoder while holding the essence of the original high-dimensional physics. Extreme aerodynamic flows can be compressed through machine learning into a low-dimensional manifold, which can enable real-time sparse reconstruction, dynamical modeling, and control of extremely unsteady gusty flows. The present findings offer support for the stable flight of next-generation small air vehicles in atmosphere conditions traditionally considered unflyable.

physics.flu-dyn↗

arXiv2023

Similarities in Massive Separation Across Reynolds Numbers for Swept and Tapered Finite Span Wings

Experimental investigations were performed to elucidate the features of flow fields occurring over cantilevered finite-aspect ratio NACA 0015 wings at high angles of attack with various sweep angles and taper ratios. Volumetric Stereoscopic Particle Image Velocimetry experiments were performed at mean chord based Reynolds number of 247,500 in a wind tunnel and 600 in a water tunnel. Direct Numerical Simulations (DNS) of the water tunnel test section, including the cantilevered model, were also performed at the lower Reynolds number. The low Reynolds number experiments, low Reynolds number simulations, and high Reynolds number experiments all showed that sweeping the leading edge back shifted the largest portion of the reversed flow towards the wingtip while sweeping the trailing edge forward shifted the reversed flow towards the wing root. A detailed parametric sweep of planform geometry systematically varied the leading and trailing edge sweep angles and taper ratios of the finite wings. It was found that the large scale vortical structures resulting from varying these parameters at the two Reynolds numbers share surprisingly many three-dimensional topological features, despite the orders of magnitude different Reynolds numbers.

physics.flu-dyn↗

arXiv2023

A cyclic perspective on transient gust encounters through the lens of persistent homology

Large amplitude gust encounters exhibit a range of separated flow phenomena, making them difficult to characterize using the traditional tools of aerodynamics. In this work, we propose a dynamical systems approach to gust encounters, viewing the flow as a cycle (or a closed trajectory) in state space. We posit that the topology of this cycle, or its shape and structure, provides a compact description of the flow, and can be used to identify coordinates in which the dynamics evolve in a simple, intuitive way. To demonstrate this idea, we consider flowfield measurements of a transverse gust encounter. For each case in the dataset, we characterize the full-state dynamics of the flow using persistent homology, a tool that identifies holes in point cloud data, and transform the dynamics to a reduced-order space using a nonlinear autoencoder. Critically, we constrain the autoencoder such that it preserves topologically relevant features of the original dynamics, or those features identified by persistent homology. Using this approach, we are able to transform six separate gust encounters to a three-dimensional latent space, in which each gust encounter reduces to a simple circle, and from which the original flow can be reconstructed. This result shows that topology can guide the creation of low-dimensional state representations for strong transverse gust encounters, a crucial step toward the modeling and control of airfoil-gust interactions.

physics.flu-dyn↗

arXiv2023

Super-Resolution Analysis via Machine Learning: A Survey for Fluid Flows

This paper surveys machine-learning-based super-resolution reconstruction for vortical flows. Super resolution aims to find the high-resolution flow fields from low-resolution data and is generally an approach used in image reconstruction. In addition to surveying a variety of recent super-resolution applications, we provide case studies of super-resolution analysis for an example of two-dimensional decaying isotropic turbulence. We demonstrate that physics-inspired model designs enable successful reconstruction of vortical flows from spatially limited measurements. We also discuss the challenges and outlooks of machine-learning-based super-resolution analysis for fluid flow applications. The insights gained from this study can be leveraged for super-resolution analysis of numerical and experimental flow data.

physics.flu-dyn↗

arXiv2023

Sparse sensor reconstruction of vortex-impinged airfoil wake with machine learning

Reconstruction of unsteady vortical flow fields from limited sensor measurements is challenging. We develop machine learning methods to reconstruct flow features from sparse sensor measurements during transient vortex-airfoil wake interaction using only a limited amount of training data. The present machine learning models accurately reconstruct the aerodynamic force coefficients, pressure distributions over airfoil surface, and two-dimensional vorticity field for a variety of untrained cases. Multi-layer perceptron is used for estimating aerodynamic forces and pressure profiles over the surface, establishing a nonlinear model between the pressure sensor measurements and the output variables. A combination of multi-layer perceptron with convolutional neural network is utilized to reconstruct the vortical wake. Furthermore, the use of transfer learning and long short-term memory algorithm combined in the training models greatly improves the reconstruction of transient wakes by embedding the dynamics. The present machine-learning methods are able to estimate the transient flow features while exhibiting robustness against noisy sensor measurements. Finally, appropriate sensor locations over different time periods are assessed for accurately estimating the wakes. The present study offers insights into the dynamics of vortex-airfoil interaction and the development of data-driven flow estimation.

physics.flu-dyn↗

arXiv2023

Image and video compression of fluid flow data

We study the compression of spatial and temporal features in fluid flow data using multimedia compression techniques. The efficacy of spatial compression techniques, including JPEG and JPEG2000 (JP2), and spatio-temporal video compression techniques, namely H.264, H.265, and AV1, in limiting the introduction of compression artifacts and preserving underlying flow physics are considered for laminar periodic wake around a cylinder, two-dimensional turbulence, and turbulent channel flow. These compression techniques significantly compress flow data while maintaining dominant flow features with negligible error. AV1 and H.265 compressions present the best performance across a variety of canonical flow regimes and outperform traditional techniques such as proper orthogonal decomposition in some cases. These image and video compression algorithms are flexible, scalable, and generalizable holding potential for a wide range of applications in fluid dynamics in the context of data storage and transfer.

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