arXiv subjects

Kunihiko Taira

Publications and source records attributed to Kunihiko Taira.

At least 55 records · Page 3Linked to original sources

arXiv2022

Triglobal resolvent analysis of swept-wing wakes

Through triglobal resolvent analysis, we reveal the effects of wing tip and sweep angle on laminar separated wakes over swept wings. For the present study, we consider wings with semi-aspect ratios from $1$ to $4$, sweep angles from $0^\circ$ to $45^\circ$, and angles of attack of $20^\circ$ and $30^\circ$ at a chord-based Reynolds number of $400$ and a Mach number of $0.1$. Using direct numerical simulations, we observe that unswept wings develop vortex shedding near the wing root with a quasi-steady tip vortex. For swept wings, vortex shedding is seen near the wing tip for low sweep angles, while the wakes are steady for wings with high sweep angles. To gain further insights into the mechanisms of flow unsteadiness, triglobal resolvent analysis is used to identify the optimal spatial input-output mode pairs and the associated gains over a range of frequencies. The three-dimensional forcing and response modes reveal that harmonic fluctuations are directed towards the root for unswept wings and towards the wing tip for swept wings. The overlapping region of the forcing-response mode pairs uncovers triglobal resolvent wavemakers associated with self-sustained unsteady wakes of swept wings. Furthermore, we show that for low aspect ratio wings optimal perturbations develop globally over the entire wingspan. The present study uncovers physical insights on the effects of tip and sweep on the growth of optimal harmonic perturbations and the wake dynamics of separated flows over swept wings.

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arXiv2022

A Database for Reduced-Complexity Modeling of Fluid Flows

We present a publicly accessible database designed to aid in the conception, training, demonstration, evaluation, and comparison of reduced-complexity models for fluid mechanics. Availability of high-quality flow data is essential for all of these aspects of model development for both data-driven and physics-based methods. The database contains time-resolved data for six distinct datasets: a large eddy simulation of a turbulent jet, direct numerical simulations of a zero-pressure-gradient turbulent boundary layer, particle-image-velocimetry measurements for the same boundary layer at several Reynolds numbers, direct numerical simulations of laminar stationary and pitching flat-plate airfoils, particle-image-velocimetry and force measurements of an airfoil encountering a gust, and a large eddy simulation of the separated, turbulent flow over an airfoil. These six cases span several key flow categories: laminar and turbulent, statistically stationary and transient, tonal and broadband spectral content, canonical and application-oriented, wall-bounded and free-shear flow, and simulation and experimental measurements. For each dataset, we describe the flow setup and computational/experimental methods, catalog the data available in the database, and provide examples of how these data can be used for reduced-complexity modeling. All data can be downloaded using a browser interface or Globus. Our vision is that the common testbed provided by this database will aid the fluid mechanics community in clarifying the distinct capabilities of new and existing methods.

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arXiv2022

Wing sweep effects on laminar separated flows

We reveal the effects of sweep on the wake dynamics around NACA 0015 wings at high angles of attack using direct numerical simulations and resolvent analysis. The influence of sweep on the wake dynamics is considered for sweep angles from $0^\circ$ to $45^\circ$ and angles of attack from $16^\circ$ to $30^\circ$ for a spanwise periodic wing at a chord-based Reynolds number of $400$ and a Mach number of $0.1$. Wing sweep affects the wake dynamics, especially in terms of stability and spanwise fluctuations with implications on the development of three-dimensional wakes. We observe that wing sweep attenuates spanwise fluctuations. Even as the sweep angle influences the wake, force and pressure coefficients can be collapsed for low angles of attack when examined in wall-normal and wingspan-normal independent flow components. Some small deviations at high sweep and incidence angles are attributed to vortical wake structures that impose secondary aerodynamic loads, revealed through the force element analysis. Furthermore, we conduct global resolvent analysis to uncover oblique modes with high disturbance amplification. The resolvent analysis also reveals the presence of wavemakers in the shear-dominated region associated with the emergence of three-dimensional wakes at high angles of attack. For flows at high sweep angles, the optimal convection speed of the response modes is shown to be faster than the optimal wavemakers speed suggesting a mechanism for the attenuation of perturbations. The present findings serve as a fundamental stepping stone to understanding separated flows at higher Reynolds numbers.

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arXiv2022

Adjoint-based phase reduction analysis of incompressible periodic flows

We establish the theoretical framework for adjoint-based phase reduction analysis for incompressible periodic flows. Through this adjoint-based method, we obtain spatiotemporal phase sensitivity fields through a single pair of forward and backward direct numerical simulations, as opposed to the impulse-based method that requires a very large number of simulations. Phase-based analysis involves perturbation analysis about a periodically varying base state and hence is tailored for the analysis of periodic flows. We formulate the phase description of periodic flows with respect to the potential and vortical perturbations in the flow field. The current phase-reduction analysis can also be implemented consistently in the immersed boundary projection method, which facilitates the analysis over arbitrarily-shaped bodies. We demonstrate the strength of the phase-based analysis for periodic flows over circular cylinder and symmetric airfoils at high incidence angles. The critical regions for phase modification in the cylinder flow are investigated and the locations of flow separation are shown to be the most sensitive regions. Further, the results reveal the influence of the angle of attack and airfoil thickness on the phase-sensitivity distribution of flows over various airfoils. The phase for such flows is defined based on the lift coefficient, and hence is influenced by the vortical structures responsible for lift production. The present framework sheds light on the connection between phase-sensitivity and vortex formation dynamics.

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arXiv2022

Transition, intermittency and phase interference effects in airfoil secondary tones and acoustic feedback loop

A large eddy simulation is performed to study secondary tones generated by a NACA0012 airfoil at angle of attack of $α= 3^{\circ}$ with freestream Mach number of $M_{\infty} = 0.3$ and Reynolds number of $Re = 5 \times 10^4$. Laminar separation bubbles are observed over the suction side and near the trailing edge, on the pressure side. Flow visualization and spectral analysis are employed to investigate vortex shedding aft of the suction side separation bubble. Vortex interaction results in merging or bursting such that coherent structures or turbulent packets are advected towards the trailing edge leading to different levels of noise emission. Despite the intermittent occurrence of laminar-turbulent transition, the noise spectrum depicts a main tone with multiple equidistant secondary tones. To understand the role of flow instabilities on the tones, the linearized Navier-Stokes equations are examined in its operator form through bi-global stability and resolvent analyses, and by time evolution of disturbances using a matrix-free method. These linear global analyses reveal amplification of disturbances over the suction side separation bubble. Non-normality of the linear operator leads to further transient amplification due to modal interaction among eigenvectors. Two-point, one time autocovariance calculations of pressure along the spanwise direction elucidate aspects of the acoustic feedback loop mechanism in the non-linear solutions. This feedback process is self-sustained by acoustic waves radiated from the trailing edge, which reach the most sensitive flow location between the leading edge and the separation bubble, as identified by the resolvent analysis. Leading edge disturbances arising from secondary diffraction and phase interference among the most unstable frequencies computed in the eigenspectrum are also shown to have an important role in the feedback loop.

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arXiv2021

Network-based analysis of fluid flows: Progress and outlook

The network of interactions among fluid elements and coherent structures gives rise to the incredibly rich dynamics of vortical flows. These interactions can be described with the use of mathematical tools from the emerging field of network science, which leverages graph theory, dynamical systems theory, data science, and control theory. The blending of network science and fluid mechanics facilitates the extraction of the key interactions and communities in terms of vortical elements, modal structures, and particle trajectories. Phase-space techniques and time-delay embedding enable network-based analysis in terms of visibility, recurrence, and cluster transitions leveraging available time-series measurements. Equipped with the knowledge of interactions and communities, the network-theoretic approach enables the analysis, modeling, and control of fluid flows, with a particular emphasis on interactive dynamics. In this article, we provide a brief introduction to network science and an overview of the progress on network-based strategies to study the complex dynamics of fluid flows. Case studies are surveyed to highlight the utility of network-based techniques to tackle a range of problems from fluid mechanics. Towards the end of the paper, we offer an outlook on network-inspired approaches.

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arXiv2021

Laminar vortex dynamics around forward-swept wings

Forward-swept wings offer unique advantages in the aerodynamic performance of air vehicles. However, the low-Reynolds-number characteristics of such wings have not been explored in the past. In this work, we numerically study laminar separated flows over forward-swept wings with semi aspect ratios $sAR=0.5$ to 2 at a chord-based Reynolds number of 400. Forward-swept wings generate wakes that are significantly different from those of backward-swept wings. For low-aspect-ratio forward wings, the wakes remain steady due to the strong downwash effects induced by the tip vortices. For larger aspect ratio, the downwash effects weaken over the inboard regions of the wing, allowing unsteady vortex shedding to occur. Further larger aspect ratio allows for the formation of streamwise vortices for highly-swept wings, stabilizing the flow. Forward-swept wings can generate enhanced lift at high angles of attack than the unswept and backward-swept wings, with the cost of high drag. We show through force element analysis that the increased lift of forward-swept wings is attributed to the vortical structure that is maintained by the tip-vortex-induced downwash over the outboard region of wing span. The current findings offer a detailed understanding of the sweep effects on laminar separated flows over forward-swept wings, and invite innovative designs of high-lift devices.

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arXiv2021

Global field reconstruction from sparse sensors with Voronoi tessellation-assisted deep learning

Achieving accurate and robust global situational awareness of a complex time-evolving field from a limited number of sensors has been a longstanding challenge. This reconstruction problem is especially difficult when sensors are sparsely positioned in a seemingly random or unorganized manner, which is often encountered in a range of scientific and engineering problems. Moreover, these sensors can be in motion and can become online or offline over time. The key leverage in addressing this scientific issue is the wealth of data accumulated from the sensors. As a solution to this problem, we propose a data-driven spatial field recovery technique founded on a structured grid-based deep-learning approach for arbitrary positioned sensors of any numbers. It should be noted that the naïve use of machine learning becomes prohibitively expensive for global field reconstruction and is furthermore not adaptable to an arbitrary number of sensors. In the present work, we consider the use of Voronoi tessellation to obtain a structured-grid representation from sensor locations enabling the computationally tractable use of convolutional neural networks. One of the central features of the present method is its compatibility with deep-learning based super-resolution reconstruction techniques for structured sensor data that are established for image processing. The proposed reconstruction technique is demonstrated for unsteady wake flow, geophysical data, and three-dimensional turbulence. The current framework is able to handle an arbitrary number of moving sensors, and thereby overcomes a major limitation with existing reconstruction methods. The presented technique opens a new pathway towards the practical use of neural networks for real-time global field estimation.

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arXiv2021

Resolvent analysis on the origin of two-dimensional transonic buffet

Resolvent analysis is performed to identify the origin of two-dimensional transonic buffet over an airfoil. The base flow for the resolvent analysis is the time-averaged flow over a NACA 0012 airfoil at a chord-based Reynolds number of 2000 and a free-stream Mach number of 0.85. We reveal that the mechanism of buffet is buried underneath the global low-Reynolds-number flow physics. At this low Reynolds number, the dominant flow feature is the von Karman shedding. However, we show that with the appropriate forcing input, buffet can appear even at a Reynolds number that is much lower than what is traditionally associated with transonic buffet. The source of buffet is identified to be at the shock foot from the windowed resolvent analysis, which is validated by companion simulations using sustained forcing inputs based on resolvent modes. We also comment on the role of perturbations in the vicinity of the trailing edge. The present study not only provides insights on the origin of buffet but also serves a building block for low-Reynolds-number compressible aerodynamics in light of the growing interests in Martian flights.

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arXiv2021

Linear modal instabilities around post-stall swept finite-aspect ratio wings at low Reynolds numbers

Linear modal instabilities of flow over finite-span untapered wings have been investigated numerically at Reynolds number 400, at a range of angles of attack and sweep on two wings having aspect ratios 4 and 8. Base flows have been generated by direct numerical simulation, marching the unsteady incompressible three-dimensional Navier-Stokes equations to a steady state, or using selective frequency damping to obtain stationary linearly unstable flows. Unstable three-dimensional linear global modes of swept wings have been identified for the first time using spectral-element time-stepping solvers. The effect of the wing geometry and flow parameters on these modes has been examined in detail. An increase of the angle of attack was found to destabilize the flow, while an increase of the sweep angle had the opposite effect. On unswept wings, TriGlobal analysis revealed that the most unstable global mode peaks in the midspan region of the wake; the peak of the mode structure moves towards the tip as sweep is increased. Data-driven analysis was then employed to study the effects of wing geometry and flow conditions on the nonlinear wake. On unswept wings, the dominant mode at low angles of attack is a Kelvin-Helmholtz-like instability, qualitatively analogous with global modes of infinite-span wings under same conditions. At higher angles of attack and moderate sweep angles, the dominant mode is a structure denominated the interaction mode. At high sweep angles, this mode evolves into elongated streamwise vortices on higher aspect ratio wings, while on shorter wings it becomes indistinguishable from tip-vortex instability.

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arXiv2020

Probabilistic neural network-based reduced-order surrogate for fluid flows

In recent years, there have been a surge in applications of neural networks (NNs) in physical sciences. Although various algorithmic advances have been proposed, there are, thus far, limited number of studies that assess the interpretability of neural networks. This has contributed to the hasty characterization of most NN methods as "black boxes" and hindering wider acceptance of more powerful machine learning algorithms for physics. In an effort to address such issues in fluid flow modeling, we use a probabilistic neural network (PNN) that provide confidence intervals for its predictions in a computationally effective manner. The model is first assessed considering the estimation of proper orthogonal decomposition (POD) coefficients from local sensor measurements of solution of the shallow water equation. We find that the present model outperforms a well-known linear method with regard to estimation. This model is then applied to the estimation of the temporal evolution of POD coefficients with considering the wake of a NACA0012 airfoil with a Gurney flap and the NOAA sea surface temperature. The present model can accurately estimate the POD coefficients over time in addition to providing confidence intervals thereby quantifying the uncertainty in the output given a particular training data set.

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arXiv2020

Aerodynamic characterization of low-aspect-ratio swept wings at $Re=400$

We perform unsteady three-dimensional direct numerical simulations to study the aerodynamic characteristics of finite-aspect-ratio swept wings with a NACA 0015 cross-section at a chord-based Reynolds number of 400. The effects of the sweep angle ($Λ=0^{\circ}-45^{\circ}$) on the aerodynamic force coefficients are examined for finite-aspect-ratio wings ($sAR=0.5$, 1, and 2) over a wide range of angles of attack ($α=0^{\circ}-30^{\circ}$). The unsteady laminar separated flows exhibit complex aerodynamic characteristics with respect to these parameters. The introduction of sweep enhances lift for wings with low aspect ratios of $sAR=0.5$ and 1, due to the lift generated by the vortical structures near the midspan. For these cases, the dependence of drag coefficients on the sweep angle is less noticeable, particularly at lower angles of attack. The lift-to-drag ratios for low-aspect-ratio wings increase with the sweep angle. However, such favorable effects of sweep angle on the lift coefficients and lift-to-drag ratios are not observed for wings with higher aspect ratios, where the midspan effects are relatively weaker over the wing span. The results herein provide a laminar aerodynamic characterization of the low-aspect-ratio wings and complement the unsteady low-Reynolds-number aerodynamic database with highlight on the effect of sweep.

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arXiv2020

Phase-locking of laminar wake to periodic vibrations of a circular cylinder

Phase synchronization between the vortex shedding behind a two-dimensional circular cylinder and its vibrations is investigated using the phase-reduction analysis. Leveraging this approach enables the development of a one-dimensional, linear model with respect to the limit-cycle attractor of the laminar wake, which accurately describes the phase dynamics of the high-dimensional, nonlinear fluid flow and its response to rotational, transverse and longitudinal vibrations of the cylinder. This phase-based model is derived by assessing the phase-response and sensitivity of the wake dynamics to impulse perturbations of the cylinder, which can be performed in simulations and experiments. The resulting model in turn yields the theoretical conditions required for phase-locking between the cylinder vibrations and the wake. We furthermore show that this synchronization mechanism can be employed to stabilize the wake and subsequently reduce drag. We also uncover the circumstances under which the concurrent occurrence of different vibrational motions can be used to promote or impede synchronization. These findings provide valuable insights for the study of vortex-induced body oscillations, the enhancement of aerodynamic performance of flyers, or the mitigation of structural vibrations by synchronizing or desynchronizing the oscillatory motions of body to the periodic wake.

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arXiv2020

Network broadcast analysis and control of turbulent flows

We present a network-based modal analysis technique that identifies key dynamical paths along which perturbations amplify over a time-varying base flow. This analysis is built upon the Katz centrality, which reveals the flow structures that can effectively spread perturbations over a time-evolving network of vortical interactions on the base flow. Motivated by the resolvent form of the Katz function, we take the singular value decomposition of the resulting communicability matrix, complementing the resolvent analysis for fluid flows. The right-singular vectors, referred to as the broadcast modes, give insights into the sensitive regions where introduced perturbations can be effectively spread and amplified over the entire fluid-flow network that evolves in time. We apply this analysis to a two-dimensional decaying isotropic turbulence. The broadcast mode reveals that vortex dipoles are important structures in spreading perturbations. By perturbing the flow with the principal broadcast mode, we demonstrate the utility of the insights gained from the present analysis to effectively modify the evolution of turbulent flows. The current network-inspired work presents a novel use of network analysis to guide flow control efforts, in particular for time-varying base flows.

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arXiv2020

Machine learning based spatio-temporal super resolution reconstruction of turbulent flows

We present a new turbulent data reconstruction method with supervised machine learning techniques inspired by super resolution and inbetweening, which can recover high-resolution turbulent flows from grossly coarse flow data in space and time. For the present machine learning based data reconstruction, we use the downsampled skip-connection/multi-scale model based on a convolutional neural network to incorporate the multi-scale nature of fluid flows into its network structure. As an initial example, the model is applied to a two-dimensional cylinder wake at $Re_D$ = 100. The reconstructed flow fields by the proposed method show great agreement with the reference data obtained by direct numerical simulation. Next, we examine the capability of the proposed model for a two-dimensional decaying homogeneous isotropic turbulence. The machine-learned models can follow the decaying evolution from coarse input data in space and time, according to the assessment with the turbulence statistics. The proposed concept is further investigated for a complex turbulent channel flow over a three-dimensional domain at $Re_τ$ =180. The present model can reconstruct high-resolved turbulent flows from very coarse input data in space, and it can also reproduce the temporal evolution when the time interval is appropriately chosen. The dependence on the amount of training snapshots and duration between the first and last frames based on a temporal two-point correlation coefficient are also assessed to reveal the capability and robustness of spatio-temporal super resolution reconstruction. These results suggest that the present method can meet a range of flow reconstructions for supporting computational and experimental efforts.

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arXiv2020

Probabilistic neural networks for fluid flow surrogate modeling and data recovery

We consider the use of probabilistic neural networks for fluid flow {surrogate modeling} and data recovery. This framework is constructed by assuming that the target variables are sampled from a Gaussian distribution conditioned on the inputs. Consequently, the overall formulation sets up a procedure to predict the hyperparameters of this distribution which are then used to compute an objective function given training data. We demonstrate that this framework has the ability to provide for prediction confidence intervals based on the assumption of a probabilistic posterior, given an appropriate model architecture and adequate training data. The applicability of the present framework to cases with noisy measurements and limited observations is also assessed. To demonstrate the capabilities of this framework, we consider canonical regression problems of fluid dynamics from the viewpoint of reduced-order modeling and spatial data recovery for four canonical data sets. The examples considered in this study arise from (1) the shallow water equations, (2) a two-dimensional cylinder flow, (3) the wake of NACA0012 airfoil with a Gurney flap, and (4) the NOAA sea surface temperature data set. The present results indicate that the probabilistic neural network not only produces a machine-learning-based fluid flow {surrogate} model but also systematically quantifies the uncertainty therein to assist with model interpretability.

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arXiv2020

Phase-synchronization properties of laminar cylinder wake for periodic external forcings

We investigate the synchronization properties of the two-dimensional periodic flow over a circular cylinder using the principles of phase-reduction theory. The influence of harmonic external forcings on the wake dynamics, and the possible synchronization of the vortex shedding behind the cylinder to these forcings, is determined by evaluating the phase response of the system to weak impulse perturbations. These horizontal and vertical perturbations are added at different phase values over a period, in order to develop a linear one-dimensional model with respect to the limit cycle that describes the high-dimensional and nonlinear dynamics of the fluid flow via only a single scalar phase variable. This model is then utilized to acquire the theoretical conditions for the synchronization between the cylinder wake and the harmonic forcings added in the global near-wake region. Valuable insights are gained by comparing the findings of the present research against those rendered by the dynamic mode decomposition and adjoint analysis of the wake dynamics in earlier works. The present analysis reveals regions in the flow which enable phase synchronization or desynchronization to periodic excitations for applications such as active flow control and fluid-structure interactions.

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arXiv2020

Resolvent analysis of an airfoil laminar separation bubble at Re = 500,000

We perform resolvent analysis to examine the perturbation dynamics over the laminar separation bubble (LSB) that forms near the leading edge of a NACA 0012 airfoil at a chord-based Reynolds number of 500,000 and an angle of attack of 8 degrees. Randomized SVD is adopted in the present analysis to relieve the computational cost associated with the high-Re global base flow. To examine the local physics over the LSB, we consider the use of exponential discounting to limit the time horizon that allows for the instability to develop with respect to the base flow. With discounting, the gain distribution over frequency accurately captures the spectral content over the LSB obtained from flow simulation. The peak-gain frequency also agrees with previous flow control results on suppressing dynamic stall over a pitching airfoil. According to the gain distribution and the modal structures, we conclude that the dominant energy-amplification mechanism is the Kelvin-Helmholtz instability. In addition to discounting, we also examine the use of spatial windows for both the forcing and response. From the response-windowed analysis, we find that the LSB serves the main role of energy amplifier, with the amplification saturating at the reattachment point. The input window imposes the constraint of surface forcing, and the results show that the optimal actuator location is slightly upstream of the separation point. The surface-forcing mode also suggest the optimal momentum forcing in the surface-tangent direction, with strong uni-directionality that is ideal for synthetic-jet-type actuators. This study demonstrates the strength of randomized resolvent analysis in tackling high-Reynolds-number base flows and calls attention to the care needed for base-flow instabilities.

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