arXiv subjects

Kunihiko Taira

Publications and source records attributed to Kunihiko Taira.

At least 73 records · Page 4Linked to original sources

arXiv2020

Identifying vortical network connectors for turbulent flow modification

We introduce a network (graph) theoretic community-based framework to extract vortical structures that serve the role of connectors for the vortical interactions in two- and three-dimensional isotropic turbulence. The present framework represents the vortical interactions on a network, where the vortical elements are viewed as the nodes and the vortical interactions are regarded as edges weighted by induced velocity. We identify closely interacting vortical elements as vortical network communities through community detection algorithms. We show that the inter- and intra-community interactions can be used to decompose the governing equation for the evolution of network nodes. These community-based interactions are used to identify the communities which have the strongest and weakest interactions amongst them. These vortical communities are referred to as connector and peripheral communities, respectively. We demonstrate the influence of the network-based structures to modify the dynamics of a collection of discrete point vortices. Taking advantage of the strong inter-community interactions, connector community can significantly modify the collective dynamics of vortices through the application of multiple impulse perturbations. We then apply the community-based framework to extract influential structures in isotropic turbulence. The connector and peripheral communities extracted from turbulent flows resemble shear-layer and vortex-core like structures, respectively. The influence of the connector structures on the flow field and their neighboring vortical structures is analyzed by adding impulse perturbations to the connectors in direct numerical simulations. The findings are compared with the cases of perturbing the strongest vortex tube and shear-layer regions. We find that perturbing the connector structures enhances local turbulent mixing beyond what are achieved by the other cases.

physics.flu-dyn↗

arXiv2020

Laminar separated flows over finite-aspect-ratio swept wings

We perform direct numerical simulations of laminar separated flows over finite-aspect-ratio swept wings at a chord-base Reynolds number of $Re = 400$ to reveal a variety of wake structures generated for a range of aspect ratios ($sAR=0.5-4$), angles of attack ($α=16^{\circ}-30^{\circ}$), and sweep angles ($Λ=0^{\circ}-45^{\circ}$). Flows behind swept wings exhibit increased complexity in their dynamical features compared to unswept-wing wakes. For unswept wings, the wake dynamics are predominantly influenced by the tip effects. Steady wakes are mainly limited to low-aspect-ratio wings. Unsteady vortex shedding takes place near the midspan of higher-$AR$ wings due to weakened downwash induced by the tip vortices. With increasing sweep angle, the source of three dimensionality transitions from the tip to the midspan. A pair of symmetric vortical structures forms along the two sides of the midspan, imposing downward velocity upon each other in a manner similar to the downwash induced by tip vortices. Such stabilizing midspan effects not only expand the steady wake region to higher aspect ratios, but also enhance lift. At higher aspect ratios, the midspan effects of swept wings diminish at outboard region, allowing unsteady vortex shedding to develop near the tip. In the wakes of highly swept wings, streamwise finger-like structures form repetitively along the wing span, providing a stabilizing effect. The insights revealed from this study can aid the design of high-lift devices and serve as a stepping stone for understanding the complex wake dynamics at higher Reynolds numbers and those generated by unsteady wing maneuvers.

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arXiv2020

Phase-based control of periodic fluid flows

Fluid flows play a central role in scientific and technological development, and many of these flows are characterized by a dominant oscillation, such as the vortex shedding in the wake of nearly all transportation vehicles. The ability to control vortex shedding is critical to improve the aerodynamic performance of these unsteady fluid flow systems. This goal requires precise characterization of how perturbations affect the long-time phase of the oscillatory flow, as well as the ability to control transient behaviors. In this work, we develop an energy-efficient flow control strategy to rapidly alter the oscillation phase of time-periodic fluid flows, leveraging theory developed for periodic biological systems. First, we perform a phase-sensitivity analysis to construct a reduced-order model for the response of the flow oscillation to impulsive control inputs at various phases. Next, we introduce two control strategies for real-time phase control based on the phase-sensitivity function: 1) optimal phase control, obtained by solving the Euler-Lagrange equations as a two-point boundary value problem, and 2) model-predictive control (MPC). Our approach is demonstrated for two unsteady flow systems, the incompressible laminar flow past a circular cylinder and the flow past an airfoil. We show that effective phase control may be achieved with several actuation strategies, including blowing and rotary control. Moreover, our control approach uses realistic measurements of the lift force on the body, rather than requiring high-dimensional measurements of the full flow field.

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arXiv2020

Unsteady control of supersonic turbulent cavity flow based on resolvent analysis

We use resolvent analysis to determine an unsteady active control setup to attenuate pressure fluctuations in turbulent supersonic flow over a rectangular cavity with a length-to-depth ratio of 6 at a Mach number of 1.4 and a Reynolds number based on cavity depth of 10,000. Large-eddy simulations (LES) and dynamic modal decomposition (DMD) of the supersonic cavity flow reveal the dominance of two-dimensional Rossiter modes II and IV. These predominantly two-dimensional vortical structures generate high-amplitude unsteadiness over the cavity through trailing-edge impingement and create oblique shock waves by obstructing the freestream. To disrupt the undesired formation of vortical structures, we introduce three-dimensional unsteady forcing along the cavity leading edge to generate streamwise vortical structures. Resolvent analysis with respect to the time-averaged base flow is leveraged to determine the optimal combination of forcing frequency and spanwise wavenumber. Instead of selecting the most amplified resolvent forcing modes, we seek the combination of control parameters that yields sustained amplification of the primary resolvent-based kinetic energy distribution over the entire length of the cavity. The sustained amplification is critical to ensure that the selected forcing input remains effective to prevent the formation of the large spanwise vortices. This resolvent-analysis-based flow control guideline is validated with a number of companion LES of the controlled cavity flows. The optimal control setup is verified to be the most effective in reducing the pressure root-mean-square level up to 52% along the aft and bottom cavity walls compared to the baseline cavity flow. The present flow control guideline derived from resolvent analysis should be applicable to flows that require the actuation input to remain effective over an extended region of interest.

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arXiv2020

Active flow control of a pump-induced wall-normal vortex with steady blowing

The emergence of a submerged vortex upstream of a pump can reduce pump intake efficiency and cause structural damage. In this study, we consider the use of active flow control with steady blowing to increase the pressure distribution within a single-phase pump-induced wall-normal vortex model, which is based on the Burgers vortex with a no-slip boundary condition prescribed along its symmetry plane. The goal of our control is to modify the vortex core velocity profile. These changes are sought to increase the core pressure such that detrimental effects on the pump are alleviated. Three-dimensional direct numerical simulations (DNS) are performed to examine the dynamics of the vortex with the application of axial momentum injection at and around the root of the vortex. We find that the active flow control approach can effectively modify the wall-normal vortical structure and significantly increase the low-core pressure by up to 81% compared to that of the uncontrolled case. The result shows that the control setup is also effective when it is introduced in an off-centered manner. Compared to the unsteady blowing and suction based actuation from our previous work (Liu et al. 2018), the current steady control technique offers an effective and simple flow control setup that can support robust operations of pumps.

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arXiv2020

Randomized resolvent analysis

Performing global resolvent analysis for high-Reynolds-number turbulent flow calls for the handling of a large discrete operator. Even though such large operator is required in the analysis, most applications of resolvent analysis extracts only a few dominant resolvent response and forcing modes. Here, we consider the use of randomized numerical linear algebra to reduce the dimension of the resolvent operator for achieving computational speed up and memory saving compared to the standard resolvent analysis. To accomplish this goal, we utilize sketching of the linear operator with random test matrices with a Gaussian distribution and with insights from the base flow incorporated to perform singular value decomposition on a low-rank matrix holding dominant characteristics of the full resolvent operator. The strength of the randomized resolvent analysis is demonstrated on a turbulent separated flow over an airfoil. This randomized approach clears the path towards tackling resolvent analysis for higher-Reynolds number bi- and tri-global base flows.

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arXiv2020

Assessment of supervised machine learning methods for fluid flows

We apply supervised machine learning techniques to a number of regression problems in fluid dynamics. Four machine learning architectures are examined in terms of their characteristics, accuracy, computational cost, and robustness for canonical flow problems. We consider the estimation of force coefficients and wakes from a limited number of sensors on the surface for flows over a cylinder and NACA0012 airfoil with a Gurney flap. The influence of the temporal density of the training data is also examined. Furthermore, we consider the use of convolutional neural network in the context of super-resolution analysis of two-dimensional cylinder wake, two-dimensional decaying isotropic turbulence, and three-dimensional turbulent channel flow. In the concluding remarks, we summarize on findings from a range of regression type problems considered herein.

physics.flu-dyn↗

arXiv2019

Resolvent analysis of compressible laminar and turbulent cavity flows

The present work demonstrates the use of resolvent analysis to obtain physical insights for open-cavity flows. Resolvent analysis identifies the flow response to harmonic forcing, given a steady base state, in terms of the response and forcing modes and the amplification gain. The response and forcing modes reveal the spatial structures associated with this amplification process. In this study, we perform resolvent analysis on both laminar and turbulent flows over a rectangular cavity with length-to-depth ratio of $L/D=6$ at a free stream Mach number of $M_\infty=0.6$ in a spanwise periodic setting. Based on the dominant instability of the base state, a discount parameter is introduced to resolvent analysis to examine the harmonic characteristics over a finite-time window. We first uncover the underlying flow physics and interpret findings from laminar flow at $Re_D = 502$. These findings from laminar flow are extended to a more practical cavity flow example at a much higher Reynolds number of $Re_D = 10^4$. The features of response and forcing modes from the laminar and turbulent cavity flows are similar to the spatial structures from the laminar analysis. We further find that the large amplification of energy in flow response is associated with high frequency for turbulent flow, while the flow is more responsive to low frequency excitation in the laminar case. These findings from resolvent analysis provide valuable insights for flow control studies with regard to parameter selection and placement of actuators and sensors.

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arXiv2019

On the formation of three-dimensional flows over finite-aspect-ratio wings under tip effects

We perform DNS of flow over finite-aspect-ratio NACA 0015 wings to characterize the tip effects on the wake dynamics. This study focuses on the development of three-dimensional separated flow over the wing, and discuss flow structures formed on the wing surface as well as in the far field wake. Vorticity is introduced into the flow in a predominantly two-dimensional manner. The vortex sheet from the wing tip rolls up around the free end to form the tip vortex. At its inception, the tip vortex is weak and its effect is spatially confined. As the flow around the tip separates, the tip effects extend farther in the spanwise direction, generating noticeable three dimensionality in the wake. For low-aspect-ratio wings, the wake remains stable due to the strong downwash over the entire span. Increasing the aspect ratio allows unsteady vortical flow to emerge away from the tip at sufficiently high angles of attack. These unsteady vortices shed and form closed vortical loops. For higher-aspect-ratio wings, the tip effects retard the near-tip shedding process, which desynchronizes from the two-dimensional shedding over the mid-span region, yielding vortex dislocation. At high angles of attack, the tip vortex exhibits noticeable undulations due to the strong interaction with the unsteady shedding vortices. The spanwise distribution of force coefficients is related to the three-dimensional wake dynamics and the tip effects. Vortical elements in the wake that are responsible for the generation of lift and drag forces are identified through the force element analysis. We note that at high angles of attack, a stationary vortical structure forms at the leading edge near the tip, giving rise to locally high lift and drag forces. The analysis performed here reveals how the vortical flow around the tip influences the separation physics, the global wake dynamics, and the spanwise force distributions.

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arXiv2019

Randomized methods to characterize large-scale vortical flow network

We demonstrate the effective use of randomized methods for linear algebra to perform network-based analysis of complex vortical flows. Network theoretic approaches can reveal the connectivity structures among a set of vortical elements and analyze their collective dynamics. These approaches have recently been generalized to analyze high-dimensional turbulent flows, for which network computations can become prohibitively expensive. In this work, we propose efficient methods to approximate network quantities, such as the leading eigendecomposition of the adjacency matrix, using randomized methods. Specifically, we use the Nyström method to approximate the leading eigenvalues and eigenvectors, achieving significant computational savings and reduced memory requirements. The effectiveness of the proposed technique is demonstrated on two high-dimensional flow fields: two-dimensional flow past an airfoil and two-dimensional turbulence. We find that quasi-uniform column sampling outperforms uniform column sampling, while both feature the same computational complexity.

math.NA↗

arXiv2019

Modal Analysis of Fluid Flows: Applications and Outlook

We present applications of modal analysis techniques to study, model, and control canonical aerodynamic flows. To illustrate how modal analysis techniques can provide physical insights in a complementary manner, we selected four fundamental examples of cylinder wakes, wall-bounded flows, airfoil wakes, and cavity flows. We also offer brief discussions on the outlook for modal analysis techniques, in light of rapid developments in data science.

physics.flu-dyn↗

arXiv2019

Active Flow Control for Drag Reduction of a Plunging Airfoil under Deep Dynamic Stall

High-fidelity simulations are performed to study active flow control techniques for alleviating deep dynamic stall of a SD7003 airfoil in plunging motion. The flow Reynolds number is $Re=60{,}000$ and the freestream Mach number is $M=0.1$. Numerical simulations are performed with a finite difference based solver that incorporates high-order compact schemes for differentiation, interpolation and filtering on a staggered grid. A mesh convergence study is conducted and results show good agreement with available data in terms of aerodynamic coefficients. Different spanwise arrangements of actuators are implemented to simulate blowing and suction at the airfoil leading edge. We observe that, for a specific frequency range of actuation, mean drag and drag fluctuations are substantially reduced while mean lift is maintained almost unaffected, especially for a 2D actuator setup. For this frequency range, 2D flow actuation disrupts the formation of the dynamic stall vortex, what leads to drag reduction due to a pressure increase along the airfoil suction side, towards the trailing edge region. At the same time, pressure is reduced on the suction side near the leading edge, increasing lift and further reducing drag.

physics.flu-dyn↗

arXiv2019

Revealing essential dynamics from high-dimensional fluid flow data and operators

We consider concepts centered around modal analysis, data science, network science, and machine learning to reveal the essential dynamics from high-dimensional fluid flow data and operators. The presentation of the material herein is example-based and follows the author's keynote talk at the 32nd Computational Fluid Dynamics Symposium (Japan Society of Fluid Mechanics, Tokyo, December 11-13, 2018). This talk was delivered as a compilation of some of the research activities undertaken by the author's research group.

physics.flu-dyn↗

arXiv2019

Super-resolution reconstruction of turbulent flows with machine learning

We use machine learning to perform super-resolution analysis of grossly under-resolved turbulent flow field data to reconstruct the high-resolution flow field. Two machine-learning models are developed; namely the convolutional neural network (CNN) and the hybrid Downsampled Skip-Connection Multi-Scale (DSC/MS) models. These machine-learning models are applied to two-dimensional cylinder wake as a preliminary test and show remarkable ability to reconstruct laminar flow from low-resolution flow field data. We further assess the performance of these models for two-dimensional homogeneous turbulence. The CNN and DSC/MS models are found to reconstruct turbulent flows from extremely coarse flow field images with remarkable accuracy. For the turbulent flow problem, the machine-leaning based super-resolution analysis can greatly enhance the spatial resolution with as little as 50 training snapshot data, holding great potential to reveal subgrid-scale physics of complex turbulent flows. With the growing availability of flow field data from high-fidelity simulations and experiments, the present approach motivates the development of effective super-resolution models for a variety of fluid flows.

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arXiv2018

Cluster-based feedback control of turbulent post-stall separated flows

We propose a novel model-free self-learning cluster-based control strategy for general nonlinear feedback flow control technique, benchmarked for high-fidelity simulations of post-stall separated flows over an airfoil. The present approach partitions the flow trajectories (force measurements) into clusters, which correspond to characteristic coarse-grained phases in a low-dimensional feature space. A feedback control law is then sought for each cluster state through iterative evaluation and downhill simplex search to minimize power consumption in flight. Unsupervised clustering of the flow trajectories for in-situ learning and optimization of coarse-grained control laws are implemented in an automated manner as key enablers. Re-routing the flow trajectories, the optimized control laws shift the cluster populations to the aerodynamically favorable states. Utilizing limited number of sensor measurements for both clustering and optimization, these feedback laws were determined in only $O(10)$ iterations. The objective of the present work is not necessarily to suppress flow separation but to minimize the desired cost function to achieve enhanced aerodynamic performance. The present control approach is applied to the control of two and three-dimensional separated flows over a NACA 0012 airfoil with large-eddy simulations at an angle of attack of $9^\circ$, Reynolds number $Re = 23,000$ and free-stream Mach number $M_\infty = 0.3$. The optimized control laws effectively minimize the flight power consumption enabling the flows to reach a low-drag state. The present work aims to address the challenges associated with adaptive feedback control design for turbulent separated flows at moderate Reynolds number.

physics.flu-dyn↗

arXiv2018

Core-pressure alleviation for a wall-normal vortex by active flow control

We consider the application of active flow control to modify the radial pressure distribution of a single-phase wall-normal vortex. The present flow is based on the Burgers vortex model but with a no-slip boundary condition prescribed along its symmetry plane. The wall-normal vortex serves as a model for vortices that emerge upstream of turbomachinaries, such as pumps. This study characterizes the baseline vortex unsteadiness through numerical simulation and dynamic mode decomposition. The insights gained from the baseline flow are used to develop an active flow control technique with rotating zero-net-mass blowing and suction for the objective of modifying the core pressure distribution. The effectiveness of the control strategy is demonstrated by achieving a widened vortex core with increased pressure. Such change in the flow field weakens the local strength of the wall-normal vortex core, potentially inhibiting the formation of hollow-core vortices, commonly encountered in liquids.

physics.flu-dyn↗

arXiv2018

Active attenuation of a trailing vortex inspired by a parabolized stability analysis

Designing effective control for complex three-dimensional flow fields proves to be non-trivial. Oftentimes, intuitive control strategies lead to suboptimal control. To navigate the control space, we utilize a linear parabolized stability analysis to guide the design of a control scheme for a trailing vortex flow field aft of a NACA0012 half-wing at an angle of attack $α= 5^\circ$ and a chord-based Reynolds number $Re = 1000$. The stability results show that the unstable mode with the smallest growth rate (fifth wake mode) provides a pathway to excite a vortex instability, whereas the principal unstable mode remains in the wake of the wing. Inspired by this finding, we perform direct numerical simulations that excite each mode with body forces matching the shape function from the stability analysis. Relative to the baseline uncontrolled case, the principal wake mode reduces the vortex length, while the fifth wake mode further shortens the tip vortex. Analogously, the streamwise circulation of the trailing vortex is found to be significantly reduced. From these results, we conclude that a rudimentary linear stability analysis can provide key insight into the underlying physics and help engineers design more effective control.

physics.flu-dyn↗

arXiv2018

Resolvent-analysis-based design of airfoil separation control

We combine three-dimensional (3D) large-eddy simulations (LES) and resolvent analysis to design active separation control techniques on a NACA 0012 airfoil. Spanwise-periodic flows over the airfoil at a chord-based Reynolds number of $23,000$ and a free-stream Mach number of $0.3$ are considered at two post-stall angles of attack of $6^\circ$ and $9^\circ$. Near the leading edge, localized unsteady thermal actuation is introduced in an open-loop manner with two tunable parameters of actuation frequency and spanwise wavelength. For the most successful control case that achieves full reattachment, we observe a reduction in drag by up to $49\%$ and increase in lift by up to $54\%$. To provide physics-based guidance for the effective choice of these control input parameters, we conduct global resolvent analysis on the baseline turbulent mean flows to identify the actuation frequency and wavenumber that provide high energy amplification. The present analysis also considers the use of a temporal filter to limit the time horizon for assessing the energy amplification to extend resolvent analysis to unstable base flows. We incorporate the amplification and response mode from resolvent analysis to provide a metric that quantifies momentum mixing associated with the modal structure. By comparing this metric from resolvent analysis and the LES results of controlled flows, we demonstrate that resolvent analysis can predict the effective range of actuation frequency as well as the global response to the actuation input. Supported by the agreements between the results from resolvent analysis and LES, we believe that this study provides insights for the use of resolvent analysis in guiding future active flow control.

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