Adjoint-based phase reduction analysis of incompressible periodic flows

Kawamura, Y.; Godavarthi, Vedasri; Taira, Kunihiko

doi:10.1103/physrevfluids.7.104401

Cited by 3 publications

(11 citation statements)

References 51 publications

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“…Here, Z (x, θ) = ∇ q Θ(q)| q=q 0 (x,θ ) is the spatial phase sensitivity field as it quantifies the phase response of the system to any given small perturbation and D is the considered spatial domain. This spatial phase sensitivity field can be obtained using either a direct impulse-based method (Taira & Nakao 2018;Khodkar & Taira 2020;Loe et al 2021;Nair et al 2021), or an adjoint-based approach (Kawamura & Nakao 2013, 2015Kawamura et al 2022), or a Jacobian-free approach (Iima 2021). We use the adjoint-based phase reduction framework to obtain the phase sensitivity fields in the present study, as we can obtain the high-fidelity Z (x, θ) in all the flow variables by solving a single pair of forward and adjoint simulations.…”

Section: Phase Reduction Approachmentioning

confidence: 99%

“…The smallest grid size is set to x min /c = 0.02, and the time step is chosen to be t = 0.005. The present computational set-up has been validated and is the same as that used in Kawamura et al (2022). The same computational set-up is used for adjoint simulations of the phase sensitivity fields.…”

Section: Computational Set-upmentioning

confidence: 99%

“…To obtain the optimal actuation waveform for fast synchronization for periodic fluid flows, we use phase reduction analysis (Taira & Nakao 2018; Kawamura et al. 2022). We identify the phase sensitivity fields that encode the effect of timing of actuation, and then analytically solve an optimization problem to obtain the synchronization waveform in terms of the phase sensitivity function.…”

Section: Fast Synchronization Analysis Through the Phase Reduction Ap...mentioning

confidence: 99%

“…2021), or an adjoint-based approach (Kawamura & Nakao 2013, 2015; Kawamura et al. 2022), or a Jacobian-free approach (Iima 2021). We use the adjoint-based phase reduction framework to obtain the phase sensitivity fields in the present study, as we can obtain the high-fidelity in all the flow variables by solving a single pair of forward and adjoint simulations.…”

Section: Fast Synchronization Analysis Through the Phase Reduction Ap...mentioning

confidence: 99%

“…The phase reduction approach expresses the perturbation dynamics using a single scalar phase variable. Recently, it has been used for studying periodic flows to reveal the phase sensitivity fields (Kawamura & Nakao 2013, 2015Khodkar & Taira 2020;Iima 2021;Loe et al 2021;Kawamura, Godavarthi & Taira 2022), synchronization characteristics to external forcing (Taira & Nakao 2018;Khodkar & Taira 2020;Khodkar, Klamo & Taira 2021;Skene & Taira 2022) and flow control (Nair et al 2021;Loe et al 2023) in a computationally inexpensive way.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Optimal waveform for fast synchronization of airfoil wakes

Godavarthi,

Kawamura,

Taira

2023

J. Fluid Mech.

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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 analyse 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.

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Section: Phase Reduction Approachmentioning

confidence: 99%

Section: Computational Set-upmentioning

confidence: 99%

Section: Fast Synchronization Analysis Through the Phase Reduction Ap...mentioning

confidence: 99%

Section: Fast Synchronization Analysis Through the Phase Reduction Ap...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal waveform for fast synchronization of airfoil wakes

Godavarthi,

Kawamura,

Taira

2023

J. Fluid Mech.

Self Cite

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Controlling fluidic oscillator flow dynamics by elastic structure vibration

Loe

Zheng

Kotani

et al. 2023

Sci Rep

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In this study, we introduce a design of a feedback-type fluidic oscillator with elastic structures surrounding its feedback channel. By employing phase reduction theory, we extract the phase sensitivity function of the complex fluid–structure coupled system, which represents the system’s oscillatory characteristics. We show that the frequency of the oscillating flow inside the fluidic oscillator can be modulated by inducing synchronization with the weak periodic forcing from the elastic structure vibration. This design approach adds controllability to the fluidic oscillator, where conventionally, the intrinsic oscillatory characteristics of such device were highly determined by its geometry. The synchronization-induced control also changes the physical characteristics of the oscillatory fluid flow, which can be beneficial for practical applications, such as promoting better fluid mixing without changing the overall geometry of the device. Furthermore, by analyzing the phase sensitivity function, we demonstrate how the use of phase reduction theory gives good estimation of the synchronization condition with minimal number of experiments, allowing for a more efficient control design process. Finally, we show how an optimal control signal can be designed to reach the fastest time to synchronization.

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Optimal external forces of the lock-in phenomena for flow past an inclined plate in uniform flow

Iima

2024

Phys. Rev. E

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Adjoint-based phase reduction analysis of incompressible periodic flows

Cited by 3 publications

References 51 publications

Optimal waveform for fast synchronization of airfoil wakes

Optimal waveform for fast synchronization of airfoil wakes

Controlling fluidic oscillator flow dynamics by elastic structure vibration

Optimal external forces of the lock-in phenomena for flow past an inclined plate in uniform flow

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