Phase-reduction for synchronization of oscillating flow by perturbation on surrounding structure

Loe, Innocentio A.; Nakao, Hiroya; Jimbo, Yasuhiko; Kotani, Kiyoshi

doi:10.1017/jfm.2020.1110

Cited by 8 publications

(8 citation statements)

References 30 publications

(56 reference statements)

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“…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%

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: Introductionmentioning

confidence: 99%

Optimal waveform for fast synchronization of airfoil wakes

Godavarthi,

Kawamura,

Taira

2023

J. Fluid Mech.

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“…In addition, phase reduction analysis is also sensor friendly as it only requires temporal measurements capturing the phase of the limit-cycle oscillation. Hence phase-based analysis is remarkably useful for analysis and control of periodic fluid flows, however such applications have been very recent [29,30,31,32,33,34,35,36,37,40,38,39].…”

Section: Introductionmentioning

confidence: 99%

“…There are mainly two methods to obtain the phase sensitivity function [12,13,14,15,16,17,18,19,20,21]: one is the direct method using impulsive perturbation applied to the system, and the other is the adjoint method using the adjoint equations derived from the governing equations of the system. The direct method has been used to characterize and control the periodic vortex shedding around cylinders [33,34,35,36,37] and airfoil [36]. The lock-on characteristics of vortex shedding for a circular cylinder to various periodic perturbations such as, periodic external forcing [33,34], periodic vibrations of cylinder [35] and fluid-structure interactions [37] are demonstrated via phase reduction using the direct method.…”

Section: Introductionmentioning

confidence: 99%

“…The direct method has been used to characterize and control the periodic vortex shedding around cylinders [33,34,35,36,37] and airfoil [36]. The lock-on characteristics of vortex shedding for a circular cylinder to various periodic perturbations such as, periodic external forcing [33,34], periodic vibrations of cylinder [35] and fluid-structure interactions [37] are demonstrated via phase reduction using the direct method. Subsequently, Nair et al [36] developed a transient control technique based on the phase sensitivity function obtained via the direct method to modify the phase of vortex shedding behavior of flows past a circular cylinder and an airfoil.…”

Section: Introductionmentioning

confidence: 99%

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Adjoint-based phase reduction analysis of incompressible periodic flows

Kawamura¹,

Godavarthi²,

Taira³

2022

Preprint

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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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“…It is only relatively recently that phase reduction has been introduced to the fluids community (Kawamura & Nakao 2015; Taira & Nakao 2018; Iima 2019; Khodkar & Taira 2020; Khodkar, Klamo & Taira 2021; Loe et al. 2021; Nair et al. 2021).…”

Section: Introductionmentioning

confidence: 99%

Phase-reduction analysis of periodic thermoacoustic oscillations in a Rijke tube

Skene

Taira

2021

J. Fluid Mech.

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Phase-reduction analysis captures the linear phase dynamics with respect to a limit cycle subjected to weak external forcing. We apply this technique to study the phase dynamics of the self-sustained oscillations produced by a Rijke tube undergoing thermoacoustic instability. Through the phase-reduction formulation, we are able to reduce these dynamics to a scalar equation for the phase, which allows us to efficiently determine the synchronisation properties of the system. For the thermoacoustic system, we find the conditions for which $m:n$ frequency locking occurs, which sheds light on the mechanisms behind asynchronous and synchronous quenching. We also reveal the optimal placement of pressure actuators that provide the most efficient route to synchronisation.

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Phase-reduction for synchronization of oscillating flow by perturbation on surrounding structure

Abstract: Abstract

Cited by 8 publications

References 30 publications

Optimal waveform for fast synchronization of airfoil wakes

Optimal waveform for fast synchronization of airfoil wakes

Adjoint-based phase reduction analysis of incompressible periodic flows

Phase-reduction analysis of periodic thermoacoustic oscillations in a Rijke tube

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