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

Khodkar, Mohammad Amin; Klamo, Joseph T.; Taira, Kunihiko

doi:10.1103/physrevfluids.6.034401

Cited by 10 publications

(7 citation statements)

References 30 publications

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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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Adjoint-based phase reduction analysis of incompressible periodic flows

Kawamura¹,

Godavarthi²,

Taira³

2022

Preprint

Self Cite

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“…Using this approach, the conditions for synchronisation (lock-on) to external excitation were determined (Munday & Taira 2013). Moreover, phase-based characterisation of the global flow field around a bluff body (Khodkar & Taira 2020) and sensitivity of phase dynamics to body motion (Khodkar, Klamo & Taira 2021) have been studied. Such a phase-reduced representation of the flow physics forms the basis of the analysis in this work.…”

Section: Introductionmentioning

confidence: 99%

Phase-based control of periodic flows

et al. 2021

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Unsteady bluff-body flows exhibit dominant oscillatory behaviour owing to periodic vortex shedding. The ability to manipulate this vortex shedding is critical to improving the aerodynamic performance of bodies in a flow. This goal requires a precise understanding of how the perturbations affect the asymptotic behaviour of the oscillatory flow and of the ability to control transient dynamics. In this work, we develop an energy-efficient flow-control strategy to alter the oscillation phase of time-periodic fluid flows rapidly. 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 a real-time optimal phase-control strategy based on the phase-sensitivity function obtained by solving the associated Euler–Lagrange equations as a two-point boundary-value problem. Our approach is demonstrated for the incompressible laminar flow past a circular cylinder and an airfoil. We show the effectiveness of phase control with different actuation inputs, including blowing and rotary control. Moreover, our control approach is a sensor-based approach without the need for access to high-dimensional measurements of the entire flow field.

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“…2018). 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.…”

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

Cited by 10 publications

References 30 publications

Adjoint-based phase reduction analysis of incompressible periodic flows

Adjoint-based phase reduction analysis of incompressible periodic flows

Phase-based control of periodic flows

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

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