Phase-based control of periodic flows

Abstract

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.

Adjoint-based phase reduction analysis of incompressible periodic flows

“…In addition to examining the influence of angle of attack and thickness, as the phase is defined based on the lift coefficient, phase modification through vortex shedding dynamics can be utilized for enhancement of lift [50]. Let us examine the contours of ∇ × Z superposed on ω for NACA0012 airfoil at α = 35 • for θ = 0, π/2, π, 3π/2 shown in figure 9.…”

“…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].…”

“…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.…”

“…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. Thus, phase sensitivity fields reveal essential physics responsible for optimal control design for periodic fluid flows.…”

Optimal waveform for fast synchronization of airfoil wakes

“…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.…”