UCLA

In this thesis, we present phase-based analysis and develop flow control strategies for unsteady fluid flows. Unsteady fluid flows of interest in this work are associated with time-varying base states. We propose phase-based control strategies by investigating the effect of the timing of actuation introduction on these time-varying base states. We apply the phase reduction approach, which has been used to study periodic nonlinear oscillators. Phase-based analysis transforms the perturbation dynamics about a periodically varying base state into a single scalar phase variable and provides sensitivity at various phases encoded in the phase sensitivity function. We implement this phase-based approach to describe the dominant oscillatory physics of both laminar and turbulent oscillatory fluid flows and investigate potential unsteady flow control strategies to achieve desirable dynamics quickly.

First, we demonstrate the potential of the phase-based approach in analyzing the vortex dynamics of laminar periodic cylinder and airfoil wakes. We establish a theoretical framework for adjoint-based phase reduction analysis to compute the spatiotemporal phase sensitivity fields for periodic flows in a computationally tractable manner. Through the spatial phase sensitivity fields, we identify the most sensitive spatial locations of these wakes for introducing actuation and investigate the influence of the angle of attack and airfoil thickness on the phase-sensitivity distribution of flows over various airfoils. We then relate the phase response to the vortical structures responsible for lift production to shed light on the connection between phase sensitivity and vortex formation dynamics.

Next, we seek quick-acting flow control strategies based on the phase-based analysis for periodic flows through the lens of synchronization with external forcing. Using the obtained spatial phase sensitivity fields for airfoil wakes, we analytically obtain the optimal actuation waveform for fast synchronization to modify the wake-shedding frequency of airfoil wakes by casting an optimization problem. The obtained optimal actuation waveform becomes increasingly non-sinusoidal for higher angles of attack. We actuate based on the obtained waveform and achieve rapid synchronization within as low as two vortex-shedding cycles, irrespective of the forcing frequency. In contrast, traditional sinusoidal actuation requires O(10) shedding cycles.

While the phase-based analysis and control have been demonstrated for periodic flows, we extend this framework for turbulent oscillatory flows with multi-modal behaviour to generalize the applicability of the phase-based approach for more complex unsteady flows. We consider supersonic turbulent flow over an open rectangular cavity with an incoming free-stream Mach number of 1.4 and a depth-based Reynolds number of 10,000 to demonstrate the applicability of phase-based analysis for high-speed flows. Open cavity flows exhibit violent fluctuations due to the feedback between the shear layer instabilities and the acoustic field, resulting in several dominant modes superposed with broadband nature owing to the turbulence. Before applying phase-based control, we perform an actuator placement study of cavity flows using windowed resolvent analysis that can suppress pressure fluctuations. The resolvent analysis provides spatial harmonic forcing and response modes based on the time-averaged base state that results in maximum amplification of perturbations. Through windowed resolvent analysis, we identify localized forcing modes that can provide insights into the actuator placement on the cavity walls. We identify the leading edge as the primary actuator location, reaffirming the previous studies using resolvent analysis.

We then propose a phase-based description and control framework to reduce the pressure fluctuations within the cavity. We formulate the phase-based flow control to effectively modify the dominant frequency, thereby breaking the feedback loop and, hence, suppressing the pressure fluctuations. We identify the phase variable by projecting the spanwise-averaged pressure field onto the spatial mode associated with vortex convection frequency obtained using dynamic mode decomposition. We introduce three-dimensional impulse perturbations from the leading edge to characterize the phase response of the cavity flow in terms of the advancement or delay of the vortex convection process. The insights from the phase sensitivity are then used to perform open-loop flow control through unsteady blowing using actuation frequencies that are slightly higher/lower than the vortex convection frequency to disturb the feedback loop and attenuate the pressure fluctuations in the cavity. By designing an actuation waveform based on the phase response optimized for quick flow modification, we also investigate the speed of fluctuation reduction and compare the performance with a sinusoidal waveform at various spanwise actuation waveforms.

The present phase-based analysis framework efficiently modifies the frequency of unsteady flows, opening potential paths for quick unsteady flow control strategies with several aerodynamic applications, such as fluid-structure interactions and transient and high-speed unsteady flows.