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Modeling the Aerodynamic Response to Impulsive Active Flow Control
Title
Modeling the Aerodynamic Response to Impulsive Active Flow Control
Creator
Asztalos, Katherine
Date
2021
Description
In unsteady aerodynamics the response to external disturbances can depend significantly on the initial condition, and the extent to which this...
Show moreIn unsteady aerodynamics the response to external disturbances can depend significantly on the initial condition, and the extent to which this impacts the ability to model the flowfield can vary. In this work, we look to develop a model that can capture and predict the long-time response to actuation, which we suspect to be sensitive to the instantaneous state. We investigate whether a physical understanding of the short-time response to impulsive actuation can be obtained, with the goal of understanding the observed physical phenomenon present in the immediate response to this type of actuation. We find that the response to impulsive actuation is sensitive to the instantaneous wake, and that the short-time response is directly proportional to the time rate of change of the actuation input. Computational simulations of a stalled NACA 0009 airfoil subject to leading-edge synthetic jet actuation were performed. Full state information, as well as force response measurements, were collected using an immersed boundary method (IBM) numerical code. The numerical simulations performed sought to characterize the response to actuation by varying the actuation parameters, such as the strength, direction, and phase at which the onset of actuation occurs. It was found that the long-time response to actuation can be sensitive to the instantaneous wake state at the onset of actuation. The ability to extract models that describe the complex behavior of the system provides additional insight into the dominant features governing the response of such systems, as well as achieves predictive capabilities of the systems' response. The data-driven models, which are identified using variants of dynamic mode decomposition, can capture both the short- and long-time response of the system to actuation. Predictive models are identified using multiple trajectories of data corresponding to varying the phase of vortex shedding at which the onset of actuation occurs. These models achieve accurate predictions for off-design cases as well. It is also shown that multiple control objectives with the same actuator can be achieved. Classical theory aids in understanding the physics governing unsteady aerodynamic motion and the response to disturbances. Theoretical models are developed using the assumptions from classical unsteady aerodynamic theory, which provide insight into the forms that the data-driven models take. The effect of short-duration momentum injection actuation is modeled through a combination of source/sink, doublet, and vortex elements. Regardless of the precise elements used in the theoretical model, the lift response is composed of a contribution directly proportional to the rate of change of actuation strength, and a contribution that persists after the actuation burst ends that arises due to the enforcement of the Kutta condition. Methodologies that retain the physics inherent to the system by projecting the governing equations of motion onto a well-suited basis are extremely valuable for gaining physical insight and understanding into the dynamics of the flowfield. A new methodology is proposed for extracting spectral content from systems with limited data available using projection-based modeling approaches. There are challenges associated with using modal decomposition-based modeling techniques for systems exhibiting large transient dynamics due to external inputs, which is applicable in this particular instance and for related systems. The methodology presented here shows how the dynamics of this system can be understood through analysis of optimal finite-time horizon transient energy growth, applied to reduced-order models identified using actuation response data with either data-driven or physics-based models. A novel methodology is proposed to guide future experimental actuation design to achieve maximal response by considering an optimal forcing mode, identified from considering the optimal perturbation of the full unactuated system, which maximizes a given output.
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Resolvent analysis of turbulent flows: Extensions, improvements and applications
Title
Resolvent analysis of turbulent flows: Extensions, improvements and applications
Creator
Lopez-Doriga Costales, Barbara
Date
2024
Description
This thesis presents several advances in both physics-based and data-driven modeling of turbulent fluid flows. In particular, the present...
Show moreThis thesis presents several advances in both physics-based and data-driven modeling of turbulent fluid flows. In particular, the present thesis focuses on resolvent analysis, a physics-based framework that identifies the coherent structures that are most amplified by the Navier-Stokes equations when they are linearized about a known turbulent mean flow via a singular value decomposition (SVD) of a discretized operator. This method has proven to effectively capture energetically-relevant features observed in various flows. However, it has some shortcomings that the present work intends to alleviate. First, the original formulation of resolvent analysis is restricted to statistically-stationary or time-periodic mean flows. To expand the applicability of this framework, this thesis presents a spatiotemporal variant of resolvent analysis that is able to account for time-varying systems. Moreover, sparsity (which manifests in localization) is also incorporated to the analysis through the addition of an l1-norm penalization term to the optimization associated with the SVD. This allows for the identification of energetically-relevant coherent structures that correspond to spatio-temporally localized amplification mechanisms, for flows with either a time-varying or stationary mean. The high computational cost associated with the discretization and analysis of a large discretized of the mean-linearized Navier-Stokes operator represents the second drawback of resolvent analysis. As a second contribution, this thesis provides an analytic form of resolvent analysis for planar flows based on wavepacket pseudomode theory, avoiding the numerical computations required in the original framework. The third contribution focuses on the characterization of the energetically-dominant coherent structures that arise in turbulent flow traveling through straight ducts with square and rectangular cross-sections. First, resolvent analysis is applied to predict the coherent structures that arise in this flow, and to study the sensitivity of this methodology to the secondary mean flow components that display a distinct pattern near the duct corners. Next, a data-driven causality analysis is performed to understand the physical mechanisms involved in the evolution of coherent structures near the duct corners. To do this, a nonlinear Granger causality analysis method is developed and applied to proper orthogonal decomposition coefficients of direct numerical simulation data, revealing that the structures associated with the secondary velocity components are behind the formation and translation of the near-wall and near-corner streamwise structures. A general discussion and future prospects are discussed at the end of this thesis.
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