Scott T. M. Dawson

Modal Analysis of Fluid Flows: An Overview

Simple aerodynamic configurations under even modest conditions can exhibit complex flows with a wide range of temporal and spatial features. It has become common practice in the analysis of these flows to look for and extract physically important features, or modes, as a first step in the analysis. This step typically starts with a modal decomposition of an experimental or numerical dataset of the flow field, or of an operator relevant to the system. We describe herein some of the dominant techniques for accomplishing these modal decompositions and analyses that have seen a surge of activity in recent decades. For a non-expert, keeping track of recent developments can be daunting, and the intent of this document is to provide an introduction to modal analysis that is accessible to the larger fluid dynamics community. In particular, we present a brief overview of several of the well-established techniques and clearly lay the framework of these methods using familiar linear algebra. The modal analysis techniques covered in this paper include the proper orthogonal decomposition (POD), balanced proper orthogonal decomposition (Balanced POD), dynamic mode decomposition (DMD), Koopman analysis, global linear stability analysis, and resolvent analysis.

State-space model identification and feedback control of unsteady aerodynamic forces

Abstract Unsteady aerodynamic models are necessary to accurately simulate forces and develop feedback controllers for wings in agile motion; however, these models are often high dimensional or incompatible with modern control techniques. Recently, reduced-order unsteady aerodynamic models have been developed for a pitching and plunging airfoil by linearizing the discretized Navier–Stokes equation with lift-force output. In this work, we extend these reduced-order models to include multiple inputs (pitch, plunge, and surge) and explicit parameterization by the pitch-axis location, inspired by Theodorsen׳s model. Next, we investigate the naive application of system identification techniques to input–output data and the resulting pitfalls, such as unstable or inaccurate models. Finally, robust feedback controllers are constructed based on these low-dimensional state-space models for simulations of a rigid flat plate at Reynolds number 100. Various controllers are implemented for models linearized at base angles of attack α 0 = 0 ° , α 0 = 10 ° , and α 0 = 20 ° . The resulting control laws are able to track an aggressive reference lift trajectory while attenuating sensor noise and compensating for strong nonlinearities.

Parameter-Varying Aerodynamics Models for Aggressive Pitching-Response Prediction

Current low-dimensional aerodynamic-modeling capabilities are greatly challenged in the face of aggressive flight maneuvers, such as rapid pitching motions that lead to aerodynamic stall. Nonlinearities associated with leading-edge vortex development and flow separation push existing real-time-capable aerodynamics models beyond their predictive limits, which puts reliable real-time flight simulation and control out of reach. In the present development, a push toward realizing real-time-capable models with enhanced predictive performance for flight operations has been made by considering the simpler problem of modeling an aggressively pitching airfoil in a low-dimensional manner. A parameter-varying model, composed of three coupled quasi-linear sub-models, is proposed to approximate the lift, drag, and pitching-moment response of an airfoil to arbitrarily prescribed aggressive ramp–hold pitching kinematics. An output-error-minimization strategy is used to identify the low-dimensional quasi-linear parameter...

A Data-Driven Modeling Framework for Predicting Forces and Pressures on a Rapidly Pitching Airfoil

This work formulates a switched linear modeling procedure to understand and predict the unsteady aerodynamic forces arising from rapid pitching motion of a NACA 0012 airfoil at a Reynolds number of 50,000. The system identification procedure applies a generalized dynamic mode decomposition algorithm to time-resolved wind tunnel measurements of the lift and drag forces, as well as the pressure at six locations on the suction surface of the airfoil. Linear state space models are identified for 5-degree pitch-up and pitchdown maneuvers within an overall angle of attack range of 0◦–20◦. The identified models accurately capture the effects of flow separation and leading-edge vortex formation and convection. It is shown that switching between different linear models can give accurate prediction of the nonlinear behavior that is present in high-amplitude maneuvers. The models are accurate for a wide range of motions, including pitch-and-hold, sinusoidal, and pseudo-random pitching maneuvers. Providing the models access to a subset of the measured data channels can allow for improved estimates of the remaining states via the use of a Kalman filter, which could be of use for aerodynamic control applications.

Unsteady aerodynamic response modeling: A parameter-varying approach

Current low-dimensional aerodynamic modeling capabilities are greatly challenged in the face of aggressive flight maneuvers, such as rapid pitching motions that lead to aerodynamic stall. Nonlinearities associated with leading-edge vortex development and flow separation push existing real-time-capable aerodynamics models beyond their predictive limits. The inability to accurately predict the aerodynamic response of an aircraft to sharp maneuvers makes flight simulation for pilot training unrealistic and, thus, ineffective at adequately preparing pilots to safely handle compromising flight scenarios. Inaccurate low-dimensional models also put practical approaches for aerodynamic optimization and control out of reach. In the present development, we make a push toward realizing real-time-capable models with enhanced predictive performance for flight operations by considering the simpler problem of modeling an aggressively pitching airfoil in a low-dimensional manner. We propose a parameter-varying model, composed of three coupled quasi-linear sub-models, to approximate the response of an airfoil to arbitrarily prescribed aggressive ramp-hold pitching kinematics. An output error minimization strategy is used to identify the lowdimensional quasi-linear parameter-varying sub-models from input-output data gathered from low-Reynolds number (Re = 100) direct numerical fluid dynamics simulations. The resulting models have noteworthy predictive capabilities for arbitrary ramp-hold pitching maneuvers spanning a broad range of operating points, thus making the models especially useful for aerodynamic optimization and real-time control and simulation.

Lift Enhancement of High Angle of Attack Airfoils using Periodic Pitching

In this work, we study a sinusoidally pitching, two-dimensional flat plate airfoil at a Reynolds number of 100, across a range of pitching amplitudes, frequencies, mean angles of attack, and pitch axis locations. We report on the lift, drag, and wake structures present in different regions of parameter space. We examine the average and spectral properties of the forces on the airfoil, and use dynamic mode decomposition to examine the structures and frequency content of the wake. We give focus to a number of regions in parameter space where interesting behavior is observed. In particular, we find that in the regime where the flow on the upper surface of the airfoil is separated, but the steady wake is stable, pitching at a specific frequency excites a vortex shedding mode in the wake, leading to substantial increase in the lift and drag forces. This phenomena is insensitive to pitchaxis location and amplitude. At higher angles of attack where the wake for a steady airfoil exhibits periodic vortex shedding, we find that, in addition to this mean lift maxima, the interaction between the natural and forced modes gives rise to more complex behavior.