Discrete Vortex Modeling of Aerodynamic Flutter of a Flat Plate with Damped Oscillations
Creators: name: Chao, Emma
Publisher: name: University of Nevada, Las Vegas
Year: 2020
Subjects: Aerospace Engineering; Engineering; Mechanical Engineering

description: Aerodynamic flutter is the unstable oscillation of a body caused by the interaction of aerodynamic forces, structural elasticity, and inertial effects induced by vortex shedding. Current models of this phenomenon require finite element analysis and extensive computational power and processing time. The purpose of this study was to develop and validate a program that is faster and more efficient than existing approaches by using the discrete vortex method (DVM). By reducing the complexities of flutter to the shedding of vortices in an inviscid model of a two-dimensional flat plate with a torsional spring constant at its center, this phenomenon can be modeled for a demonstration. A discrete vortex model of inviscid flow past a cylinder is transformed through conformal mappings to model the behavior of a flat plate in an impulsively started streamline flow. Discrete vortices are shed at the tips of the plate and the moment induced by the vortices on the flat plate result in its angular displacement varying over time to simulate flutter. The results of this study provide a rudimentary example of the potential benefit of implementing DVM in the field of structural dynamics.
A FreeBASIC program was developed for this thesis and utilized in several parametric studies. The program includes an iterative time loop in which discrete vortices are added to the flow field and the angle of the flat plate is updated in every time step. The program is fast enough that it runs in almost real time though it slows down as more vortices are added into the field. The resulting flow field displays like a video which allows the viewer to visually observe how a plate of user-defined properties will behave in a uniform flow. Furthermore, the user can observe the force and pressure distributions on the plate in the same window to visualize the aerodynamic forces acting on the plate due to the wake. Finally, the deflection angle, drag force, and pressure at a specified probe location in the wake are calculated in each time step and recorded in a text file; for data analysis, these values can be extracted and plotted with respect to time.
Throughout development, the program was validated for realistic results by plotting inviscid streamlines, observing the wake generated by discrete vortices, and analyzing the flutter simulation results. Once the program development was complete, the parameters varied in this study included plate width, uniform velocity, mass moment of inertia, damping coefficient, and torsional stiffness. By performing Fast Fourier Transforms on the deflection angle and pressure data, the damped frequency and the Strouhal number of the wake, respectively, were approximated for each case simulated in the program. The correspondence between the predicted and actual values for damped frequencies was extremely accurate. However, the Strouhal numbers were less conclusive as they were difficult to extract from autospectral plots; this can be attributed to various minor issues within the program due to singularities at the tips of the plate and at the center of each vortex. Additionally, the times at which specimens failed were recorded for each parametric study. It was expected that the failure time would increase for stiffer specimens with more damping; the results generated by the model supported this prediction by demonstrating positive correlations between these parameters and failure time yet no clear correlation between mass moment of inertia and failure time. The correlation between predictions and simulated results provides support that the program used is viable. With future adjustments and developments, the discrete vortex model has the potential to revolutionize the industry of flutter simulation, providing a faster and more efficient analysis technique that can be implemented early on in a structures design process.