Department of Structural Mechanics and Computer Aided Engineering

A Physics‐Based Model for Computing Flow Forces on Vibrating Aerodynamic Structures
Ahmed M. Naguib
Michigan State University, East Lansing, USA
Motivated by interest in the aerodynamics of unsteady airfoils, the present study is focused on obtaining a simplified, vortex‐array model of the unsteady flow in the wake of an airfoil undergoing small‐amplitude but high‐reduced‐frequency pitch oscillations.
The model is used to predict the mean and unsteady velocity field in the wake of a NACA 0012 airfoil executing sinusoidal as well as non‐sinusoidal pitch oscillation. The model predictive accuracy is assessed by comparison to the LDV measurements of the
streamwise velocity by Koochesfahani (AIAA J. 37, 1999) at chord Reynolds number of 12,000 and a reduced frequency as high as 10. The results demonstrate the ability of the vortex‐array model to successfully reproduce the experimentally measured mean and phase‐averaged streamwise velocity profiles in the wake of the airfoil. Moreover, by using the model to reconstruct the complete velocity field in the wake, the mean streamwise force acting on the airfoil is computed for different frequencies and amplitudes of oscillation. The computed force coefficient is found to agree with computational and experimental data in literature.
Subsequent to verification of the appropriateness of the model to represent the wake of oscillating airfoils, the model is capitalized upon to explore how the thrust force varies with wake vortex parameters; i.e. circulation and streamwise/cross‐flow spacing of the
vortices. Insight from this exploration has the potential for providing a rational approach for manipulation of the trailing edge flow in order to obtain desirable characteristics of the forces acting on airfoils that vibrate in a steady approach flow, or static airfoils that are subject to oscillatory change in the approach flow direction. Such situations are encountered in a wide range of engineering applications, including unmanned micro air vehicles (UMAVs) and wind turbines.