American Institute of Aeronautics and Astronautics
1
High-Accuracy Viscous Analysis of Unsteady Flexible Airfoil
Response to Impinging Gust
Vladimir V. Golubev
1
, Brian D. Dreyer
2
and Timothy M. Hollenshade
3
Florida Center for Advanced Aero Propulsion, Computational Aero Propulsion Group
Embry-Riddle Aeronautical University, Daytona Beach, FL 32114, USA
Miguel R. Visbal
4
Air Force Research Laboratory, WPAFB, OH 80906, USA
The current work extends the previously developed high-accuracy inviscid analysis of unsteady, nonlinear,
aeroelastic gust-airfoil interaction, to include viscous effects. In the implemented iterative procedure, a set of
governing Navier-Stokes equations is solved simultaneously with equations of motion of the structure, so that
the fluid and structure are treated as a coupled dynamic system. The numerical procedure employs a high-
order low-pass filter operator which selectively damps the poorly resolved high-frequency content to retain
numerical accuracy and stability over a wide range of flow regimes. An efficient analytical model is developed
to introduce an unsteady incompressible 2D vortical flow perturbation inside the computational domain
through a source term in the momentum equations. Strongly coupled unsteady aerodynamic, aeroelastic and
aeroacoustic responses of rigid and flexible Joukowski airfoil subject to a viscous upstream flow with imposed
harmonic, high-amplitude, vortical gust are examined in test studies.
I. INTRODUCTION
A gust encounter generally produces a significant impact on the wing unsteady aerodynamic response, with even
more severe effect anticipated for light-weight micro air vehicles (MAV’s) where such impact may compromise the
flight stability and performance. Particularly for low-Reynolds number MAV applications, a flexible wing structure
may actually be designed to alleviate the severity of the gust impact, a fixture so wide-spread in natural flyers [1].
Modeling such problems, however, requires truly multidisciplinary approaches going beyond the current practices of
split flow and structural analyses that, for the purpose of aeroelastic predictions, primarily rely on time-linearization
procedures and reduced-order models for obtaining unsteady aerodynamic forces [2]. Indeed, as was previously
noted [3], the latter may not be adequate when inherently nonlinear aerodynamic phenomena are present, such as the
formation of dynamic-stall-like vortices due to high-intensity unsteady forcing of low-speed wings [4] and
associated nonlinear hysteresis phenomena observed in unsteady aerodynamic characteristics of oscillating airfoils
[5], or local transonic zones associated with shocks and their interaction with boundary layers that may occur even at
moderate flow Mach number for structures subject to high-intensity flow disturbances [6]. Hence, a comprehensive
prediction tool is required that would enable a clear understanding of the physics of unsteady, nonlinear, aeroelastic
flow-structure interaction through efficient coupling of high-accuracy flow and structural motion solvers treating
fluid and structure as a single dynamic system. The current paper addresses the development of such unified
prediction tool on the basis of a high-accuracy Navier-Stokes solver FDL3DI [7, 8] that has been successfully
applied to a variety of steady and unsteady flow problems as recently reviewed, e.g., in Ref. [9], including several
computational aeroacoustics benchmarks [10]. We start with reviewing the implemented numerical model and, for
the sake of future fully 3D unsteady viscous analyses, emphasize the code Implicit Large Eddy Simulation (ILES)
approach [11, 12] based on combining high-order compact schemes with Pade-type low-pass filtering procedure to
ensure stability, with the method being particularly attractive for current applications due to its ability to seamlessly
handle mixed laminar, transitional and turbulent flows.
The foundation for this work was laid in our previous study [3] which developed an efficient two-degrees-of-
freedom (2-DOF) structural motion module integrated with a high-order nonlinear aeroacoustic code for an inviscid
1
Associate Professor, Associate Fellow AIAA
2
Graduate Research Assistant
3
Graduate Research Assistant
4
Technical Area Leader, Associate Fellow AIAA
15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference)
11 - 13 May 2009, Miami, Florida
AIAA 2009-3271
Copyright © 2009 by Golubev et al. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.