Abstract
The present paper highlights results derived from the application of a high-fidelity simulation technique to the analysis of low-Reynolds-number transitional flows over moving and flexible canonical configurations motivated by small natural and man-made flyers. This effort addresses three separate fluid dynamic phenomena relevant to small fliers, including: laminar separation and transition over a stationary airfoil, transition effects on the dynamic stall vortex generated by a plunging airfoil, and the effect of flexibility on the flow structure above a membrane airfoil. The specific cases were also selected to permit comparison with available experimental measurements. First, the process of transition on a stationary SD7003 airfoil section over a range of Reynolds numbers and angles of attack is considered. Prior to stall, the flow exhibits a separated shear layer which rolls up into spanwise vortices. These vortices subsequently undergo spanwise instabilities, and ultimately breakdown into fine-scale turbulent structures as the boundary layer reattaches to the airfoil surface. In a time-averaged sense, the flow displays a closed laminar separation bubble which moves upstream and contracts in size with increasing angle of attack for a fixed Reynolds number. For a fixed angle of attack, as the Reynolds number decreases, the laminar separation bubble grows in vertical extent producing a significant increase in drag. For the lowest Reynolds number considered (Re c = 104), transition does not occur over the airfoil at moderate angles of attack prior to stall. Next, the impact of a prescribed high-frequency small-amplitude plunging motion on the transitional flow over the SD7003 airfoil is investigated. The motion-induced high angle of attack results in unsteady separation in the leading edge and in the formation of dynamic-stall-like vortices which convect downstream close to the airfoil. At the lowest value of Reynolds number (Re c = 104), transition effects are observed to be minor and the dynamic stall vortex system remains fairly coherent. For Re c = 4 × 104, the dynamic-stall vortex system is laminar at is inception, however shortly afterwards, it experiences an abrupt breakdown associated with the onset of spanwise instability effects. The computed phased-averaged structures for both values of Reynolds number are found to be in good agreement with the experimental data. Finally, the effect of structural compliance on the unsteady flow past a membrane airfoil is investigated. The membrane deformation results in mean camber and large fluctuations which improve aerodynamic performance. Larger values of lift and a delay in stall are achieved relative to a rigid airfoil configuration. For Re c = 4.85 × 104, it is shown that correct prediction of the transitional process is critical to capturing the proper membrane structural response.
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Acknowledgments
The authors are grateful for AFOSR sponsorship under tasks monitored by Dr. J. Schmisseur. This work was also supported in part by a grant of HPC time from the DoD HPC Major Shared Resource Center at AFRL, WPAFB. The authors are grateful to M. OL, R. Radespiel and J. Windte for their kind assistance with their experimental data sets.
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Visbal, M.R., Gordnier, R.E. & Galbraith, M.C. High-fidelity simulations of moving and flexible airfoils at low Reynolds numbers. Exp Fluids 46, 903–922 (2009). https://doi.org/10.1007/s00348-009-0635-4
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DOI: https://doi.org/10.1007/s00348-009-0635-4