Numerical study of two-airfoil arrangements by a discrete vortex method

• Published in: Theoretical and computational fluid dynamics 2020-04, Vol.34 (1-2), p.79-103
• Main Authors: Faure, Thierry M., Dumas, Laurent, Montagnier, Olivier
• Format: Article
• Language: English
• Subjects: Adaptation; Aerodynamic characteristics; Aerodynamic coefficients; Aerodynamics; Airfoil oscillations; Analysis; Angle of attack; Classical and Continuum Physics; Coefficients; Computational fluid dynamics; Computational Science and Engineering; Engineering; Engineering Fluid Dynamics; Flow; Fluid flow; Fluid mechanics; Mechanics; Methods; Numerical analysis; Numerical methods; Original Article; Physics; Reynolds number; Shear layers; Suction; Theorems; Vortex shedding; Vortices
• ISSN: 0935-4964; 1432-2250
• DOI: 10.1007/s00162-019-00511-0

The aerodynamic characteristics of two neighboring airfoils are greatly different from those of a single airfoil, for both attached and detached flow conditions. In order to study the features of a two-airfoil arrangement with variations in the angle of attack and distances between the airfoils, and considering possible flow detachments, an adaptation of a discrete-time vortex numerical method is conducted. It is based on the fact that for a given airfoil and Reynolds number, there is a critical value of the leading-edge suction parameter. If its instantaneous value exceeds the critical value, vortex shedding occurs at the leading edge, representing the shear layer associated with flow detachment. In addition, Kelvin’s theorem imposes for each time step that the total circulation equals zero. In the present paper, Kelvin’s theorem is extended for a two-airfoil arrangement with the initial starting flow condition. That numerical method allows to obtain instantaneous flow features and airfoil forces for different arrangements. It is validated first for unsteady motions of airfoils in oscillation and plunge. Then, steady airfoils cases are considered without plunging motion and a constant angle-of-attack. Comparisons with available experimental data are presented in terms of flow field and aerodynamic coefficients both for unsteady motions or steady airfoils. In particular, in order to show the possible improvement in the two-airfoil arrangement performance, the averaged lift coefficient is compared with the single-airfoil configuration. A discussion on the lift efficiency ratio with previous measurements and time development of the flow field permits to understand the mechanisms contributing to a positive interaction.