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.

中文翻译：

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离散涡法对双翼型布置的数值研究

对于附着和分离的流动条件，两个相邻翼型的空气动力学特性与单个翼型的空气动力学特性有很大不同。为了研究具有不同攻角和翼型间距离变化的双翼型布置的特征，并考虑可能的流动分离，对离散时间涡数值方法进行了改进。它基于这样一个事实，即对于给定的翼型和雷诺数，前缘吸力参数存在一个临界值。如果其瞬时值超过临界值，则在前缘发生涡脱落，代表与流动脱离相关的剪切层。此外，开尔文定理对每个时间步长规定总循环量为零。在本文中，开尔文定理扩展到具有初始起始流动条件的两翼型布置。该数值方法允许获得不同布置的瞬时流动特征和翼型力。它首先针对翼型在振荡和俯冲中的不稳定运动进行了验证。然后，在没有俯冲运动和恒定迎角的情况下考虑稳定翼型的情况。在非定常运动或稳定翼型的流场和空气动力学系数方面与可用的实验数据进行了比较。特别地，为了显示双翼型布置性能的可能改进，将平均升力系数与单翼型配置进行比较。