Numerical calculations were carried out in order to investigate the delay of transition to turbulence on a wing section by means of local dynamic surface deformation. Physically, the deformation may be produced by piezoelectrically driven actuators located below a compliant aerodynamic surface, which have been explored experimentally. One actuator was located in the upstream region of the wing, and it was oscillated at the most unstable frequency in order to develop small disturbances corresponding to Tollmien–Schlichting instabilities. A second controlling actuator was placed further downstream, and then it was oscillated at the same frequency but with an appropriate phase shift and modified amplitude in order to decrease the disturbance growth and delay the transition process. The configuration consists of a NLF(1) 0414F natural laminar flow wing section in subsonic flow at a chord-based Reynolds number of $1\times {10}^6$. Angles of attack of both 3.0 and 4.0 deg were considered. Large-eddy simulations were carried out via solution of the unsteady three-dimensional compressible Navier–Stokes equations using a high-fidelity computational scheme and an implicit time-marching approach. Two-dimensional simulations were used to develop an empirical process that was applied to determine the optimal phase shift and amplitude of the controlling actuator. Results of the simulations are described, features of the flowfields are elucidated, and comparisons are made between solutions for the uncontrolled and controlled cases in order quantify effectiveness of the control. It is shown that dynamic surface control can return approximately 20% of the upper wing surface to laminar flow that is lost to premature transition when disturbances are present.

为了研究通过局部动态表面变形在机翼截面上过渡到湍流的延迟，进行了数值计算。在物理上，变形可以由位于顺应性气动表面下方的压电驱动致动器产生，该致动器已通过实验进行了探索。一个执行器位于机翼的上游区域，它以最不稳定的频率振荡，以便产生对应于托尔米恩-施利希特不稳定性的小扰动。将第二个控制执行器放置在更下游，然后以相同的频率振荡，但具有适当的相移和改变的幅度，以减少干扰的增长并延迟过渡过程。$\mathrm{1个}\times {10}^6$。考虑了3.0和4.0度的迎角。大涡模拟是通过使用高保真计算方案和隐式时间前进方法通过求解不稳定的三维可压缩Navier-Stokes方程进行的。二维模拟用于开发经验过程，该过程可用于确定控制执行器的最佳相移和幅度。描述了仿真结果，阐明了流场的特征，并对非受控案例和受控案例的解决方案进行了比较，以量化控制的有效性。结果表明，动态表面控制可以使大约20％的上机翼表面返回层流，当存在扰动时，层流会因过早过渡而丢失。