A computational study is conducted on thin flat plates to simulate flows of Reynolds numbers at ${10}^4$ to provide understanding and guidance for micro air vehicles and other low-Reynolds-number airfoil designs. A synergistic effort between experiments and validated and computational fluid dynamics (CFD) tools were used as part of this study. The CFD tool used in this study is an established Reynolds-averaged Navier–Stokes (RANS) solver with a Spalart–Allmaras turbulence model and a correlation-based laminar–turbulent boundary-layer transition model. The computational method was validated against experimental data for flat plates under steady and unsteady kinematic conditions. The objective of the study was to understand unsteady characteristics of a thin flat plate undergoing harmonic pitching (no plunging) around the quarter chord under incompressible flow conditions. Pitching amplitudes were limited to 10 deg to ensure there was no effect of dynamic stall. The focus of this study is to characterize unsteady aerodynamics based on reduced frequency, which was varied between 0.005, 0.05, and 0.5. The unsteady condition of 0.05 was compared against experiments, 2-D RANS, and 3-D hybrid RANS/large-eddy simulation formulations. It was observed that the lift characteristics were reasonably well predicted by the CFD tools when compared to experimental observations. At a reduced frequency of $0.05$, the pitching motion causes an apparent stabilization of vortices resulting in higher oscillatory lift amplitude than the static value. The 3-D RANS better predicted the pitching-moment characteristics compared to the 2-D RANS, attributed to the breakdown of the leading-edge vortex. It was observed that, although thinner flat-plate airfoils have a higher maximum lift coefficient compared to the thicker NACA 0012, they also produce higher instantaneous pitching moment.

在薄平板上进行了计算研究，以模拟雷诺数在 ${10}^4$为微型飞行器和其他低雷诺数的机翼设计提供理解和指导。实验与经过验证的流体动力学和计算流体动力学（CFD）工具之间的协同努力被用作本研究的一部分。本研究中使用的CFD工具是建立的雷诺平均Navier-Stokes（RANS）求解器，具有Spalart-Allmaras湍流模型和基于相关的层流-湍流边界层过渡模型。针对稳态和非稳态运动条件下平板的实验数据对计算方法进行了验证。这项研究的目的是了解在不可压缩的流动条件下，四分之一弦周围经历谐波俯仰（无骤降）的薄平板的不稳定特性。俯仰幅度限制在10度以确保没有动态失速的影响。这项研究的重点是基于降低的频率来表征不稳定的空气动力学特性，降低的频率在0.005、0.05和0.5之间变化。将0.05的不稳定条件与实验，2-D RANS和3-D混合RANS /大涡模拟配方进行了比较。观察到，与实验观察相比，CFD工具可以很好地预测升力特性。以降低的频率 观察到，与实验观察相比，CFD工具可以很好地预测升力特性。以降低的频率 观察到，与实验观察相比，CFD工具可以很好地预测升力特性。以降低的频率$0.05$，俯仰运动会引起涡流的明显稳定，从而导致振荡升力幅度高于静态值。与3-D RANS相比，3-D RANS可以更好地预测俯仰力矩特性，这归因于前沿涡旋的破坏。观察到，尽管较薄的平板翼型与较厚的NACA 0012相比具有更高的最大升力系数，但它们也会产生更高的瞬时俯仰力矩。