Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou 310027, P. R. China and Department of Mechanics, Zhejiang University, Hangzhou 310027, P. R. China.
Phys Rev E. 2018 Jan;97(1-1):013110. doi: 10.1103/PhysRevE.97.013110.
This paper investigates the three-dimensional instabilities of the flow past a periodically heaving airfoil. By comparison with a pitching foil [Deng et al., Phys. Rev. E 92, 063013 (2015)PLEEE81539-375510.1103/PhysRevE.92.063013], here we present distinctive characteristics for the heaving foil, particulary regarding its Floquet modes. By increasing the frequency (Sr), or equivalently decreasing the amplitude (A_{D}) along the marginal stability curve in the (Sr,A_{D}) phase space, the critical Floquet mode emerges sequentially as A, quasiperiodic (QP), and B. It is interesting to note that both modes A and B are synchronous with the base flow, in contrast to the quasiperiodic mode QP. To further investigate the instability across the marginal curve, we fix the frequency at Sr=0.187, of which the critical Floquet mode is located in the synchronous regime, while varying A_{D} around the critical point. We find that the dominant mode switches from mode A to mode B, while mode QP never becomes critical as we increase A_{D}. We note that mode S, a subharmonic mode, can also be unstable, which, however, is not physically realizable, because the magnitude of its Floquet multiplier is always smaller than that of mode B. We have also studied the influence of various Reynolds numbers at the same critical point on the marginal stability curve, with the results resembling that by varying the amplitude A_{D}.
本文研究了周期性激励翼型绕流的三维不稳定性。与俯仰翼型相比[Deng 等人，Phys. Rev. E 92, 063013 (2015)PLEEE81539-375510.1103/PhysRevE.92.063013]，本文呈现了激励翼型的独特特征，特别是其 Floquet 模式。通过增加频率(Sr)，或者等效地沿(Sr,A_{D})相空间中的临界限减少振幅(A_{D})，临界 Floquet 模式依次作为 A、拟周期(QP)和 B 出现。有趣的是，注意到模式 A 和 B 都与基流同步，而 QP 模式则不同。为了进一步研究临界限上的不稳定性，我们将频率固定在 Sr=0.187，其临界 Floquet 模式位于同步区域，而在临界点周围变化 A_{D}。我们发现主导模式从模式 A 切换到模式 B，而随着 A_{D}的增加，模式 QP 从未变得临界。我们注意到，次谐波模式 S 也可能不稳定，但实际上是不可能的，因为其 Floquet 乘子的大小始终小于模式 B。我们还在相同的临界点研究了各种雷诺数对临界限稳定性的影响，结果与通过改变振幅 A_{D}相似。
