Time-delayed feedback technique for suppressing instabilities in time-periodic flow
Time-delayed feedback technique for suppressing instabilities in time-periodic flow
复制标题
用于抑制时间周期流不稳定性的延时反馈技术
DOI：
10.1103/physrevfluids.2.113904
复制
发表时间：
2017
影响因子：
2.6
通讯作者：
L. Lesshafft
中科院分区：
文献类型：
--
作者：
L. Shaabani;D. Sipp;L. Lesshafft
提出了一种数值方法，允许计算时间周期性的湍流状态，即使在存在流体动力学不稳定性。该方法基于通过延迟反馈控制的方式来滤波非谐波分量，如Pyragas [ Phys. Lett. A 170，421-428（1992）]。它的使用在湍流问题的情况下，这里展示了一个周期性的强迫层流射流，受亚谐不稳定性，引起涡对。滤波器增益的最优选择，这是一个自由参数的稳定化过程中，在低维模型问题的背景下进行了研究，它表明，该模型预测滤波器性能在高维EQUILOW系统。有效地抑制了喷流中的涡对，从而准确地恢复了响应于谐波强迫的不稳定的周期性湍流状态。该过程可以直接在任何标准的并行求解器中实现。延迟反馈控制的存储器需求可以通过检查点之间的时间插值来显著减少。最后，该方法被扩展为治疗周期性问题的频率是不知道的先验。这一过程被证明为一个三维立方盖驱动腔在超临界条件下。
A numerical method is presented that allows to compute time-periodic flow states, even in the presence of hydrodynamic instabilities. The method is based on filtering non-harmonic components by way of delayed feedback control, as introduced by Pyragas [ Phys. Lett. A 170 , 421-428 (1992)]. Its use in flow problems is demonstrated here for the case of a periodically forced laminar jet, subject to a subharmonic instability that gives rise to vortex pairing. The optimal choice of the filter gain, which is a free parameter in the stabilization procedure, is investigated in the context of a low-dimensional model problem, and it is shown that this model predicts well the filter performance in the high-dimensional flow system. Vortex pairing in the jet is efficiently suppressed, so that the unstable periodic flow state in response to harmonic forcing is accurately retrieved. The procedure is straightforward to implement inside any standard flow solver. Memory requirements for the delayed feedback control can be significantly reduced by means of time interpolation between checkpoints. Finally, the method is extended for the treatment of periodic problems where the frequency is not known a priori . This procedure is demonstrated for a three-dimensional cubic lid-driven cavity in supercritical conditions.