Systems & Controls Engineering, United Technologies Corporation, East Hartford, Connecticut 06108, USA.
Chaos. 2013 Sep;23(3):033133. doi: 10.1063/1.4820819.
We present a strategy for control of chaos in open flows and provide its experimental validation in the near field of a transitional jet flow system. The low-dimensional chaotic dynamics studied here results from vortex ring formation and their pairings over a spatially extended region of the flow that was excited by low level periodic forcing of the primary instability. The control method utilizes unstable periodic orbits (UPO) embedded within the chaotic attractor. Since hydrodynamic instabilities in the open flow system are convective, both monitoring and control can be implemented at a few locations, resulting in a simple and effective control algorithm. Experiments were performed in an incompressible, initially laminar, 4 cm diameter circular air jet, at a Reynolds number of 23,000, housed in a low-noise, large anechoic chamber. Distinct trajectory bundles surrounding the dominant UPOs were found from experimentally derived, time-delayed embedding of the chaotic attractor. Velocity traces from a pair of probes placed at the jet flow exit and farther downstream were used to empirically model the UPOs and compute control perturbations to be applied at the jet nozzle lip. Open loop control was used to sustain several nearly periodic states.
我们提出了一种控制开流混沌的策略，并在过渡射流系统的近场中验证了其有效性。这里研究的低维混沌动力学是由涡旋环形成及其在流场的空间扩展区域中的配对引起的，该区域受到初级不稳定性的低水平周期激励。控制方法利用混沌吸引子中嵌入的不稳定周期轨道（UPO）。由于开流系统中的流体动力不稳定性是对流的，因此可以在少数几个位置进行监测和控制，从而形成一种简单而有效的控制算法。实验在一个不可压缩的、初始层流的 4cm 直径圆形空气射流中进行，雷诺数为 23000，安装在一个低噪声、大型无回声室中。从混沌吸引子的实验衍生的时滞嵌入中发现了围绕主要 UPO 的不同轨迹束。从放置在射流出口和更远下游的一对探头的速度迹线中，我们可以经验地对 UPO 进行建模，并计算要在射流喷嘴唇口施加的控制扰动。开环控制可维持几个近周期性状态。
