Minimizing transient energy growth in plane Poiseuille flow
Minimizing transient energy growth in plane Poiseuille flow
复制标题
最小化平面泊肃叶流中的瞬态能量增长
DOI：
--
复制
发表时间：
2008
期刊：
影响因子：
--
通讯作者：
George Papadakis
中科院分区：
文献类型：
--
作者：
J. Whidborne;J. McKernan;George Papadakis
研究了层流平面波塞维尔流的反馈控制问题。与许多流动一样，平面泊泽维尔流动的动力学是非正态的。因此，小的扰动迅速增长，而大的瞬态可能引发非线性并导致湍流，即使这种扰动在线性流动中最终会衰减。这种灵敏度可以用最大瞬态能量增长来测量。采用谱法对线性化的流动方程进行离散，然后在一个波数对上考虑，从而得到适合高级控制设计的流动动力学模型。通过对一组线性矩阵不等式的重复求解，得到了使最大瞬态能量增长上界最小的状态反馈控制器。采用全Navier-Stokes解算器对控制器进行了测试，结果表明，与不受控制的情况相比，控制器的瞬态能量响应幅度明显减小。
The feedback control of laminar plane Poiseuille flow is considered. In common with many flows, the dynamics of plane Poiseuille flow is very non-normal. Consequently, small perturbations grow rapidly with a large transient that may trigger non-linearities and lead to turbulence, even though such perturbations would, in a linear flow, eventually decay. This sensitivity can be measured using the maximum transient energy growth. The linearized flow equations are discretized using spectral methods and then considered at one wave-number pair in order to obtain a model of the flow dynamics in a form suitable for advanced control design. State feedback controllers that minimize an upper bound on the maximum transient energy growth are obtained by the repeated solution of a set of linear matrix inequalities. The controllers are tested using a full Navier—Stokes solver, and the transient energy response magnitudes are significantly reduced compared with the uncontrolled case.