Nonlinear control of unsteady finite-amplitude perturbations in the Blasius boundary-layer flow
Nonlinear control of unsteady finite-amplitude perturbations in the Blasius boundary-layer flow
复制标题
Blasius 边界层流中非定常有限振幅扰动的非线性控制
DOI：
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发表时间：
2013
影响因子：
3.7
通讯作者：
P. D. Palma
中科院分区：
文献类型：
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作者：
S. Cherubini;J. Robinet;P. D. Palma
摘要本文基于非线性Navier-Stokes方程，提出了一种最优控制策略，旨在抑制Blasius边界层流中非定常有限幅扰动的快速增长。变分过程是用来找到吹吸控制律在壁面提供最大阻尼的能量，一个给定的扰动在一个给定的目标时间，最终的目的是导致流回到层流状态。两个最佳增长的有限振幅初始扰动能够导致非常迅速的过渡已被用来初始化流。已经发现的非线性控制程序能够驱动这种扰动回到层流状态，提供的目标时间的最小化和区域中的吹吸应用已被适当地选择。另一方面，基于线性化Navier-Stokes方程的等效控制过程被发现效果较差，在考虑有限振幅扰动时无法将流动引导到层流状态。对于给定的初始扰动，也已经确定了对吹气和吸气具有强敏感性的区域：当在这些区域中致动控制时，也观察到致动区域的较短范围的层流化。非线性最佳吹吸律由交替的壁面法向速度扰动组成，它似乎通过两种不同的机制来改变核心流结构：（i）在小时间内的壁面法向速度补偿;（ii）在大时间内的旋转平衡效应。对于不同的目标时间、成本参数值以及吹扫区和抽吸区的流向范围，已经观察到类似的控制律，这意味着这两种机制是最优控制策略的鲁棒特征，只要考虑到非线性效应。
Abstract The present work provides an optimal control strategy, based on the nonlinear Navier–Stokes equations, aimed at hampering the rapid growth of unsteady finite-amplitude perturbations in a Blasius boundary-layer flow. A variational procedure is used to find the blowing and suction control law at the wall providing the maximum damping of the energy of a given perturbation at a given target time, with the final aim of leading the flow back to the laminar state. Two optimally growing finite-amplitude initial perturbations capable of leading very rapidly to transition have been used to initialize the flow. The nonlinear control procedure has been found able to drive such perturbations back to the laminar state, provided that the target time of the minimization and the region in which the blowing and suction is applied have been suitably chosen. On the other hand, an equivalent control procedure based on the linearized Navier–Stokes equations has been found much less effective, being not able to lead the flow to the laminar state when finite-amplitude disturbances are considered. Regions of strong sensitivity to blowing and suction have been also identified for the given initial perturbations: when the control is actuated in such regions, laminarization is also observed for a shorter extent of the actuation region. The nonlinear optimal blowing and suction law consists of alternating wall-normal velocity perturbations, which appear to modify the core flow structures by means of two distinct mechanisms: (i) a wall-normal velocity compensation at small times; (ii) a rotation-counterbalancing effect al larger times. Similar control laws have been observed for different target times, values of the cost parameter, and streamwise extents of the blowing and suction zone, meaning that these two mechanisms are robust features of the optimal control strategy, provided that the nonlinear effects are taken into account.