This work extends the input-output approach to the study of wall-bounded shear flows manipulated using actuators common in experimental flow control studies. In particular, we adapt this powerful analytical framework to investigate the flow response to specified geometric actuation patterns (e.g., different plasma actuators) that can be applied over a range of different temporal input signals. For example, the commonly studied steady-state (time-averaged) flow response corresponds to a superposition of step responses in our modeling framework. The approach takes advantage of the linearity of the transfer function representation to construct the actuated flow field as a weighted superposition of the flow responses to point sources of varying intensity comprising the actuation model. We first validate the proposed method through comparisons with numerical and experimental studies of the time-averaged behavior of a transitional boundary layer actuated using a dielectric-barrier discharge plasma actuator operating in constricted discharge mode. The method is shown to reproduce the streamwise velocity field and the vortical structures observed downstream from the tested plasma actuator configurations. We then demonstrate that the method provides even better agreement with the steady-state response of the boundary layer subject to actuation from arrays of symmetric plasma actuators arranged in both spanwise and serpentine geometries. These results indicate the utility of this extension to the widely used input-output framework in analyzing the effects of certain actuation modalities that have shown promise in flow manipulation strategies for drag reduction. An important benefit of this analytical method is the low computational cost associated with its use in extensive parametric studies that would be cost-prohibitive using experiments or high-fidelity simulations.

中文翻译：

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致动边界层的输入输出框架

这项工作将输入-输出方法扩展到研究使用实验流量控制研究中常见的执行器操纵的有边界的剪切流的研究。尤其是，我们采用了这种强大的分析框架，以研究对指定几何驱动模式（例如，不同的等离子体驱动器）的流量响应，该模式可应用于一系列不同的时间输入信号。例如，通常研究的稳态（时间平均）流动响应对应于我们建模框架中阶跃响应的叠加。该方法利用传递函数表示的线性来构造被驱动的流场，作为对包括驱动模型的强度变化的点源的流响应的加权叠加。我们首先通过与数值和实验研究的比较来验证所提出的方法，该数值和实验研究是使用在受限放电模式下工作的介电势垒放电等离子体致动器来驱动过渡边界层的时间平均行为。示出了该方法以再现从测试的等离子体致动器构造的下游观察到的沿流速度场和涡旋结构。然后，我们证明了该方法与边界层的稳态响应提供了更好的一致性，该边界层受到以沿展向和蛇形几何形状布置的对称等离子致动器阵列的驱动。这些结果表明，此扩展到广泛使用的输入-输出框架在分析某些驱动方式的效果方面具有实用性，这些方式已在减少阻力的流量操纵策略中显示出了希望。这种分析方法的一个重要优点是与在广泛的参数研究中使用相关的计算成本较低，而使用实验或高保真度模拟可能会抑制成本。