Abstract We present a numerical study on the fluid–structure interaction of an incompressible laminar flow around a slender blunt-based body implementing a rear cavity of flexible plates. The study focuses on the use of this type of device to control the wake dynamics and the aerodynamic forces acting on the body, as well as to harvest energy from the flow. To that aim, the effects on the plates flow-induced vibrations (FIV) and on the dynamics of the flow of three control parameters, namely the reduced velocity, 0 ≤ U ∗ 12 , the mass ratio, m ∗ = [ 500 , 1000 ] and the cavity height h c , are evaluated at Reynolds number R e = 500 . Four different branches are identified in terms of dynamic response, as U ∗ increases, regardless of the values of h c and m ∗ . At low values of U ∗ , an initial branch with a local peak of moderate amplitude response is observed, where the plates oscillate in counter-phase, in a varicose mode, with a frequency f p that is synchronized with the second harmonic of the vortex shedding frequency, 2 f v s , and similar to the natural frequency of the solid, f n ≃ f 1 , n . For intermediate values of U ∗ , a transition towards a sinuous mode of oscillation occurs, where the plate frequency is synchronized with the vortex shedding frequency, f p = f v s . Initially, after such transition, the oscillation frequency is lower than the natural frequency of the plates f p f 1 , n , so that a weak response defines a lower branch in the amplitude response curve. When U ∗ increases, a lock-in regime develops with f p = f v s = f 1 , n , that is characterized by a response amplification, giving rise to the emergence of the upper branch, where the FIV amplitude of plates is the highest. Finally, a fourth desynchronization branch of moderate amplitude appears for larger values of U ∗ , where the plates present a complex, multi-mode regime, characterized by the vibration at multiple frequencies within the range 5 f 1 , n f p 6 . 5 f 1 , n . The analysis of the plates deformation through POD analysis reveals that they mainly oscillate following the first Euler–Bernoulli mode for the first three branches, and a combination of the second and first Euler–Bernoulli modes for the desynchronization branch. The effect of increasing the mass ratio is to mitigate the response at higher values of U ∗ , while reducing the cavity height h c leads to the fostering of oscillations within the upper and desynchronization branches. In general, the FIV response of plates alters the wake dynamics and the force coefficient, especially within the lock-in regime, where the drag is strongly amplified, although the fluctuations of the lift are attenuated (nearly a 40% reduction). Besides, reductions of the drag of approximately 2% are obtained within the initial and lower branches. Finally, a simple quantification of the energy transfer from the plates, through a linearized Euler–Bernoulli approach, shows that the lock-in regime represents the best regime to extract energy from the flow.

中文翻译：

---

具有后柔性腔的钝体后面层流尾流中流动引起的振动的数值分析

摘要 我们提出了一个关于不可压缩层流的流体-结构相互作用的数值研究，该层流围绕一个细长的钝基体，实现了一个柔性板的后腔。该研究的重点是使用这种类型的设备来控制尾流动力学和作用在身体上的空气动力，以及从流动中获取能量。为此，对板流致振动 (FIV) 和三个控制参数的流动动力学的影响，即降低的速度，0 ≤ U ∗ 12，质量比，m ∗ = [ 500 , 1000 ] 和空腔高度 hc 在雷诺数 Re = 500 下进行评估。随着 U ∗ 增加，无论 hc 和 m ∗ 的值如何，根据动态响应确定了四个不同的分支。在 U ∗ 的低值下，观察到具有中等幅度响应的局部峰值的初始分支，其中板以反相、曲张模式振荡，其频率 fp 与涡旋脱落频率的二次谐波同步，2 fvs 等到固体的固有频率，fn ≃ f 1 , n 。对于 U ∗ 的中间值，会发生向正弦振荡模式的转变，其中板频率与涡旋脱落频率 fp = fvs 同步。最初，在这种转变之后，振荡频率低于板的固有频率 fpf 1 , n ，因此弱响应定义了振幅响应曲线中的下分支。当 U ∗ 增加时，锁定机制发展为 fp = fvs = f 1 , n ，其特征在于响应放大，导致出现上部分支，其中板块的 FIV 幅度最高。最后，对于较大的 U ∗ 值，出现中等幅度的第四个去同步分支，其中板块呈现复杂的多模式状态，其特征是在 5 f 1 ，nfp 6 范围内的多个频率下振动。5 f 1 , n 。通过 POD 分析对板块变形的分析表明，它们的前三个分支主要遵循第一 Euler-Bernoulli 模式，而去同步分支则主要遵循第二和第一 Euler-Bernoulli 模式的组合。增加质量比的效果是在更高的 U * 值时减轻响应，同时降低腔高度 hc 导致在上部和不同步分支内产生振荡。一般来说，板块的 FIV 响应改变了尾流动力学和力系数，特别是在锁定状态下，尽管升力的波动被减弱（减少近 40%），但阻力被强烈放大。此外，在初始和下部分支内获得了大约 2% 的阻力减少。最后，通过线性化的 Euler-Bernoulli 方法对来自板的能量转移进行简单量化，表明锁定状态代表了从流动中提取能量的最佳状态。在初始和较低的分支内获得了大约 2% 的阻力减少。最后，通过线性化的 Euler-Bernoulli 方法对来自板的能量转移进行简单量化，表明锁定状态代表了从流动中提取能量的最佳状态。在初始和较低的分支内获得了大约 2% 的阻力减少。最后，通过线性化的 Euler-Bernoulli 方法对来自板的能量转移进行简单量化，表明锁定状态代表了从流动中提取能量的最佳状态。