Abstract The paper performs simulation of a rectangular plate excited by turbulent channel flow at friction Reynolds numbers of 180 and 400. The fluid–structure interaction is assumed to be one-way coupled, i.e, the fluid affects the solid and not vice versa. We solve the incompressible Navier–Stokes equations using finite volume direct numerical simulation in the fluid domain. In the solid domain, we solve the dynamic linear elasticity equations using a time-domain finite element method. The obtained plate averaged displacement spectra collapse in the low frequency region in outer scaling. However, the high frequency spectral levels do not collapse in inner units. This spectral behavior is reasoned using theoretical arguments. The resonant vibration is stronger at the third natural frequency than at the first natural frequency. We explain this behavior by comparing the fluid and solid length scales. We further study the sources of plate excitation using a novel formulation. This formulation expresses the average displacement spectrum of the plate as an integrated contribution from the fluid sources within the channel. Analysis of the sources reveals that at the plate natural frequencies, the contribution of the fluid sources to the plate excitation peaks in the buffer layer. The corresponding wall-normal width is found to be ≈ 0 . 75 δ . The integrated contribution of the overlap and outer regions together to the plate response is comparable to that from the buffer region for R e τ = 180 and exceeds the buffer region contribution for R e τ = 400 . We analyze the decorrelated features of the sources using spectral Proper Orthogonal Decomposition (POD) of the net displacement source. We enforce the orthogonality of the modes in an inner product with a symmetric positive definite kernel. The dominant spectral POD mode contributes to the entire plate excitation. The contribution of the remaining modes from the different wall-normal regions undergo destructive interference resulting in zero net contribution. The envelope of the dominant mode further shows that the intensity of the sources peaks in the buffer region and the wall-normal width of the sources extend well into the outer region of the channel.

中文翻译：

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湍流通道流动中的板响应：流固耦合分析

摘要 本文对摩擦雷诺数为180 和400 时由湍流通道流激发的矩形板进行了模拟。假定流固耦合是单向耦合的，即流体影响固体，反之亦然。我们在流体域中使用有限体积直接数值模拟来求解不可压缩的 Navier-Stokes 方程。在实体域中，我们使用时域有限元方法求解动态线性弹性方程。获得的板平均位移谱在外标度的低频区域坍塌。然而，高频频谱水平不会在内部单元中崩溃。这种光谱行为是使用理论论证来推理的。共振振动在第三固有频率比在第一固有频率更强。我们通过比较流体和固体长度尺度来解释这种行为。我们使用一种新的配方进一步研究了板激发的来源。该公式将板的平均位移谱表示为通道内流体源的综合贡献。源分析表明，在板固有频率处，流体源对缓冲层中板激发峰值的贡献。发现相应的壁法线宽度为 ≈ 0 。75 δ。重叠区域和外部区域对板块响应的综合贡献与 Re τ = 180 的缓冲区的贡献相当，并且超过了 Re τ = 400 的缓冲区贡献。我们使用净位移源的光谱真正交分解 (POD) 来分析源的去相关特征。我们在具有对称正定核的内积中强制模式的正交性。主要的光谱 POD 模式有助于整个板激发。来自不同壁法线区域的剩余模式的贡献经历相消干涉，导致零净贡献。主模式的包络进一步表明，源的强度在缓冲区达到峰值，并且源的壁法向宽度很好地延伸到通道的外部区域。来自不同壁法线区域的剩余模式的贡献经历相消干涉，导致零净贡献。主模式的包络进一步表明，源的强度在缓冲区达到峰值，并且源的壁法向宽度很好地延伸到通道的外部区域。来自不同壁法线区域的剩余模式的贡献经历相消干涉，导致零净贡献。主模式的包络进一步表明，源的强度在缓冲区达到峰值，并且源的壁法向宽度很好地延伸到通道的外部区域。