标题： 基于Eddy的群体模型用于高雷诺数下的壁面压力谱 显示英文标题

标题： Eddy population based model for the wall-pressure spectrum at high Reynolds number

摘要： 湍流边界层下方的壁面压力脉动通过流体和结构模态之间的相互作用引发噪声和结构疲劳。 传统的频谱预测模型——如广泛接受的Goody模型——无法捕捉高雷诺数下次对流区域中的能量增长，同时又过度预测了方差。 为解决这些不足，提出了两种半经验模型，用于规范湍流边界层、管道和通道中的壁面压力频谱，摩擦雷诺数$\delta^+$范围从180到47 000。 这些模型基于对两种涡旋群体的考虑，这些涡旋群体大致代表了内尺度运动和外尺度运动对壁面压力脉动的贡献。 第一个模型将预乘频谱表示为两个重叠的对数正态分布：一个与$\delta^+$无关的内尺度项和一个幅度随$\delta^+$平滑扩大的外尺度项。 经过与大涡模拟、直接数值模拟和最近的高$\delta^+$管道数据校准，它再现了对流脊和在大$\delta^+$下次对流脊的出现。 第二个模型围绕新获得的管道数据开发，利用理论论证来规定内尺度和外尺度分布的频谱形状。 通过将$\delta^+$依赖性嵌入平滑渐近函数中，它得出一个随着$\delta^+$连续变化的公式。 这两个模型都捕捉了整个频谱及其方差的对数增长，为更准确的工程预测壁面压力脉动奠定了基础。 显示英文摘要

摘要： Wall-pressure fluctuations beneath turbulent boundary layers drive noise and structural fatigue through interactions between fluid and structural modes. Conventional predictive models for the spectrum--such as the widely accepted Goody model--fail to capture the energetic growth in the subconvective regime that occurs at high Reynolds number, while at the same time over-predicting the variance. To address these shortcomings, two semi-empirical models are proposed for the wall-pressure spectrum in canonical turbulent boundary layers, pipes and channels for friction Reynolds numbers $\delta^+$ ranging from 180 to 47 000. The models are based on consideration of two eddy populations that broadly represent the contributions to the wall pressure fluctuations from inner-scale motions and outer-scale motions. The first model expresses the premultiplied spectrum as the sum of two overlapping log-normal populations: an inner-scaled term that is $\delta^+$-invariant and an outer-scaled term whose amplitude broadens smoothly with $\delta^+$. Calibrated against large-eddy simulations, direct numerical simulations, and recent high-$\delta^+$ pipe data, it reproduces the convective ridge and the emergence of a sub-convective ridge at large $\delta^+$. The second model, developed around newly-available pipe data, uses theoretical arguments to prescribe the spectral shapes of the inner and outer populations. By embedding the $\delta^+$ dependence in smooth asymptotic functions, it yields a formulation that varies continuously with $\delta^+$. Both models capture the full spectrum and the logarithmic growth of its variance, laying the groundwork for more accurate engineering predictions of wall-pressure fluctuations.