论文标题
湍流边界层中表面压力光谱与涡度之间的关系
The Relationship Between Surface Pressure Spectra and Vorticity in a Turbulent Boundary Layer
论文作者
论文摘要
根据流动涡度的涡度，审查并重新考虑了湍流边界层下面的表面压力波数模型。使用基于Chase（1991）给出的基于涡度方程的解决方案和Squires定理，这表明可以使用非线性湍流扰动相互作用作为源来指定表面压力谱的完整解决方案。然后证明表面压力可以与流动中的涡度直接相关。根据通道流配置的直接数值模拟检查结果。结果表明，与壁剪应力相关的涡度在约七个壁单元的距离上迅速衰减，因此外部涡度在大多数流动中占主导地位。评估了涡度相关函数，并表明涡度正常的长度尺度仅大约十个壁单元，因此可以将流量建模为不相关的涡流板的叠加。最后，通过基于基于均方根（RMS）涡度的分布来建模涡度光谱的模型，并通过对流量中的涡度（RMS）涡度的分布进行建模，以及大约十个壁单元的积分长度尺度。使用来自数值模拟的输入，获得了表面压力光谱的现有经验模型的良好拟合。
The modeling of surface pressure wave number spectra beneath a turbulent boundary layer is reviewed and reconsidered in terms of the vorticity in the flow. Using a solution based on the vorticity equation and Squires theorem, which was originally given by Chase(1991), it is shown that the complete solution for surface pressure spectrum can be specified using the non-linear turbulence-turbulence interaction terms as sources. It is then shown that the surface pressure can be directly related to the vorticity in the flow. The results are checked against a Direct Numerical Simulation of a channel flow configuration. It is shown that the vorticity associated with the wall shear stress decays rapidly over a distance of about seven wall units and so the outer vorticity dominates in the majority of the flow. The vorticity correlation functions are evaluated and it is shown that the length scale of the vorticity normal the wall is only about ten wall units so the flow can be modeled as the superposition of uncorrelated vortex sheets. Finally a model for the surface pressure wave number spectrum is developed by modeling the vorticity spectrum based on the distribution of root mean square (rms) vorticity in the flow, and an integral length scale that is about ten wall units. Using inputs from the numerical simulation, a good fit to existing empirical models for surface pressure spectra is obtained.
