Analytical models of the wall-pressure spectrum under a turbulent boundary layer with adverse pressure gradient
Analytical models of the wall-pressure spectrum under a turbulent boundary layer with adverse pressure gradient
复制标题
逆压梯度湍流边界层壁面压力谱解析模型
DOI：
10.1017/jfm.2019.616
复制
发表时间：
2019
影响因子：
3.7
通讯作者：
M. Roger
中科院分区：
文献类型：
--
作者：
G. Grasso;Prateek Jaiswal;Hao Wu;S. Moreau;M. Roger
本文提出了一个全面的分析方法，湍流边界层下的壁压波动的建模，统一和扩展的分析模型，已经提出了几十年。将控制压力波动的泊松方程在波数域中进行傅里叶变换，得到修正的亥姆霍兹方程，并采用绿色函数技术求解。微分方程的源项由湍流平均切变项和湍流湍流相互作用项组成，它们分别在湍流场的联合正态概率分布的假设下建模。湍流统计的函数表达式被证明是壁压谱的正确表示的最关键点。各种假设对湍流的纵向相关函数的形状的影响进行评估，在第一位与纯粹的分析考虑，使用理想化的流动模型。然后，将边界层湍流谱分布假设对所得壁面压力谱的影响与直接数值模拟计算结果和控制扩散翼型上的压力测量结果进行了比较。在试验条件下，在该翼型吸力面上形成的附面层的特征是具有逆压力梯度。最后讨论了壁压谱计算的数值方法。一个Monte Carlo技术用于快速评价的多维积分制定的理论部分。
This paper presents a comprehensive analytical approach to the modelling of wall-pressure fluctuations under a turbulent boundary layer, unifying and expanding the analytical models that have been proposed over many decades. The Poisson equation governing pressure fluctuations is Fourier transformed in the wavenumber domain to obtain a modified Helmholtz equation, which is solved with a Green’s function technique. The source term of the differential equations is composed of turbulence–mean shear and turbulence–turbulence interaction terms, which are modelled separately within the hypothesis of a joint normal probability distribution of the turbulent field. The functional expression of the turbulence statistics is shown to be the most critical point for a correct representation of the wall-pressure spectrum. The effect of various assumptions on the shape of the longitudinal correlation function of turbulence is assessed in the first place with purely analytical considerations using an idealised flow model. Then, the effect of the hypothesis on the spectral distribution of boundary-layer turbulence on the resulting wall-pressure spectrum is compared with the results of direct numerical simulation computations and pressure measurements on a controlled-diffusion aerofoil. The boundary layer developing over the suction side of this aerofoil in test conditions is characterised by an adverse pressure gradient. The final part of the paper discusses the numerical aspect of wall-pressure spectrum computation. A Monte Carlo technique is used for a fast evaluation of the multi-dimensional integral formulation developed in the theoretical part.
影响因子：
3.7
作者：
Jones, L. E.;Sandberg, R. D.;Sandham, N. D.
通讯作者：
Sandham, N. D.