激波/湍流边界层干扰物面剪切应力统计特性

为了揭示激波/湍流边界层干扰区内物面剪切应力统计特性的演化规律，采用直接数值模拟方法对来流马赫数2.9、12°激波角的入射激波与平板湍流边界层相互作用问题进行了研究。通过与风洞试验数据的比较分析，验证了计算结果的可靠性。系统地探究了干扰区内物面剪切应力的典型特征，如预乘谱、概率密度分布和相干结构等。研究结果表明，分离激波的低频振荡运动对流向及展向分量的预乘谱均没有实质影响，其脉动仍以高频特征为主，低频能量变化较小。干扰区内流向剪切应力概率密度函数分布变化剧烈，分离泡内对数正态分布规律不再适用，而展向剪切应力在干扰区内与正态分布较为接近。相较于上游湍流边界层，分离泡内物面剪切应力矢量夹角与幅值的联合概率密度变化显著，峰值概率降低，峰值范围增大。此外，流向剪切应力脉动场的本征正交分解分析指出，主能量模态与分离激波的低频振荡以及下游再附边界层内的Görtler-like流向涡结构密切相关。

Statistical characteristics of wall shear stress in shock wave and turbulent boundary layer interactions

To reveal the evolution of wall shear stress characteristics in the interaction region, direct numerical simulation of a reflected shock wave and turbulent boundary layer interaction for the incident shock of 12° at Mach number 2.9 is performed. The accuracy of numerical results has been validated against the experimental data and previous direct numerical simulations under matching conditions. The statistical characteristics of wall shear stress, including pre-multiplied power spectral density, probability density function and coherent structures have been analyzed in detail. Results indicate that the low-frequency motions of separated shock wave have no substantial influence on the power spectrum of streamwise and spanwise components of wall shear stress vector. The fluctuations are dominated by high-frequency content and the low-frequency energy exhibits little change. The distribution of probability density functions of streamwise wall shear stress varies dramatically through the interaction region and the law of logarithmic normal distribution is not applicable to the separation bubble, but the distribution of spanwise component is approximately of normal distribution throughout the interaction region. Compared with the upstream undisturbed turbulent boundary layer, the joint probability density function between the angle and magnitude of wall shear stress vector is significantly changed in the separation bubble, with the peak of probability decreasing and the range of maximum values increasing. The proper orthogonal decomposition analysis of the fluctuating streamwise shear stress indicates that the dominant modes are closely associated with the low-frequency oscillations of the separated shock wave and the Görtler-like streamwise vortex structures in the reattachment boundary layer downstream.