Turbulent flat-plate boundary layer flows have been widely employed for numerical validation in the aero-optical field. In present study, the laminar-to-turbulent evolution induced by wavy roughness in high-Reynolds-number supersonic freestream is investigated using a numerical technique based on the fifth-order weighted compact nonlinear scheme (WCNS-E-5). The computational procedure and post-processing method are described in detail, and the acquired instantaneous flow structure and statistical data are compared with other theoretical, experimental, and numerical results to demonstrate the feasibility of predicting turbulence using WCNS-E-5. Further, to reduce the computational resources required to simulate turbulent flow, a velocity correlation function is introduced to decrease the computational domain in the spanwise direction. Additionally, the effects of different grid sizes on the simulation results are examined by reducing the number of cells in the streamwise, wall-normal, and spanwise directions. Finally, the authors conduct a tentative investigation into the aero-optical effects of the laminar-to-turbulent flowfield using a ray-tracing method, considering both the feasibility of aero-optical detection and the effect of grid scale on the time-averaged imaging quality, as well as a deeper probe into the characteristic structures reflected by aero-optical frequency spectrum. The results elucidated that the wall-normal grid number has the strongest influence on the transitional location, and undoubtedly affects wavefront aberrations. However, different gird scales lead to similar aero-optical spectrum, and revealed the Kolmogorov-type turbulence at small-scale regime. As a prelude to further aero-optical simulations of wall-bounded flows, the current study provides some reference for the code validation process and aero-optical interrogation.

中文翻译：

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WCNS-E-5对高雷诺数自由流中超音速边界层和湍流气动光学研究的验证案例

湍流平板边界层流已广泛用于航空光学领域的数值验证。在本研究中，使用基于五阶加权紧凑非线性方案 (WCNS-E-5) 的数值技术研究了高雷诺数超音速自由流中由波浪粗糙度引起的层流到湍流的演变。详细描述了计算过程和后处理方法，并将获得的瞬时流动结构和统计数据与其他理论、实验和数值结果进行了比较，以证明使用 WCNS-E-5 预测湍流的可行性。此外，为了减少模拟湍流所需的计算资源，引入速度相关函数以减少展向方向的计算域。此外，通过减少流向、壁法向和展向方向上的单元数量来检查不同网格大小对模拟结果的影响。最后，考虑到气动光学探测的可行性和网格尺度对时间平均成像的影响，作者使用射线追踪方法对层流到湍流流场的气动光学效应进行了初步研究。质量，以及对航空光学频谱反射的特征结构的更深入探索。结果表明，壁法向网格数对过渡位置的影响最大，无疑会影响波前像差。然而，不同的网格尺度导致相似的航空光谱，并揭示了小尺度区域的 Kolmogorov 型湍流。