激波/边界层干扰非定常特性的高精度数值模拟与物理分析

The shock wave/boundary layer interaction (SBLI) is an important phenomenon which extensively exists in supersonic flow. As a typical characteristic of SBLI, the unsteadiness has received much attention ever since it was discovered. In the past two or three decades, many experiments and numerical simulations had been conducted to study the unsteadiness of SBLI. However, there is still no definite answer to the cause of this phenomenon. This project studied the unsteady low-frequency oscillation and the related phenomena of the supersonic/hypersonic SBLI using high order numerical scheme. First, an optimized symmetric fourth-order WENO scheme is developed to simulate the supersonic/hypersonic SBLI by optimizing the dispersion and dissipation of the linear fifth-order WENO scheme. Then, the relativity and frequency of the unsteadiness are analyzed in detail. And the discrete mode composing the low-frequency motion are obtained by using proper orthogonal decomposition and dynamic mode decomposition. Further, the causes of the three-dimensional structure and their effects on the unsteady motion are investigated. At last, the low-frequency oscillation and its effects on the pressure load and heat flux at the hypersonic condition are studied and analyzed the effects of the strong compressibility on the SBLI at high Mach numbers.

激波/边界层干扰是超声速流动中广泛存在且具有显著影响的流动现象。低频非定常效应作为激波/边界层干扰的典型特征，自发现以来就引起了研究者的广泛重视，但直到现在对这种现象的原因仍没有一个公认的答案。本项目采用高精度数值方法对超声速以及高超声速激波/边界层干扰中的非定常低频振荡以及相关物理现象开展直接数值模拟研究。首先，在计算方法上通过改善对称型WENO5格式的色散和耗散关系，发展高分辨率、低耗散的对称优化四阶WENO格式，开展超声速条件下激波/边界层干扰的高精度数值模拟；接着，采用特征正交分解和动态模式分解等两种分析手段，对低频振荡开展相关性分析和频谱特性分析，得到构成低频振荡的主要模态；进一步，分析了流场中典型三维流动结构的形成机制以及此流动结构对非定常振荡的影响；最后，在高超声速条件下研究激波/边界层干扰的低频特性以及流场压力载荷和热流载荷特征，探讨高马赫数所引起的强压缩效应对干扰的影响。

本项目在计算方法上通过改善对称型WENO5格式的色散和耗散关系，发展了适用于高精度数值模拟的对称优化四阶WENO格式，该格式在可压缩湍流、高超声速激波边界层干扰均得到应用，且具有较高的分辨率和鲁棒性；接着，采用特征正交分解和动态模态分解，对低频运动开展相关性分析和频谱特性分析，得到构成低频运动的主要模态，发现了分离泡内摩阻脉动具有Gortler涡特征；进一步，发展了适用于可压缩湍流边界层壁面热流的分解方法，定量刻画了边界层内的能量输运过程对壁面热流的贡献；最后，在考虑存在较强可压缩效应的高超声速流动情况下，研究了激波/边界层干扰低频运动及其对流场压力载荷和热流载荷的影响。