边界层由层流向湍流的转捩是高超声速飞行器设计面临的重大空气动力学问题。随着飞行速域与空域的不断拓展，高超声速高焓边界层中的高温气体效应、尤其是热化学非平衡（TCNE）效应使得量热完全气体（CPG）假设失效，并深刻影响流动转捩过程，导致新物理、新现象的产生。相关研究涉及多个学科，是近年国际上的热点领域，但是目前研究手段尚不健全，耦合作用机理尚不明晰。本文考虑TCNE效应和空气五组分模型，针对高超声速高焓边界层，在流场精确计算、流动稳定性分析和转捩机理等方面开展了研究，取得的主要成果包括：针对高阶激波装配法，建立了广义最小残差法（GMRES）和线松弛两种隐式时间推进格式，有效克服了TCNE流动的强数值刚性，对定常层流的收敛速度可达显式或半隐式格式的4至20倍。两种格式都适合并行计算，GMRES便于实现无矩阵化，线松弛则易处理流场迭代与激波运动的强耦合，且求解成本低。利用线性稳定性理论研究了来流马赫数最高达20的高焓边界层的稳定性，边界层中出现了更高频的第三模态，但第二模态仍占主导。扰动相比基本流更趋向热化学冻结态，基本流改变带来的影响占主导，即TCNE效应引起的边界层温度和厚度的降低使得第二模态更不稳定、频率升高。给出了高焓边界层中的扰动能量传输机制，得到了第二模态下游区域的超声速模态的演化特性。发展了TCNE边界层的非线性抛物化扰动方程（NPSE）和Floquet二次失稳理论（SIT）方法，实现了二次失稳分析在TCNE边界层中的首次应用。研究发现，相较于亚谐共振，基本共振是第二模态二次失稳的主导机制。相比于CPG算例，TCNE效应使得基本共振的增长率更大，也使得斜波转捩过程中流向涡及其他模态的增长均更快。同时，发现非定常模态和它们的谐波模态之间的能量传递集中发生在它们与平均流强烈相互作用的地方。进一步地，利用NPSE和SIT方法研究了来流马赫数为16的高焓后掠抛物体三维边界层中横流的首次和二次失稳，发现TCNE效应使得横流模态更不稳定。在饱和的定常横流涡中观察到与低速流动相同的经典同向卷起结构。对于定常横流涡的二次失稳，CPG算例中I型模态的增长率最大，但在TCNE算例中，发现IV型模态具有最大的增长率。IV型模态位于横流涡的下洗区，且其增长由法向产生项（位于涡的顶部和底部）和展向产生项（位于下洗区）共同贡献。
Boundary layer transition from laminar to turbulence is of vital importance to the design of hypersonic vehicles. With continuous expansion of flight speed and altitude domains, the high-temperature gas effects, especially the thermochemical non-equilibrium (TCNE) effects in hypersonic high-enthalpy boundary layers invalidate the calorically perfect gas (CPG) assumption. They can also largely influence the flow transition process, resulting in new physics and new phenomena. Relevant research is multi-interdisciplinary and has been a worldwide hotspot in recent years. However, the research methods are still in development, and the coupling mechanisms remain unclear. In this thesis, the boundary-layer instability and transition in hypersonic high-enthalpy boundary layers are investigated considering the TCNE effects and the five-species model of air. The works are on accurate flow calculations, flow instability analyses and transition mechanisms. The main results are summarized as follows.For the high-order shock-fitting method, two implicit time-stepping schemes are established, including the generalized minimum residual (GMRES) and line relaxation (LR) methods. The implicit schemes effectively overcome strong numerical stiffness in TCNE flows. Furthermore, the convergence rate is accelerated by 4~20 times for steady laminar flow calculations, in comparison with the explicit or semi-implicit schemes. Besides, both implicit schemes are suitable for parallel computations. GMRES can be matrix-free, while LR is cheap to solve and easily deals with the strong coupling between the flow iteration and shock wave motion.Linear stability theory is used to study the modal instability of high-enthalpy boundary layers with free-stream Mach numbers of up to 20. The unstable third mode appears at a higher frequency, but the second mode is still dominant. The disturbance tends to be more thermochemical frozen than the basic flow. The influence caused by the basic flow modification is dominant. Therefore, the cooler and thinner boundary layer in the TCNE flow destabilizes the second mode and increases its frequency. The energy transfer mechanisms of disturbances in high-enthalpy boundary layers are obtained. The evolution of supersonic modes in the downstream region of the second mode is investigated.The nonlinear parabolized stability equations (NPSE) and Floquet-based secondary instability theory (SIT) are developed for TCNE boundary layers. They are first employed to analyze the secondary instability in TCNE boundary layers. The fundamental resonance is the dominant secondary instability mechanism of the second mode, compared with the subharmonic resonance. Furthermore, compared with the CPG cases, the TCNE effects increase the growth rate of the fundamental resonance and, in the oblique-mode breakdown case, lead to faster growth of the streamwise vortex mode and other modes. In this process, intensive energy transfer between the selected modes and their harmonic waves occurs where they interact strongly with the basic flow.The NPSE and SIT methods are further utilized to study the primary and secondary crossflow instabilities in high-enthalpy flows. The case studied is a three-dimensional boundary layer over a swept parabola with a free-stream Mach number of 16. TCNE effects are found to destabilize the crossflow mode. The classical co-rotating rollover structures, like those in lower speed flows, are observed in saturated stationary crossflow vortices. In terms of the secondary instability of stationary crossflow vortices, the type-I mode has the largest growth rate in the CPG case. However, in the TCNE case, the type-IV mode is found to have the largest growth rate. The type-IV mode is located in the downwash region of the crossflow vortex. Its growth is contributed by both the wall-normal production term (at the top and bottom of the vortex) and the spanwise production term (at the downwash region).
