高超声速流动中，气体来流经激波压缩后温度升高，高温导致气体分子的内能激发，甚至引起离解、电离等化学反应。这些物理化学过程的特征时间通常大于流动特征时间，因此高超声速流动一般处于热化学非平衡状态。如何准确刻画这样的非平衡流动状态至今仍是一个开放的课题。

本文采用物理力学的方法，研究了高温热化学非平衡流动的建模与模拟。首先，通过分子内态的态-态方法实现了高温热化学非平衡流动的精细模拟；然后为提高态-态模拟的工程可行性，发展了流动降维模型并研究了物理降维模型；最后从微观分子碰撞着手，构建了体系碰撞势能面，结合量子-经典动力学模拟得到了大量的振动态-态速率常数，为空气组分高置信度振动态-态模拟提供坚实的数据支持。通过研究，初步打通了从微观分子碰撞的量子化学计算出发，态-态方法为桥梁的高温热化学非平衡流动模拟链条。主要研究内容和研究成果如下：

1）分析了热化学非平衡效应对典型高超声速流动的影响。针对高焓来流的二维双楔激波-边界层干扰流动，分别采用冻结（Fr）、热非平衡（TN）和热化学非平衡（TCN）三种热化学模型进行了数值模拟。二维基本流结果表明，不同热化学模型得到的分离区大小差别很大，但初始分离和二次分离发生的临界折转角几乎一样。采用全局稳定性分析发现，当超过不稳定临界折转角后，流动中出现三维全局不稳定模态，而热化学非平衡效应推迟了全局不稳定的发生，相当于起稳定流动的作用。

2）开展了一维流动的高置信度态-态模拟。首先，采用振动态-态模拟方法求解了正激波后O₂/O气体混合物的松弛过程。相比于常用的双温度模型，振动态-态模拟预测的振动温度峰值更靠近实验结果，并且氧原子质量分数分布也与实验数据符合最好，说明了振动态-态模拟有较高的置信度。进一步地，实现了正激波后五组分空气N₂/N/O₂/O/NO气体混合物的热化学松弛过程的振动态-态模拟，得到了激波后N₂、O₂和NO分子所有振动能级的演化曲线，从中可以明显看出振动松弛和化学反应（主要是离解）各自主导的区域。其次，根据本文新补充的C₂电子态HPIE及HPID速率常数实现了EAST激波管实验条件（Shot 92-102）的电子态-态模拟，得到的高温非平衡C₂的Red辐射和CO的VUV辐射与EAST激波管的实验测量值符合很好，而文献中的双温QSS方法计算结果与实验数据有较大差别，说明了电子态-态模拟有更高的置信度。以上结果表明，高置信度的态-态模拟可以得到更准确的流场信息和详细的非平衡演化规律。

3）发展了适用于热化学非平衡流动计算的准一维驻点线模型。通过与轴对称CFD计算结果、文献中的流动降维模型DRNSE结果以及球头驻点热流实验测量值比较，验证了驻点线模型的可靠性。然后借助驻点线模型实现了球头绕流驻点线上空气五组分混合物的振动态-态模拟（包括46、61和48个O₂、N₂和NO振动态），给出了驻点线上O₂、N₂和NO所有振动态的精细分布，并发现在激波后、边界层内这两个关键区域由于振动松弛-化学反应的强烈耦合作用气体分子内态呈现强非Boltzmann分布。此外，采用Park双温度模型得到的结果与振动态-态模拟有较大差别，主要原因是双温度模型采用的假设没有考虑非Boltzmann分布效应的影响。以上结果表明驻点线模型是高效、准确地求解驻点线流动的有力工具，其与态-态模拟的结合有助于从微观上了解流场关键区域的热化学非平衡特征。

4）研究了两种考虑非Boltzmann修正的高保真度热化学非平衡模型。首先，在Macheret-Fridman双温度模型基础上，引入非平衡离解速率和离解振动能变化的非Boltzmann分布修正因子，构建了MMF模型。采用MMF模型计算了O₂/O气体混合物在正激波后的松弛过程以及球头绕流的激波脱体距离，计算结果与实验数据和振动态-态模拟符合较好。其次，对振动态-态模拟进行粗粒化，将振动态按能量均分为不同的组，构建了粗粒化模型。采用粗粒化模型计算了O₂/O气体混合物在正激波后的松弛过程，发现对于Case2和3这两个离解反应占优的情况，“2 groups”可以给出与振动态-态模拟近乎一致的结果。而对于Case6复合占优的情况，“2 groups”的结果稍差，随着分组的增多，粗粒化模型结果逐渐趋近于振动态-态模拟结果。以上结果表明两种热化学模型通过考虑内能能级的非Boltzmann修正，可以在接近于态-态模拟精度的前提下有效减少计算量，有希望应用到工程实际中。

5）开展了振动松弛速率常数的量子化学计算。首先，采用Improved Lennard-Jones（ILJ）势能函数构建了O₂(³Σ_g⁻)+O₂(³Σ_g⁻)体系的自旋平均势能面（PES），并改进了N₂(¹Σ_g⁺)+N₂(¹Σ_g⁺)体系的ILJ PES。通过与ab initio数据点以及色散系数、第二维里系数、输运系数等实验数据比较，验证了上述PES的可靠性。在此基础上，采用量子-经典动力学方法分别计算了O₂+O₂和N₂+N₂的大量V-T和V-V-T速率常数，通过与实验结果比较验证了所采用的PES及动力学方法适合于计算振动松弛速率常数，且计算量上优于文献中采用的方法。新得到的速率常数数据可以替代精度较低的半经典FHO模型数据，对提高态-态模拟结果的精度有重要意义。其次，采用ILJ势函数构建了N₂(¹Σ_g⁺)+O(³P)体系的³Π PES和³Σ PES，通过与ab initio数据点以及分子束实验的总碰撞截面比较，验证了新构建的PES的可靠性。然后分析了文献中振动松弛速率常数的计算结果和实验数据有很大差别的原因，排除了采用不同动力学方法以及不同PES带来的影响。随后通过引入非绝热振动-电子态（V-E）传能过程的贡献，首次定量得到了与实验数据吻合的总振动松弛速率，说明了V-E过程在含O(³P)等开壳层原子碰撞中起关键作用。

In hypersonic flows, the temperature of the flow field is very high due to the shock wave compression, which leads to the internal energy excitation of gas molecules and even causes chemical reactions such as dissociation and ionization. The characteristic time of a hypersonic flow is usually much less than the characteristic time of the above-mentioned physical and chemical processes, so the flow is in a thermochemical nonequilibrium state. How to describe this thermochemical nonequilibrium flow accurately is still an open topic. In this thesis, a detailed simulation of high-temperature thermochemical nonequilibrium flow is realized by state-to-state approach; A dimensionally reduced model is developed and two physically reduced models are investigated to improve the feasibility of state-to-state simulation in engineering application; Finally, potential energy surfaces of various systems are constructed for the microscopic molecular collision, and a large number of vibrational state-to-state rate coefficients are obtained by mixed quantum-classical dynamics simulation, which provides solid data support for high confidence vibrational state-to-state simulation of air species. The simulation chain from the quantum chemistry calculation of microscopic molecular collision with the state-to-state approach as the bridge is built. The main work accomplished in this thesis are summarized as follows:

1) The influence of thermochemical nonequilibrium effect on typical hypersonic flow is analyzed. Three different thermochemical models, namely frozen (Fr), thermal nonequilibrium (TN), and thermochemical nonequilibrium (TCN), are used to calculate the two-dimensional double-wedge shock-wave/boundary-layer interaction with high enthalpy incoming flow. The results of two-dimensional basic flow show that although the sizes of separation zones obtained by different thermochemical models are very different, the critical deflected angles of the incipient separation and secondary separation are almost the same. Through the global stability analysis of the basic flow, it is found that when the critical deflected angle of instability is exceeded, three-dimensional global instability modes appear. And the thermochemical nonequilibrium effect postpones the occurrence of global instability, which is equivalent to stabilizing the flow.

2) The high confidence state-to-state simulation of one-dimensional flow is carried out. Firstly, the relaxation process of O₂/O gas mixture behind the normal shock wave is solved by vibrational state-to-state approach. Compared with the commonly used two-temperature model, the peak value of vibrational temperature predicted by vibrational state-to-state simulation is closer to the experimental result. And the distribution of oxygen atom mass fraction is in good agreement with the experimental data, indicating that vibrational state-to-state simulation has high confidence. Furthermore, the thermochemical relaxation process of the five species N₂/N/O₂/O/NO gas mixture behind the normal shock wave is simulated, and the evolution curves of all the vibrational energy levels of N₂, O₂, and NO molecules after the shock wave are obtained, from which the dominant regions of vibrational relaxation and chemical reaction (mainly dissociation) can be clearly seen. Secondly, according to the newly added C₂ electronic state HPIE and HPID rate constants in this thesis, the electronic state-to-state simulations of the experimental conditions of the EAST shock tube (Shot92-102) are realized. The obtained high-temperature nonequilibrium C₂ Red radiation and CO VUV radiation are in good agreement with the experimentally measured values of the EAST shock tube. However, the results calculated by the 2T-QSS method in the literature are quite different from the experimental data, indicating that the electronic state-to-state simulation has higher confidence. The above results show that more accurate flow field information and detailed nonequilibrium evolution law can be obtained by state-to-state simulation with high confidence.

3) A quasi-one-dimensional stagnation streamline model for thermochemical nonequilibrium flow calculation is developed. The reliability of the stagnation streamline model is verified by comparing with the results of axisymmetric CFD calculation, the DRNSE model in the literature, and the experimental measurement of the stagnation point heat flux of the sphere. With the help of the stagnation streamline model, the vibrational state-to-state simulation of the five species air mixture (including 46, 61 and 48 of O₂, N₂ and NO vibrational states) along the stagnation streamline is realized, and the detailed distributions of all the O2, N2 and NO vibrational state along the stagnation streamline are given. It is found that the vibrational states of the gas molecules show strong non-Boltzmann distribution due to the strong coupling effect of vibrational relaxation and chemical reaction both behind the shock wave and inside the boundary layer. In addition, the results obtained by Park's two-temperature model are quite different from the vibrational state-to-state simulation, which is mainly because the hypothesis adopted by the two-temperature model does not consider the effect of the non-Boltzmann distribution. The above results show that the stagnation streamline model is a powerful tool to solve the stagnation streamline flow efficiently and accurately, and its combination with state-to-state simulation is helpful to understand the thermochemical nonequilibrium characteristics of the key regions of the flow field microscopically.

4) Two high-fidelity thermochemical nonequilibrium models considering the non-Boltzmann correction are studied. Firstly, based on Macheret-Fridman two-temperature model, non-Boltzmann correction factors  and  are introduced to construct the MMF model. The relaxation process of O₂/O gas mixture behind the normal shock wave and the shock standoff distance of the sphere are calculated by the MMF model. The calculated results are in good agreement with the experimental data and vibrational state-to-state simulation. Secondly, the coarse-grained model vibrational state-to-state approach is constructed by dividing the vibrational states into different groups according to energy. The relaxation process of O₂/O gas mixture behind a normal shock wave is calculated by using the coarse-grained model. It is found that "2 groups" can give nearly the same results as the vibrational state-to-state simulation for Case2 and Case3 in which dissociation reactions dominate. However, in the recombination dominating Case6, the result of "2 groups" is slightly worse. With the increase of groups, results of the coarse-grained model gradually approaches that of vibrational state-to-state simulation. The above results show that the two physically reduced models can effectively reduce the calculation cost and keep the accuracy of the state-to-state simulation by considering the non-Boltzmann correction, which is expected to be applied to engineering practice.

5) The quantum chemistry calculation of the vibrational relaxation rate coefficient is carried out. Firstly, the spin-average potential energy surface (PES) of O₂(³Σ_g⁻)+O₂(³Σ_g⁻) system is constructed by using the Improved Lennard-Jones (ILJ) potential energy function, and the ILJ PES of N₂(¹Σ_g⁺)+N₂(¹Σ_g⁺) system is improved. The reliability of the above PESs is verified by comparing with ab initio data, experimental data such as dispersion coefficient, second virial coefficient, and transport coefficient. On this basis, a large number of V-T and V-V-T rate coefficients of O₂+O₂ and N₂+N₂ are calculated respectively by the mixed quantum-classical method. It is verified by comparing with the experimental data that the PES and the dynamical method are suitable for the calculation of vibrational relaxation rate coefficient, and the computational cost is better than that used in the literature. The new data of rate coefficient can replace the low accurate ones calculated by the semi-classical FHO model, which is of great significance to improve the accuracy of the state-to-state simulation. Secondly, the ³Π PES and ³Σ PES of N₂(¹Σ_g⁺)+O(³P) system are constructed by using ILJ potential function, and the reliability of the newly built PES is verified by comparing with ab initio data and the total collision cross sections of molecular beam experiments. Moreover, the reason for the rate coefficient anomaly in the literature is analyzed, and the influences of different dynamical methods and PESs are first excluded. Furthermore, by introducing the contribution of the non-adiabatic vibrational-electronic (V-E) energy transfer process, the total vibrational relaxation rate is obtained quantitatively for the first time with good agreement with the experimental data. It is indicated that the V-E process plays a crucial role in the collisions involving O(³P) and other open-shell molecules.