在高超声速飞行的应用背景下，飞行器的表面会出现极大的摩阻和热流，它们会极大程度地威胁到飞行器的安全，因此热防护系统往往是必不可少的。在被动式热防护系统中，往往会在最外层附加一层辐射层，其能够将大部分的热流以表面辐射的形式传递至外部环境，从而降低表面的热流负担。当存在表面辐射效应时，飞行器表面的温度将会随空间位置出现变化，使得整体流场与具有等温壁面或绝热壁面的流场出现一定的偏差。考虑到热防护系统的现实意义，对受到表面辐射影响的流场进行系统的分析是必要的。

本文从层流流动特性、湍流流动特性和边界层稳定性三个方面分析了受到表面辐射影响的二维高超声速平板边界层流动。为更好地模拟表面辐射，我们引入了一种穿透型辐射平衡边界，其同时考虑了表面辐射与通过固液分界面穿透入结构内部的热量，理论上能够更好地贴近实际情况。为对层流和湍流的流场进行求解，我们使用了Du Fort-Frankel类的差分方法进行了计算。其中湍流模型使用的是经典的Baldwin-Lomax模型，但我们并未考虑转捩的影响，而是假定流场在最前缘便已达到完全湍流状态。无论是层流还是湍流情况，表面辐射均导致壁面温度沿流向逐渐减小。整体而言，壁面温度与来流马赫数成正相关，与对应大气高度和表面辐射率成反相关，且湍流情况的壁面温度要远大于层流情况。在将穿透型辐射平衡情况的剖面图和在同一位置处具有相同壁面温度的等温壁情况进行对比之后，我们发现两种情况的速度剖面基本没有区别，而穿透型辐射平衡情况的温度剖面的最大温度更高、达到最大温度的位置更远离壁面，这样的现象对于层流而言较为显著。进一步地，我们对穿透型辐射平衡情况和对应的等温壁情况的表面热通量进行了定量比较，发现对于层流而言两者的相对差异在10%的量级，且沿流向逐渐减小；对于湍流而言两者的相对差异仅在2%的量级。此外，在层流情况下此相对差异与来流马赫数、对应大气高度和表面辐射率均成负相关。这些结果表明，若使用基于层流等温壁情况的方法来预测受到表面辐射影响的层流边界层流动的表面热通量，很大可能会造成一定程度的对热通量的低估；而若使用基于湍流等温壁情况的方法来预测受到表面辐射影响的湍流边界层流动的表面热通量，表面辐射不会对结果的准确性造成过多的影响。为预测受到表面辐射影响的层流边界层流动的表面热通量，我们提出了一种修正参考焓方法，其能够在一定的参数范围内较好地预测层流穿透型辐射平衡情况的表面热通量，与差分方法的结果在多种情况下的最大相对差异仅为2.5%左右。在边界层厚度方面，层流穿透型辐射平衡情况的速度边界层厚度、位移边界层厚度和动量边界层厚度均与流向的坐标近似地成指数关系，其中速度边界层厚度对应的指数约为0.46，位移边界层和动量边界层对应的指数大约为0.51。对于湍流穿透型辐射平衡情况，我们仅考虑了由时均速度定义的速度边界层厚度，其同样也与流向的坐标近似地成指数关系，但指数受参数的影响更大，在0.68-0.76之间变化。对于边界层稳定性，我们使用了平行流动假设，计算得到了一些模态函数以及其对应的特征值。

In the context of hypersonic flights, the surface of aircraft can experience significant friction and heat flux, which can greatly threaten the safety of the aircraft. Therefore, Thermal Protection Systems are often essential. In passive Thermal Protection Systems, a radiation-shielding layer is often present as the outermost layer, which can transfer most of the heat flow to the external environment in the form of surface radiation, thereby reducing the heat flow burden on the surface. When there is surface radiation effect, the temperature of the aircraft surface will change with spatial position, resulting in a certain deviation between the overall flow field and the flow field with isothermal or adiabatic walls. Considering the practical significance of thermal protection systems, it is necessary to conduct a systematic analysis of the flow field affected by surface radiation.
In this paper, the two-dimensional hypersonic boundary layer flow on a flat plate affected by surface radiation is analyzed from three aspects: laminar flow characteristics, turbulent flow characteristics and boundary layer stability. To better simulate surface radiation, we have introduced a penetrating radiation equilibrium boundary that takes into account both surface radiation and the heat penetrating into the structure through the interface, theoretically better fitting the actual situation. To solve the flow fields of laminar and turbulent flow, we used the Du Fort-Frankel type difference method for calculation. Turbulence is modelled using the classic Baldwin-Lomax model, but we did not consider the influence of transition, instead we assumed that the flow field had reached a fully turbulent state at the leading edge. Whether in laminar or turbulent cases, surface radiation leads to a gradual decrease in wall temperature along the flow direction. On the whole, the wall temperature is positively correlated with the Mach number, and inversely correlated with the corresponding atmospheric height and surface emissivity, and the wall temperature in turbulent cases is much greater than that in laminar cases. After comparing the profile of penetrating-radiation-equilibrium cases with isothermal cases with the same wall temperature at the same location, we found that the velocity profiles of the two cases were basically the same. However, the temperature profile of penetrating-radiation-equilibrium cases had a higher maximum temperature, and the position where the maximum temperature was reached was further away from the wall. Such difference is more significant for laminar flow than for turbulent flow. Furthermore, we quantitatively compared the surface heat fluxes of penetrating-radiation-equilibrium cases and the corresponding isothermal cases. We found that the relative difference between the two for laminar flow is on the order of 10%, and gradually decreases along the flow direction; For turbulent flow, the relative difference between the two is only on the order of 2%. In addition, in the case of laminar flow, this relative difference is negatively correlated with the incoming Mach number, the corresponding atmospheric height and the surface radiance. These results show that if a method based on laminar isothermal cases is used to predict the surface heat flux of laminar boundary layer flow affected by surface radiation, it may underestimate the surface heat flux to a certain degree; However, if a method based on turbulent isothermal cases is used to predict the surface heat flux of turbulent boundary layer flow affected by surface radiation, the surface radiation will not have too much impact on the accuracy of the results. In order to predict the surface heat flux of laminar boundary layer flow affected by surface radiation, we proposed a modified reference enthalpy method, which have been shown to better predict the surface heat flux of laminar penetrating-radiation-equilibrium cases within a certain parameter range, and the maximum relative difference between its predictions and the results of the difference method in multiple cases is only about 2.5%. In terms of the thickness of the boundary layer, the velocity thickness, the displacement thickness and the momentum thickness of laminar penetrating-radiation-equilibrium cases are all approximately exponential with the coordinate in the direction of external flow. The exponent corresponding to the velocity thickness is about 0.46, while the exponent corresponding to the displacement thickness and the momentum thickness is about 0.51. For turbulent penetrating-radiation-equilibrium cases, we only considered the velocity thickness of boundary layer, which is defined by the time-averaged velocity. The thickness is also approximately exponential with the coordinate in the direction of external flow, but the exponent is more affected by the parameters, ranging from 0.68 to 0.76. As for the stability of the boundary layer, we used the parallel flow hypothesis, and obtained some modal functions and their corresponding eigenvalues.