超声速三维边界层感受性问题的研究

超声速三维边界层感受性问题是可压缩三维边界层转捩过程预测与控制的关键阶段，其对超声速飞行器的研究和设计至关重要。目前，有关超声速三维边界层感受性的实验、理论和数值研究的相关报道甚少；因此，开展超声速三维边界层感受性关键问题的研究不仅具有十分重要的理论意义，而且还有着广阔的实际应用前景。本课题以无限薄后掠翼平板三维边界层为物理模型，构造无振荡的、高精度高分辨的WENO格式和四阶精度修正的TVD Runge-Kutta来进行时间推进与展向采用傅利叶展开相结合的方法；研究在自由来流扰动(如声波、涡波和熵波扰动)作用下激发超声速三维边界层内形成感受性过程的起因；揭示不同自由来流扰动与激波相互作用所激发超声速三维边界层内形成初始失稳模态的感受性过程的异同点；建立自由来流扰动在超声速三维边界层内被诱导出感受性过程中所起的作用和地位；寻找在超声速三维边界层内被诱导出失稳模态向下游演化的机制转换等。

The supersonic receptivity in the three-dimensional boundary layer is the key stage of the prediction and control of the laminar-turbulent transition in the compressible three-dimensional boundary layer, which is crucial to the design and research for the supersonic aircraft. By now, the reports about the experiments, theories or numerical studies on the receptivity in the supersonic three-dimensional boundary layers are little. Therefore, the studies of the key issues on the receptivity in the supersonic three-dimensional boundary layers are not only of theoretical significance, but also of practical application. This project is formulated by the physical model of the three-dimensional boundary layer over an infinite-thin swept flat plate. The non-oscillation, high-resolution WENO spatial schemes and fourth-order modified Runge-Kutta with TVD temporal scheme combined with the fast Fourier transform in the spanwise direction are introduced for the numerical simulation. DNS is performed to study the formation of the instability in the supersonic three-dimensional boundary layers under the free-stream disturbances such as acoustic, vortical and entropy waves. It is going to reveal the similarities and differences among the receptivity in the supersonic three-dimensional boundary layers triggered by different types of the free-stream disturbances interacting with the shock wave. The effect and position of the free-stream disturbances on the receptivity in the supersonic three-dimensional boundary layers are established. And find the transfer mechanism of downstream evolution of the unstable modes induced by free-stream disturbances in the supersonic three-dimensional boundary layers.