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The hypersonic flow field around a blunt cone was simulated using a high-order finite difference method. Fast acoustic waves, slow acoustic waves, entropy waves, and vortical waves were introduced into the free-stream to determine the influence of a free-stream with disturbances on the hypersonic flow field and boundary layer. The effect of disturbance type on the evolution of perturbations in the hypersonic boundary layer was analyzed. Fast Fourier Transform was adopted to analyze the effect of the disturbance type on the evolution of different modes in the boundary layer. A roughness element was introduced into the flow field to reveal the impact of the roughness element on hypersonic boundary layer receptivity. The results showed that a free-stream with disturbances affected the hypersonic flow field and boundary layer; acoustic waves had the greatest influence. The impact of slow acoustic waves on the flow field was mainly concentrated in the region between the shock and the boundary layer, whereas the influence of fast acoustic waves was mainly concentrated in the boundary layer. Multi-mode perturbations formed in the boundary layer were caused by the free-stream with disturbances, wherein the fundamental mode was the dominant mode of the perturbations in the boundary layer caused by fast acoustic waves, entropy waves, and vortical waves. The dominant modes of the perturbations in the boundary layer caused by slow acoustic waves were both the fundamental mode and the second harmonic mode. The roughness element changed the propagation process of different modes of perturbations in the boundary layer. In the downstream region of the roughness element, perturbations in the boundary layer caused by the slow acoustic waves had the greatest influence. The second harmonic mode in the boundary layer was significantly suppressed, and the fundamental mode became the dominant mode. The effects of fast acoustic waves and entropy waves on the boundary layer receptivity were similar, except the amplitude of the perturbations in the boundary layer caused by the fast acoustic waves was larger.

Effect of a Roughness Element on the Hypersonic Boundary Layer Receptivity Due to Different Types of Free-Stream Disturbance with a Single Frequency