Three-dimensional receptivity of hypersonic sharp and blunt cones to free-stream planar waves using hierarchical input-output analysis

Understanding the receptivity of hypersonic flows to free-stream disturbances is crucial for predicting laminar to turbulent boundary layer transition. Input-output analysis as a receptivity tool considers which free-stream disturbances lead to the largest response from the boundary layer using the global linear dynamics. Two technical challenges are addressed. First, we restrict the allowable forcing to physically realizable inputs via a free-stream boundary modification to the classic input-output formulation. Second, we develop a hierarchical input-output (H-IO) analysis which allows us to solve the three-dimensional problem at a fraction of the computational cost otherwise associated with directly inverting the fully three-dimensional resolvent operator. Next, we consider Mach 5.8 flows over a sharp cone and two blunt cones with 3.6mm and 7.2mm spherically blunt tips. H-IO correctly predicts that the sharp cone boundary layer is most receptive to slow acoustic waves at an optimal incidence angle of 10°, validating the method. We then investigate the effect of free-stream disturbances on the blunt cone boundary layer and identify two distinct vorticity-dominated receptivity mechanisms for the oblique first-mode instability at 10kHz and an entropy layer instability at 40 and 70kHz. Our results reveal these receptivity processes to be highly three-dimensional in nature, involving both the nose tip and excitation along narrow bands at certain azimuthal angles along the oblique shock downstream. We interpret these processes in terms of critical angles from linear shock/perturbation interaction theory. Finally, we show how these receptivity processes vary with frequency and nose tip bluntness, and demonstrate how this methodology might be applied to transition prediction from first principles.