Receptivity and Forced Response to Acoustic Disturbances in High-Speed Boundary Layers

Abstract

Supersonic boundary-layer receptivity to freestream acoustic disturbances is investigated by solving the Navier-Stokes equations for Mach 3.5 flow over a sharp flat plate and a 7-deg halfangle cone. The freestream disturbances are generated from a wavy wall placed at the nozzle wall. The freestream acoustic disturbances radiated by the wavy wall are obtained by solving the linearized Euler equations. The results for the flat plate show that instability modes are generated at all the incident angles ranging from zero to highly oblique. However, the receptivity coefficient decreases by about 20 times when the incident angle increases from zero to a highly oblique angle of 68 degrees. The results for the cone show that no instability modes are generated when the acoustic disturbances impinge the cone obliquely. The results show that the perturbations generated inside the boundary layer by the acoustic disturbances are the response of the boundary layer to the external forcing. The amplitude of the forced disturbances inside the boundary layer are about 2.5 times larger than the incoming field for zero azimuthal wavenumber and they are about 1.5 times for large azimuthal wavenumbers.

IUTAM Laminar-Turbulent Transition

“…[Duck, 1990] also studied this topic in the high Reynolds number limit but he did not obtain quantitative agreement with the results of Mack. Other works based on forced linear stability equations are by [Choudhari, 1994] in the context of subsonic acoustic receptivity and [Balakumar et al, 2016] in the context of supersonic acoustic receptivity. On the one hand, the linear stability equations make no simplifying assumptions based on the order of magnitude of the disturbances, unlike the LUBLE.…”

On the Effects of Sound in Subsonic Boundary Layer Flows

“…[Duck, 1990] also studied this topic in the high Reynolds number limit but he did not obtain quantitative agreement with the results of Mack. Other works based on forced linear stability equations are by [Choudhari, 1994] in the context of subsonic acoustic receptivity and [Balakumar et al, 2016] in the context of supersonic acoustic receptivity. On the one hand, the linear stability equations make no simplifying assumptions based on the order of magnitude of the disturbances, unlike the LUBLE.…”

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

“…For example, hypersonic boundary layer receptivity under free-stream disturbance refers to the process that occurs when disturbances in the free-stream enter the boundary layer and result in the generation of perturbations in the boundary layer. Many scholars have researched hypersonic boundary layer receptivity [ 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 ], but it is not yet fully understood because the hypersonic boundary layer receptivity is affected by many factors. These factors interact with each other, which increases the complexity of the hypersonic boundary layer receptivity.…”

“…The parameters of free-stream disturbances, such as amplitude, frequency, and incident angle, also significantly impact hypersonic boundary layer receptivity. Balakumar et al [ 12 ] analyzed the receptivity of the supersonic boundary layer under acoustic waves. They found that the perturbations in the boundary layer are a response to the free-stream acoustic waves, and the amplitude of the perturbations in the boundary layer is related to the incident angle of the free-stream disturbances.…”